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                       Semantic Analysis of SPARK Text
                             Examiner GPL Edition

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

procedure Process_Dns_Request.Set_TTL_Data_SOA_Response






@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_1.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
***  Proved C1:  fld_ttlinseconds(fld_inherit(soa_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H9.
***  Proved C2:  fld_ttlinseconds(fld_inherit(soa_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H10.
***  Proved C3:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H7.
***  Proved C4:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H8.
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C5:  start_byte <= 8177
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H28 (true-hypothesis).
---  Eliminated hypothesis H1 (redundant, given H25).
---  Eliminated hypothesis H3 (redundant, given H27).
---  Eliminated hypothesis H8 (redundant, given H5, H25 & H27).
     +++  New H29:  integer__size >= 0
     +++  New H30:  character__size >= 0
     +++  New H31:  positive__size >= 0
     +++  New H32:  dns_types__packet_bytes_range__size >= 0
     +++  New H33:  unsigned_types__unsigned16__size >= 0
     +++  New H34:  unsigned_types__unsigned32__size >= 0
     +++  New H35:  rr_type__classtype__size >= 0
     +++  New H36:  rr_type__wirestringtypeindex__size >= 0
     +++  New H37:  rr_type__wirestringtype__size >= 0
     +++  New H38:  rr_type__resourcerecordtype__size >= 0
     +++  New H39:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_2.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H7.
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New C1:  nameserver_name_length + (mailbox_name_length + 20) >= 0
<S>  New C6:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New C2:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
<S>  New C7:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H6:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H34:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte <= 8176
<S>  New C5:  start_byte <= 8175
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C8:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New C10:  mailbox_name_length >= - 2147483668
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C9:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New C11:  mailbox_name_length <= 2147483627
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C12:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C13:  start_byte <= 2147483643
***  Proved C1:  nameserver_name_length + (mailbox_name_length + 20) >= 0
     using hypotheses H1 & H3.
***  Proved C6:  nameserver_name_length + (mailbox_name_length + 20) >= 0
     using hypotheses H1 & H3.
***  Proved C8:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
     using hypotheses H1 & H3.
***  Proved C10:  mailbox_name_length >= - 2147483668
     using hypothesis H3.
***  Proved C13:  start_byte <= 2147483643
     using hypothesis H8.
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C2:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
     using hypotheses H2 & H4.
***  Proved C7:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
     using hypotheses H2 & H4.
***  Proved C9:  nameserver_name_length + (mailbox_name_length + 20) <= 
          2147483647
     using hypotheses H2 & H4.
***  Proved C11:  mailbox_name_length <= 2147483627
     using hypothesis H4.
***  Proved C12:  start_byte >= - 2147483652
     using hypothesis H7.
---  Eliminated hypothesis H26 (true-hypothesis).
---  Eliminated hypothesis H28 (true-hypothesis).
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H30 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H1 (redundant, given H25).
---  Eliminated hypothesis H3 (redundant, given H27).
---  Eliminated hypothesis H8 (redundant, given H33).
---  Eliminated hypothesis H33 (redundant, given H5, H25 & H27).
     +++  New H35:  integer__size >= 0
     +++  New H36:  character__size >= 0
     +++  New H37:  positive__size >= 0
     +++  New H38:  dns_types__packet_bytes_range__size >= 0
     +++  New H39:  unsigned_types__unsigned16__size >= 0
     +++  New H40:  unsigned_types__unsigned32__size >= 0
     +++  New H41:  rr_type__classtype__size >= 0
     +++  New H42:  rr_type__wirestringtypeindex__size >= 0
     +++  New H43:  rr_type__wirestringtype__size >= 0
     +++  New H44:  rr_type__resourcerecordtype__size >= 0
     +++  New H45:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_3.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  nameserver_name_length >= - 2147483648
<S>  New C3:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  nameserver_name_length <= 2147483647
<S>  New C4:  true
***  Proved C1:  nameserver_name_length >= - 2147483648
     using hypothesis H1.
***  Proved C3:  true
***  Proved C4:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C2:  nameserver_name_length <= 2147483647
     using hypothesis H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_4.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
***  Proved C1:  1 <= nameserver_name_length -> nameserver_name_length >= 
          rr_type__wirestringtypeindex__first and nameserver_name_length <= 
          rr_type__wirestringtypeindex__last
     using hypotheses H2 & H25.
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
<S>  New C2:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
<S>  New C2:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_5.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  true
***  Proved C1:  start_byte <= dns_types__packet_bytes_range__last - 20 - (
          mailbox_name_length + nameserver_name_length)
     using hypothesis H5.
***  Proved C3:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H2 & H55.
***  Proved C4:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
     using hypothesis H48.
***  Proved C5:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H7.
***  Proved C6:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H8.
***  Proved C7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H9.
***  Proved C8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H10.
***  Proved C9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
     using hypothesis H11.
***  Proved C10:  fld_class(fld_inherit(soa_record)) <= rr_type__classtype__last
     using hypothesis H12.
***  Proved C11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
     using hypothesis H13.
***  Proved C12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
     using hypothesis H14.
***  Proved C13:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C14:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C15:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C16:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C17:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C18:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C19:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H21.
***  Proved C20:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H22.
***  Proved C21:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H23.
***  Proved C22:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H24.
***  Proved C23:  nameserver_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H25.
***  Proved C24:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H2.
***  Proved C25:  mailbox_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H27.
***  Proved C26:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H4.
***  Proved C27:  nameserver_name_length >= 0
     using hypothesis H1.
***  Proved C28:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H2.
***  Proved C29:  mailbox_name_length >= 0
     using hypothesis H3.
***  Proved C30:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H4.
***  Proved C31:  start_byte <= dns_types__packet_bytes_range__last - 26 - (
          nameserver_name_length + mailbox_name_length)
     using hypothesis H5.
***  Proved C33:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H2 & H55.
***  Proved C34:  true
***  Proved C35:  1 <= nameserver_name_length
     using hypothesis H55.
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New C2:  true
<S>  New C32:  true
***  Proved C2:  true
***  Proved C32:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_6.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  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(update(bytes, [start_byte + 5 + 
          loop__1__i], element(fld_nameserver(soa_record), [loop__1__i])), [
          i___1]) and element(update(bytes, [start_byte + 5 + loop__1__i], 
          element(fld_nameserver(soa_record), [loop__1__i])), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  loop__1__i >= 0
***  Proved C1:  start_byte <= dns_types__packet_bytes_range__last - 20 - (
          mailbox_name_length + nameserver_name_length)
     using hypothesis H1.
***  Proved C2:  loop__1__i + 1 >= rr_type__wirestringtypeindex__first
     using hypothesis H2.
***  Proved C4:  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(update(bytes, [start_byte + 5 + 
          loop__1__i], element(fld_nameserver(soa_record), [loop__1__i])), [
          i___1]) and element(update(bytes, [start_byte + 5 + loop__1__i], 
          element(fld_nameserver(soa_record), [loop__1__i])), [i___1]) <= 
          dns_types__byte__last)
     using hypotheses H4, H36, H37, H42 & H43.
***  Proved C5:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H5.
***  Proved C6:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H6.
***  Proved C7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H7.
***  Proved C8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H8.
***  Proved C9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
     using hypothesis H9.
***  Proved C10:  fld_class(fld_inherit(soa_record)) <= rr_type__classtype__last
     using hypothesis H10.
***  Proved C11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
     using hypothesis H11.
***  Proved C12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
     using hypothesis H12.
***  Proved C13:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C14:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C15:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C16:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C17:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C18:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C19:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C20:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C21:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H21.
***  Proved C22:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H22.
***  Proved C23:  nameserver_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H23.
***  Proved C24:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H24.
***  Proved C25:  mailbox_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H25.
***  Proved C26:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H26.
***  Proved C27:  nameserver_name_length >= 0
     using hypothesis H27.
***  Proved C28:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H24.
***  Proved C29:  mailbox_name_length >= 0
     using hypothesis H29.
***  Proved C30:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H26.
***  Proved C31:  start_byte <= dns_types__packet_bytes_range__last - 26 - (
          nameserver_name_length + mailbox_name_length)
     using hypothesis H31.
***  Proved C32:  loop__1__i + 1 >= rr_type__wirestringtypeindex__first
     using hypothesis H2.
***  Proved C34:  loop__1__i >= 0
     using hypothesis H34.
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= 129 -> character__first <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= 129 -> character__first <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          character__last)
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New C3:  loop__1__i <= 128
<S>  New C33:  loop__1__i <= 128
***  Proved C3:  loop__1__i <= 128
     using hypotheses H24, H35 & H50.
***  Proved C33:  loop__1__i <= 128
     using hypotheses H24, H35 & H50.
>>>  Restructured hypothesis H50 into:
     >>>  H50:  loop__1__i <> nameserver_name_length
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= 129 -> 0 <= element(fld_nameserver(soa_record), [
          i___1]) and element(fld_nameserver(soa_record), [i___1]) <= 
          character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= 129 -> 0 <= element(fld_email(soa_record), [i___2])
           and element(fld_email(soa_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= 129 -> 0 <= element(fld_nameserver(soa_record), [
          i___1]) and element(fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= 129 -> 0 <= element(fld_email(soa_record), [i___2])
           and element(fld_email(soa_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
%%%  Hypotheses H35 & H50 together imply that
          loop__1__i < nameserver_name_length.
