*****************************************************************************
                       Semantic Analysis of SPARK Text
                             Examiner GPL Edition

*****************************************************************************



SPARK Simplifier GPL 2012
Copyright (C) 2012 Altran Praxis Limited, Bath, U.K.

procedure Process_Dns_Request.Create_Response_SOA






@@@@@@@@@@  VC: procedure_create_response_soa_1.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
***  Proved C1:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C2:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H4.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_2.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
***  Proved C1:  num_found__1 >= rr_type__numberofrecordstype__first
     using hypothesis H36.
***  Proved C2:  num_found__1 <= rr_type__numberofrecordstype__last
     using hypothesis H37.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_3.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New C1:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_4.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New C1:  true
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(
          replies__1, [i___1]))) and fld_class(fld_inherit(element(replies__1, [
          i___1]))) <= rr_type__classtype__last)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, rr_type__wirestringtypeindex__first <= i___2 and 
          i___2 <= rr_type__wirestringtypeindex__last -> character__first <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, rr_type__wirestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__wirestringtypeindex__last -> character__first <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_5.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
***  Proved C1:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) >= rr_type__wirestringtypeindex__first
     using hypothesis H58.
***  Proved C2:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) <= rr_type__wirestringtypeindex__last
     using hypothesis H59.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_6.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
***  Proved C1:  1 >= rr_type__returnedrecordsindextype__first
     using hypothesis H56.
***  Proved C2:  1 <= rr_type__returnedrecordsindextype__last
     using hypothesis H57.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_7.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
***  Proved C1:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) 
          >= rr_type__wirestringtypeindex__first
     using hypothesis H76.
***  Proved C2:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) 
          <= rr_type__wirestringtypeindex__last
     using hypothesis H77.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_8.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  true
***  Proved C11:  true
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C1:  dns_types__packet_size - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= - 
          2147483648
<S>  New C3:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) 
          + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C2:  dns_types__packet_size - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          2147483647
<S>  New C4:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) 
          + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New C5:  dns_types__packet_size - (32 + dns_types__header_bits div 8) >= - 
          9223372036854775808
<S>  New C7:  dns_types__header_bits div 8 >= - 9223372036854775840
<S>  New C9:  dns_types__header_bits div 8 >= - 9223372036854775808
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New C6:  dns_types__packet_size - (32 + dns_types__header_bits div 8) <= 
          9223372036854775807
<S>  New C8:  dns_types__header_bits div 8 <= 9223372036854775775
<S>  New C10:  dns_types__header_bits div 8 <= 9223372036854775807
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C12:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C13:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New C1:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= - 
          2147483648
<S>  New C2:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          2147483647
<S>  New C5:  32 + dns_types__header_bits div 8 <= 9223372036854784000
<S>  New C6:  - 9223372036854767615 <= 32 + dns_types__header_bits div 8
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New C7:  true
<S>  New C9:  true
<S>  New C8:  true
<S>  New C10:  true
<S>  New C1:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) 
          + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
<S>  New C2:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
<S>  New C5:  true
<S>  New C6:  true
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C3:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 
          - 2147483648
     using hypotheses H58 & H76.
***  Proved C4:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
     using hypotheses H59 & H77.
***  Proved C12:  start_byte >= - 2147483648
     using hypothesis H3.
***  Proved C13:  start_byte <= 2147483647
     using hypothesis H1.
***  Proved C7:  true
***  Proved C9:  true
***  Proved C8:  true
***  Proved C10:  true
***  Proved C1:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
     using hypotheses H59 & H77.
***  Proved C2:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
     using hypotheses H58 & H76.
***  Proved C5:  true
***  Proved C6:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_9.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
***  Proved C3:  start_byte + 1 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New C1:  (qname_location + 49152) mod unsigned_types__unsigned16__modulus 
          >= 0
<S>  New C6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New C2:  (qname_location + 49152) mod unsigned_types__unsigned16__modulus 
          <= 65535
<S>  New C7:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New C4:  start_byte <= 8179
<S>  New C5:  start_byte <= 8178
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C8:  start_byte >= - 2147483649
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C9:  start_byte <= 2147483646
***  Proved C9:  start_byte <= 2147483646
     using hypothesis H4.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New C1:  (qname_location + 49152) mod 65536 >= 0
<S>  New C2:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C6:  qname_location >= 0
     using hypothesis H6.
***  Proved C7:  qname_location <= 65535
     using hypothesis H7.
***  Proved C8:  start_byte >= - 2147483649
     using hypothesis H98.
***  Proved C1:  (qname_location + 49152) mod 65536 >= 0
***  Proved C2:  (qname_location + 49152) mod 65536 <= 65535
---  Eliminated hypothesis H25 (true-hypothesis).
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H48 (true-hypothesis).
---  Eliminated hypothesis H49 (true-hypothesis).
---  Eliminated hypothesis H50 (true-hypothesis).
---  Eliminated hypothesis H51 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H54 (true-hypothesis).
---  Eliminated hypothesis H55 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H64 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H74 (true-hypothesis).
---  Eliminated hypothesis H75 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H81 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H101 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H95 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H94 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H1 (redundant, given H4).
---  Eliminated hypothesis H24 (redundant, given H2).
---  Eliminated hypothesis H36 (redundant, given H42).
---  Eliminated hypothesis H87 (redundant, given H90).
---  Eliminated hypothesis H89 (redundant, given H88).
---  Eliminated hypothesis H90 (redundant, given H3 & H100).
---  Eliminated hypothesis H98 (redundant, given H3).
---  Eliminated hypothesis H99 (redundant, given H4).
     +++  New H103:  integer__size >= 0
     +++  New H104:  character__size >= 0
     +++  New H105:  natural__size >= 0
     +++  New H106:  positive__size >= 0
     +++  New H107:  dns_types__qname_ptr_range__size >= 0
     +++  New H108:  dns_types__qname_ptr_range__base__first <= 
          dns_types__qname_ptr_range__base__last
     +++  New H109:  dns_types__packet_length_range__size >= 0
     +++  New H110:  dns_types__packet_bytes_range__size >= 0
     +++  New H111:  dns_types__dns_packet__size >= 0
     +++  New H112:  unsigned_types__unsigned16__size >= 0
     +++  New H113:  unsigned_types__unsigned32__size >= 0
     +++  New H114:  rr_type__classtype__size >= 0
     +++  New H115:  rr_type__wirestringtypeindex__size >= 0
     +++  New H116:  rr_type__wirestringtype__size >= 0
     +++  New H117:  rr_type__resourcerecordtype__size >= 0
     +++  New H118:  rr_type__returnedrecordsindextype__size >= 0
     +++  New H119:  rr_type__numberofrecordstype__size >= 0
     +++  New H120:  rr_type__soa_record_type__soarecordtype__size >= 0
     +++  New H121:  dns_types__qname_ptr_range__base__first <= 0
     +++  New H122:  dns_types__qname_ptr_range__base__last >= 16383


@@@@@@@@@@  VC: procedure_create_response_soa_10.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
***  Proved C3:  start_byte + 3 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C5:  start_byte + 3 >= dns_types__packet_bytes_range__base__first
     using hypothesis H110.
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New C1:  true
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
<S>  New C2:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(fld_bytes(output_packet), [
          i___1]) and element(fld_bytes(output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> 0 <= element(fld_bytes(output_packet__2)
          , [i___1]) and element(fld_bytes(output_packet__2), [i___1]) <= 255)
<S>  New C4:  start_byte <= 8177
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New C6:  start_byte <= 2147483644
***  Proved C1:  true
***  Proved C2:  true
***  Proved C6:  start_byte <= 2147483644
     using hypothesis H4.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
---  Eliminated hypothesis H25 (true-hypothesis).
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H48 (true-hypothesis).
---  Eliminated hypothesis H49 (true-hypothesis).
---  Eliminated hypothesis H50 (true-hypothesis).
---  Eliminated hypothesis H51 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H54 (true-hypothesis).
---  Eliminated hypothesis H55 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H64 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H74 (true-hypothesis).
---  Eliminated hypothesis H75 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H81 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H101 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H95 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H94 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H108 (duplicate of H6).
---  Eliminated hypothesis H1 (redundant, given H4).
---  Eliminated hypothesis H4 (redundant, given H106).
---  Eliminated hypothesis H24 (redundant, given H2).
---  Eliminated hypothesis H36 (redundant, given H42).
---  Eliminated hypothesis H87 (redundant, given H90).
---  Eliminated hypothesis H89 (redundant, given H88).
---  Eliminated hypothesis H90 (redundant, given H3 & H100).
---  Eliminated hypothesis H98 (redundant, given H3).
---  Eliminated hypothesis H99 (redundant, given H106).
---  Eliminated hypothesis H105 (redundant, given H3).
---  Eliminated hypothesis H106 (redundant, given H107).
---  Eliminated hypothesis H109 (redundant, given H7).
---  Eliminated hypothesis H110 (redundant, given H3).
---  Eliminated hypothesis H111 (redundant, given H107).
---  Substituted hypothesis H113, which specifies an equivalence for fld_header(
          output_packet__2).
