%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP060^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:33 AM UTC 2026
% Result : Theorem 10.16s 1.85s
% Output : Refutation 10.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP060^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:44:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.08/0.95 % (2565319)Will run a generic schedule for satisfiability detection.
% 4.08/0.95 % (2565328)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3792640990:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.08/0.95 % (2565325)% WARNING: option uhcvi not known.
% 4.08/0.95 % (2565328)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.08/0.95 % (2565325)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3641360400:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.08/0.95 % (2565324)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3110510589_2999 on theBenchmark for (2999ds/0Mi)
% 4.08/0.95 % (2565326)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2322949633:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.08/0.95 % (2565327)dis+10_1_sil=32000:sp=arity:random_seed=3796477395:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.08/0.95 % (2565325)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.08/0.95 % (2565330)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1460904326:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.08/0.95 % (2565329)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1801719831:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.08/0.95 % (2565328)Instruction limit reached!
% 4.08/0.95 % (2565328)------------------------------
% 4.08/0.95 % (2565328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.95 % (2565328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.95 % (2565328)CaDiCaL version: 2.1.3
% 4.08/0.95 % (2565328)Termination reason: Instruction limit
% 4.08/0.95 % (2565328)Termination phase: Saturation
% 4.08/0.95 % (2565328)Time elapsed: 0.028 s
% 4.08/0.95 % (2565328)Peak memory usage: 13 MB
% 4.08/0.95 % (2565328)Instructions burned: 120 (million)
% 4.08/0.95 % (2565325)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.08/0.95 % Exception at run slice level
% 4.08/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.08/0.95 % (2565338)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3315388411:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.08/0.95 % (2565327)Instruction limit reached!
% 4.08/0.95 % (2565327)------------------------------
% 4.08/0.95 % (2565327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.95 % (2565327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.95 % (2565327)CaDiCaL version: 2.1.3
% 4.08/0.95 % (2565327)Termination reason: Instruction limit
% 4.08/0.95 % (2565327)Termination phase: Saturation
% 4.08/0.95 % (2565327)Time elapsed: 0.044 s
% 4.08/0.95 % (2565327)Peak memory usage: 13 MB
% 4.08/0.95 % (2565327)Instructions burned: 103 (million)
% 4.08/0.95 % Exception at run slice level
% 4.08/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.08/0.95 % (2565339)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1924532271:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.08/0.95 % (2565342)ott-21_1_sil=16000:fs=off:random_seed=1020885150:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.08/0.95 % (2565341)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2957792961:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.08/0.95 % (2565329)Instruction limit reached!
% 4.08/0.95 % (2565329)------------------------------
% 4.08/0.95 % (2565329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.95 % (2565329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.95 % (2565329)CaDiCaL version: 2.1.3
% 4.08/0.95 % (2565329)Termination reason: Instruction limit
% 4.08/0.95 % (2565329)Termination phase: Saturation
% 4.08/0.95 % (2565329)Time elapsed: 0.059 s
% 4.08/0.95 % (2565329)Peak memory usage: 13 MB
% 4.08/0.95 % (2565329)Instructions burned: 132 (million)
% 4.08/0.95 % (2565341)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.08/0.95 % (2565330)Instruction limit reached!
% 4.08/0.95 % (2565330)------------------------------
% 4.08/0.95 % (2565330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565330)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565330)Termination reason: Instruction limit
% 10.16/1.85 % (2565330)Termination phase: Saturation
% 10.16/1.85 % (2565330)Time elapsed: 0.084 s
% 10.16/1.85 % (2565330)Peak memory usage: 14 MB
% 10.16/1.85 % (2565330)Instructions burned: 161 (million)
% 10.16/1.85 % (2565341)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.16/1.85 % (2565342)Instruction limit reached!
% 10.16/1.85 % (2565342)------------------------------
% 10.16/1.85 % (2565342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565342)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565342)Termination reason: Instruction limit
% 10.16/1.85 % (2565342)Termination phase: Saturation
% 10.16/1.85 % (2565342)Time elapsed: 0.042 s
% 10.16/1.85 % (2565342)Peak memory usage: 13 MB
% 10.16/1.85 % (2565342)Instructions burned: 182 (million)
% 10.16/1.85 % (2565348)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2232995180:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 10.16/1.85 % (2565346)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1958413464:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 10.16/1.85 % (2565347)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4230141934:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 10.16/1.85 % (2565339)Instruction limit reached!
% 10.16/1.85 % (2565339)------------------------------
% 10.16/1.85 % (2565339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565339)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565339)Termination reason: Instruction limit
% 10.16/1.85 % (2565339)Termination phase: Saturation
% 10.16/1.85 % (2565339)Time elapsed: 0.069 s
% 10.16/1.85 % (2565339)Peak memory usage: 13 MB
% 10.16/1.85 % (2565339)Instructions burned: 131 (million)
% 10.16/1.85 % (2565352)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=872870278:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % (2565354)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=211799631:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % (2565354)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.16/1.85 % (2565356)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3620272602:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 10.16/1.85 % (2565356)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.16/1.85 % (2565341)Instruction limit reached!
% 10.16/1.85 % (2565341)------------------------------
% 10.16/1.85 % (2565341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565341)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565341)Termination reason: Instruction limit
% 10.16/1.85 % (2565341)Termination phase: Saturation
% 10.16/1.85 % (2565341)Time elapsed: 0.329 s
% 10.16/1.85 % (2565341)Peak memory usage: 17 MB
% 10.16/1.85 % (2565341)Instructions burned: 685 (million)
% 10.16/1.85 % (2565348)Instruction limit reached!
% 10.16/1.85 % (2565348)------------------------------
% 10.16/1.85 % (2565348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565348)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565348)Termination reason: Instruction limit
% 10.16/1.85 % (2565348)Termination phase: Saturation
% 10.16/1.85 % (2565348)Time elapsed: 0.293 s
% 10.16/1.85 % (2565348)Peak memory usage: 19 MB
% 10.16/1.85 % (2565348)Instructions burned: 1180 (million)
% 10.16/1.85 % (2565358)fmb+10_1_sil=64000:random_seed=3854802612:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 10.16/1.85 % (2565359)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3909557255:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 10.16/1.85 % (2565354)Instruction limit reached!
% 10.16/1.85 % (2565354)------------------------------
% 10.16/1.85 % (2565354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565354)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565354)Termination reason: Instruction limit
% 10.16/1.85 % (2565354)Termination phase: Saturation
% 10.16/1.85 % (2565354)Time elapsed: 0.267 s
% 10.16/1.85 % (2565354)Peak memory usage: 16 MB
% 10.16/1.85 % (2565354)Instructions burned: 695 (million)
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % (2565358)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % (2565363)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2237851872:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 10.16/1.85 % (2565362)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3592703856:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 10.16/1.85 % (2565363)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.16/1.85 % (2565365)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1486322992:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 10.16/1.85 % (2565346)Instruction limit reached!
% 10.16/1.85 % (2565346)------------------------------
% 10.16/1.85 % (2565346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565346)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565346)Termination reason: Instruction limit
% 10.16/1.85 % (2565346)Termination phase: Saturation
% 10.16/1.85 % (2565346)Time elapsed: 0.352 s
% 10.16/1.85 % (2565346)Peak memory usage: 14 MB
% 10.16/1.85 % (2565346)Instructions burned: 478 (million)
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % (2565368)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4141832695:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 10.16/1.85 % (2565365)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.16/1.85 % (2565365)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.16/1.85 % (2565369)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1133040457:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % (2565372)ott-2_1_sil=16000:newcnf=on:random_seed=445358621:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 10.16/1.85 % (2565372)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.16/1.85 % (2565373)ott+10_1_sil=32000:tgt=ground:random_seed=846898542:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 10.16/1.85 % (2565356)Instruction limit reached!