     H35 & H50 have therefore been deleted and a new H51 added to this effect.
***  Proved C35:  loop__1__i + 1 <= nameserver_name_length
     via its standard form, which is:
     Std.Fm C35:  - loop__1__i + nameserver_name_length > 0
     using hypothesis H51.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_7.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C5:  loop__1__i >= rr_type__wirestringtypeindex__first
     using hypothesis H2.
***  Proved C6:  loop__1__i <= rr_type__wirestringtypeindex__last
     using hypothesis H3.
***  Proved C7:  start_byte + 5 + loop__1__i >= 
          dns_types__packet_bytes_range__first
     using hypotheses H5 & H34.
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H4:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New C1:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New C3:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H4:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C2:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New C4:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H4:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes, [i___1]) and element(
          bytes, [i___1]) <= 255)
<S>  New C8:  start_byte + 5 + loop__1__i <= 8180
<S>  New C12:  loop__1__i <= 8180
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C9:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New C13:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C10:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New C14:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  start_byte >= 1
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C11:  loop__1__i >= 1
***  Proved C9:  start_byte + 5 + loop__1__i >= - 2147483648
     using hypotheses H5 & H34.
***  Proved C13:  start_byte >= - 2147483653
     using hypothesis H5.
***  Proved C14:  start_byte <= 2147483642
     using hypothesis H6.
***  Proved C11:  loop__1__i >= 1
     using hypothesis H34.
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C1:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
     using hypotheses H3, H11 & H34.
***  Proved C3:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
     using hypotheses H3, H11 & H34.
***  Proved C2:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
     using hypotheses H3, H11 & H34.
***  Proved C4:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
     using hypotheses H3, H11 & H34.
***  Proved C12:  loop__1__i <= 8180
     using hypothesis H3.
***  Proved C10:  start_byte + 5 + loop__1__i <= 2147483647
     using hypotheses H3 & H6.
---  Eliminated hypothesis H28 (true-hypothesis).
---  Eliminated hypothesis H30 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (duplicate of H2).
---  Eliminated hypothesis H1 (redundant, given H31).
---  Eliminated hypothesis H27 (redundant, given H23).
---  Eliminated hypothesis H29 (redundant, given H25).
     +++  New H36:  integer__size >= 0
     +++  New H37:  character__size >= 0
     +++  New H38:  positive__size >= 0
     +++  New H39:  dns_types__packet_bytes_range__size >= 0
     +++  New H40:  unsigned_types__unsigned16__size >= 0
     +++  New H41:  unsigned_types__unsigned32__size >= 0
     +++  New H42:  rr_type__classtype__size >= 0
     +++  New H43:  rr_type__wirestringtypeindex__size >= 0
     +++  New H44:  rr_type__wirestringtype__size >= 0
     +++  New H45:  rr_type__resourcerecordtype__size >= 0
     +++  New H46:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_8.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
***  Proved C6:  5 + nameserver_name_length <= integer__base__last
     using hypotheses H1, H3, H43 & H55.
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New C1:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New C3:  nameserver_name_length >= - 4
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New C4:  nameserver_name_length <= 8175
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New C5:  nameserver_name_length >= - 2147483653
***  Proved C1:  start_byte + (5 + nameserver_name_length) >= 1
     using hypotheses H1 & H7.
***  Proved C3:  nameserver_name_length >= - 4
     using hypothesis H1.
***  Proved C2:  start_byte + (5 + nameserver_name_length) <= 8180
     using hypotheses H39 & H55.
***  Proved C4:  nameserver_name_length <= 8175
     using hypothesis H55.
***  Proved C5:  nameserver_name_length >= - 2147483653
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_9.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C3:  5 + nameserver_name_length >= 
          dns_types__packet_bytes_range__first
     using hypotheses H35 & H46.
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New C1:  start_byte + (5 + nameserver_name_length) >= 1
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New C4:  nameserver_name_length <= 8175
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C5:  nameserver_name_length >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C6:  nameserver_name_length <= 2147483642
***  Proved C1:  start_byte + (5 + nameserver_name_length) >= 1
     using hypotheses H5 & H27.
***  Proved C5:  nameserver_name_length >= - 2147483653
     using hypothesis H27.
***  Proved C6:  nameserver_name_length <= 2147483642
     using hypotheses H47 & H50.
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C4:  nameserver_name_length <= 8175
     using hypothesis H24.
---  Eliminated hypothesis H28 (true-hypothesis).
---  Eliminated hypothesis H30 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H46 (duplicate of H34).
---  Eliminated hypothesis H34 (duplicate of H2).
---  Eliminated hypothesis H1 (redundant, given H31).
---  Eliminated hypothesis H6 (redundant, given H2 & H43).
---  Eliminated hypothesis H27 (redundant, given H23).
---  Eliminated hypothesis H29 (redundant, given H25).
---  Eliminated hypothesis H35 (redundant, given H50).
---  Eliminated hypothesis H44 (redundant, given H42).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H47 (redundant, given H3).
---  Eliminated hypothesis H48 (redundant, given H5).
---  Eliminated hypothesis H49 (redundant, given H2 & H43).
-S-  Eliminated hypothesis H50.
     This was achieved by replacing all occurrences of loop__1__i by:
          nameserver_name_length.
<S>  New H42:  start_byte + 5 + nameserver_name_length >= 1
<S>  New H43:  start_byte + 5 + nameserver_name_length <= 8180
<S>  New H36:  element(fld_nameserver(soa_record), [nameserver_name_length]) >= 
          0
<S>  New H37:  element(fld_nameserver(soa_record), [nameserver_name_length]) <= 
          255
<S>  New H2:  nameserver_name_length >= 1
<S>  New H3:  nameserver_name_length <= 129
***  Proved C2:  start_byte + (5 + nameserver_name_length) <= 8180
     via its standard form, which is:
     Std.Fm C2:  - nameserver_name_length - start_byte > - 8176
     using hypothesis H43.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_10.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
***  Proved C1:  mailbox_name_length >= integer__first
     using hypotheses H3, H49 & H55.
***  Proved C3:  1 >= integer__first
     using hypothesis H51.
***  Proved C4:  1 <= integer__last
     using hypothesis H52.
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New C2:  mailbox_name_length <= 2147483647
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C2:  mailbox_name_length <= 2147483647
     using hypothesis H45.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_11.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  mailbox_name_length >= - 2147483648
<S>  New C3:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  mailbox_name_length <= 2147483647
<S>  New C4:  true
***  Proved C1:  mailbox_name_length >= - 2147483648
     using hypothesis H29.
***  Proved C3:  true
***  Proved C4:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C2:  mailbox_name_length <= 2147483647
     using hypothesis H26.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_12.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
***  Proved C1:  1 <= mailbox_name_length -> mailbox_name_length >= 
          rr_type__wirestringtypeindex__first and mailbox_name_length <= 
          rr_type__wirestringtypeindex__last
     using hypotheses H4 & H27.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
<S>  New C2:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
<S>  New C2:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_13.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C1:  1 <= mailbox_name_length -> mailbox_name_length >= 
          rr_type__wirestringtypeindex__first and mailbox_name_length <= 
          rr_type__wirestringtypeindex__last
     using hypotheses H25 & H26.
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
<S>  New C2:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
<S>  New C2:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_14.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
%%%  Simplified C10 on reading formula in, to give:
     %%%  C10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified C13 on reading formula in, to give:
     %%%  C13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  true
***  Proved C3:  1 >= rr_type__wirestringtypeindex__first
     using hypotheses H25 & H55.
***  Proved C4:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H4 & H68.
***  Proved C5:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
     using hypothesis H48.
***  Proved C6:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H7.
***  Proved C7:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H8.
***  Proved C8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H9.
***  Proved C9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H10.
***  Proved C10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record)
          )
     using hypothesis H11.
***  Proved C11:  fld_class(fld_inherit(soa_record)) <= rr_type__classtype__last
     using hypothesis H12.
***  Proved C12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
     using hypothesis H13.
***  Proved C13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
     using hypothesis H14.
***  Proved C14:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C15:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C16:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C17:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C18:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C19:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C20:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H21.
***  Proved C21:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H22.
***  Proved C22:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H23.
***  Proved C23:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H24.
***  Proved C24:  nameserver_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H25.
***  Proved C25:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H2.
***  Proved C26:  mailbox_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H27.
***  Proved C27:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H4.
***  Proved C28:  nameserver_name_length >= 0
     using hypothesis H1.
***  Proved C29:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H2.
***  Proved C30:  mailbox_name_length >= 0
     using hypothesis H3.
***  Proved C31:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H4.
***  Proved C32:  start_byte <= dns_types__packet_bytes_range__last - 26 - (
          nameserver_name_length + mailbox_name_length)
     using hypothesis H5.