%%%  Simplified H103 further (given H6 & H7), to give:
     %%%  H103:  qname_location >= - 49152
%%%  Simplified H104 further (given H6 & H7), to give:
     %%%  H104:  qname_location <= 16383
     +++  New H115:  integer__size >= 0
     +++  New H116:  character__size >= 0
     +++  New H117:  natural__size >= 0
     +++  New H118:  positive__size >= 0
     +++  New H119:  dns_types__qname_ptr_range__size >= 0
     +++  New H120:  dns_types__qname_ptr_range__base__first <= 
          dns_types__qname_ptr_range__base__last
     +++  New H121:  dns_types__packet_length_range__size >= 0
     +++  New H122:  dns_types__packet_bytes_range__size >= 0
     +++  New H123:  dns_types__dns_packet__size >= 0
     +++  New H124:  unsigned_types__unsigned16__size >= 0
     +++  New H125:  unsigned_types__unsigned32__size >= 0
     +++  New H126:  rr_type__classtype__size >= 0
     +++  New H127:  rr_type__wirestringtypeindex__size >= 0
     +++  New H128:  rr_type__wirestringtype__size >= 0
     +++  New H129:  rr_type__resourcerecordtype__size >= 0
     +++  New H130:  rr_type__returnedrecordsindextype__size >= 0
     +++  New H131:  rr_type__numberofrecordstype__size >= 0
     +++  New H132:  rr_type__soa_record_type__soarecordtype__size >= 0
     +++  New H133:  dns_types__qname_ptr_range__base__first <= 0
     +++  New H134:  dns_types__qname_ptr_range__base__last >= 16383


@@@@@@@@@@  VC: procedure_create_response_soa_11.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
***  Proved C1:  6 >= dns_types__byte__first
     using hypothesis H115.
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C5:  start_byte + 4 >= dns_types__packet_bytes_range__base__first
     using hypothesis H110.
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 255)
<S>  New H116:  true
<S>  New C2:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H118:  start_byte <= 8177
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
<S>  New C4:  start_byte <= 8176
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New C6:  start_byte <= 2147483643
***  Proved C2:  true
***  Proved C6:  start_byte <= 2147483643
     using hypothesis H4.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 255)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 255)
<S>  New H117:  start_byte >= - 2
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H115:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
---  Eliminated hypothesis H25 (true-hypothesis).
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H48 (true-hypothesis).
---  Eliminated hypothesis H49 (true-hypothesis).
---  Eliminated hypothesis H50 (true-hypothesis).
---  Eliminated hypothesis H51 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H54 (true-hypothesis).
---  Eliminated hypothesis H55 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H64 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H74 (true-hypothesis).
---  Eliminated hypothesis H75 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H81 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H101 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H95 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H94 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H108 (duplicate of H6).
---  Eliminated hypothesis H1 (redundant, given H4).
---  Eliminated hypothesis H4 (redundant, given H106).
---  Eliminated hypothesis H24 (redundant, given H2).
---  Eliminated hypothesis H36 (redundant, given H42).
---  Eliminated hypothesis H87 (redundant, given H90).
---  Eliminated hypothesis H89 (redundant, given H88).
---  Eliminated hypothesis H90 (redundant, given H3 & H100).
---  Eliminated hypothesis H98 (redundant, given H3).
---  Eliminated hypothesis H99 (redundant, given H106).
---  Eliminated hypothesis H105 (redundant, given H3).
---  Eliminated hypothesis H106 (redundant, given H107).
---  Eliminated hypothesis H107 (redundant, given H118).
---  Eliminated hypothesis H109 (redundant, given H7).
---  Eliminated hypothesis H110 (redundant, given H3).
---  Eliminated hypothesis H111 (redundant, given H118).
---  Eliminated hypothesis H117 (redundant, given H3).
---  Eliminated hypothesis H119 (redundant, given H3).
---  Eliminated hypothesis H120 (redundant, given H118).
---  Substituted hypothesis H113, which specifies an equivalence for fld_header(
          output_packet__2).
%%%  Simplified H103 further (given H6 & H7), to give:
     %%%  H103:  qname_location >= - 49152
%%%  Simplified H104 further (given H6 & H7), to give:
     %%%  H104:  qname_location <= 16383
     +++  New H121:  integer__size >= 0
     +++  New H122:  character__size >= 0
     +++  New H123:  natural__size >= 0
     +++  New H124:  positive__size >= 0
     +++  New H125:  dns_types__qname_ptr_range__size >= 0
     +++  New H126:  dns_types__qname_ptr_range__base__first <= 
          dns_types__qname_ptr_range__base__last
     +++  New H127:  dns_types__packet_length_range__size >= 0
     +++  New H128:  dns_types__packet_bytes_range__size >= 0
     +++  New H129:  dns_types__dns_packet__size >= 0
     +++  New H130:  unsigned_types__unsigned16__size >= 0
     +++  New H131:  unsigned_types__unsigned32__size >= 0
     +++  New H132:  rr_type__classtype__size >= 0
     +++  New H133:  rr_type__wirestringtypeindex__size >= 0
     +++  New H134:  rr_type__wirestringtype__size >= 0
     +++  New H135:  rr_type__resourcerecordtype__size >= 0
     +++  New H136:  rr_type__returnedrecordsindextype__size >= 0
     +++  New H137:  rr_type__numberofrecordstype__size >= 0
     +++  New H138:  rr_type__soa_record_type__soarecordtype__size >= 0
     +++  New H139:  dns_types__qname_ptr_range__base__first <= 0
     +++  New H140:  dns_types__qname_ptr_range__base__last >= 16383


@@@@@@@@@@  VC: procedure_create_response_soa_12.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
***  Proved C1:  0 >= dns_types__byte__first
     using hypothesis H115.
***  Proved C2:  0 <= dns_types__byte__last
     using hypothesis H116.
***  Proved C3:  start_byte + 5 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C5:  start_byte + 5 >= dns_types__packet_bytes_range__base__first
     using hypothesis H110.
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H118:  start_byte <= 8177
<S>  New H124:  start_byte <= 8176
<S>  New C4:  start_byte <= 8175
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New H126:  start_byte <= 2147483643
<S>  New C6:  start_byte <= 2147483642
***  Proved C6:  start_byte <= 2147483642
     using hypothesis H4.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
<S>  New H117:  start_byte >= - 2
<S>  New H123:  start_byte >= - 3
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
<S>  New H125:  start_byte >= - 2147483652
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H115:  true
<S>  New H121:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H116:  true
<S>  New H122:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
---  Eliminated hypothesis H25 (true-hypothesis).
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H48 (true-hypothesis).
---  Eliminated hypothesis H49 (true-hypothesis).
---  Eliminated hypothesis H50 (true-hypothesis).
---  Eliminated hypothesis H51 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H54 (true-hypothesis).
---  Eliminated hypothesis H55 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H64 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H74 (true-hypothesis).
---  Eliminated hypothesis H75 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H81 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H101 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H95 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H94 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H121 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H122 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H108 (duplicate of H6).
---  Eliminated hypothesis H1 (redundant, given H4).
---  Eliminated hypothesis H4 (redundant, given H106).
---  Eliminated hypothesis H24 (redundant, given H2).
---  Eliminated hypothesis H36 (redundant, given H42).
---  Eliminated hypothesis H87 (redundant, given H90).
---  Eliminated hypothesis H89 (redundant, given H88).
---  Eliminated hypothesis H90 (redundant, given H3 & H100).
---  Eliminated hypothesis H98 (redundant, given H3).
---  Eliminated hypothesis H99 (redundant, given H106).
---  Eliminated hypothesis H105 (redundant, given H3).
---  Eliminated hypothesis H106 (redundant, given H107).
---  Eliminated hypothesis H107 (redundant, given H118).
---  Eliminated hypothesis H109 (redundant, given H7).
---  Eliminated hypothesis H110 (redundant, given H3).
---  Eliminated hypothesis H111 (redundant, given H118).
---  Eliminated hypothesis H117 (redundant, given H3).
---  Eliminated hypothesis H118 (redundant, given H124).
---  Eliminated hypothesis H119 (redundant, given H3).
---  Eliminated hypothesis H120 (redundant, given H124).
---  Eliminated hypothesis H123 (redundant, given H3).
---  Eliminated hypothesis H125 (redundant, given H3).
---  Eliminated hypothesis H126 (redundant, given H124).
---  Substituted hypothesis H113, which specifies an equivalence for fld_header(
          output_packet__2).
%%%  Simplified H103 further (given H6 & H7), to give:
     %%%  H103:  qname_location >= - 49152
%%%  Simplified H104 further (given H6 & H7), to give:
     %%%  H104:  qname_location <= 16383
     +++  New H127:  integer__size >= 0
     +++  New H128:  character__size >= 0
     +++  New H129:  natural__size >= 0
     +++  New H130:  positive__size >= 0
     +++  New H131:  dns_types__qname_ptr_range__size >= 0
     +++  New H132:  dns_types__qname_ptr_range__base__first <= 
          dns_types__qname_ptr_range__base__last
     +++  New H133:  dns_types__packet_length_range__size >= 0
     +++  New H134:  dns_types__packet_bytes_range__size >= 0
     +++  New H135:  dns_types__dns_packet__size >= 0
     +++  New H136:  unsigned_types__unsigned16__size >= 0
     +++  New H137:  unsigned_types__unsigned32__size >= 0
     +++  New H138:  rr_type__classtype__size >= 0
     +++  New H139:  rr_type__wirestringtypeindex__size >= 0
     +++  New H140:  rr_type__wirestringtype__size >= 0
     +++  New H141:  rr_type__resourcerecordtype__size >= 0
     +++  New H142:  rr_type__returnedrecordsindextype__size >= 0
     +++  New H143:  rr_type__numberofrecordstype__size >= 0
     +++  New H144:  rr_type__soa_record_type__soarecordtype__size >= 0
     +++  New H145:  dns_types__qname_ptr_range__base__first <= 0
     +++  New H146:  dns_types__qname_ptr_range__base__last >= 16383


@@@@@@@@@@  VC: procedure_create_response_soa_13.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H127 has been replaced by "true".  (It is already present, as 
          H115).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H116).
***  Proved C1:  1 >= dns_types__byte__first
     using hypothesis H115.