% 10.16/1.85 % (2565356)------------------------------
% 10.16/1.85 % (2565356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565356)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565356)Termination reason: Instruction limit
% 10.16/1.85 % (2565356)Termination phase: Saturation
% 10.16/1.85 % (2565356)Time elapsed: 0.434 s
% 10.16/1.85 % (2565356)Peak memory usage: 18 MB
% 10.16/1.85 % (2565356)Instructions burned: 880 (million)
% 10.16/1.85 % (2565376)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1285999540:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 10.16/1.85 % Exception at run slice level
% 10.16/1.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.16/1.85 % (2565378)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3146422224:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 10.16/1.85 % (2565378)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.16/1.85 % (2565372)Instruction limit reached!
% 10.16/1.85 % (2565372)------------------------------
% 10.16/1.85 % (2565372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565372)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565372)Termination reason: Instruction limit
% 10.16/1.85 % (2565372)Termination phase: Saturation
% 10.16/1.85 % (2565372)Time elapsed: 0.501 s
% 10.16/1.85 % (2565372)Peak memory usage: 19 MB
% 10.16/1.85 % (2565372)Instructions burned: 870 (million)
% 10.16/1.85 % (2565380)dis+21_1_sil=32000:sas=cadical:random_seed=139216028:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 10.16/1.85 % (2565365)Instruction limit reached!
% 10.16/1.85 % (2565365)------------------------------
% 10.16/1.85 % (2565365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565365)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565365)Termination reason: Instruction limit
% 10.16/1.85 % (2565365)Termination phase: Saturation
% 10.16/1.85 % (2565365)Time elapsed: 0.680 s
% 10.16/1.85 % (2565365)Peak memory usage: 16 MB
% 10.16/1.85 % (2565365)Instructions burned: 1473 (million)
% 10.16/1.85 % (2565382)ott+11_1_sil=16000:gs=on:random_seed=1201184538:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 10.16/1.85 % (2565382)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.16/1.85 % (2565363) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2565319-2565363"...
% 10.16/1.85 % (2565363)...printing done.
% 10.16/1.85 % (2565363)Refutation found. Thanks to Tanya!
% 10.16/1.85 % SZS status Theorem for theBenchmark
% 10.16/1.85 % SZS output start Proof for theBenchmark
% 10.16/1.85 thf(type_def_5, type, list_c1059388851t_unit: $tType).
% 10.16/1.85 thf(type_def_6, type, config256849571t_unit: $tType).
% 10.16/1.85 thf(type_def_7, type, list_message_p_v: $tType).
% 10.16/1.85 thf(type_def_8, type, message_p_v: $tType).
% 10.16/1.85 thf(type_def_9, type, nat: $tType).
% 10.16/1.85 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 10.16/1.85 thf(func_def_0, type, enabled_p_v_s: (config256849571t_unit > message_p_v > $o)).
% 10.16/1.85 thf(func_def_1, type, firstO1414030372_p_v_s: (list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o)).
% 10.16/1.85 thf(func_def_2, type, fLPThe1519354920_p_v_s: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_3, type, fLPThe536531371_p_v_s: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > list_message_p_v)).
% 10.16/1.85 thf(func_def_4, type, minus_minus_nat: (nat > nat > nat)).
% 10.16/1.85 thf(func_def_5, type, one_one_nat: nat).
% 10.16/1.85 thf(func_def_6, type, zero_zero_nat: nat).
% 10.16/1.85 thf(func_def_7, type, prefix1615116500t_unit: (list_c1059388851t_unit > list_c1059388851t_unit > $o)).
% 10.16/1.85 thf(func_def_8, type, prefix47729710ge_p_v: (list_message_p_v > list_message_p_v > $o)).
% 10.16/1.85 thf(func_def_9, type, last_c571238084t_unit: (list_c1059388851t_unit > config256849571t_unit)).
% 10.16/1.85 thf(func_def_10, type, last_message_p_v: (list_message_p_v > message_p_v)).
% 10.16/1.85 thf(func_def_11, type, nil_co1338500125t_unit: list_c1059388851t_unit).
% 10.16/1.85 thf(func_def_12, type, nil_message_p_v: list_message_p_v).
% 10.16/1.85 thf(func_def_13, type, nth_co1649820636t_unit: (list_c1059388851t_unit > nat > config256849571t_unit)).
% 10.16/1.85 thf(func_def_14, type, nth_message_p_v: (list_message_p_v > nat > message_p_v)).
% 10.16/1.85 thf(func_def_15, type, suc: (nat > nat)).
% 10.16/1.85 thf(func_def_16, type, size_s1406904903t_unit: (list_c1059388851t_unit > nat)).
% 10.16/1.85 thf(func_def_17, type, size_s1168481041ge_p_v: (list_message_p_v > nat)).
% 10.16/1.85 thf(func_def_18, type, ord_less_nat: (nat > nat > $o)).
% 10.16/1.85 thf(func_def_19, type, ord_less_eq_nat: (nat > nat > $o)).
% 10.16/1.85 thf(func_def_20, type, fe: (nat > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_21, type, ft: (nat > list_message_p_v)).
% 10.16/1.85 thf(func_def_22, type, index: nat).
% 10.16/1.85 thf(func_def_23, type, msgInSet: message_p_v).
% 10.16/1.85 thf(func_def_24, type, msg: message_p_v).
% 10.16/1.85 thf(func_def_25, type, n0: nat).
% 10.16/1.85 thf(func_def_26, type, n1: nat).
% 10.16/1.85 thf(func_def_27, type, nMsg: nat).
% 10.16/1.85 thf(func_def_28, type, n: nat).
% 10.16/1.85 thf(func_def_32, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 10.16/1.85 thf(func_def_33, type, vNOT: ($o > $o)).
% 10.16/1.85 thf(func_def_34, type, vAND: ($o > $o > $o)).
% 10.16/1.85 thf(func_def_35, type, db1: !>[X0: $tType]:(X0)).
% 10.16/1.85 thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
% 10.16/1.85 thf(func_def_37, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 10.16/1.85 thf(func_def_38, type, vOR: ($o > $o > $o)).
% 10.16/1.85 thf(func_def_39, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 10.16/1.85 thf(func_def_40, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 10.16/1.85 thf(func_def_41, type, vIMP: ($o > $o > $o)).
% 10.16/1.85 thf(func_def_42, type, db2: !>[X0: $tType]:(X0)).
% 10.16/1.85 thf(func_def_43, type, sP0: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > $o)).
% 10.16/1.85 thf(func_def_44, type, sP1: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > $o)).
% 10.16/1.85 thf(func_def_45, type, sK2: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_46, type, sK3: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_47, type, sK4: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_48, type, sK5: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_49, type, sK6: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_50, type, sK7: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_51, type, sK8: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_52, type, sK9: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_53, type, sK10: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_54, type, sK11: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_55, type, sK12: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_56, type, sK13: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_57, type, sK14: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_58, type, sK15: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_59, type, sK16: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_60, type, sK17: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_61, type, sK18: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_62, type, sK19: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_63, type, sK20: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_64, type, sK21: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_65, type, sK22: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_66, type, sK23: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_67, type, sK24: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_68, type, sK25: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_69, type, sK26: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_70, type, sK27: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit)).