***  Proved C33:  1 >= rr_type__wirestringtypeindex__first
     using hypotheses H25 & H55.
***  Proved C34:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H4 & H68.
***  Proved C35:  true
***  Proved C36:  1 <= mailbox_name_length
     using hypothesis H68.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
+++  Using "A->B, A |- B" on hypotheses H66 & H68 yields a new hypothesis:
     +++  H69:  mailbox_name_length >= rr_type__wirestringtypeindex__first and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
+++  Using "A->B, A |- B" on hypotheses H67 & H68 yields a new hypothesis:
     +++  H70:  1 >= rr_type__wirestringtypeindex__first and 1 <= 
          rr_type__wirestringtypeindex__last
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + (5 + nameserver_name_length) <= 8160 - 
          mailbox_name_length
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H67:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H69:  mailbox_name_length >= 1 and mailbox_name_length <= 
          rr_type__wirestringtypeindex__last
<S>  New H70:  1 <= rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H67:  true
<S>  New H69:  mailbox_name_length >= 1 and mailbox_name_length <= 129
<S>  New H70:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C1:  start_byte + (5 + nameserver_name_length) >= 1
     using hypothesis H56.
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_15.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  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(update(bytes, [start_byte + 5 + 
          loop__1__i], element(fld_nameserver(soa_record), [loop__1__i])), [
          i___1]) and element(update(bytes, [start_byte + 5 + loop__1__i], 
          element(fld_nameserver(soa_record), [loop__1__i])), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified C10 on reading formula in, to give:
     %%%  C10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified C13 on reading formula in, to give:
     %%%  C13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  true
***  Proved C4:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H3 & H34.
***  Proved C5:  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(update(bytes, [start_byte + 5 + 
          loop__1__i], element(fld_nameserver(soa_record), [loop__1__i])), [
          i___1]) and element(update(bytes, [start_byte + 5 + loop__1__i], 
          element(fld_nameserver(soa_record), [loop__1__i])), [i___1]) <= 
          dns_types__byte__last)
     using hypotheses H4, H36, H37, H42 & H43.
***  Proved C6:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H5.
***  Proved C7:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H6.
***  Proved C8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H7.
***  Proved C9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H8.
***  Proved C10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record)
          )
     using hypothesis H9.
***  Proved C11:  fld_class(fld_inherit(soa_record)) <= rr_type__classtype__last
     using hypothesis H10.
***  Proved C12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
     using hypothesis H11.
***  Proved C13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
     using hypothesis H12.
***  Proved C14:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C15:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C16:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C17:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C18:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C19:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C20:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C21:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C22:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H21.
***  Proved C23:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H22.
***  Proved C24:  nameserver_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H23.
***  Proved C25:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H24.
***  Proved C26:  mailbox_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H25.
***  Proved C27:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H26.
***  Proved C28:  nameserver_name_length >= 0
     using hypothesis H27.
***  Proved C29:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H24.
***  Proved C30:  mailbox_name_length >= 0
     using hypothesis H29.
***  Proved C31:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H26.
***  Proved C32:  start_byte <= dns_types__packet_bytes_range__last - 26 - (
          nameserver_name_length + mailbox_name_length)
     using hypothesis H31.
***  Proved C34:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H3 & H34.
***  Proved C35:  true
***  Proved C36:  1 <= mailbox_name_length
     using hypothesis H63.
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H62:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New C3:  true
<S>  New C33:  true
***  Proved C3:  true
***  Proved C33:  true
+++  Using "A->B, A |- B" on hypotheses H61 & H63 yields a new hypothesis:
     +++  H64:  mailbox_name_length >= 1 and mailbox_name_length <= 
          rr_type__wirestringtypeindex__last
+++  Using "A->B, A |- B" on hypotheses H62 & H63 yields a new hypothesis:
     +++  H65:  1 <= rr_type__wirestringtypeindex__last
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= character__last)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + (5 + nameserver_name_length) <= 8160 - 
          mailbox_name_length
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H62:  true
<S>  New H64:  mailbox_name_length >= 1 and mailbox_name_length <= 129
<S>  New H65:  true
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C1:  start_byte + (5 + nameserver_name_length) >= 1
     using hypothesis H51.
---  Eliminated hypothesis H28 (true-hypothesis).
---  Eliminated hypothesis H30 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H38 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H60 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H65 (true-hypothesis).
---  Eliminated hypothesis H34 (duplicate of H2).
---  Eliminated hypothesis H46 (duplicate of H2).
---  Eliminated hypothesis H63 (duplicate of H25).
>>>  Using "A->B, A |- B" on H61, given H63, we simplify the former to:
     >>>  H61:  mailbox_name_length >= 1 and mailbox_name_length <= 129
---  Eliminated hypothesis H1 (redundant, given H31).
---  Eliminated hypothesis H6 (redundant, given H2 & H43).
---  Eliminated hypothesis H27 (redundant, given H23).
---  Eliminated hypothesis H29 (redundant, given H25).
---  Eliminated hypothesis H35 (redundant, given H50).
---  Eliminated hypothesis H44 (redundant, given H42).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H47 (redundant, given H3).
---  Eliminated hypothesis H48 (redundant, given H5).
---  Eliminated hypothesis H49 (redundant, given H2 & H43).
---  Eliminated hypothesis H53 (redundant, given H23).
---  Eliminated hypothesis H54 (redundant, given H24).
---  Eliminated hypothesis H55 (redundant, given H23).
---  Eliminated hypothesis H56 (redundant, given H24).
---  Eliminated hypothesis H57 (redundant, given H25).
---  Eliminated hypothesis H58 (redundant, given H26).
-S-  Eliminated hypothesis H50.
     This was achieved by replacing all occurrences of loop__1__i by:
          nameserver_name_length.
<S>  New H2:  nameserver_name_length >= 1
<S>  New H42:  start_byte + 5 + nameserver_name_length >= 1
<S>  New H43:  start_byte + 5 + nameserver_name_length <= 8180
<S>  New H36:  element(fld_nameserver(soa_record), [nameserver_name_length]) >= 
          0
<S>  New H37:  element(fld_nameserver(soa_record), [nameserver_name_length]) <= 
          255
<S>  New H3:  nameserver_name_length <= 129
---  Attempted addition of new hypothesis:
          mailbox_name_length >= 1
     eliminated: this already exists (as H25).
---  Attempted addition of new hypothesis:
          mailbox_name_length <= 129
     eliminated: this already exists (as H26).
>>>  Hypothesis H61 has now been split into two, giving:
     >>>  H25:  mailbox_name_length >= 1
     >>>  H26:  mailbox_name_length <= 129
---  Attempted addition of new hypothesis:
          mailbox_name_length >= 1
     eliminated: this already exists (as H25).
---  Attempted addition of new hypothesis:
          mailbox_name_length <= 129
     eliminated: this already exists (as H26).
>>>  Hypothesis H64 has now been split into two, giving:
     >>>  H25:  mailbox_name_length >= 1
     >>>  H26:  mailbox_name_length <= 129
     +++  New H66:  integer__size >= 0
     +++  New H67:  character__size >= 0
     +++  New H68:  positive__size >= 0
     +++  New H69:  dns_types__packet_bytes_range__size >= 0
     +++  New H70:  unsigned_types__unsigned16__size >= 0
     +++  New H71:  unsigned_types__unsigned32__size >= 0
     +++  New H72:  rr_type__classtype__size >= 0
     +++  New H73:  rr_type__wirestringtypeindex__size >= 0
     +++  New H74:  rr_type__wirestringtype__size >= 0
     +++  New H75:  rr_type__resourcerecordtype__size >= 0
     +++  New H76:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_16.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
---  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 
          H38).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  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(update(bytes, [current_byte + 
          loop__2__i], element(fld_email(soa_record), [loop__2__i])), [i___1]) 
          and element(update(bytes, [current_byte + loop__2__i], element(
          fld_email(soa_record), [loop__2__i])), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified C10 on reading formula in, to give:
     %%%  C10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified C13 on reading formula in, to give:
     %%%  C13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  loop__2__i >= 0
***  Proved C1:  current_byte >= 1
     using hypothesis H1.
***  Proved C2:  current_byte <= dns_types__packet_bytes_range__last - 20 - 
          mailbox_name_length
     using hypothesis H2.
***  Proved C3:  loop__2__i + 1 >= rr_type__wirestringtypeindex__first
     using hypothesis H3.
***  Proved C5:  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(update(bytes, [current_byte + 
          loop__2__i], element(fld_email(soa_record), [loop__2__i])), [i___1]) 
          and element(update(bytes, [current_byte + loop__2__i], element(
          fld_email(soa_record), [loop__2__i])), [i___1]) <= 
          dns_types__byte__last)
     using hypotheses H5, H37, H38, H43 & H44.
***  Proved C6:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H6.
***  Proved C7:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H7.
***  Proved C8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H8.
***  Proved C9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H9.
***  Proved C10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record)
          )
     using hypothesis H10.
***  Proved C11:  fld_class(fld_inherit(soa_record)) <= rr_type__classtype__last
     using hypothesis H11.
***  Proved C12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
     using hypothesis H12.