***  Proved C2:  1 <= dns_types__byte__last
     using hypothesis H122.
***  Proved C3:  start_byte + 6 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C5:  start_byte + 6 >= dns_types__packet_bytes_range__base__first
     using hypothesis H110.
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H118:  start_byte <= 8177
<S>  New H124:  start_byte <= 8176
<S>  New H130:  start_byte <= 8175
<S>  New C4:  start_byte <= 8174
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New H126:  start_byte <= 2147483643
<S>  New H132:  start_byte <= 2147483642
<S>  New C6:  start_byte <= 2147483641
***  Proved C6:  start_byte <= 2147483641
     using hypothesis H4.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
<S>  New H117:  start_byte >= - 2
<S>  New H123:  start_byte >= - 3
<S>  New H129:  start_byte >= - 4
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
<S>  New H125:  start_byte >= - 2147483652
<S>  New H131:  start_byte >= - 2147483653
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H115:  true
<S>  New H121:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H116:  true
<S>  New H122:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
---  Eliminated hypothesis H25 (true-hypothesis).
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H48 (true-hypothesis).
---  Eliminated hypothesis H49 (true-hypothesis).
---  Eliminated hypothesis H50 (true-hypothesis).
---  Eliminated hypothesis H51 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H54 (true-hypothesis).
---  Eliminated hypothesis H55 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H64 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H74 (true-hypothesis).
---  Eliminated hypothesis H75 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H81 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H101 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H127 (true-hypothesis).
---  Eliminated hypothesis H128 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H95 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H94 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H121 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H122 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H108 (duplicate of H6).
---  Eliminated hypothesis H1 (redundant, given H4).
---  Eliminated hypothesis H4 (redundant, given H106).
---  Eliminated hypothesis H24 (redundant, given H2).
---  Eliminated hypothesis H36 (redundant, given H42).
---  Eliminated hypothesis H87 (redundant, given H90).
---  Eliminated hypothesis H89 (redundant, given H88).
---  Eliminated hypothesis H90 (redundant, given H3 & H100).
---  Eliminated hypothesis H98 (redundant, given H3).
---  Eliminated hypothesis H99 (redundant, given H106).
---  Eliminated hypothesis H105 (redundant, given H3).
---  Eliminated hypothesis H106 (redundant, given H107).
---  Eliminated hypothesis H107 (redundant, given H118).
---  Eliminated hypothesis H109 (redundant, given H7).
---  Eliminated hypothesis H110 (redundant, given H3).
---  Eliminated hypothesis H111 (redundant, given H118).
---  Eliminated hypothesis H117 (redundant, given H3).
---  Eliminated hypothesis H118 (redundant, given H124).
---  Eliminated hypothesis H119 (redundant, given H3).
---  Eliminated hypothesis H120 (redundant, given H124).
---  Eliminated hypothesis H123 (redundant, given H3).
---  Eliminated hypothesis H124 (redundant, given H130).
---  Eliminated hypothesis H125 (redundant, given H3).
---  Eliminated hypothesis H126 (redundant, given H130).
---  Eliminated hypothesis H129 (redundant, given H3).
---  Eliminated hypothesis H131 (redundant, given H3).
---  Eliminated hypothesis H132 (redundant, given H130).
---  Substituted hypothesis H113, which specifies an equivalence for fld_header(
          output_packet__2).
%%%  Simplified H103 further (given H6 & H7), to give:
     %%%  H103:  qname_location >= - 49152
%%%  Simplified H104 further (given H6 & H7), to give:
     %%%  H104:  qname_location <= 16383
     +++  New H133:  integer__size >= 0
     +++  New H134:  character__size >= 0
     +++  New H135:  natural__size >= 0
     +++  New H136:  positive__size >= 0
     +++  New H137:  dns_types__qname_ptr_range__size >= 0
     +++  New H138:  dns_types__qname_ptr_range__base__first <= 
          dns_types__qname_ptr_range__base__last
     +++  New H139:  dns_types__packet_length_range__size >= 0
     +++  New H140:  dns_types__packet_bytes_range__size >= 0
     +++  New H141:  dns_types__dns_packet__size >= 0
     +++  New H142:  unsigned_types__unsigned16__size >= 0
     +++  New H143:  unsigned_types__unsigned32__size >= 0
     +++  New H144:  rr_type__classtype__size >= 0
     +++  New H145:  rr_type__wirestringtypeindex__size >= 0
     +++  New H146:  rr_type__wirestringtype__size >= 0
     +++  New H147:  rr_type__resourcerecordtype__size >= 0
     +++  New H148:  rr_type__returnedrecordsindextype__size >= 0
     +++  New H149:  rr_type__numberofrecordstype__size >= 0
     +++  New H150:  rr_type__soa_record_type__soarecordtype__size >= 0
     +++  New H151:  dns_types__qname_ptr_range__base__first <= 0
     +++  New H152:  dns_types__qname_ptr_range__base__last >= 16383


@@@@@@@@@@  VC: procedure_create_response_soa_14.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H127 has been replaced by "true".  (It is already present, as 
          H115).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H140 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H141 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H142 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H143 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H144 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H147 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H148 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H149 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H150 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H151 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H152 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H153 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H154 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H155 has been replaced by "true".  (It is already present, as 
          H77).
***  Proved C1:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) 
          >= rr_type__wirestringtypeindex__first
     using hypothesis H76.
***  Proved C2:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) 
          <= rr_type__wirestringtypeindex__last
     using hypothesis H77.
***  Proved C3:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) >= rr_type__wirestringtypeindex__first
     using hypothesis H58.
***  Proved C4:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) <= rr_type__wirestringtypeindex__last
     using hypothesis H59.
***  Proved C5:  start_byte + 7 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C8:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) <= rr_type__wirestringtypeindex__last
     using hypothesis H59.
***  Proved C10:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) 
          <= rr_type__wirestringtypeindex__last
     using hypothesis H77.
***  Proved C12:  1 >= rr_type__returnedrecordsindextype__first
     using hypothesis H56.
***  Proved C13:  1 <= rr_type__returnedrecordsindextype__last
     using hypothesis H57.
***  Proved C14:  start_byte + 7 >= dns_types__packet_bytes_range__base__first
     using hypothesis H110.
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H118:  start_byte <= 8177
<S>  New H124:  start_byte <= 8176
<S>  New H130:  start_byte <= 8175
<S>  New H136:  start_byte <= 8174
<S>  New C6:  start_byte <= 8173
<S>  New C11:  start_byte + 7 <= 8154 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New H126:  start_byte <= 2147483643
<S>  New H132:  start_byte <= 2147483642
<S>  New H138:  start_byte <= 2147483641
<S>  New C15:  start_byte <= 2147483640
***  Proved C15:  start_byte <= 2147483640
     using hypothesis H4.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
<S>  New H117:  start_byte >= - 2
<S>  New H123:  start_byte >= - 3
<S>  New H129:  start_byte >= - 4
<S>  New H135:  start_byte >= - 5
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
<S>  New H125:  start_byte >= - 2147483652
<S>  New H131:  start_byte >= - 2147483653
<S>  New H137:  start_byte >= - 2147483654
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H115:  true
<S>  New H121:  true
<S>  New H133:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H116:  true
<S>  New H122:  true
<S>  New H134:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C7:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) >= 0
     using hypothesis H58.
***  Proved C9:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) 
          >= 0
     using hypothesis H76.
***  Proved C11:  start_byte + 7 <= 8154 - (rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) + rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))))
     via its standard form, which is:
     Std.Fm C11:  - start_byte - rr_type__wirenamelength(fld_email(element(
          replies__1, [1]))) - rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) > - 8148
     using hypothesis H100.
---  Eliminated hypothesis H25 (true-hypothesis).
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H48 (true-hypothesis).
---  Eliminated hypothesis H49 (true-hypothesis).
---  Eliminated hypothesis H50 (true-hypothesis).
---  Eliminated hypothesis H51 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H54 (true-hypothesis).
---  Eliminated hypothesis H55 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H64 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H74 (true-hypothesis).
---  Eliminated hypothesis H75 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H81 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H101 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H127 (true-hypothesis).
---  Eliminated hypothesis H128 (true-hypothesis).
---  Eliminated hypothesis H139 (true-hypothesis).
---  Eliminated hypothesis H140 (true-hypothesis).
---  Eliminated hypothesis H141 (true-hypothesis).
---  Eliminated hypothesis H142 (true-hypothesis).
---  Eliminated hypothesis H143 (true-hypothesis).
---  Eliminated hypothesis H144 (true-hypothesis).
---  Eliminated hypothesis H145 (true-hypothesis).
---  Eliminated hypothesis H146 (true-hypothesis).
---  Eliminated hypothesis H147 (true-hypothesis).
---  Eliminated hypothesis H148 (true-hypothesis).
---  Eliminated hypothesis H149 (true-hypothesis).
---  Eliminated hypothesis H150 (true-hypothesis).
---  Eliminated hypothesis H151 (true-hypothesis).
---  Eliminated hypothesis H152 (true-hypothesis).
---  Eliminated hypothesis H153 (true-hypothesis).
---  Eliminated hypothesis H154 (true-hypothesis).
---  Eliminated hypothesis H155 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H95 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H94 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H121 (true-hypothesis).
---  Eliminated hypothesis H133 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H122 (true-hypothesis).
---  Eliminated hypothesis H134 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H108 (duplicate of H6).
---  Eliminated hypothesis H1 (redundant, given H4).
---  Eliminated hypothesis H4 (redundant, given H106).
---  Eliminated hypothesis H24 (redundant, given H2).
---  Eliminated hypothesis H36 (redundant, given H42).
---  Eliminated hypothesis H87 (redundant, given H90).