% 10.16/1.85 thf(func_def_71, type, sK28: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_72, type, sK29: ((config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v)).
% 10.16/1.85 thf(func_def_73, type, sK30: (nat > (nat > $o) > nat)).
% 10.16/1.85 thf(func_def_74, type, sK31: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_75, type, sK32: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_76, type, sK33: (nat > (nat > $o) > nat)).
% 10.16/1.85 thf(func_def_77, type, sK34: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_78, type, sK35: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_79, type, sK36: (nat > (nat > $o) > nat)).
% 10.16/1.85 thf(func_def_80, type, sK37: ((nat > nat) > nat)).
% 10.16/1.85 thf(func_def_81, type, sK38: ((nat > nat) > nat)).
% 10.16/1.85 thf(func_def_82, type, sK39: ((nat > nat) > nat)).
% 10.16/1.85 thf(func_def_83, type, sK40: ((nat > nat) > nat)).
% 10.16/1.85 thf(func_def_84, type, sK41: ((nat > $o) > nat > nat > nat)).
% 10.16/1.85 thf(func_def_85, type, sK42: ((nat > $o) > nat > nat > nat)).
% 10.16/1.85 thf(func_def_86, type, sK43: (nat > nat)).
% 10.16/1.85 thf(func_def_87, type, sK44: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_88, type, sK45: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_89, type, sK46: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_90, type, sK47: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_91, type, sK48: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_92, type, sK49: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_93, type, sK50: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_94, type, sK51: (nat > nat)).
% 10.16/1.85 thf(func_def_95, type, sK52: (nat > nat)).
% 10.16/1.85 thf(func_def_96, type, sK53: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_97, type, sK54: (nat > nat)).
% 10.16/1.85 thf(func_def_98, type, sK55: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_99, type, sK56: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_100, type, sK57: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_101, type, sK58: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_102, type, sK59: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_103, type, sK60: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_104, type, sK61: ((nat > nat) > nat)).
% 10.16/1.85 thf(func_def_105, type, sK62: ((nat > nat) > nat)).
% 10.16/1.85 thf(func_def_106, type, sK63: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_107, type, sK64: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_108, type, sK65: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_109, type, sK66: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_110, type, sK67: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_111, type, sK68: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_112, type, sK69: ((nat > nat > $o) > nat)).
% 10.16/1.85 thf(func_def_113, type, sK70: (nat > nat > nat)).
% 10.16/1.85 thf(func_def_114, type, sK71: (nat > nat > nat)).
% 10.16/1.85 thf(func_def_115, type, sK72: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_116, type, sK73: (nat > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_117, type, sK74: (nat > list_message_p_v)).
% 10.16/1.85 thf(func_def_118, type, sK75: ((list_c1059388851t_unit > $o) > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_119, type, sK76: ((list_message_p_v > $o) > list_message_p_v)).
% 10.16/1.85 thf(func_def_120, type, sK77: (list_c1059388851t_unit > list_c1059388851t_unit > nat)).
% 10.16/1.85 thf(func_def_121, type, sK78: (list_message_p_v > list_message_p_v > nat)).
% 10.16/1.85 thf(func_def_122, type, sK79: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_123, type, sK80: ((nat > $o) > (nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_124, type, sK81: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_125, type, sK82: ((nat > $o) > nat)).
% 10.16/1.85 thf(func_def_126, type, sK83: (list_message_p_v > nat > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > config256849571t_unit > nat)).
% 10.16/1.85 thf(func_def_127, type, sK84: (message_p_v > nat > nat > nat)).
% 10.16/1.85 thf(func_def_128, type, sK85: nat).
% 10.16/1.85 thf(func_def_129, type, sK86: nat).
% 10.16/1.85 thf(func_def_130, type, sK87: ((nat > message_p_v > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_131, type, sK88: ((nat > message_p_v > $o) > nat > list_message_p_v)).
% 10.16/1.85 thf(func_def_132, type, sK89: (list_message_p_v > (nat > message_p_v > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_133, type, sK90: ((nat > message_p_v > $o) > nat > message_p_v)).
% 10.16/1.85 thf(func_def_134, type, sK91: ((nat > config256849571t_unit > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_135, type, sK92: ((nat > config256849571t_unit > $o) > nat > list_c1059388851t_unit)).
% 10.16/1.85 thf(func_def_136, type, sK93: (list_c1059388851t_unit > (nat > config256849571t_unit > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_137, type, sK94: ((nat > config256849571t_unit > $o) > nat > config256849571t_unit)).
% 10.16/1.85 thf(func_def_138, type, sK95: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_139, type, sK96: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_140, type, sK97: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_141, type, sK98: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_142, type, sK99: (nat > nat > nat)).
% 10.16/1.85 thf(func_def_143, type, sK100: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_144, type, sK101: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_145, type, sK102: (nat > nat)).
% 10.16/1.85 thf(func_def_146, type, sK103: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_147, type, sK104: ((nat > $o) > nat > nat)).
% 10.16/1.85 thf(func_def_148, type, sK105: (nat > nat > nat)).
% 10.16/1.85 thf(func_def_150, type, db3: !>[X0: $tType]:(X0)).
% 10.16/1.85 thf(func_def_151, type, db6: !>[X0: $tType]:(X0)).
% 10.16/1.85 thf(func_def_152, type, db5: !>[X0: $tType]:(X0)).
% 10.16/1.85 thf(func_def_153, type, db4: !>[X0: $tType]:(X0)).
% 10.16/1.85 thf(f1,axiom,(
% 10.16/1.85 (ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index)))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Occ3_H)).
% 10.16/1.85 thf(f2,axiom,(
% 10.16/1.85 ! [X0 : nat] : ((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) => (((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_SameCfgOnLow)).
% 10.16/1.85 thf(f6,axiom,(
% 10.16/1.85 (ord_less_nat @ zero_zero_nat @ n1)),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_AssumpOcc6_H_I1_J)).
% 10.16/1.85 thf(f7,axiom,(
% 10.16/1.85 ! [X0 : nat] : (((minus_minus_nat @ (suc @ X0) @ one_one_nat)) = X0)),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_diff__Suc__1)).
% 10.16/1.85 thf(f9,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat,X2 : nat] : (((minus_minus_nat @ (minus_minus_nat @ (suc @ X0) @ X1) @ (suc @ X2))) = ((minus_minus_nat @ (minus_minus_nat @ X0 @ X1) @ X2)))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Suc__diff__diff)).
% 10.16/1.85 thf(f12,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : (((minus_minus_nat @ X0 @ (suc @ X1))) = ((minus_minus_nat @ (minus_minus_nat @ X0 @ one_one_nat) @ X1)))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_diff__Suc__eq__diff__pred)).
% 10.16/1.85 thf(f30,axiom,(
% 10.16/1.85 ! [X0 : nat] : (ord_less_eq_nat @ zero_zero_nat @ X0)),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_le0)).
% 10.16/1.85 thf(f32,axiom,(
% 10.16/1.85 ! [X0 : nat] : (((minus_minus_nat @ X0 @ X0)) = zero_zero_nat)),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_diff__self__eq__0)).
% 10.16/1.85 thf(f33,axiom,(
% 10.16/1.85 ! [X0 : nat] : (((minus_minus_nat @ zero_zero_nat @ X0)) = zero_zero_nat)),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_diff__0__eq__0)).
% 10.16/1.85 thf(f42,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => (((minus_minus_nat @ X0 @ X1)) = zero_zero_nat))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_diff__is__0__eq_H)).