***  Proved C13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first 
          <= i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
     using hypothesis H13.
***  Proved C14:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H14.
***  Proved C15:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H15.
***  Proved C16:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H16.
***  Proved C17:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H17.
***  Proved C18:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H18.
***  Proved C19:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H19.
***  Proved C20:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H20.
***  Proved C21:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H21.
***  Proved C22:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H22.
***  Proved C23:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H23.
***  Proved C24:  nameserver_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H24.
***  Proved C25:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H25.
***  Proved C26:  mailbox_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H26.
***  Proved C27:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H27.
***  Proved C28:  nameserver_name_length >= 0
     using hypothesis H28.
***  Proved C29:  nameserver_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H25.
***  Proved C30:  mailbox_name_length >= 0
     using hypothesis H30.
***  Proved C31:  mailbox_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H27.
***  Proved C32:  start_byte <= dns_types__packet_bytes_range__last - 26 - (
          nameserver_name_length + mailbox_name_length)
     using hypothesis H32.
***  Proved C33:  loop__2__i + 1 >= rr_type__wirestringtypeindex__first
     using hypothesis H3.
***  Proved C35:  loop__2__i >= 0
     using hypothesis H35.
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= 129 -> character__first <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= 129 -> character__first <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          character__last)
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New C4:  loop__2__i <= 128
<S>  New C34:  loop__2__i <= 128
***  Proved C4:  loop__2__i <= 128
     using hypotheses H27, H36 & H49.
***  Proved C34:  loop__2__i <= 128
     using hypotheses H27, H36 & H49.
>>>  Restructured hypothesis H49 into:
     >>>  H49:  loop__2__i <> mailbox_name_length
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= 129 -> 0 <= element(fld_nameserver(soa_record), [
          i___1]) and element(fld_nameserver(soa_record), [i___1]) <= 
          character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= 129 -> 0 <= element(fld_email(soa_record), [i___2])
           and element(fld_email(soa_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= 129 -> 0 <= element(fld_nameserver(soa_record), [
          i___1]) and element(fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= 129 -> 0 <= element(fld_email(soa_record), [i___2])
           and element(fld_email(soa_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H6:  start_byte >= 1
<S>  New H43:  current_byte + loop__2__i >= 1
<S>  New H47:  loop__2__i >= 1
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H44:  current_byte + loop__2__i <= 8180
<S>  New H48:  loop__2__i <= 8180
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H45:  current_byte + loop__2__i >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H46:  current_byte + loop__2__i <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H37:  element(fld_email(soa_record), [loop__2__i]) >= 0
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H38:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
%%%  Hypotheses H36 & H49 together imply that
          loop__2__i < mailbox_name_length.
     H36 & H49 have therefore been deleted and a new H50 added to this effect.
***  Proved C36:  loop__2__i + 1 <= mailbox_name_length
     via its standard form, which is:
     Std.Fm C36:  - loop__2__i + mailbox_name_length > 0
     using hypothesis H50.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_17.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
***  Proved C5:  loop__2__i >= rr_type__wirestringtypeindex__first
     using hypothesis H3.
***  Proved C6:  loop__2__i <= rr_type__wirestringtypeindex__last
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H5:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New C1:  element(fld_email(soa_record), [loop__2__i]) >= 0
<S>  New C3:  element(fld_email(soa_record), [loop__2__i]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H5:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C2:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New C4:  element(fld_email(soa_record), [loop__2__i]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  start_byte >= 1
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New C7:  current_byte + loop__2__i >= 1
<S>  New C11:  loop__2__i >= 1
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C8:  current_byte + loop__2__i <= 8180
<S>  New C12:  loop__2__i <= 8180
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C9:  current_byte + loop__2__i >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C10:  current_byte + loop__2__i <= 2147483647
***  Proved C7:  current_byte + loop__2__i >= 1
     using hypotheses H1 & H35.
***  Proved C11:  loop__2__i >= 1
     using hypothesis H35.
***  Proved C9:  current_byte + loop__2__i >= - 2147483648
     using hypotheses H1 & H35.
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C1:  element(fld_email(soa_record), [loop__2__i]) >= 0
     using hypotheses H4, H13 & H35.
***  Proved C3:  element(fld_email(soa_record), [loop__2__i]) >= 0
     using hypotheses H4, H13 & H35.
***  Proved C2:  element(fld_email(soa_record), [loop__2__i]) <= 255
     using hypotheses H4, H13 & H35.
***  Proved C4:  element(fld_email(soa_record), [loop__2__i]) <= 255
     using hypotheses H4, H13 & H35.
***  Proved C12:  loop__2__i <= 8180
     using hypothesis H4.
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H35 (duplicate of H3).
---  Eliminated hypothesis H7 (redundant, given H24, H26 & H32).
---  Eliminated hypothesis H28 (redundant, given H24).
---  Eliminated hypothesis H30 (redundant, given H26).
     +++  New H37:  integer__size >= 0
     +++  New H38:  character__size >= 0
     +++  New H39:  positive__size >= 0
     +++  New H40:  dns_types__packet_bytes_range__size >= 0
     +++  New H41:  unsigned_types__unsigned16__size >= 0
     +++  New H42:  unsigned_types__unsigned32__size >= 0
     +++  New H43:  rr_type__classtype__size >= 0
     +++  New H44:  rr_type__wirestringtypeindex__size >= 0
     +++  New H45:  rr_type__wirestringtype__size >= 0
     +++  New H46:  rr_type__resourcerecordtype__size >= 0
     +++  New H47:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_18.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
***  Proved C8:  nameserver_name_length + mailbox_name_length <= 
          integer__base__last
     using hypotheses H61 & H68.
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
<S>  New C1:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          >= 1
<S>  New C3:  nameserver_name_length + mailbox_name_length >= - 5
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8180
<S>  New C4:  nameserver_name_length + mailbox_name_length <= 8174
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
<S>  New C5:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New C7:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
<S>  New C6:  nameserver_name_length + mailbox_name_length <= 2147483641
***  Proved C1:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= 1
     using hypotheses H1, H3 & H7.
***  Proved C3:  nameserver_name_length + mailbox_name_length >= - 5
     using hypotheses H1 & H3.
***  Proved C4:  nameserver_name_length + mailbox_name_length <= 8174
     using hypotheses H55 & H68.
***  Proved C5:  nameserver_name_length + mailbox_name_length >= - 2147483654
     using hypotheses H1 & H3.
***  Proved C7:  nameserver_name_length + mailbox_name_length >= - 2147483648
     using hypotheses H1 & H3.
***  Proved C6:  nameserver_name_length + mailbox_name_length <= 2147483641
     using hypotheses H55 & H68.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
>>>  Restructured hypothesis H68 into:
     >>>  H68:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H67:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H67:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_19.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C3:  6 + (nameserver_name_length + mailbox_name_length) >= 
          dns_types__packet_bytes_range__first
     using hypotheses H29, H35 & H46.
***  Proved C8:  nameserver_name_length + mailbox_name_length <= 
          integer__base__last
     using hypotheses H56 & H63.
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
<S>  New C1:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          >= 1
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8180
<S>  New C4:  nameserver_name_length + mailbox_name_length <= 8174
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
<S>  New C5:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New C7:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
<S>  New C6:  nameserver_name_length + mailbox_name_length <= 2147483641
***  Proved C1:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= 1
     using hypotheses H5, H27 & H29.
***  Proved C5:  nameserver_name_length + mailbox_name_length >= - 2147483654
     using hypotheses H27 & H29.
***  Proved C7:  nameserver_name_length + mailbox_name_length >= - 2147483648
     using hypotheses H27 & H29.
***  Proved C6:  nameserver_name_length + mailbox_name_length <= 2147483641
     using hypotheses H54 & H63.
>>>  Restructured hypothesis H63 into:
     >>>  H63:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H62:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H62:  true
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C4:  nameserver_name_length + mailbox_name_length <= 8174
     using hypotheses H24 & H63.
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_20.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
---  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 
          H38).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H4)
          .
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H6:  start_byte >= 1
<S>  New H43:  current_byte + loop__2__i >= 1
<S>  New H47:  loop__2__i >= 1
<S>  New C1:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          >= 1
<S>  New C3:  nameserver_name_length + mailbox_name_length >= - 5
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H44:  current_byte + loop__2__i <= 8180
<S>  New H48:  loop__2__i <= 8180
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8180
<S>  New C4:  nameserver_name_length + mailbox_name_length <= 8174
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C5:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New C7:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C6:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New C8:  nameserver_name_length + mailbox_name_length <= 2147483647
***  Proved C1:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= 1
     using hypotheses H6, H28 & H30.
***  Proved C3:  nameserver_name_length + mailbox_name_length >= - 5
     using hypotheses H28 & H30.
***  Proved C5:  nameserver_name_length + mailbox_name_length >= - 2147483654
     using hypotheses H28 & H30.
***  Proved C7:  nameserver_name_length + mailbox_name_length >= - 2147483648
     using hypotheses H28 & H30.