---  Eliminated hypothesis H89 (redundant, given H88).
---  Eliminated hypothesis H90 (redundant, given H3 & H100).
---  Eliminated hypothesis H98 (redundant, given H3).
---  Eliminated hypothesis H99 (redundant, given H106).
---  Eliminated hypothesis H105 (redundant, given H3).
---  Eliminated hypothesis H106 (redundant, given H107).
---  Eliminated hypothesis H107 (redundant, given H118).
---  Eliminated hypothesis H109 (redundant, given H7).
---  Eliminated hypothesis H110 (redundant, given H3).
---  Eliminated hypothesis H111 (redundant, given H118).
---  Eliminated hypothesis H117 (redundant, given H3).
---  Eliminated hypothesis H118 (redundant, given H124).
---  Eliminated hypothesis H119 (redundant, given H3).
---  Eliminated hypothesis H120 (redundant, given H124).
---  Eliminated hypothesis H123 (redundant, given H3).
---  Eliminated hypothesis H124 (redundant, given H130).
---  Eliminated hypothesis H125 (redundant, given H3).
---  Eliminated hypothesis H126 (redundant, given H130).
---  Eliminated hypothesis H129 (redundant, given H3).
---  Eliminated hypothesis H130 (redundant, given H136).
---  Eliminated hypothesis H131 (redundant, given H3).
---  Eliminated hypothesis H132 (redundant, given H136).
---  Eliminated hypothesis H135 (redundant, given H3).
---  Eliminated hypothesis H137 (redundant, given H3).
---  Eliminated hypothesis H138 (redundant, given H136).
---  Substituted hypothesis H113, which specifies an equivalence for fld_header(
          output_packet__2).
%%%  Simplified H103 further (given H6 & H7), to give:
     %%%  H103:  qname_location >= - 49152
%%%  Simplified H104 further (given H6 & H7), to give:
     %%%  H104:  qname_location <= 16383
     +++  New H156:  integer__size >= 0
     +++  New H157:  character__size >= 0
     +++  New H158:  natural__size >= 0
     +++  New H159:  positive__size >= 0
     +++  New H160:  dns_types__qname_ptr_range__size >= 0
     +++  New H161:  dns_types__qname_ptr_range__base__first <= 
          dns_types__qname_ptr_range__base__last
     +++  New H162:  dns_types__packet_length_range__size >= 0
     +++  New H163:  dns_types__packet_bytes_range__size >= 0
     +++  New H164:  dns_types__dns_packet__size >= 0
     +++  New H165:  unsigned_types__unsigned16__size >= 0
     +++  New H166:  unsigned_types__unsigned32__size >= 0
     +++  New H167:  rr_type__classtype__size >= 0
     +++  New H168:  rr_type__wirestringtypeindex__size >= 0
     +++  New H169:  rr_type__wirestringtype__size >= 0
     +++  New H170:  rr_type__resourcerecordtype__size >= 0
     +++  New H171:  rr_type__returnedrecordsindextype__size >= 0
     +++  New H172:  rr_type__numberofrecordstype__size >= 0
     +++  New H173:  rr_type__soa_record_type__soarecordtype__size >= 0
     +++  New H174:  dns_types__qname_ptr_range__base__first <= 0
     +++  New H175:  dns_types__qname_ptr_range__base__last >= 16383


@@@@@@@@@@  VC: procedure_create_response_soa_15.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H127 has been replaced by "true".  (It is already present, as 
          H115).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H140 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H141 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H142 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H143 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H144 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H147 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H148 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H149 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H150 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H151 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H152 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H153 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H154 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H155 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H156 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H157 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H158 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H159 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H163 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H165 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H167 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H168 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H171 on reading formula in, to give:
     %%%  H171:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified H172 on reading formula in, to give:
     %%%  H172:  fld_header(output_packet__3) = fld_header(output_packet__2)
%%%  Simplified H173 on reading formula in, to give:
     %%%  H173:  output_packet__3 = upf_bytes(output_packet__2, fld_bytes(
          output_packet__3))
---  Hypothesis H174 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H175 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H176 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H177 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H178 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H179 has been replaced by "true".  (It is already present, as 
          H77).
***  Proved C5:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 
          integer__base__first
     using hypothesis H89.
***  Proved C6:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          integer__base__last
     using hypothesis H90.
***  Proved C7:  start_byte + 32 >= dns_types__packet_bytes_range__base__first
     using hypothesis H110.
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H117:  start_byte >= - 2
<S>  New H123:  start_byte >= - 3
<S>  New H129:  start_byte >= - 4
<S>  New H135:  start_byte >= - 5
<S>  New H160:  start_byte >= - 6
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
<S>  New C1:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= 1
<S>  New C3:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) 
          + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H118:  start_byte <= 8177
<S>  New H124:  start_byte <= 8176
<S>  New H130:  start_byte <= 8175
<S>  New H136:  start_byte <= 8174
<S>  New H161:  start_byte <= 8173
<S>  New H166:  start_byte + 7 <= 8154 - (rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) + rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))))
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
<S>  New C2:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= 8180
<S>  New C4:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) 
          + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 8180
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New H126:  start_byte <= 2147483643
<S>  New H132:  start_byte <= 2147483642
<S>  New H138:  start_byte <= 2147483641
<S>  New H170:  start_byte <= 2147483640
<S>  New C8:  start_byte <= 2147483615
***  Proved C8:  start_byte <= 2147483615
     using hypothesis H4.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
<S>  New H125:  start_byte >= - 2147483652
<S>  New H131:  start_byte >= - 2147483653
<S>  New H137:  start_byte >= - 2147483654
<S>  New H169:  start_byte >= - 2147483655
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H115:  true
<S>  New H121:  true
<S>  New H133:  true
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H116:  true
<S>  New H122:  true
<S>  New H134:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= 1
     via its standard form, which is:
     Std.Fm C1:  32 + (start_byte + rr_type__wirenamelength(fld_email(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1])))) >= 1
     using hypotheses H3, H162 & H164.
***  Proved C3:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
     using hypotheses H76 & H162.
***  Proved C4:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])
          )) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          8180
     using hypotheses H59 & H77.
---  Eliminated hypothesis H25 (true-hypothesis).
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H48 (true-hypothesis).
---  Eliminated hypothesis H49 (true-hypothesis).
---  Eliminated hypothesis H50 (true-hypothesis).
---  Eliminated hypothesis H51 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H54 (true-hypothesis).
---  Eliminated hypothesis H55 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H64 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H74 (true-hypothesis).
---  Eliminated hypothesis H75 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H81 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H101 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H127 (true-hypothesis).
---  Eliminated hypothesis H128 (true-hypothesis).
---  Eliminated hypothesis H139 (true-hypothesis).
---  Eliminated hypothesis H140 (true-hypothesis).
---  Eliminated hypothesis H141 (true-hypothesis).
---  Eliminated hypothesis H142 (true-hypothesis).
---  Eliminated hypothesis H143 (true-hypothesis).
---  Eliminated hypothesis H144 (true-hypothesis).
---  Eliminated hypothesis H145 (true-hypothesis).
---  Eliminated hypothesis H146 (true-hypothesis).
---  Eliminated hypothesis H147 (true-hypothesis).
---  Eliminated hypothesis H148 (true-hypothesis).
---  Eliminated hypothesis H149 (true-hypothesis).
---  Eliminated hypothesis H150 (true-hypothesis).
---  Eliminated hypothesis H151 (true-hypothesis).
---  Eliminated hypothesis H152 (true-hypothesis).
---  Eliminated hypothesis H153 (true-hypothesis).
---  Eliminated hypothesis H154 (true-hypothesis).
---  Eliminated hypothesis H155 (true-hypothesis).
---  Eliminated hypothesis H156 (true-hypothesis).
---  Eliminated hypothesis H157 (true-hypothesis).
---  Eliminated hypothesis H158 (true-hypothesis).
---  Eliminated hypothesis H159 (true-hypothesis).
---  Eliminated hypothesis H163 (true-hypothesis).
---  Eliminated hypothesis H165 (true-hypothesis).
---  Eliminated hypothesis H167 (true-hypothesis).
---  Eliminated hypothesis H168 (true-hypothesis).
---  Eliminated hypothesis H174 (true-hypothesis).
---  Eliminated hypothesis H175 (true-hypothesis).
---  Eliminated hypothesis H176 (true-hypothesis).
---  Eliminated hypothesis H177 (true-hypothesis).
---  Eliminated hypothesis H178 (true-hypothesis).
---  Eliminated hypothesis H179 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H95 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H94 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H121 (true-hypothesis).
---  Eliminated hypothesis H133 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H122 (true-hypothesis).
---  Eliminated hypothesis H134 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H108 (duplicate of H6).
---  Eliminated hypothesis H166 (duplicate of H100).
---  Eliminated hypothesis H1 (redundant, given H4).
---  Eliminated hypothesis H4 (redundant, given H106).
---  Eliminated hypothesis H24 (redundant, given H2).
---  Eliminated hypothesis H36 (redundant, given H42).
---  Eliminated hypothesis H87 (redundant, given H90).
---  Eliminated hypothesis H89 (redundant, given H88).
---  Eliminated hypothesis H90 (redundant, given H3 & H100).
---  Eliminated hypothesis H98 (redundant, given H3).
---  Eliminated hypothesis H99 (redundant, given H106).
---  Eliminated hypothesis H105 (redundant, given H3).
---  Eliminated hypothesis H106 (redundant, given H107).
---  Eliminated hypothesis H107 (redundant, given H118).
---  Eliminated hypothesis H109 (redundant, given H7).
---  Eliminated hypothesis H110 (redundant, given H3).