% 10.16/1.85 thf(f56,axiom,(
% 10.16/1.85 (ord_less_nat = (^[X0 : nat, X1 : nat] : ((X0 != X1) & (ord_less_eq_nat @ X0 @ X1))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_nat__less__le)).
% 10.16/1.85 thf(f59,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X1 @ X0) | (ord_less_eq_nat @ X0 @ X1))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_nat__le__linear)).
% 10.16/1.85 thf(f91,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => (ord_less_eq_nat @ (suc @ X0) @ X1))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Suc__leI)).
% 10.16/1.85 thf(f97,axiom,(
% 10.16/1.85 ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0)) = ? [X1 : nat] : (X0 = ((suc @ X1))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_gr0__conv__Suc)).
% 10.16/1.85 thf(f117,axiom,(
% 10.16/1.85 ! [X0 : nat] : ((X0 != zero_zero_nat) => ? [X1 : nat] : (X0 = ((suc @ X1))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_not0__implies__Suc)).
% 10.16/1.85 thf(f119,axiom,(
% 10.16/1.85 ! [X0 : nat] : ((X0 != zero_zero_nat) => ~ ! [X1 : nat] : (X0 != ((suc @ X1))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_old_Onat_Oexhaust)).
% 10.16/1.85 thf(f120,axiom,(
% 10.16/1.85 ! [X0 : nat] : (zero_zero_nat != ((suc @ X0)))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Zero__not__Suc)).
% 10.16/1.85 thf(f130,axiom,(
% 10.16/1.85 ! [X0 : nat] : (((minus_minus_nat @ X0 @ zero_zero_nat)) = X0)),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_minus__nat_Odiff__0)).
% 10.16/1.85 thf(f136,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => (((minus_minus_nat @ (suc @ X1) @ X0)) = ((suc @ (minus_minus_nat @ X1 @ X0)))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Suc__diff__le)).
% 10.16/1.85 thf(f137,axiom,(
% 10.16/1.85 (one_one_nat = ((suc @ zero_zero_nat)))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_One__nat__def)).
% 10.16/1.85 thf(f157,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ zero_zero_nat @ X0) => (((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Suc__diff__eq__diff__pred)).
% 10.16/1.85 thf(f160,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((suc @ X0)) = ((suc @ X1))) => (X0 = X1))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Suc__inject)).
% 10.16/1.85 thf(f161,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat,X2 : nat] : (((minus_minus_nat @ (minus_minus_nat @ X0 @ X1) @ X2)) = ((minus_minus_nat @ (minus_minus_nat @ X0 @ X2) @ X1)))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_diff__commute)).
% 10.16/1.85 thf(f163,axiom,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => (((suc @ (minus_minus_nat @ X1 @ (suc @ X0)))) = ((minus_minus_nat @ X1 @ X0))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Suc__diff__Suc)).
% 10.16/1.85 thf(f245,conjecture,(
% 10.16/1.85 (((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat))) = ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat))))),
% 10.16/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 10.16/1.85 thf(f246,negated_conjecture,(
% 10.16/1.85 ~ (((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat))) = ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat))))),
% 10.16/1.85 inference(negated_conjecture,[status(cth)],[f245])).
% 10.16/1.85 thf(f247,plain,(
% 10.16/1.85 (ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index)))),
% 10.16/1.85 inference(rectify,[],[f1])).
% 10.16/1.85 thf(f248,plain,(
% 10.16/1.85 (((ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index)))) = $true)),
% 10.16/1.85 inference(fool_elimination,[],[f247])).
% 10.16/1.85 thf(f249,plain,(
% 10.16/1.85 ! [X0 : nat] : ((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) => (((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))))),
% 10.16/1.85 inference(rectify,[],[f2])).
% 10.16/1.85 thf(f250,plain,(
% 10.16/1.85 ! [X0 : nat] : ((((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index)))) = $true) => (((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))))),
% 10.16/1.85 inference(fool_elimination,[],[f249])).
% 10.16/1.85 thf(f255,plain,(
% 10.16/1.85 (ord_less_nat @ zero_zero_nat @ n1)),
% 10.16/1.85 inference(rectify,[],[f6])).
% 10.16/1.85 thf(f256,plain,(
% 10.16/1.85 (((ord_less_nat @ zero_zero_nat @ n1)) = $true)),
% 10.16/1.85 inference(fool_elimination,[],[f255])).
% 10.16/1.85 thf(f283,plain,(
% 10.16/1.85 ! [X0 : nat] : (ord_less_eq_nat @ zero_zero_nat @ X0)),
% 10.16/1.85 inference(rectify,[],[f30])).
% 10.16/1.85 thf(f284,plain,(
% 10.16/1.85 ! [X0 : nat] : (((ord_less_eq_nat @ zero_zero_nat @ X0)) = $true)),
% 10.16/1.85 inference(fool_elimination,[],[f283])).
% 10.16/1.85 thf(f299,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => (((minus_minus_nat @ X0 @ X1)) = zero_zero_nat))),
% 10.16/1.85 inference(rectify,[],[f42])).
% 10.16/1.85 thf(f300,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) = $true) => (zero_zero_nat = ((minus_minus_nat @ X0 @ X1))))),
% 10.16/1.85 inference(fool_elimination,[],[f299])).
% 10.16/1.85 thf(f325,plain,(
% 10.16/1.85 (ord_less_nat = (^[X0 : nat, X1 : nat] : ((X0 != X1) & (ord_less_eq_nat @ X0 @ X1))))),
% 10.16/1.85 inference(rectify,[],[f56])).
% 10.16/1.85 thf(f326,plain,(
% 10.16/1.85 (ord_less_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))))),
% 10.16/1.85 inference(fool_elimination,[],[f325])).
% 10.16/1.85 thf(f331,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X1 @ X0) | (ord_less_eq_nat @ X0 @ X1))),
% 10.16/1.85 inference(rectify,[],[f59])).
% 10.16/1.85 thf(f332,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) = $true) | (((ord_less_eq_nat @ X0 @ X1)) = $true))),
% 10.16/1.85 inference(fool_elimination,[],[f331])).
% 10.16/1.85 thf(f385,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => (ord_less_eq_nat @ (suc @ X0) @ X1))),
% 10.16/1.85 inference(rectify,[],[f91])).
% 10.16/1.85 thf(f386,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1)) = $true) => (((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true))),
% 10.16/1.85 inference(fool_elimination,[],[f385])).
% 10.16/1.85 thf(f397,plain,(
% 10.16/1.85 ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0)) = ((?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X0)))))),
% 10.16/1.85 inference(fool_elimination,[],[f97])).
% 10.16/1.85 thf(f452,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => (((minus_minus_nat @ (suc @ X1) @ X0)) = ((suc @ (minus_minus_nat @ X1 @ X0)))))),
% 10.16/1.85 inference(rectify,[],[f136])).
% 10.16/1.85 thf(f453,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) = $true) => (((minus_minus_nat @ (suc @ X1) @ X0)) = ((suc @ (minus_minus_nat @ X1 @ X0)))))),
% 10.16/1.85 inference(fool_elimination,[],[f452])).
% 10.16/1.85 thf(f492,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ zero_zero_nat @ X0) => (((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))))),
% 10.16/1.85 inference(rectify,[],[f157])).
% 10.16/1.85 thf(f493,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ zero_zero_nat @ X0)) = $true) => (((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))))),
% 10.16/1.85 inference(fool_elimination,[],[f492])).