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H45:  current_byte + loop__2__i >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H46:  current_byte + loop__2__i <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  element(fld_email(soa_record), [loop__2__i]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H38:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C4:  nameserver_name_length + mailbox_name_length <= 8174
     using hypotheses H25 & H27.
***  Proved C6:  nameserver_name_length + mailbox_name_length <= 2147483641
     using hypotheses H25 & H27.
***  Proved C8:  nameserver_name_length + mailbox_name_length <= 2147483647
     using hypotheses H25 & H27.
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H47 (duplicate of H35).
---  Eliminated hypothesis H35 (duplicate of H3).
---  Eliminated hypothesis H28 (redundant, given H24).
---  Eliminated hypothesis H30 (redundant, given H26).
---  Eliminated hypothesis H36 (redundant, given H49).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H46 (redundant, given H44).
---  Eliminated hypothesis H48 (redundant, given H4).
-S-  Eliminated hypothesis H49.
     This was achieved by replacing all occurrences of loop__2__i by:
          mailbox_name_length.
<S>  New H43:  current_byte + mailbox_name_length >= 1
<S>  New H44:  current_byte + mailbox_name_length <= 8180
<S>  New H37:  element(fld_email(soa_record), [mailbox_name_length]) >= 0
<S>  New H38:  element(fld_email(soa_record), [mailbox_name_length]) <= 255
<S>  New H3:  mailbox_name_length >= 1
<S>  New H4:  mailbox_name_length <= 129
     +++  New H50:  integer__size >= 0
     +++  New H51:  character__size >= 0
     +++  New H52:  positive__size >= 0
     +++  New H53:  dns_types__packet_bytes_range__size >= 0
     +++  New H54:  unsigned_types__unsigned16__size >= 0
     +++  New H55:  unsigned_types__unsigned32__size >= 0
     +++  New H56:  rr_type__classtype__size >= 0
     +++  New H57:  rr_type__wirestringtypeindex__size >= 0
     +++  New H58:  rr_type__wirestringtype__size >= 0
     +++  New H59:  rr_type__resourcerecordtype__size >= 0
     +++  New H60:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_21.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H70).
***  Proved C1:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C2:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= dns_types__packet_bytes_range__first
     using hypothesis H69.
***  Proved C4:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= dns_types__packet_bytes_range__last
     using hypothesis H70.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
>>>  Restructured hypothesis H68 into:
     >>>  H68:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
<S>  New H73:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H75:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
<S>  New H74:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H76:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
<S>  New H69:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H71:  nameserver_name_length + mailbox_name_length >= - 5
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H72:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8177
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H67:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H67:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_22.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
***  Proved C1:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C2:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= dns_types__packet_bytes_range__first
     using hypothesis H64.
***  Proved C4:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= dns_types__packet_bytes_range__last
     using hypothesis H65.
>>>  Restructured hypothesis H63 into:
     >>>  H63:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
<S>  New H68:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H70:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
<S>  New H69:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H71:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H66:  nameserver_name_length + mailbox_name_length >= - 5
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H65:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H67:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8177
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H62:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H62:  true
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_23.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
---  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 
          H38).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H51).
***  Proved C1:  fld_serialnumber(soa_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H14.
***  Proved C2:  fld_serialnumber(soa_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H15.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= dns_types__packet_bytes_range__first
     using hypothesis H50.
***  Proved C4:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= dns_types__packet_bytes_range__last
     using hypothesis H51.
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H54:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H56:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H55:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H57:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H6:  start_byte >= 1
<S>  New H43:  current_byte + loop__2__i >= 1
<S>  New H47:  loop__2__i >= 1
<S>  New H50:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H52:  nameserver_name_length + mailbox_name_length >= - 5
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H44:  current_byte + loop__2__i <= 8180
<S>  New H48:  loop__2__i <= 8180
<S>  New H51:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H53:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8177
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H45:  current_byte + loop__2__i >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H46:  current_byte + loop__2__i <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H37:  element(fld_email(soa_record), [loop__2__i]) >= 0
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H38:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H47 (duplicate of H35).
---  Eliminated hypothesis H35 (duplicate of H3).
---  Eliminated hypothesis H28 (redundant, given H24).
---  Eliminated hypothesis H30 (redundant, given H26).
---  Eliminated hypothesis H36 (redundant, given H49).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H46 (redundant, given H44).
---  Eliminated hypothesis H48 (redundant, given H4).
---  Eliminated hypothesis H51 (redundant, given H32).
---  Eliminated hypothesis H53 (redundant, given H6 & H32).
---  Eliminated hypothesis H54 (redundant, given H52).
---  Eliminated hypothesis H55 (redundant, given H6 & H32).
---  Eliminated hypothesis H56 (redundant, given H52).
---  Eliminated hypothesis H57 (redundant, given H6 & H32).
-S-  Eliminated hypothesis H49.
     This was achieved by replacing all occurrences of loop__2__i by:
          mailbox_name_length.
<S>  New H43:  current_byte + mailbox_name_length >= 1
<S>  New H44:  current_byte + mailbox_name_length <= 8180
<S>  New H37:  element(fld_email(soa_record), [mailbox_name_length]) >= 0
<S>  New H38:  element(fld_email(soa_record), [mailbox_name_length]) <= 255
<S>  New H3:  mailbox_name_length >= 1
<S>  New H4:  mailbox_name_length <= 129
     +++  New H60:  integer__size >= 0
     +++  New H61:  character__size >= 0
     +++  New H62:  positive__size >= 0
     +++  New H63:  dns_types__packet_bytes_range__size >= 0
     +++  New H64:  unsigned_types__unsigned16__size >= 0
     +++  New H65:  unsigned_types__unsigned32__size >= 0
     +++  New H66:  rr_type__classtype__size >= 0
     +++  New H67:  rr_type__wirestringtypeindex__size >= 0
     +++  New H68:  rr_type__wirestringtype__size >= 0
     +++  New H69:  rr_type__resourcerecordtype__size >= 0
     +++  New H70:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_24.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H70).
%%%  Simplified H84 on reading formula in, to give:
     %%%  H84:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H70).
***  Proved C1:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C2:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H69.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H6:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H34:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H48:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H72:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H83:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H84:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8176
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8173
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
<S>  New C6:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483643
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= - 2147483652
     using hypotheses H1, H3 & H46.
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483643
     using hypothesis H70.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
>>>  Restructured hypothesis H68 into:
     >>>  H68:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
<S>  New H73:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H75:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
<S>  New H74:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H76:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
<S>  New H69:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H71:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H67:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H67:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_25.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H65).
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H65).
***  Proved C1:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C2:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H64.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H4:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H65:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H67:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H78:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H79:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8176
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8173
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
<S>  New C6:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483643
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= - 2147483652
     using hypotheses H27, H29 & H48.
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483643
     using hypothesis H65.
>>>  Restructured hypothesis H63 into:
     >>>  H63:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
<S>  New H68:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H70:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
<S>  New H69:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H71:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H66:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H62:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H62:  true
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_26.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
---  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 
          H38).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H51).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H51).
***  Proved C1:  fld_refresh(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H16.
***  Proved C2:  fld_refresh(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H17.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H50.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H5:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H44:  current_byte + loop__2__i <= 8180
<S>  New H48:  loop__2__i <= 8180
<S>  New H51:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H53:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H65:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8176
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8173
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H45:  current_byte + loop__2__i >= - 2147483648
<S>  New C6:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H46:  current_byte + loop__2__i <= 2147483647
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483643
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483643
     using hypothesis H51.
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H54:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H56:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H55:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H57:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte >= 1
<S>  New H43:  current_byte + loop__2__i >= 1
<S>  New H47:  loop__2__i >= 1
<S>  New H50:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H52:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H37:  element(fld_email(soa_record), [loop__2__i]) >= 0
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H38:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) >= - 2147483652
     using hypothesis H50.
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H60 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H47 (duplicate of H35).
---  Eliminated hypothesis H35 (duplicate of H3).
---  Eliminated hypothesis H28 (redundant, given H24).
---  Eliminated hypothesis H30 (redundant, given H26).
---  Eliminated hypothesis H36 (redundant, given H49).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H46 (redundant, given H44).
---  Eliminated hypothesis H48 (redundant, given H4).
---  Eliminated hypothesis H51 (redundant, given H32).
---  Eliminated hypothesis H53 (redundant, given H6 & H32).
---  Eliminated hypothesis H54 (redundant, given H52).
---  Eliminated hypothesis H55 (redundant, given H6 & H32).
---  Eliminated hypothesis H56 (redundant, given H52).
---  Eliminated hypothesis H57 (redundant, given H6 & H32).
---  Eliminated hypothesis H64 (redundant, given H32).
-S-  Eliminated hypothesis H49.
     This was achieved by replacing all occurrences of loop__2__i by:
          mailbox_name_length.