---  Eliminated hypothesis H111 (redundant, given H118).
---  Eliminated hypothesis H117 (redundant, given H3).
---  Eliminated hypothesis H118 (redundant, given H124).
---  Eliminated hypothesis H119 (redundant, given H3).
---  Eliminated hypothesis H120 (redundant, given H124).
---  Eliminated hypothesis H123 (redundant, given H3).
---  Eliminated hypothesis H124 (redundant, given H130).
---  Eliminated hypothesis H125 (redundant, given H3).
---  Eliminated hypothesis H126 (redundant, given H130).
---  Eliminated hypothesis H129 (redundant, given H3).
---  Eliminated hypothesis H130 (redundant, given H136).
---  Eliminated hypothesis H131 (redundant, given H3).
---  Eliminated hypothesis H132 (redundant, given H136).
---  Eliminated hypothesis H135 (redundant, given H3).
---  Eliminated hypothesis H136 (redundant, given H161).
---  Eliminated hypothesis H137 (redundant, given H3).
---  Eliminated hypothesis H138 (redundant, given H161).
---  Eliminated hypothesis H160 (redundant, given H3).
---  Eliminated hypothesis H162 (redundant, given H58).
---  Eliminated hypothesis H164 (redundant, given H76).
---  Eliminated hypothesis H169 (redundant, given H3).
---  Eliminated hypothesis H170 (redundant, given H161).
-S-  Substituted hypothesis H113.
     This was achieved by replacing all occurrences of fld_header(
          output_packet__2) by:
          fld_header(output_packet).
---  Substituted hypothesis H172, which specifies an equivalence for fld_header(
          output_packet__3).
%%%  Simplified H103 further (given H6 & H7), to give:
     %%%  H103:  qname_location >= - 49152
%%%  Simplified H104 further (given H6 & H7), to give:
     %%%  H104:  qname_location <= 16383
     +++  New H180:  integer__size >= 0
     +++  New H181:  character__size >= 0
     +++  New H182:  natural__size >= 0
     +++  New H183:  positive__size >= 0
     +++  New H184:  dns_types__qname_ptr_range__size >= 0
     +++  New H185:  dns_types__qname_ptr_range__base__first <= 
          dns_types__qname_ptr_range__base__last
     +++  New H186:  dns_types__packet_length_range__size >= 0
     +++  New H187:  dns_types__packet_bytes_range__size >= 0
     +++  New H188:  dns_types__dns_packet__size >= 0
     +++  New H189:  unsigned_types__unsigned16__size >= 0
     +++  New H190:  unsigned_types__unsigned32__size >= 0
     +++  New H191:  rr_type__classtype__size >= 0
     +++  New H192:  rr_type__wirestringtypeindex__size >= 0
     +++  New H193:  rr_type__wirestringtype__size >= 0
     +++  New H194:  rr_type__resourcerecordtype__size >= 0
     +++  New H195:  rr_type__returnedrecordsindextype__size >= 0
     +++  New H196:  rr_type__numberofrecordstype__size >= 0
     +++  New H197:  rr_type__soa_record_type__soarecordtype__size >= 0
     +++  New H198:  dns_types__qname_ptr_range__base__first <= 0
     +++  New H199:  dns_types__qname_ptr_range__base__last >= 16383


@@@@@@@@@@  VC: procedure_create_response_soa_16.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H127 has been replaced by "true".  (It is already present, as 
          H115).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H140 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H141 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H142 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H143 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H144 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H147 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H148 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H149 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H150 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H151 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H152 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H153 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H154 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H155 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H156 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H157 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H158 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H159 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H163 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H165 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H167 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H168 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H171 on reading formula in, to give:
     %%%  H171:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified H172 on reading formula in, to give:
     %%%  H172:  fld_header(output_packet__3) = fld_header(output_packet__2)
%%%  Simplified H173 on reading formula in, to give:
     %%%  H173:  output_packet__3 = upf_bytes(output_packet__2, fld_bytes(
          output_packet__3))
---  Hypothesis H174 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H175 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H176 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H177 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H178 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H179 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H184 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H185 has been replaced by "true".  (It is already present, as 
          H90).
---  Hypothesis H188 has been replaced by "true".  (It is already present, as 
          H180).
---  Hypothesis H189 has been replaced by "true".  (It is already present, as 
          H181).
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  true
***  Proved C9:  dns_types__header_bits div 8 >= system__min_int
     using hypothesis H95.
***  Proved C10:  dns_types__header_bits div 8 <= system__max_int
     using hypothesis H96.
***  Proved C11:  true
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New C1:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) + dns_types__header_bits div 8 >= 0
<S>  New C3:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) + dns_types__header_bits div 8 >= 0
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New C2:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) + dns_types__header_bits div 8 <= 8192
<S>  New C4:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) + dns_types__header_bits div 8 <= 8192
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
<S>  New H125:  start_byte >= - 2147483652
<S>  New H131:  start_byte >= - 2147483653
<S>  New H137:  start_byte >= - 2147483654
<S>  New H169:  start_byte >= - 2147483655
<S>  New H186:  start_byte >= - 2147483680
<S>  New C5:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) + dns_types__header_bits div 8 >= - 2147483648
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New H126:  start_byte <= 2147483643
<S>  New H132:  start_byte <= 2147483642
<S>  New H138:  start_byte <= 2147483641
<S>  New H170:  start_byte <= 2147483640
<S>  New H187:  start_byte <= 2147483615
<S>  New C6:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) + dns_types__header_bits div 8 <= 2147483647
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H117:  start_byte >= - 2
<S>  New H123:  start_byte >= - 3
<S>  New H129:  start_byte >= - 4
<S>  New H135:  start_byte >= - 5
<S>  New H160:  start_byte >= - 6
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
<S>  New H180:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= 1
<S>  New H182:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New C7:  dns_types__header_bits div 8 >= 1
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H118:  start_byte <= 8177
<S>  New H124:  start_byte <= 8176
<S>  New H130:  start_byte <= 8175
<S>  New H136:  start_byte <= 8174
<S>  New H161:  start_byte <= 8173
<S>  New H166:  start_byte + 7 <= 8154 - (rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) + rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))))
<S>  New H181:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
<S>  New H183:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          8180
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
<S>  New C8:  dns_types__header_bits div 8 <= 8180
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
<S>  New C1:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= - 12
<S>  New C3:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= - 12
<S>  New C2:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= 8180
<S>  New C4:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= 8180
<S>  New C5:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= - 2147483660
<S>  New C6:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= 2147483635
<S>  New C7:  true
<S>  New C8:  true
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H115:  true
<S>  New H121:  true
<S>  New H133:  true
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H116:  true
<S>  New H122:  true
<S>  New H134:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= - 12
     using hypothesis H180.
***  Proved C3:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= - 12
     using hypothesis H180.
***  Proved C2:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
     using hypothesis H181.
***  Proved C4:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
     using hypothesis H181.
***  Proved C5:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= - 2147483660
     using hypothesis H180.
***  Proved C6:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 2147483635
     using hypothesis H181.
***  Proved C7:  true
***  Proved C8:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_17.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  true
***  Proved C9:  dns_types__header_bits div 8 >= system__min_int
     using hypothesis H95.
***  Proved C10:  dns_types__header_bits div 8 <= system__max_int
     using hypothesis H96.
***  Proved C11:  true
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New C1:  start_byte + dns_types__header_bits div 8 >= 0
<S>  New C3:  start_byte + dns_types__header_bits div 8 >= 0
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New C2:  start_byte + dns_types__header_bits div 8 <= 8192
<S>  New C4:  start_byte + dns_types__header_bits div 8 <= 8192
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C5:  start_byte + dns_types__header_bits div 8 >= - 2147483648
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C6:  start_byte + dns_types__header_bits div 8 <= 2147483647
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New C7:  dns_types__header_bits div 8 >= 1
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New C8:  dns_types__header_bits div 8 <= 8180
>>>  Restructured hypothesis H100 into:
     >>>  H100:  dns_types__packet_size - (32 + dns_types__header_bits div 8) - 
          (rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          start_byte
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          start_byte
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= start_byte
<S>  New C1:  start_byte >= - 12
<S>  New C3:  start_byte >= - 12
<S>  New C2:  start_byte <= 8180
<S>  New C4:  start_byte <= 8180
<S>  New C5:  start_byte >= - 2147483660
<S>  New C6:  start_byte <= 2147483635
<S>  New C7:  true
<S>  New C8:  true
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  start_byte >= - 12
     using hypothesis H3.
***  Proved C3:  start_byte >= - 12
     using hypothesis H3.
***  Proved C2:  start_byte <= 8180
     using hypothesis H4.
***  Proved C4:  start_byte <= 8180
     using hypothesis H4.
***  Proved C5:  start_byte >= - 2147483660
     using hypothesis H3.
***  Proved C6:  start_byte <= 2147483635
     using hypothesis H4.
***  Proved C7:  true
***  Proved C8:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_18.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  true
***  Proved C11:  true
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New C1:  start_byte + dns_types__header_bits div 8 >= 0
<S>  New C3:  start_byte + dns_types__header_bits div 8 >= 0
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New C2:  start_byte + dns_types__header_bits div 8 <= 8192
<S>  New C4:  start_byte + dns_types__header_bits div 8 <= 8192
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C5:  start_byte + dns_types__header_bits div 8 >= - 2147483648
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C6:  start_byte + dns_types__header_bits div 8 <= 2147483647
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New C7:  dns_types__header_bits div 8 >= 1
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New C8:  dns_types__header_bits div 8 <= 8180
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New C9:  dns_types__header_bits div 8 >= - 9223372036854775808
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New C10:  dns_types__header_bits div 8 <= 9223372036854775807
>>>  Restructured hypothesis H42 into:
     >>>  H42:  num_found__1 < 1
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New C1:  start_byte >= - 12
<S>  New C3:  start_byte >= - 12
<S>  New C2:  start_byte <= 8180
<S>  New C4:  start_byte <= 8180
<S>  New C5:  start_byte >= - 2147483660
<S>  New C6:  start_byte <= 2147483635
<S>  New C7:  true
<S>  New C8:  true
<S>  New C9:  true
<S>  New C10:  true
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  start_byte >= - 12
     using hypothesis H3.