% 10.16/1.85 thf(f498,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => (((suc @ (minus_minus_nat @ X1 @ (suc @ X0)))) = ((minus_minus_nat @ X1 @ X0))))),
% 10.16/1.85 inference(rectify,[],[f163])).
% 10.16/1.85 thf(f499,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1)) = $true) => (((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))))),
% 10.16/1.85 inference(fool_elimination,[],[f498])).
% 10.16/1.85 thf(f639,plain,(
% 10.16/1.85 (((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat))) != ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat))))),
% 10.16/1.85 inference(flattening,[],[f246])).
% 10.16/1.85 thf(f640,plain,(
% 10.16/1.85 ! [X0 : nat] : ((((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))) | (((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index)))) != $true))),
% 10.16/1.85 inference(ennf_transformation,[],[f250])).
% 10.16/1.85 thf(f647,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((zero_zero_nat = ((minus_minus_nat @ X0 @ X1))) | (((ord_less_eq_nat @ X0 @ X1)) != $true))),
% 10.16/1.85 inference(ennf_transformation,[],[f300])).
% 10.16/1.85 thf(f691,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true) | (((ord_less_nat @ X0 @ X1)) != $true))),
% 10.16/1.85 inference(ennf_transformation,[],[f386])).
% 10.16/1.85 thf(f719,plain,(
% 10.16/1.85 ! [X0 : nat] : (? [X1 : nat] : (X0 = ((suc @ X1))) | (zero_zero_nat = X0))),
% 10.16/1.85 inference(ennf_transformation,[],[f117])).
% 10.16/1.85 thf(f722,plain,(
% 10.16/1.85 ! [X0 : nat] : (? [X1 : nat] : (((suc @ X1)) = X0) | (zero_zero_nat = X0))),
% 10.16/1.85 inference(ennf_transformation,[],[f119])).
% 10.16/1.85 thf(f738,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((suc @ (minus_minus_nat @ X1 @ X0)))) | (((ord_less_eq_nat @ X0 @ X1)) != $true))),
% 10.16/1.85 inference(ennf_transformation,[],[f453])).
% 10.16/1.85 thf(f761,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | (((ord_less_nat @ zero_zero_nat @ X0)) != $true))),
% 10.16/1.85 inference(ennf_transformation,[],[f493])).
% 10.16/1.85 thf(f763,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((X0 = X1) | (((suc @ X0)) != ((suc @ X1))))),
% 10.16/1.85 inference(ennf_transformation,[],[f160])).
% 10.16/1.85 thf(f764,plain,(
% 10.16/1.85 ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))) | (((ord_less_nat @ X0 @ X1)) != $true))),
% 10.16/1.85 inference(ennf_transformation,[],[f499])).
% 10.16/1.85 thf(f846,plain,(
% 10.16/1.85 ! [X0 : nat] : ((((suc @ (sK52 @ X0))) = X0) | (zero_zero_nat = X0))),
% 10.16/1.85 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK5 @ X1 @ X0)],[f719])).
% 10.16/1.85 thf(f848,plain,(
% 10.16/1.85 ! [X0 : nat] : ((((suc @ (sK54 @ X0))) = X0) | (zero_zero_nat = X0))),
% 10.16/1.85 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK5 @ X1 @ X0)],[f722])).
% 10.16/1.85 thf(f880,plain,(
% 10.16/1.85 (((ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index)))) = $true)),
% 10.16/1.85 inference(cnf_transformation,[],[f248])).
% 10.16/1.85 thf(f881,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))) | (((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index)))) != $true)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f640])).
% 10.16/1.85 thf(f885,plain,(
% 10.16/1.85 (((ord_less_nat @ zero_zero_nat @ n1)) = $true)),
% 10.16/1.85 inference(cnf_transformation,[],[f256])).
% 10.16/1.85 thf(f886,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((minus_minus_nat @ (suc @ X0) @ one_one_nat)) = X0)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f7])).
% 10.16/1.85 thf(f888,plain,(
% 10.16/1.85 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((minus_minus_nat @ (minus_minus_nat @ (suc @ X0) @ X1) @ (suc @ X2))) = ((minus_minus_nat @ (minus_minus_nat @ X0 @ X1) @ X2)))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f9])).
% 10.16/1.85 thf(f891,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X0 @ (suc @ X1))) = ((minus_minus_nat @ (minus_minus_nat @ X0 @ one_one_nat) @ X1)))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f12])).
% 10.16/1.85 thf(f919,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((ord_less_eq_nat @ zero_zero_nat @ X0)) = $true)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f284])).
% 10.16/1.85 thf(f921,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((zero_zero_nat = ((minus_minus_nat @ X0 @ X0)))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f32])).
% 10.16/1.85 thf(f922,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((zero_zero_nat = ((minus_minus_nat @ zero_zero_nat @ X0)))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f33])).
% 10.16/1.85 thf(f931,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) != $true) | (zero_zero_nat = ((minus_minus_nat @ X0 @ X1)))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f647])).
% 10.16/1.85 thf(f945,plain,(
% 10.16/1.85 (ord_less_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))))),
% 10.16/1.85 inference(cnf_transformation,[],[f326])).
% 10.16/1.85 thf(f948,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) = $true) | (((ord_less_eq_nat @ X0 @ X1)) = $true)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f332])).
% 10.16/1.85 thf(f999,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true) | (((ord_less_nat @ X0 @ X1)) != $true)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f691])).
% 10.16/1.85 thf(f1005,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((ord_less_nat @ zero_zero_nat @ X0)) = ((?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X0)))))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f397])).
% 10.16/1.85 thf(f1030,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((suc @ (sK52 @ X0))) = X0) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f846])).
% 10.16/1.85 thf(f1033,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((suc @ (sK54 @ X0))) = X0) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f848])).
% 10.16/1.85 thf(f1034,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((zero_zero_nat != ((suc @ X0)))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f120])).
% 10.16/1.85 thf(f1047,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((minus_minus_nat @ X0 @ zero_zero_nat)) = X0)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f130])).
% 10.16/1.85 thf(f1055,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) != $true) | (((minus_minus_nat @ (suc @ X1) @ X0)) = ((suc @ (minus_minus_nat @ X1 @ X0))))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f738])).
% 10.16/1.85 thf(f1056,plain,(
% 10.16/1.85 (one_one_nat = ((suc @ zero_zero_nat)))),
% 10.16/1.85 inference(cnf_transformation,[],[f137])).
% 10.16/1.85 thf(f1087,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | (((ord_less_nat @ zero_zero_nat @ X0)) != $true)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f761])).
% 10.16/1.85 thf(f1090,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X0)) != ((suc @ X1))) | (X0 = X1)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f763])).
% 10.16/1.85 thf(f1091,plain,(
% 10.16/1.85 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((minus_minus_nat @ (minus_minus_nat @ X0 @ X1) @ X2)) = ((minus_minus_nat @ (minus_minus_nat @ X0 @ X2) @ X1)))) )),
% 10.16/1.85 inference(cnf_transformation,[],[f161])).
% 10.16/1.85 thf(f1093,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))) | (((ord_less_nat @ X0 @ X1)) != $true)) )),
% 10.16/1.85 inference(cnf_transformation,[],[f764])).
% 10.16/1.85 thf(f1194,plain,(
% 10.16/1.85 (((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat))) != ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat))))),
% 10.16/1.85 inference(cnf_transformation,[],[f639])).
% 10.16/1.85 thf(f1198,plain,(
% 10.16/1.85 ($true = (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ n1 @ (size_s1406904903t_unit @ (fe @ index)))))),
% 10.16/1.85 inference(definition_unfolding,[],[f880,f945])).