<S>  New H44:  current_byte + mailbox_name_length <= 8180
<S>  New H43:  current_byte + mailbox_name_length >= 1
<S>  New H37:  element(fld_email(soa_record), [mailbox_name_length]) >= 0
<S>  New H38:  element(fld_email(soa_record), [mailbox_name_length]) <= 255
<S>  New H3:  mailbox_name_length >= 1
<S>  New H4:  mailbox_name_length <= 129
     +++  New H68:  integer__size >= 0
     +++  New H69:  character__size >= 0
     +++  New H70:  positive__size >= 0
     +++  New H71:  dns_types__packet_bytes_range__size >= 0
     +++  New H72:  unsigned_types__unsigned16__size >= 0
     +++  New H73:  unsigned_types__unsigned32__size >= 0
     +++  New H74:  rr_type__classtype__size >= 0
     +++  New H75:  rr_type__wirestringtypeindex__size >= 0
     +++  New H76:  rr_type__wirestringtype__size >= 0
     +++  New H77:  rr_type__resourcerecordtype__size >= 0
     +++  New H78:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_27.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H70).
%%%  Simplified H84 on reading formula in, to give:
     %%%  H84:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H94 on reading formula in, to give:
     %%%  H94:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H95 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H70).
***  Proved C1:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C2:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 8 >= dns_types__packet_bytes_range__first
     using hypothesis H69.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 8 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H92.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H6:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H34:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H48:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H72:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H83:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H84:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H90:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H91:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H94:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8172
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8169
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
<S>  New H93:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483639
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483639
     using hypothesis H70.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
>>>  Restructured hypothesis H68 into:
     >>>  H68:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
<S>  New H73:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H75:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
<S>  New H74:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H76:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
<S>  New H69:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H71:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H89:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
<S>  New H92:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H67:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H67:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_28.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H65).
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H89 on reading formula in, to give:
     %%%  H89:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H65).
***  Proved C1:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C2:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 8 >= dns_types__packet_bytes_range__first
     using hypothesis H64.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 8 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H87.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H4:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H65:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H67:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H78:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H79:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H85:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H86:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H89:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8172
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8169
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
<S>  New H88:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483639
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483639
     using hypothesis H65.
>>>  Restructured hypothesis H63 into:
     >>>  H63:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
<S>  New H68:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H70:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
<S>  New H69:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H71:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H66:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H84:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
<S>  New H87:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H62:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H62:  true
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_29.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
---  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 
          H38).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H51).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H17).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H51).
***  Proved C1:  fld_retry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H18.
***  Proved C2:  fld_retry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H19.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 8 >= dns_types__packet_bytes_range__first
     using hypothesis H50.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 8 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H73.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H5:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H44:  current_byte + loop__2__i <= 8180
<S>  New H48:  loop__2__i <= 8180
<S>  New H51:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H53:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H65:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H71:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H72:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8172
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8169
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H46:  current_byte + loop__2__i <= 2147483647
<S>  New H74:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483639
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483639
     using hypothesis H51.
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H54:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H56:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H55:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H57:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte >= 1
<S>  New H43:  current_byte + loop__2__i >= 1
<S>  New H47:  loop__2__i >= 1
<S>  New H50:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H52:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H45:  current_byte + loop__2__i >= - 2147483648
<S>  New H73:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H37:  element(fld_email(soa_record), [loop__2__i]) >= 0
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H38:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H60 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H47 (duplicate of H35).
---  Eliminated hypothesis H35 (duplicate of H3).
---  Eliminated hypothesis H28 (redundant, given H24).
---  Eliminated hypothesis H30 (redundant, given H26).
---  Eliminated hypothesis H36 (redundant, given H49).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H46 (redundant, given H44).
---  Eliminated hypothesis H48 (redundant, given H4).
---  Eliminated hypothesis H51 (redundant, given H32).
---  Eliminated hypothesis H53 (redundant, given H6 & H32).
---  Eliminated hypothesis H54 (redundant, given H52).
---  Eliminated hypothesis H55 (redundant, given H6 & H32).
---  Eliminated hypothesis H56 (redundant, given H52).
---  Eliminated hypothesis H57 (redundant, given H6 & H32).
---  Eliminated hypothesis H64 (redundant, given H32).
---  Eliminated hypothesis H70 (redundant, given H50).
---  Eliminated hypothesis H71 (redundant, given H32).
---  Eliminated hypothesis H72 (redundant, given H32).
---  Eliminated hypothesis H73 (redundant, given H50).
---  Eliminated hypothesis H74 (redundant, given H32).
-S-  Eliminated hypothesis H49.
     This was achieved by replacing all occurrences of loop__2__i by:
          mailbox_name_length.
<S>  New H44:  current_byte + mailbox_name_length <= 8180
<S>  New H43:  current_byte + mailbox_name_length >= 1
<S>  New H37:  element(fld_email(soa_record), [mailbox_name_length]) >= 0
<S>  New H38:  element(fld_email(soa_record), [mailbox_name_length]) <= 255
<S>  New H3:  mailbox_name_length >= 1
<S>  New H4:  mailbox_name_length <= 129
     +++  New H78:  integer__size >= 0
     +++  New H79:  character__size >= 0
     +++  New H80:  positive__size >= 0
     +++  New H81:  dns_types__packet_bytes_range__size >= 0
     +++  New H82:  unsigned_types__unsigned16__size >= 0
     +++  New H83:  unsigned_types__unsigned32__size >= 0
     +++  New H84:  rr_type__classtype__size >= 0
     +++  New H85:  rr_type__wirestringtypeindex__size >= 0
     +++  New H86:  rr_type__wirestringtype__size >= 0
     +++  New H87:  rr_type__resourcerecordtype__size >= 0
     +++  New H88:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_30.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H70).
%%%  Simplified H84 on reading formula in, to give:
     %%%  H84:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H94 on reading formula in, to give:
     %%%  H94:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H95 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H98 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  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(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H70).
***  Proved C1:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H21.
***  Proved C2:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H22.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 12 >= dns_types__packet_bytes_range__first
     using hypothesis H69.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 12 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H92.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H6:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H34:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H48:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H72:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H83:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H84:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H90:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H91:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H94:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H100:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8172
<S>  New H101:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8169
<S>  New H104:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8168
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8165
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
<S>  New H93:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New H103:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 2147483639
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483635
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483635
     using hypothesis H70.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
>>>  Restructured hypothesis H68 into:
     >>>  H68:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
<S>  New H73:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H75:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
<S>  New H74:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H76:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
<S>  New H69:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H71:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H89:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H99:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 7
<S>  New H104:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
<S>  New H92:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
<S>  New H102:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) >= - 2147483656
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H104:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H104:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H67:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H67:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_31.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H65).
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H89 on reading formula in, to give:
     %%%  H89:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  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(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H100 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H65).
***  Proved C1:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C2:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 12 >= dns_types__packet_bytes_range__first
     using hypothesis H64.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 12 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H87.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H4:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H65:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H67:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H78:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H79:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H85:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H86:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H89:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H95:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8172
<S>  New H96:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8169
<S>  New H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8168
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8165
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
<S>  New H88:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New H98:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483639
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483635
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483635
     using hypothesis H65.
>>>  Restructured hypothesis H63 into:
     >>>  H63:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
<S>  New H68:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H70:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
<S>  New H69:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H71:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H66:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H84:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H94:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 7
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
<S>  New H87:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
<S>  New H97:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483656
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H62:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H62:  true
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_32.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
---  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 
          H38).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H51).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H17).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H18).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H19).
%%%  Simplified H85 on reading formula in, to give:
     %%%  H85:  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(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H51).
***  Proved C1:  fld_expiry(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H20.
***  Proved C2:  fld_expiry(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H21.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 12 >= dns_types__packet_bytes_range__first
     using hypothesis H50.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 12 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H73.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H5:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H44:  current_byte + loop__2__i <= 8180
<S>  New H48:  loop__2__i <= 8180
<S>  New H51:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H53:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H65:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H71:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H72:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H81:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8172
<S>  New H82:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8169
<S>  New H85:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8168
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8165
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H46:  current_byte + loop__2__i <= 2147483647
<S>  New H74:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New H84:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483639
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483635
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483635
     using hypothesis H51.
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H54:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H56:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H55:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H57:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte >= 1
<S>  New H43:  current_byte + loop__2__i >= 1
<S>  New H47:  loop__2__i >= 1
<S>  New H50:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H52:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H80:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 7
<S>  New H85:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H45:  current_byte + loop__2__i >= - 2147483648
<S>  New H73:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
<S>  New H83:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483656
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H37:  element(fld_email(soa_record), [loop__2__i]) >= 0
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H85:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H38:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H85:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H60 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H78 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H87 (true-hypothesis).
---  Eliminated hypothesis H47 (duplicate of H35).
---  Eliminated hypothesis H35 (duplicate of H3).
---  Eliminated hypothesis H28 (redundant, given H24).
---  Eliminated hypothesis H30 (redundant, given H26).
---  Eliminated hypothesis H36 (redundant, given H49).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H46 (redundant, given H44).
---  Eliminated hypothesis H48 (redundant, given H4).
---  Eliminated hypothesis H51 (redundant, given H32).
---  Eliminated hypothesis H53 (redundant, given H6 & H32).
---  Eliminated hypothesis H54 (redundant, given H52).
---  Eliminated hypothesis H55 (redundant, given H6 & H32).
---  Eliminated hypothesis H56 (redundant, given H52).