***  Proved C3:  start_byte >= - 12
     using hypothesis H3.
***  Proved C2:  start_byte <= 8180
     using hypothesis H4.
***  Proved C4:  start_byte <= 8180
     using hypothesis H4.
***  Proved C5:  start_byte >= - 2147483660
     using hypothesis H3.
***  Proved C6:  start_byte <= 2147483635
     using hypothesis H4.
***  Proved C7:  true
***  Proved C8:  true
***  Proved C9:  true
***  Proved C10:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_19.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H127 has been replaced by "true".  (It is already present, as 
          H115).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H140 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H141 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H142 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H143 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H144 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H147 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H148 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H149 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H150 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H151 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H152 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H153 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H154 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H155 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H156 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H157 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H158 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H159 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H163 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H165 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H167 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H168 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H171 on reading formula in, to give:
     %%%  H171:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified H172 on reading formula in, to give:
     %%%  H172:  fld_header(output_packet__3) = fld_header(output_packet__2)
%%%  Simplified H173 on reading formula in, to give:
     %%%  H173:  output_packet__3 = upf_bytes(output_packet__2, fld_bytes(
          output_packet__3))
---  Hypothesis H174 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H175 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H176 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H177 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H178 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H179 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H184 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H185 has been replaced by "true".  (It is already present, as 
          H90).
---  Hypothesis H188 has been replaced by "true".  (It is already present, as 
          H180).
---  Hypothesis H189 has been replaced by "true".  (It is already present, as 
          H181).
---  Hypothesis H192 has been replaced by "true".  (It is already present, as 
          H190).
---  Hypothesis H193 has been replaced by "true".  (It is already present, as 
          H191).
---  Hypothesis H198 has been replaced by "true".  (It is already present, as 
          H95).
---  Hypothesis H199 has been replaced by "true".  (It is already present, as 
          H96).
---  Hypothesis H200 has been replaced by "true".  (It is already present, as 
          H97).
---  Hypothesis H201 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H202 has been replaced by "true".  (It is already present, as 
          H37).
***  Proved C1:  answer_count + num_found__1 >= dns_types__unsigned_short__first
     using hypotheses H23 & H42.
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H2:  answer_count <= 65535 - rr_type__maxnumrecords
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New C2:  answer_count + num_found__1 <= 65535
<S>  New C4:  num_found__1 <= 65535
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
<S>  New C3:  num_found__1 >= 0
***  Proved C3:  num_found__1 >= 0
     using hypothesis H42.
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H190:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 >= 
          dns_types__packet_length_range__first
<S>  New H191:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 <= 
          dns_types__packet_length_range__last
<S>  New H194:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 >= 
          dns_types__packet_bytes_range__base__first
<S>  New H195:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 <= 
          dns_types__packet_bytes_range__base__last
<S>  New H196:  12 >= dns_types__packet_bytes_range__first
<S>  New H197:  12 <= dns_types__packet_bytes_range__last
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New H190:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= - 12
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New H191:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H117:  start_byte >= - 2
<S>  New H123:  start_byte >= - 3
<S>  New H129:  start_byte >= - 4
<S>  New H135:  start_byte >= - 5
<S>  New H160:  start_byte >= - 6
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
<S>  New H180:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= 1
<S>  New H182:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H196:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H118:  start_byte <= 8177
<S>  New H124:  start_byte <= 8176
<S>  New H130:  start_byte <= 8175
<S>  New H136:  start_byte <= 8174
<S>  New H161:  start_byte <= 8173
<S>  New H166:  start_byte + 7 <= 8154 - (rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) + rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))))
<S>  New H181:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
<S>  New H183:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          8180
<S>  New H197:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
<S>  New H125:  start_byte >= - 2147483652
<S>  New H131:  start_byte >= - 2147483653
<S>  New H137:  start_byte >= - 2147483654
<S>  New H169:  start_byte >= - 2147483655
<S>  New H186:  start_byte >= - 2147483680
<S>  New H194:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= - 2147483660
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New H126:  start_byte <= 2147483643
<S>  New H132:  start_byte <= 2147483642
<S>  New H138:  start_byte <= 2147483641
<S>  New H170:  start_byte <= 2147483640
<S>  New H187:  start_byte <= 2147483615
<S>  New H195:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 2147483635
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H115:  true
<S>  New H121:  true
<S>  New H133:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H116:  true
<S>  New H122:  true
<S>  New H134:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C2:  answer_count + num_found__1 <= 65535
     using hypotheses H2 & H37.
***  Proved C4:  num_found__1 <= 65535
     using hypothesis H37.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_20.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H104).
---  Hypothesis H111 has been replaced by "true".  (It is already present, as 
          H95).
---  Hypothesis H112 has been replaced by "true".  (It is already present, as 
          H96).
---  Hypothesis H113 has been replaced by "true".  (It is already present, as 
          H97).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H37).
***  Proved C1:  answer_count + num_found__1 >= dns_types__unsigned_short__first
     using hypotheses H23 & H42.
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H2:  answer_count <= 65535 - rr_type__maxnumrecords
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New C2:  answer_count + num_found__1 <= 65535
<S>  New C4:  num_found__1 <= 65535
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
<S>  New C3:  num_found__1 >= 0
***  Proved C3:  num_found__1 >= 0
     using hypothesis H42.
>>>  Restructured hypothesis H100 into:
     >>>  H100:  dns_types__packet_size - (32 + dns_types__header_bits div 8) - 
          (rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          start_byte
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          start_byte
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H103:  start_byte + 12 >= dns_types__packet_length_range__first
<S>  New H104:  start_byte + 12 <= dns_types__packet_length_range__last
<S>  New H107:  start_byte + 12 >= dns_types__packet_bytes_range__base__first
<S>  New H108:  start_byte + 12 <= dns_types__packet_bytes_range__base__last
<S>  New H109:  12 >= dns_types__packet_bytes_range__first
<S>  New H110:  12 <= dns_types__packet_bytes_range__last
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H100:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= start_byte
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H93:  true
<S>  New H95:  true
<S>  New H91:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H94:  true
<S>  New H96:  true
<S>  New H92:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New H103:  start_byte >= - 12
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New H104:  start_byte <= 8180
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H109:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H110:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H107:  start_byte >= - 2147483660
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H108:  start_byte <= 2147483635
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C2:  answer_count + num_found__1 <= 65535
     using hypotheses H2 & H37.
***  Proved C4:  num_found__1 <= 65535
     using hypothesis H37.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_21.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H45).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H46).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  true
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H37).
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
<S>  New C1:  answer_count + num_found__1 >= 0
<S>  New C3:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H2:  answer_count <= 65535 - rr_type__maxnumrecords
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New C2:  answer_count + num_found__1 <= 65535
<S>  New C4:  num_found__1 <= 65535
***  Proved C2:  answer_count + num_found__1 <= 65535
     using hypotheses H24 & H42.
***  Proved C4:  num_found__1 <= 65535
     using hypothesis H42.
>>>  Restructured hypothesis H42 into:
     >>>  H42:  num_found__1 < 1
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H45:  start_byte + 12 >= dns_types__packet_length_range__first
<S>  New H46:  start_byte + 12 <= dns_types__packet_length_range__last
<S>  New H49:  start_byte + 12 >= dns_types__packet_bytes_range__base__first
<S>  New H50:  start_byte + 12 <= dns_types__packet_bytes_range__base__last
<S>  New H51:  12 >= dns_types__packet_bytes_range__first
<S>  New H52:  12 <= dns_types__packet_bytes_range__last
<S>  New H53:  12 >= system__min_int
<S>  New H54:  12 <= system__max_int
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H53:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H54:  true
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New H45:  start_byte >= - 12
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New H46:  start_byte <= 8180
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H51:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H52:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H49:  start_byte >= - 2147483660
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H50:  start_byte <= 2147483635
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  answer_count + num_found__1 >= 0
     using hypotheses H23 & H36.
***  Proved C3:  num_found__1 >= 0
     using hypothesis H36.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_22.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
%%%  Simplified H112 on reading formula in, to give:
     %%%  H112:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H127 has been replaced by "true".  (It is already present, as 
          H115).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H140 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H141 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H142 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H143 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H144 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H147 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H148 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H149 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H150 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H151 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H152 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H153 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H154 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H155 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H156 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H157 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H158 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H159 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H163 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H165 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H167 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H168 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H171 on reading formula in, to give:
     %%%  H171:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified H172 on reading formula in, to give:
     %%%  H172:  fld_header(output_packet__3) = fld_header(output_packet__2)
%%%  Simplified H173 on reading formula in, to give:
     %%%  H173:  output_packet__3 = upf_bytes(output_packet__2, fld_bytes(
          output_packet__3))
---  Hypothesis H174 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H175 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H176 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H177 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H178 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H179 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H184 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H185 has been replaced by "true".  (It is already present, as 
          H90).
---  Hypothesis H188 has been replaced by "true".  (It is already present, as 
          H180).
---  Hypothesis H189 has been replaced by "true".  (It is already present, as 
          H181).
---  Hypothesis H192 has been replaced by "true".  (It is already present, as 
          H190).
---  Hypothesis H193 has been replaced by "true".  (It is already present, as 
          H191).