% 10.16/1.85 thf(f1199,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))) | ($true != (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ X0 @ (size_s1406904903t_unit @ (fe @ index)))))) )),
% 10.16/1.85 inference(definition_unfolding,[],[f881,f945])).
% 10.16/1.85 thf(f1202,plain,(
% 10.16/1.85 ($true = (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ zero_zero_nat @ n1)))),
% 10.16/1.85 inference(definition_unfolding,[],[f885,f945])).
% 10.16/1.85 thf(f1248,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true) | ($true != (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ X0 @ X1)))) )),
% 10.16/1.85 inference(definition_unfolding,[],[f999,f945])).
% 10.16/1.85 thf(f1254,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X0)))) = (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ zero_zero_nat @ X0)))) )),
% 10.16/1.85 inference(definition_unfolding,[],[f1005,f945])).
% 10.16/1.85 thf(f1293,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | ($true != (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ zero_zero_nat @ X0)))) )),
% 10.16/1.85 inference(definition_unfolding,[],[f1087,f945])).
% 10.16/1.85 thf(f1296,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))) | ($true != (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ X0 @ X1)))) )),
% 10.16/1.85 inference(definition_unfolding,[],[f1093,f945])).
% 10.16/1.85 thf(f1740,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))) | ($true != (((ord_less_eq_nat @ X0 @ X1) & (~ (X0 = X1)))))) )),
% 10.16/1.85 inference(beta-eta_normalization,[],[f1296])).
% 10.16/1.85 thf(f1741,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))) | (((~ (X0 = X1))) = $false) | (((ord_less_eq_nat @ X0 @ X1)) = $false)) )),
% 10.16/1.85 inference(and_proxy_clausification,[],[f1740])).
% 10.16/1.85 thf(f1742,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))) | ($true = ((X0 = X1))) | (((ord_less_eq_nat @ X0 @ X1)) = $false)) )),
% 10.16/1.85 inference(not_proxy_clausification,[],[f1741])).
% 10.16/1.85 thf(f1743,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ X1 @ X0)) = ((suc @ (minus_minus_nat @ X1 @ (suc @ X0))))) | (X0 = X1) | (((ord_less_eq_nat @ X0 @ X1)) = $false)) )),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f1742])).
% 10.16/1.85 thf(f1753,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | ($true != (((ord_less_eq_nat @ zero_zero_nat @ X0) & (~ (zero_zero_nat = X0)))))) )),
% 10.16/1.85 inference(beta-eta_normalization,[],[f1293])).
% 10.16/1.85 thf(f1754,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | (((~ (zero_zero_nat = X0))) = $false) | (((ord_less_eq_nat @ zero_zero_nat @ X0)) = $false)) )),
% 10.16/1.85 inference(and_proxy_clausification,[],[f1753])).
% 10.16/1.85 thf(f1755,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | ($true = ((zero_zero_nat = X0))) | (((ord_less_eq_nat @ zero_zero_nat @ X0)) = $false)) )),
% 10.16/1.85 inference(not_proxy_clausification,[],[f1754])).
% 10.16/1.85 thf(f1756,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | (zero_zero_nat = X0) | (((ord_less_eq_nat @ zero_zero_nat @ X0)) = $false)) )),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f1755])).
% 10.16/1.85 thf(f2348,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X0)))) = $false) | ($true = (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ zero_zero_nat @ X0)))) )),
% 10.16/1.85 inference(iff_proxy_clausification,[],[f1254])).
% 10.16/1.85 thf(f2349,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : (($false = (((^[Y0 : nat]: ((suc @ Y0) = X0)) @ X1))) | ($true = (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ zero_zero_nat @ X0)))) )),
% 10.16/1.85 inference(pi_proxy_clausification,[],[f2348])).
% 10.16/1.85 thf(f2350,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : (((((suc @ X1) = X0)) = $false) | ($true = (((ord_less_eq_nat @ zero_zero_nat @ X0) & (~ (zero_zero_nat = X0)))))) )),
% 10.16/1.85 inference(beta-eta_normalization,[],[f2349])).
% 10.16/1.85 thf(f2351,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != X0) | ($true = (((ord_less_eq_nat @ zero_zero_nat @ X0) & (~ (zero_zero_nat = X0)))))) )),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f2350])).
% 10.16/1.85 thf(f2352,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != X0) | ($true = ((~ (zero_zero_nat = X0))))) )),
% 10.16/1.85 inference(and_proxy_clausification,[],[f2351])).
% 10.16/1.85 thf(f2354,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != X0) | (((zero_zero_nat = X0)) = $false)) )),
% 10.16/1.85 inference(not_proxy_clausification,[],[f2352])).
% 10.16/1.85 thf(f2355,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((zero_zero_nat != X0) | (((suc @ X1)) != X0)) )),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f2354])).
% 10.16/1.85 thf(f2484,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true) | ($true != (((ord_less_eq_nat @ X0 @ X1) & (~ (X0 = X1)))))) )),
% 10.16/1.85 inference(beta-eta_normalization,[],[f1248])).
% 10.16/1.85 thf(f2485,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true) | (((~ (X0 = X1))) = $false) | (((ord_less_eq_nat @ X0 @ X1)) = $false)) )),
% 10.16/1.85 inference(and_proxy_clausification,[],[f2484])).
% 10.16/1.85 thf(f2486,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true) | ($true = ((X0 = X1))) | (((ord_less_eq_nat @ X0 @ X1)) = $false)) )),
% 10.16/1.85 inference(not_proxy_clausification,[],[f2485])).
% 10.16/1.85 thf(f2487,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ (suc @ X0) @ X1)) = $true) | (X0 = X1) | (((ord_less_eq_nat @ X0 @ X1)) = $false)) )),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f2486])).
% 10.16/1.85 thf(f2855,plain,(
% 10.16/1.85 ($true = (((ord_less_eq_nat @ zero_zero_nat @ n1) & (~ (zero_zero_nat = n1)))))),
% 10.16/1.85 inference(beta-eta_normalization,[],[f1202])).
% 10.16/1.85 thf(f2856,plain,(
% 10.16/1.85 ($true = ((~ (zero_zero_nat = n1))))),
% 10.16/1.85 inference(and_proxy_clausification,[],[f2855])).
% 10.16/1.85 thf(f2858,plain,(
% 10.16/1.85 ($false = ((zero_zero_nat = n1)))),
% 10.16/1.85 inference(not_proxy_clausification,[],[f2856])).
% 10.16/1.85 thf(f2859,plain,(
% 10.16/1.85 (n1 != zero_zero_nat)),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f2858])).
% 10.16/1.85 thf(f2870,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))) | ($true != (((ord_less_eq_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) & (~ (X0 = (size_s1406904903t_unit @ (fe @ index)))))))) )),
% 10.16/1.85 inference(beta-eta_normalization,[],[f1199])).
% 10.16/1.85 thf(f2871,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))) | ($false = ((~ (X0 = (size_s1406904903t_unit @ (fe @ index)))))) | ($false = ((ord_less_eq_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index)))))) )),
% 10.16/1.85 inference(and_proxy_clausification,[],[f2870])).
% 10.16/1.85 thf(f2872,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))) | ($true = ((X0 = (size_s1406904903t_unit @ (fe @ index))))) | ($false = ((ord_less_eq_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index)))))) )),
% 10.16/1.85 inference(not_proxy_clausification,[],[f2871])).