---  Eliminated hypothesis H57 (redundant, given H6 & H32).
---  Eliminated hypothesis H64 (redundant, given H32).
---  Eliminated hypothesis H70 (redundant, given H50).
---  Eliminated hypothesis H71 (redundant, given H32).
---  Eliminated hypothesis H72 (redundant, given H32).
---  Eliminated hypothesis H73 (redundant, given H50).
---  Eliminated hypothesis H74 (redundant, given H32).
---  Eliminated hypothesis H80 (redundant, given H50).
---  Eliminated hypothesis H81 (redundant, given H32).
---  Eliminated hypothesis H82 (redundant, given H32).
---  Eliminated hypothesis H83 (redundant, given H50).
---  Eliminated hypothesis H84 (redundant, given H32).
-S-  Eliminated hypothesis H49.
     This was achieved by replacing all occurrences of loop__2__i by:
          mailbox_name_length.
<S>  New H44:  current_byte + mailbox_name_length <= 8180
<S>  New H43:  current_byte + mailbox_name_length >= 1
<S>  New H37:  element(fld_email(soa_record), [mailbox_name_length]) >= 0
<S>  New H38:  element(fld_email(soa_record), [mailbox_name_length]) <= 255
<S>  New H3:  mailbox_name_length >= 1
<S>  New H4:  mailbox_name_length <= 129
     +++  New H88:  integer__size >= 0
     +++  New H89:  character__size >= 0
     +++  New H90:  positive__size >= 0
     +++  New H91:  dns_types__packet_bytes_range__size >= 0
     +++  New H92:  unsigned_types__unsigned16__size >= 0
     +++  New H93:  unsigned_types__unsigned32__size >= 0
     +++  New H94:  rr_type__classtype__size >= 0
     +++  New H95:  rr_type__wirestringtypeindex__size >= 0
     +++  New H96:  rr_type__wirestringtype__size >= 0
     +++  New H97:  rr_type__resourcerecordtype__size >= 0
     +++  New H98:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_33.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H8)
          .
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  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(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  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(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H70).
%%%  Simplified H84 on reading formula in, to give:
     %%%  H84:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H94 on reading formula in, to give:
     %%%  H94:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H95 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H98 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  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(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H107 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H108 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H114 on reading formula in, to give:
     %%%  H114:  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(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H70).
***  Proved C1:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H23.
***  Proved C2:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H24.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 16 >= dns_types__packet_bytes_range__first
     using hypothesis H69.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 16 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H92.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H5:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H6:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H8:  start_byte <= 8180
<S>  New H33:  start_byte <= 8177
<S>  New H34:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H38:  start_byte <= 8176
<S>  New H39:  start_byte <= 8175
<S>  New H48:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H59:  nameserver_name_length <= 8175
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H72:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H83:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H84:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H90:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H91:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H94:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H100:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8172
<S>  New H101:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8169
<S>  New H104:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H110:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8168
<S>  New H111:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8165
<S>  New H114:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8164
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8161
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H47:  start_byte <= 2147483643
<S>  New H93:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New H103:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 2147483639
<S>  New H113:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 2147483635
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483631
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483631
     using hypothesis H70.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  nameserver_name_length < 1
>>>  Restructured hypothesis H68 into:
     >>>  H68:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H49:  nameserver_name_length >= - 2147483648
<S>  New H51:  true
<S>  New H62:  mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H50:  nameserver_name_length <= 2147483647
<S>  New H52:  true
<S>  New H63:  mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H42:  nameserver_name_length + (mailbox_name_length + 20) >= - 
          2147483648
<S>  New H44:  mailbox_name_length >= - 2147483668
<S>  New H60:  nameserver_name_length >= - 2147483653
<S>  New H73:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H75:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H43:  nameserver_name_length + (mailbox_name_length + 20) <= 2147483647
<S>  New H45:  mailbox_name_length <= 2147483627
<S>  New H61:  nameserver_name_length <= 2147483642
<S>  New H74:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H76:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H13:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte >= 1
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H37:  start_byte >= - 3
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H58:  nameserver_name_length >= - 4
<S>  New H69:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H71:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H89:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H99:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 7
<S>  New H104:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H109:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) >= - 11
<S>  New H114:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H46:  start_byte >= - 2147483652
<S>  New H92:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
<S>  New H102:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) >= - 2147483656
<S>  New H112:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) >= - 2147483660
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H104:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H114:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H6:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H84:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H94:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H104:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H114:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H35:  nameserver_name_length + (mailbox_name_length + 20) >= 0
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H36:  nameserver_name_length + (mailbox_name_length + 20) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H15:  fld_serialnumber(soa_record) >= 0
<S>  New H17:  fld_refresh(soa_record) >= 0
<S>  New H19:  fld_retry(soa_record) >= 0
<S>  New H21:  fld_expiry(soa_record) >= 0
<S>  New H23:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H10:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H16:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H18:  fld_refresh(soa_record) <= 4294967295
<S>  New H20:  fld_retry(soa_record) <= 4294967295
<S>  New H22:  fld_expiry(soa_record) <= 4294967295
<S>  New H24:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H11:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H12:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H25:  nameserver_name_length >= 1
<S>  New H27:  mailbox_name_length >= 1
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= rr_type__wirestringtypeindex__last
<S>  New H54:  1 <= nameserver_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H67:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H2:  nameserver_name_length <= 129
<S>  New H4:  mailbox_name_length <= 129
<S>  New H53:  1 <= nameserver_name_length -> nameserver_name_length >= 1 and 
          nameserver_name_length <= 129
<S>  New H54:  true
<S>  New H66:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H67:  true
<S>  New H13:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H14:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_34.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  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 H2)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H65).
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H89 on reading formula in, to give:
     %%%  H89:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  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(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H100 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H101 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H109 on reading formula in, to give:
     %%%  H109:  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(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H110 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H111 has been replaced by "true".  (It is already present, as 
          H65).
***  Proved C1:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H21.
***  Proved C2:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H22.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 16 >= dns_types__packet_bytes_range__first
     using hypothesis H64.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 16 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H87.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8160 - (mailbox_name_length + 
          nameserver_name_length)
<S>  New H4:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte <= 8180
<S>  New H31:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H43:  start_byte + 5 + loop__1__i <= 8180
<S>  New H47:  loop__1__i <= 8180
<S>  New H52:  start_byte + (5 + nameserver_name_length) <= 8180
<S>  New H54:  nameserver_name_length <= 8175
<S>  New H65:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H67:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H78:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H79:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H85:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H86:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H89:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H95:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8172
<S>  New H96:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8169
<S>  New H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H105:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8168
<S>  New H106:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 8165
<S>  New H109:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8164
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8161
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H45:  start_byte + 5 + loop__1__i <= 2147483647
<S>  New H49:  start_byte <= 2147483642
<S>  New H88:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New H98:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483639
<S>  New H108:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) <= 2147483635
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483631
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483631
     using hypothesis H65.
>>>  Restructured hypothesis H63 into:
     >>>  H63:  mailbox_name_length < 1
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  mailbox_name_length >= - 2147483648
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  mailbox_name_length <= 2147483647
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H55:  nameserver_name_length >= - 2147483653
<S>  New H68:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H70:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H56:  nameserver_name_length <= 2147483642
<S>  New H69:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H71:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H11:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H5:  start_byte >= 1
<S>  New H42:  start_byte + 5 + loop__1__i >= 1
<S>  New H46:  loop__1__i >= 1
<S>  New H51:  start_byte + (5 + nameserver_name_length) >= 1
<S>  New H53:  nameserver_name_length >= - 4
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H66:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H84:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H94:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 7
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H104:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) >= - 11
<S>  New H109:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H44:  start_byte + 5 + loop__1__i >= - 2147483648
<S>  New H48:  start_byte >= - 2147483653
<S>  New H87:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
<S>  New H97:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483656
<S>  New H107:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)
          ) >= - 2147483660
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H36:  element(fld_nameserver(soa_record), [loop__1__i]) >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H109:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H37:  element(fld_nameserver(soa_record), [loop__1__i]) <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H79:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H89:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H109:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H13:  fld_serialnumber(soa_record) >= 0
<S>  New H15:  fld_refresh(soa_record) >= 0
<S>  New H17:  fld_retry(soa_record) >= 0
<S>  New H19:  fld_expiry(soa_record) >= 0
<S>  New H21:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H14:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H16:  fld_refresh(soa_record) <= 4294967295
<S>  New H18:  fld_retry(soa_record) <= 4294967295
<S>  New H20:  fld_expiry(soa_record) <= 4294967295
<S>  New H22:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H23:  nameserver_name_length >= 1
<S>  New H25:  mailbox_name_length >= 1
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= rr_type__wirestringtypeindex__last
<S>  New H62:  1 <= mailbox_name_length -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H24:  nameserver_name_length <= 129
<S>  New H26:  mailbox_name_length <= 129
<S>  New H61:  1 <= mailbox_name_length -> mailbox_name_length >= 1 and 
          mailbox_name_length <= 129
<S>  New H62:  true
<S>  New H11:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H12:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H25 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_35.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  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(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  rr_type__classtype__first <= fld_class(fld_inherit(soa_record))
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_nameserver(soa_record), [i___1]) and 
          element(fld_nameserver(soa_record), [i___1]) <= character__last)
%%%  Simplified H13 on reading formula in, to give:
     %%%  H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(fld_email(soa_record), [i___2]) and 
          element(fld_email(soa_record), [i___2]) <= character__last)
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H4)
          .