---  Hypothesis H198 has been replaced by "true".  (It is already present, as 
          H95).
---  Hypothesis H199 has been replaced by "true".  (It is already present, as 
          H96).
---  Hypothesis H200 has been replaced by "true".  (It is already present, as 
          H97).
---  Hypothesis H201 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H202 has been replaced by "true".  (It is already present, as 
          H37).
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
<S>  New C2:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) + dns_types__header_bits div 8 <= 8192
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H100:  start_byte < 8148 - (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1]))))
<S>  New H190:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 >= 
          dns_types__packet_length_range__first
<S>  New H191:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 <= 
          dns_types__packet_length_range__last
<S>  New H194:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 >= 
          dns_types__packet_bytes_range__base__first
<S>  New H195:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) + 12 <= 
          dns_types__packet_bytes_range__base__last
<S>  New H196:  12 >= dns_types__packet_bytes_range__first
<S>  New H197:  12 <= dns_types__packet_bytes_range__last
<S>  New C1:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= 1
<S>  New C2:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= 8180
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
<S>  New C3:  answer_count + num_found__1 <= answer_count + 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H91:  true
<S>  New H93:  true
<S>  New H95:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H92:  true
<S>  New H94:  true
<S>  New H96:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New H190:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= - 12
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New H191:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H105:  start_byte >= 0
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H117:  start_byte >= - 2
<S>  New H123:  start_byte >= - 3
<S>  New H129:  start_byte >= - 4
<S>  New H135:  start_byte >= - 5
<S>  New H160:  start_byte >= - 6
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
<S>  New H180:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= 1
<S>  New H182:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H196:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H106:  start_byte <= 8179
<S>  New H107:  start_byte <= 8178
<S>  New H118:  start_byte <= 8177
<S>  New H124:  start_byte <= 8176
<S>  New H130:  start_byte <= 8175
<S>  New H136:  start_byte <= 8174
<S>  New H161:  start_byte <= 8173
<S>  New H166:  start_byte + 7 <= 8154 - (rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) + rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))))
<S>  New H181:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
<S>  New H183:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          8180
<S>  New H197:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__2), [i___1]
          ) and element(fld_bytes(output_packet__2), [i___1]) <= 
          dns_types__byte__last)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet__3), [i___1]
          ) and element(fld_bytes(output_packet__3), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H110:  start_byte >= - 2147483649
<S>  New H119:  start_byte >= - 2147483651
<S>  New H125:  start_byte >= - 2147483652
<S>  New H131:  start_byte >= - 2147483653
<S>  New H137:  start_byte >= - 2147483654
<S>  New H169:  start_byte >= - 2147483655
<S>  New H186:  start_byte >= - 2147483680
<S>  New H194:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= - 2147483660
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H111:  start_byte <= 2147483646
<S>  New H120:  start_byte <= 2147483644
<S>  New H126:  start_byte <= 2147483643
<S>  New H132:  start_byte <= 2147483642
<S>  New H138:  start_byte <= 2147483641
<S>  New H170:  start_byte <= 2147483640
<S>  New H187:  start_byte <= 2147483615
<S>  New H195:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 2147483635
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H115:  true
<S>  New H121:  true
<S>  New H133:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= dns_types__byte__last)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H116:  true
<S>  New H122:  true
<S>  New H134:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
<S>  New H112:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__2), [i___1]) and element(fld_bytes(
          output_packet__2), [i___1]) <= 255)
<S>  New H171:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet__3), [i___1]) and element(fld_bytes(
          output_packet__3), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
<S>  New H203:  answer_count + num_found__1 >= 0
<S>  New H205:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H204:  answer_count + num_found__1 <= 65535
<S>  New H206:  num_found__1 <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(120).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H103:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H108:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(121).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H104:  (qname_location + 49152) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H109:  qname_location <= 65535
-S-  Applied substitution rule create_respo_rules(124).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H103:  (qname_location + 49152) mod 65536 >= 0
<S>  New H104:  (qname_location + 49152) mod 65536 <= 65535
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) >= 1
     using hypothesis H180.
***  Proved C2:  start_byte + 32 + (rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1]))) + rr_type__wirenamelength(fld_email(
          element(replies__1, [1])))) <= 8180
     using hypothesis H191.
***  Proved C3:  answer_count + num_found__1 <= answer_count + 64
     using hypothesis H37.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_23.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H35).
%%%  Simplified H60 on reading formula in, to give:
     %%%  H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))
          ) = rr_type__maxdomainnamelength + 1 or element(fld_nameserver(
          element(replies__1, [1])), [rr_type__wirenamelength(fld_nameserver(
          element(replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ 
          and q_ <= rr_type__wirenamelength(fld_nameserver(element(replies__1, [
          1]))) - 1 -> element(fld_nameserver(element(replies__1, [1])), [q_]) 
          <> 0)
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H44).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H29).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          rr_type__maxdomainnamelength + 1 or element(fld_email(element(
          replies__1, [1])), [rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))]) = 0 and for_all(q_ : integer, 1 <= q_ and q_ <= 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))) - 1 -> 
          element(fld_email(element(replies__1, [1])), [q_]) <> 0)
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H82 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H76).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H77).
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  true
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H3).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H4).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H104).
---  Hypothesis H111 has been replaced by "true".  (It is already present, as 
          H95).
---  Hypothesis H112 has been replaced by "true".  (It is already present, as 
          H96).
---  Hypothesis H113 has been replaced by "true".  (It is already present, as 
          H97).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H37).
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New H87:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) >= 
          integer__base__first
<S>  New H88:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          integer__base__last
<S>  New H91:  8192 - (32 + dns_types__header_bits div 8) >= system__min_int
<S>  New H92:  8192 - (32 + dns_types__header_bits div 8) <= system__max_int
<S>  New H100:  not start_byte < 8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1]))))
<S>  New C2:  start_byte + dns_types__header_bits div 8 <= 8192
>>>  Restructured hypothesis H100 into:
     >>>  H100:  8192 - (32 + dns_types__header_bits div 8) - (
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1]))) + 
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))) <= 
          start_byte
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H87:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) >= integer__base__first
<S>  New H88:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= integer__base__last
<S>  New H91:  8148 >= system__min_int
<S>  New H92:  8148 <= system__max_int
<S>  New H93:  44 >= system__min_int
<S>  New H94:  44 <= system__max_int
<S>  New H95:  12 >= system__min_int
<S>  New H96:  12 <= system__max_int
<S>  New H100:  8148 - (rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))) <= start_byte
<S>  New H103:  start_byte + 12 >= dns_types__packet_length_range__first
<S>  New H104:  start_byte + 12 <= dns_types__packet_length_range__last
<S>  New H107:  start_byte + 12 >= dns_types__packet_bytes_range__base__first
<S>  New H108:  start_byte + 12 <= dns_types__packet_bytes_range__base__last
<S>  New H109:  12 >= dns_types__packet_bytes_range__first
<S>  New H110:  12 <= dns_types__packet_bytes_range__last
<S>  New C1:  start_byte >= 1
<S>  New C2:  start_byte <= 8180
-S-  Applied substitution rule create_respo_rules(3).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H60:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           = 129 or element(fld_nameserver(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))]) = 
          0 and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_nameserver(element(replies__1, [1]))) - 1 -> element(
          fld_nameserver(element(replies__1, [1])), [q_]) <> 0)
<S>  New H78:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) = 
          129 or element(fld_email(element(replies__1, [1])), [
          rr_type__wirenamelength(fld_email(element(replies__1, [1])))]) = 0 
          and for_all(q_ : integer, 1 <= q_ and q_ <= rr_type__wirenamelength(
          fld_email(element(replies__1, [1]))) - 1 -> element(fld_email(element(
          replies__1, [1])), [q_]) <> 0)
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
<S>  New C3:  answer_count + num_found__1 <= answer_count + 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H91:  true
<S>  New H93:  true
<S>  New H95:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H92:  true
<S>  New H94:  true
<S>  New H96:  true
-S-  Applied substitution rule create_respo_rules(8).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H98:  start_byte >= - 2147483648
-S-  Applied substitution rule create_respo_rules(9).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H99:  start_byte <= 2147483647
-S-  Applied substitution rule create_respo_rules(10).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H89:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= - 
          2147483648
<S>  New H87:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147491796
-S-  Applied substitution rule create_respo_rules(11).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H90:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           + rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          2147483647
<S>  New H88:  - 2147475499 <= rr_type__wirenamelength(fld_nameserver(element(
          replies__1, [1]))) + rr_type__wirenamelength(fld_email(element(
          replies__1, [1])))
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H43:  true
-S-  Applied substitution rule create_respo_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H44:  true
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New H103:  start_byte >= - 12
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New H104:  start_byte <= 8180
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H109:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H110:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H107:  start_byte >= - 2147483660
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H108:  start_byte <= 2147483635
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
<S>  New H116:  answer_count + num_found__1 >= 0
<S>  New H118:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H117:  answer_count + num_found__1 <= 65535
<S>  New H119:  num_found__1 <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H58:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           >= 1
<S>  New H76:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H59:  rr_type__wirenamelength(fld_nameserver(element(replies__1, [1])))
           <= 129
<S>  New H77:  rr_type__wirenamelength(fld_email(element(replies__1, [1]))) <= 
          129
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H56:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H57:  true
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  start_byte >= 1
     using hypothesis H3.
***  Proved C2:  start_byte <= 8180
     using hypothesis H104.