% 10.16/1.85 thf(f2873,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((nth_co1649820636t_unit @ (fe @ index) @ X0)) = ((nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0))) | (((size_s1406904903t_unit @ (fe @ index))) = X0) | ($false = ((ord_less_eq_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index)))))) )),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f2872])).
% 10.16/1.85 thf(f2874,plain,(
% 10.16/1.85 ($true = (((ord_less_eq_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))) & (~ (n1 = (size_s1406904903t_unit @ (fe @ index)))))))),
% 10.16/1.85 inference(beta-eta_normalization,[],[f1198])).
% 10.16/1.85 thf(f2875,plain,(
% 10.16/1.85 ($true = ((~ (n1 = (size_s1406904903t_unit @ (fe @ index))))))),
% 10.16/1.85 inference(and_proxy_clausification,[],[f2874])).
% 10.16/1.85 thf(f2876,plain,(
% 10.16/1.85 ($true = ((ord_less_eq_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index)))))),
% 10.16/1.85 inference(and_proxy_clausification,[],[f2874])).
% 10.16/1.85 thf(f2877,plain,(
% 10.16/1.85 ($false = ((n1 = (size_s1406904903t_unit @ (fe @ index)))))),
% 10.16/1.85 inference(not_proxy_clausification,[],[f2875])).
% 10.16/1.85 thf(f2878,plain,(
% 10.16/1.85 (n1 != ((size_s1406904903t_unit @ (fe @ index))))),
% 10.16/1.85 inference(equality_proxy_clausification,[],[f2877])).
% 10.16/1.85 thf(f2911,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != X0) | (((sK52 @ X0)) = X1) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(constrained_superposition,[],[f1090,f1030])).
% 10.16/1.85 thf(f2912,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != X0) | (((sK54 @ X0)) = X1) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(constrained_superposition,[],[f1090,f1033])).
% 10.16/1.85 thf(f2914,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != X0) | (((sK54 @ X0)) = X1)) )),
% 10.16/1.85 inference(forward_subsumption_resolution,[],[f2912,f2355])).
% 10.16/1.85 thf(f2915,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != X0) | (((sK52 @ X0)) = X1)) )),
% 10.16/1.85 inference(forward_subsumption_resolution,[],[f2911,f2355])).
% 10.16/1.85 thf(f4502,plain,(
% 10.16/1.85 ( ! [X0 : nat] : (($true = ((ord_less_eq_nat @ one_one_nat @ X0))) | (zero_zero_nat = X0) | (((ord_less_eq_nat @ zero_zero_nat @ X0)) = $false)) )),
% 10.16/1.85 inference(constrained_superposition,[],[f2487,f1056])).
% 10.16/1.85 thf(f4581,plain,(
% 10.16/1.85 ( ! [X0 : nat] : (($true = $false) | ($true = ((ord_less_eq_nat @ one_one_nat @ X0))) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(forward_demodulation,[],[f4502,f919])).
% 10.16/1.85 thf(f4582,plain,(
% 10.16/1.85 ( ! [X0 : nat] : (($true = ((ord_less_eq_nat @ one_one_nat @ X0))) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f4581])).
% 10.16/1.85 thf(f8072,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : (($true = $false) | (((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(forward_demodulation,[],[f1756,f919])).
% 10.16/1.85 thf(f8073,plain,(
% 10.16/1.85 ( ! [X0 : nat,X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ X0)) = ((minus_minus_nat @ X1 @ (minus_minus_nat @ X0 @ one_one_nat)))) | (zero_zero_nat = X0)) )),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f8072])).
% 10.16/1.85 thf(f11219,plain,(
% 10.16/1.85 (((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat))) != ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat)))) | (((size_s1406904903t_unit @ (fe @ index))) = ((minus_minus_nat @ n1 @ one_one_nat))) | ($false = ((ord_less_eq_nat @ (minus_minus_nat @ n1 @ one_one_nat) @ (size_s1406904903t_unit @ (fe @ index)))))),
% 10.16/1.85 inference(constrained_superposition,[],[f1194,f2873])).
% 10.16/1.85 thf(f11250,plain,(
% 10.16/1.85 (((size_s1406904903t_unit @ (fe @ index))) = ((minus_minus_nat @ n1 @ one_one_nat))) | ($false = ((ord_less_eq_nat @ (minus_minus_nat @ n1 @ one_one_nat) @ (size_s1406904903t_unit @ (fe @ index)))))),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f11219])).
% 10.16/1.85 thf(f11342,definition,(
% 10.16/1.85 spl106_4 <=> ($false = ((ord_less_eq_nat @ (minus_minus_nat @ n1 @ one_one_nat) @ (size_s1406904903t_unit @ (fe @ index)))))),
% 10.16/1.85 introduced(definition,[new_symbols(definition,[spl106_4])],[avatar_definition])).
% 10.16/1.85 thf(f11344,plain,(
% 10.16/1.85 ($false = ((ord_less_eq_nat @ (minus_minus_nat @ n1 @ one_one_nat) @ (size_s1406904903t_unit @ (fe @ index))))) | ~spl106_4),
% 10.16/1.85 inference(avatar_component_clause,[],[f11342])).
% 10.16/1.85 thf(f11346,definition,(
% 10.16/1.85 spl106_5 <=> (((size_s1406904903t_unit @ (fe @ index))) = ((minus_minus_nat @ n1 @ one_one_nat)))),
% 10.16/1.85 introduced(definition,[new_symbols(definition,[spl106_5])],[avatar_definition])).
% 10.16/1.85 thf(f11348,plain,(
% 10.16/1.85 (((size_s1406904903t_unit @ (fe @ index))) = ((minus_minus_nat @ n1 @ one_one_nat))) | ~spl106_5),
% 10.16/1.85 inference(avatar_component_clause,[],[f11346])).
% 10.16/1.85 thf(f11349,plain,(
% 10.16/1.85 spl106_4 | spl106_5),
% 10.16/1.85 inference(avatar_split_clause,[],[f11250,f11346,f11342])).
% 10.16/1.85 thf(f11419,plain,(
% 10.16/1.85 ($true = $false) | ($true = ((ord_less_eq_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f948,f11344])).
% 10.16/1.85 thf(f11551,plain,(
% 10.16/1.85 ($true = ((ord_less_eq_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))) | ~spl106_4),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f11419])).
% 10.16/1.85 thf(f11585,plain,(
% 10.16/1.85 ($true != $true) | (zero_zero_nat = ((minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f931,f11551])).
% 10.16/1.85 thf(f11763,plain,(
% 10.16/1.85 (zero_zero_nat = ((minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))) | ~spl106_4),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f11585])).
% 10.16/1.85 thf(f11886,plain,(
% 10.16/1.85 (zero_zero_nat = ((minus_minus_nat @ (suc @ (size_s1406904903t_unit @ (fe @ index))) @ n1))) | (n1 = zero_zero_nat) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f8073,f11763])).
% 10.16/1.85 thf(f11888,plain,(
% 10.16/1.85 (zero_zero_nat = ((minus_minus_nat @ (suc @ (size_s1406904903t_unit @ (fe @ index))) @ n1))) | ~spl106_4),
% 10.16/1.85 inference(forward_subsumption_resolution,[],[f11886,f2859])).
% 10.16/1.85 thf(f11907,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((((minus_minus_nat @ zero_zero_nat @ (suc @ X0))) = ((minus_minus_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ n1) @ X0)))) ) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f888,f11888])).
% 10.16/1.85 thf(f11909,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((zero_zero_nat = ((minus_minus_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ n1) @ X0)))) ) | ~spl106_4),
% 10.16/1.85 inference(forward_demodulation,[],[f11907,f922])).