---  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 
          H38).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H4)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H51).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  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(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H17).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  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(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H18).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H19).
%%%  Simplified H85 on reading formula in, to give:
     %%%  H85:  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(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H21).
%%%  Simplified H95 on reading formula in, to give:
     %%%  H95:  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(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H51).
***  Proved C1:  fld_minimum(soa_record) >= unsigned_types__unsigned32__first
     using hypothesis H22.
***  Proved C2:  fld_minimum(soa_record) <= unsigned_types__unsigned32__last
     using hypothesis H23.
***  Proved C3:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 16 >= dns_types__packet_bytes_range__first
     using hypothesis H50.
***  Proved C6:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) + 16 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H73.
-S-  Applied substitution rule set_ttl_data_rules(18).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H2:  current_byte <= 8160 - mailbox_name_length
<S>  New H5:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H7:  start_byte <= 8180
<S>  New H32:  start_byte <= 8154 - (nameserver_name_length + 
          mailbox_name_length)
<S>  New H44:  current_byte + loop__2__i <= 8180
<S>  New H48:  loop__2__i <= 8180
<S>  New H51:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8180
<S>  New H53:  nameserver_name_length + mailbox_name_length <= 8174
<S>  New H64:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8177
<S>  New H65:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H71:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8176
<S>  New H72:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8173
<S>  New H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H81:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8172
<S>  New H82:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8169
<S>  New H85:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8168
<S>  New H92:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 8165
<S>  New H95:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8164
<S>  New C5:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 8161
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H46:  current_byte + loop__2__i <= 2147483647
<S>  New H74:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483643
<S>  New H84:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483639
<S>  New H94:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           <= 2147483635
<S>  New C7:  start_byte + (6 + (nameserver_name_length + mailbox_name_length)) 
          <= 2147483631
***  Proved C7:  start_byte + (6 + (nameserver_name_length + 
          mailbox_name_length)) <= 2147483631
     using hypothesis H51.
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H54:  nameserver_name_length + mailbox_name_length >= - 2147483654
<S>  New H56:  nameserver_name_length + mailbox_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H55:  nameserver_name_length + mailbox_name_length <= 2147483641
<S>  New H57:  nameserver_name_length + mailbox_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= character__last)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_nameserver(soa_record), [i___1]) and element(fld_nameserver(
          soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, rr_type__wirestringtypeindex__first <= 
          i___2 and i___2 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          fld_email(soa_record), [i___2]) and element(fld_email(soa_record), [
          i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(17).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H6:  start_byte >= 1
<S>  New H43:  current_byte + loop__2__i >= 1
<S>  New H47:  loop__2__i >= 1
<S>  New H50:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= 1
<S>  New H52:  nameserver_name_length + mailbox_name_length >= - 5
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H70:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 3
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H80:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 7
<S>  New H85:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H90:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 11
<S>  New H95:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H45:  current_byte + loop__2__i >= - 2147483648
<S>  New H73:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483652
<S>  New H83:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483656
<S>  New H93:  start_byte + (6 + (nameserver_name_length + mailbox_name_length))
           >= - 2147483660
-S-  Applied substitution rule set_ttl_data_rules(23).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H37:  element(fld_email(soa_record), [loop__2__i]) >= 0
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H85:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H95:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H38:  element(fld_email(soa_record), [loop__2__i]) <= 255
<S>  New H5:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H65:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H85:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H95:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(35).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H8:  fld_ttlinseconds(fld_inherit(soa_record)) >= 0
<S>  New H14:  fld_serialnumber(soa_record) >= 0
<S>  New H16:  fld_refresh(soa_record) >= 0
<S>  New H18:  fld_retry(soa_record) >= 0
<S>  New H20:  fld_expiry(soa_record) >= 0
<S>  New H22:  fld_minimum(soa_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H9:  fld_ttlinseconds(fld_inherit(soa_record)) <= 4294967295
<S>  New H15:  fld_serialnumber(soa_record) <= 4294967295
<S>  New H17:  fld_refresh(soa_record) <= 4294967295
<S>  New H19:  fld_retry(soa_record) <= 4294967295
<S>  New H21:  fld_expiry(soa_record) <= 4294967295
<S>  New H23:  fld_minimum(soa_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(41).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H10:  rr_type__internet <= fld_class(fld_inherit(soa_record))
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H11:  fld_class(fld_inherit(soa_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(68).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H3:  loop__2__i >= 1
<S>  New H24:  nameserver_name_length >= 1
<S>  New H26:  mailbox_name_length >= 1
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_nameserver(
          soa_record), [i___1]) and element(fld_nameserver(soa_record), [i___1])
           <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(fld_email(
          soa_record), [i___2]) and element(fld_email(soa_record), [i___2]) <= 
          255)
-S-  Applied substitution rule set_ttl_data_rules(69).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H4:  loop__2__i <= 129
<S>  New H25:  nameserver_name_length <= 129
<S>  New H27:  mailbox_name_length <= 129
<S>  New H12:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(fld_nameserver(soa_record), [i___1]) and element(
          fld_nameserver(soa_record), [i___1]) <= 255)
<S>  New H13:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 129 -> 0 <= 
          element(fld_email(soa_record), [i___2]) and element(fld_email(
          soa_record), [i___2]) <= 255)
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H31 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H39 (true-hypothesis).
---  Eliminated hypothesis H40 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H60 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H66 (true-hypothesis).
---  Eliminated hypothesis H67 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H78 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H87 (true-hypothesis).
---  Eliminated hypothesis H88 (true-hypothesis).
---  Eliminated hypothesis H89 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H47 (duplicate of H35).
---  Eliminated hypothesis H35 (duplicate of H3).
---  Eliminated hypothesis H28 (redundant, given H24).
---  Eliminated hypothesis H30 (redundant, given H26).
---  Eliminated hypothesis H36 (redundant, given H49).
---  Eliminated hypothesis H45 (redundant, given H43).
---  Eliminated hypothesis H46 (redundant, given H44).
---  Eliminated hypothesis H48 (redundant, given H4).
---  Eliminated hypothesis H51 (redundant, given H32).
---  Eliminated hypothesis H53 (redundant, given H6 & H32).
---  Eliminated hypothesis H54 (redundant, given H52).
---  Eliminated hypothesis H55 (redundant, given H6 & H32).
---  Eliminated hypothesis H56 (redundant, given H52).
---  Eliminated hypothesis H57 (redundant, given H6 & H32).
---  Eliminated hypothesis H64 (redundant, given H32).
---  Eliminated hypothesis H70 (redundant, given H50).
---  Eliminated hypothesis H71 (redundant, given H32).
---  Eliminated hypothesis H72 (redundant, given H32).
---  Eliminated hypothesis H73 (redundant, given H50).
---  Eliminated hypothesis H74 (redundant, given H32).
---  Eliminated hypothesis H80 (redundant, given H50).
---  Eliminated hypothesis H81 (redundant, given H32).
---  Eliminated hypothesis H82 (redundant, given H32).
---  Eliminated hypothesis H83 (redundant, given H50).
---  Eliminated hypothesis H84 (redundant, given H32).
---  Eliminated hypothesis H90 (redundant, given H50).
---  Eliminated hypothesis H91 (redundant, given H32).
---  Eliminated hypothesis H92 (redundant, given H32).
---  Eliminated hypothesis H93 (redundant, given H50).
---  Eliminated hypothesis H94 (redundant, given H32).
-S-  Eliminated hypothesis H49.
     This was achieved by replacing all occurrences of loop__2__i by:
          mailbox_name_length.
<S>  New H44:  current_byte + mailbox_name_length <= 8180
<S>  New H43:  current_byte + mailbox_name_length >= 1
<S>  New H37:  element(fld_email(soa_record), [mailbox_name_length]) >= 0
<S>  New H38:  element(fld_email(soa_record), [mailbox_name_length]) <= 255
<S>  New H3:  mailbox_name_length >= 1
<S>  New H4:  mailbox_name_length <= 129
     +++  New H98:  integer__size >= 0
     +++  New H99:  character__size >= 0
     +++  New H100:  positive__size >= 0
     +++  New H101:  dns_types__packet_bytes_range__size >= 0
     +++  New H102:  unsigned_types__unsigned16__size >= 0
     +++  New H103:  unsigned_types__unsigned32__size >= 0
     +++  New H104:  rr_type__classtype__size >= 0
     +++  New H105:  rr_type__wirestringtypeindex__size >= 0
     +++  New H106:  rr_type__wirestringtype__size >= 0
     +++  New H107:  rr_type__resourcerecordtype__size >= 0
     +++  New H108:  rr_type__soa_record_type__soarecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_36.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_37.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_soa_response_38.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.