***  Proved C3:  answer_count + num_found__1 <= answer_count + 64
     using hypothesis H37.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_create_response_soa_24.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(domainname, [i___1]) and element(
          domainname, [i___1]) <= character__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  dns_types__opcode_type__first <= fld_opcode(fld_header(
          output_packet))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  dns_types__response_code__first <= fld_rcode(fld_header(
          output_packet))
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) and fld_ttlinseconds(fld_inherit(
          element(replies__1, [i___1]))) <= unsigned_types__unsigned32__last)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 
          character__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= character__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_serialnumber(element(
          replies__1, [i___1])) and fld_serialnumber(element(replies__1, [i___1]
          )) <= unsigned_types__unsigned32__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_refresh(element(replies__1, [
          i___1])) and fld_refresh(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_retry(element(replies__1, [
          i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_expiry(element(replies__1, [
          i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_minimum(element(replies__1, [
          i___1])) and fld_minimum(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H45).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H46).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  true
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H37).
-S-  Applied substitution rule create_respo_rules(1).
     This was achieved by replacing all occurrences of dns_types__packet_size 
          by:
          8192.
<S>  New H1:  start_byte <= 8192
<S>  New C2:  start_byte + dns_types__header_bits div 8 <= 8192
>>>  Restructured hypothesis H42 into:
     >>>  H42:  num_found__1 < 1
-S-  Applied substitution rule create_respo_rules(2).
     This was achieved by replacing all occurrences of dns_types__header_bits 
          by:
          96.
<S>  New H45:  start_byte + 12 >= dns_types__packet_length_range__first
<S>  New H46:  start_byte + 12 <= dns_types__packet_length_range__last
<S>  New H49:  start_byte + 12 >= dns_types__packet_bytes_range__base__first
<S>  New H50:  start_byte + 12 <= dns_types__packet_bytes_range__base__last
<S>  New H51:  12 >= dns_types__packet_bytes_range__first
<S>  New H52:  12 <= dns_types__packet_bytes_range__last
<S>  New H53:  12 >= system__min_int
<S>  New H54:  12 <= system__max_int
<S>  New C1:  start_byte >= 1
<S>  New C2:  start_byte <= 8180
-S-  Applied substitution rule create_respo_rules(4).
     This was achieved by replacing all occurrences of rr_type__maxnumrecords 
          by:
          64.
<S>  New H2:  answer_count <= dns_types__unsigned_short__last - 64
<S>  New C3:  answer_count + num_found__1 <= answer_count + 64
-S-  Applied substitution rule create_respo_rules(5).
     This was achieved by replacing all occurrences of system__min_int by:
          - 9223372036854775808.
<S>  New H53:  true
-S-  Applied substitution rule create_respo_rules(6).
     This was achieved by replacing all occurrences of system__max_int by:
          9223372036854775807.
<S>  New H54:  true
-S-  Applied substitution rule create_respo_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 
          character__last)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= character__last))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= character__last))
-S-  Applied substitution rule create_respo_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 
          rr_type__wirestringtypeindex__first <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) and element(fld_nameserver(
          element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(28).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__first by:
          0.
<S>  New H6:  qname_location >= 0
-S-  Applied substitution rule create_respo_rules(29).
     This was achieved by replacing all occurrences of 
          dns_types__qname_ptr_range__last by:
          16383.
<S>  New H7:  qname_location <= 16383
-S-  Applied substitution rule create_respo_rules(34).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__first by:
          0.
<S>  New H45:  start_byte >= - 12
-S-  Applied substitution rule create_respo_rules(35).
     This was achieved by replacing all occurrences of 
          dns_types__packet_length_range__last by:
          8192.
<S>  New H46:  start_byte <= 8180
-S-  Applied substitution rule create_respo_rules(39).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H3:  start_byte >= 1
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
<S>  New H51:  true
-S-  Applied substitution rule create_respo_rules(40).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H52:  true
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(fld_bytes(output_packet), [i___1]) 
          and element(fld_bytes(output_packet), [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(41).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H49:  start_byte >= - 2147483660
-S-  Applied substitution rule create_respo_rules(42).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H50:  start_byte <= 2147483635
-S-  Applied substitution rule create_respo_rules(45).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule create_respo_rules(46).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H22:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(fld_bytes(output_packet), [i___1]) and element(fld_bytes(
          output_packet), [i___1]) <= 255)
-S-  Applied substitution rule create_respo_rules(52).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__first by:
          0.
<S>  New H8:  fld_messageid(fld_header(output_packet)) >= 0
<S>  New H14:  fld_qdcount(fld_header(output_packet)) >= 0
<S>  New H16:  fld_ancount(fld_header(output_packet)) >= 0
<S>  New H18:  fld_nscount(fld_header(output_packet)) >= 0
<S>  New H20:  fld_arcount(fld_header(output_packet)) >= 0
<S>  New H23:  answer_count >= 0
<S>  New H58:  answer_count + num_found__1 >= 0
<S>  New H60:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(53).
     This was achieved by replacing all occurrences of 
          dns_types__unsigned_short__last by:
          65535.
<S>  New H9:  fld_messageid(fld_header(output_packet)) <= 65535
<S>  New H15:  fld_qdcount(fld_header(output_packet)) <= 65535
<S>  New H17:  fld_ancount(fld_header(output_packet)) <= 65535
<S>  New H19:  fld_nscount(fld_header(output_packet)) <= 65535
<S>  New H21:  fld_arcount(fld_header(output_packet)) <= 65535
<S>  New H24:  answer_count <= 65535
<S>  New H59:  answer_count + num_found__1 <= 65535
<S>  New H61:  num_found__1 <= 65535
<S>  New H2:  answer_count <= 65471
-S-  Applied substitution rule create_respo_rules(58).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__first by:
          dns_types__query.
<S>  New H10:  dns_types__query <= fld_opcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(59).
     This was achieved by replacing all occurrences of 
          dns_types__opcode_type__last by:
          dns_types__status.
<S>  New H11:  fld_opcode(fld_header(output_packet)) <= dns_types__status
-S-  Applied substitution rule create_respo_rules(84).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__first by:
          dns_types__no_error.
<S>  New H12:  dns_types__no_error <= fld_rcode(fld_header(output_packet))
-S-  Applied substitution rule create_respo_rules(85).
     This was achieved by replacing all occurrences of 
          dns_types__response_code__last by:
          dns_types__refused.
<S>  New H13:  fld_rcode(fld_header(output_packet)) <= dns_types__refused
-S-  Applied substitution rule create_respo_rules(126).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 
          unsigned_types__unsigned32__last)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= unsigned_types__unsigned32__last)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          unsigned_types__unsigned32__last)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= unsigned_types__unsigned32__last)
-S-  Applied substitution rule create_respo_rules(127).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H27:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
-S-  Applied substitution rule create_respo_rules(132).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__classtype__last)
-S-  Applied substitution rule create_respo_rules(133).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
-S-  Applied substitution rule create_respo_rules(159).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(domainname, [i___1]
          ) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) and 
          element(fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255)
          )
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> 0 <= 
          element(fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(160).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(domainname, [i___1]) and element(domainname, [i___1]) <= 255)
<S>  New H29:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 
          rr_type__returnedrecordsindextype__first <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(167).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) and fld_ttlinseconds(
          fld_inherit(element(replies__1, [i___1]))) <= 4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_serialnumber(
          element(replies__1, [i___1])) and fld_serialnumber(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_refresh(element(
          replies__1, [i___1])) and fld_refresh(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_retry(element(
          replies__1, [i___1])) and fld_retry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_expiry(element(
          replies__1, [i___1])) and fld_expiry(element(replies__1, [i___1])) <= 
          4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> 0 <= fld_minimum(element(
          replies__1, [i___1])) and fld_minimum(element(replies__1, [i___1])) 
          <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__internet <= 
          fld_class(fld_inherit(element(replies__1, [i___1]))) and fld_class(
          fld_inherit(element(replies__1, [i___1]))) <= rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___2 : integer, 1 
          <= i___2 and i___2 <= 129 -> 0 <= element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) and element(fld_nameserver(element(
          replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 1 
          <= i___3 and i___3 <= 129 -> 0 <= element(fld_email(element(
          replies__1, [i___1])), [i___3]) and element(fld_email(element(
          replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(168).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) and 
          fld_ttlinseconds(fld_inherit(element(replies__1, [i___1]))) <= 
          4294967295)
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_serialnumber(element(replies__1, [i___1])) and fld_serialnumber(
          element(replies__1, [i___1])) <= 4294967295)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_refresh(element(replies__1, [i___1])) and fld_refresh(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_retry(element(replies__1, [i___1])) and fld_retry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_expiry(element(replies__1, [i___1])) and fld_expiry(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= 
          fld_minimum(element(replies__1, [i___1])) and fld_minimum(element(
          replies__1, [i___1])) <= 4294967295)
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 
          rr_type__internet <= fld_class(fld_inherit(element(replies__1, [i___1]
          ))) and fld_class(fld_inherit(element(replies__1, [i___1]))) <= 
          rr_type__hs)
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) and element(
          fld_nameserver(element(replies__1, [i___1])), [i___2]) <= 255))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___3 : integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(
          fld_email(element(replies__1, [i___1])), [i___3]) and element(
          fld_email(element(replies__1, [i___1])), [i___3]) <= 255))
-S-  Applied substitution rule create_respo_rules(172).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__first by:
          0.
<S>  New H36:  num_found__1 >= 0
-S-  Applied substitution rule create_respo_rules(173).
     This was achieved by replacing all occurrences of 
          rr_type__numberofrecordstype__last by:
          64.
<S>  New H37:  num_found__1 <= 64
***  Proved C1:  start_byte >= 1
     using hypothesis H3.
***  Proved C2:  start_byte <= 8180
     using hypothesis H46.
***  Proved C3:  answer_count + num_found__1 <= answer_count + 64
     using hypothesis H37.
***  PROVED VC.