% 10.16/1.85 thf(f11916,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((zero_zero_nat = ((minus_minus_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ X0) @ n1)))) ) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f11909,f1091])).
% 10.16/1.85 thf(f11918,plain,(
% 10.16/1.85 (zero_zero_nat = ((minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ n1))) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f11909,f1047])).
% 10.16/1.85 thf(f12038,plain,(
% 10.16/1.85 (zero_zero_nat = ((minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ n1)))) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f11916,f891])).
% 10.16/1.85 thf(f12242,plain,(
% 10.16/1.85 (((suc @ zero_zero_nat)) = ((minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ n1))) | (n1 = ((size_s1406904903t_unit @ (fe @ index)))) | ($false = ((ord_less_eq_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))))) | ~spl106_4),
% 10.16/1.85 inference(constrained_superposition,[],[f1743,f12038])).
% 10.16/1.85 thf(f12244,plain,(
% 10.16/1.85 (((suc @ zero_zero_nat)) = ((minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ n1))) | ($false = ((ord_less_eq_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))))) | ~spl106_4),
% 10.16/1.85 inference(forward_subsumption_resolution,[],[f12242,f2878])).
% 10.16/1.85 thf(f12247,plain,(
% 10.16/1.85 (zero_zero_nat = ((suc @ zero_zero_nat))) | ($false = ((ord_less_eq_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))))) | ~spl106_4),
% 10.16/1.85 inference(forward_demodulation,[],[f12244,f11918])).
% 10.16/1.85 thf(f12248,plain,(
% 10.16/1.85 ($false = ((ord_less_eq_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))))) | ~spl106_4),
% 10.16/1.85 inference(forward_subsumption_resolution,[],[f12247,f1034])).
% 10.16/1.85 thf(f16974,definition,(
% 10.16/1.85 spl106_8 <=> ($true = ((ord_less_eq_nat @ one_one_nat @ n1)))),
% 10.16/1.85 introduced(definition,[new_symbols(definition,[spl106_8])],[avatar_definition])).
% 10.16/1.85 thf(f16975,plain,(
% 10.16/1.85 ($true != ((ord_less_eq_nat @ one_one_nat @ n1))) | spl106_8),
% 10.16/1.85 inference(avatar_component_clause,[],[f16974])).
% 10.16/1.85 thf(f16976,plain,(
% 10.16/1.85 ($true = ((ord_less_eq_nat @ one_one_nat @ n1))) | ~spl106_8),
% 10.16/1.85 inference(avatar_component_clause,[],[f16974])).
% 10.16/1.85 thf(f17006,plain,(
% 10.16/1.85 ($true != $true) | (((suc @ (minus_minus_nat @ n1 @ one_one_nat))) = ((minus_minus_nat @ (suc @ n1) @ one_one_nat))) | ~spl106_8),
% 10.16/1.85 inference(constrained_superposition,[],[f1055,f16976])).
% 10.16/1.85 thf(f17193,plain,(
% 10.16/1.85 (((suc @ (minus_minus_nat @ n1 @ one_one_nat))) = ((minus_minus_nat @ (suc @ n1) @ one_one_nat))) | ~spl106_8),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f17006])).
% 10.16/1.85 thf(f17224,plain,(
% 10.16/1.85 (n1 = ((suc @ (minus_minus_nat @ n1 @ one_one_nat)))) | ~spl106_8),
% 10.16/1.85 inference(forward_demodulation,[],[f17193,f886])).
% 10.16/1.85 thf(f17844,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((n1 != X0) | (((minus_minus_nat @ n1 @ one_one_nat)) = ((sK54 @ X0)))) ) | ~spl106_8),
% 10.16/1.85 inference(constrained_superposition,[],[f2914,f17224])).
% 10.16/1.85 thf(f18026,plain,(
% 10.16/1.85 (((minus_minus_nat @ n1 @ one_one_nat)) = ((sK54 @ n1))) | ~spl106_8),
% 10.16/1.85 inference(equality_resolution,[],[f17844])).
% 10.16/1.85 thf(f18371,plain,(
% 10.16/1.85 (n1 = ((suc @ (sK54 @ n1)))) | ~spl106_8),
% 10.16/1.85 inference(constrained_superposition,[],[f17224,f18026])).
% 10.16/1.85 thf(f18983,plain,(
% 10.16/1.85 ( ! [X0 : nat] : ((n1 != X0) | (((sK52 @ X0)) = ((sK54 @ n1)))) ) | ~spl106_8),
% 10.16/1.85 inference(constrained_superposition,[],[f2915,f18371])).
% 10.16/1.85 thf(f19587,plain,(
% 10.16/1.85 (((sK54 @ n1)) = ((sK52 @ n1))) | ~spl106_8),
% 10.16/1.85 inference(equality_resolution,[],[f18983])).
% 10.16/1.85 thf(f21323,plain,(
% 10.16/1.85 (n1 = ((suc @ (sK52 @ n1)))) | ~spl106_8),
% 10.16/1.85 inference(constrained_superposition,[],[f18371,f19587])).
% 10.16/1.85 thf(f31563,plain,(
% 10.16/1.85 ($true = $false) | ~spl106_4),
% 10.16/1.85 inference(forward_demodulation,[],[f2876,f12248])).
% 10.16/1.85 thf(f31564,plain,(
% 10.16/1.85 $false | ~spl106_4),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f31563])).
% 10.16/1.85 thf(f31565,plain,(
% 10.16/1.85 ~spl106_4),
% 10.16/1.85 inference(avatar_contradiction_clause,[],[f31564])).
% 10.16/1.85 thf(f31567,plain,(
% 10.16/1.85 (((size_s1406904903t_unit @ (fe @ index))) = ((sK54 @ n1))) | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(forward_demodulation,[],[f11348,f18026])).
% 10.16/1.85 thf(f31569,plain,(
% 10.16/1.85 (((size_s1406904903t_unit @ (fe @ index))) = ((sK52 @ n1))) | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(forward_demodulation,[],[f31567,f19587])).
% 10.16/1.85 thf(f31692,plain,(
% 10.16/1.85 ($true = ((ord_less_eq_nat @ n1 @ (sK52 @ n1)))) | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(forward_demodulation,[],[f2876,f31569])).
% 10.16/1.85 thf(f31728,plain,(
% 10.16/1.85 ($true != $true) | (((minus_minus_nat @ (suc @ (sK52 @ n1)) @ n1)) = ((suc @ (minus_minus_nat @ (sK52 @ n1) @ n1)))) | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(constrained_superposition,[],[f1055,f31692])).
% 10.16/1.85 thf(f31940,plain,(
% 10.16/1.85 (((minus_minus_nat @ (suc @ (sK52 @ n1)) @ n1)) = ((suc @ (minus_minus_nat @ (sK52 @ n1) @ n1)))) | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f31728])).
% 10.16/1.85 thf(f31997,plain,(
% 10.16/1.85 (((minus_minus_nat @ n1 @ n1)) = ((suc @ (minus_minus_nat @ (sK52 @ n1) @ n1)))) | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(forward_demodulation,[],[f31940,f21323])).
% 10.16/1.85 thf(f32000,plain,(
% 10.16/1.85 (zero_zero_nat = ((suc @ (minus_minus_nat @ (sK52 @ n1) @ n1)))) | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(forward_demodulation,[],[f31997,f921])).
% 10.16/1.85 thf(f32001,plain,(
% 10.16/1.85 $false | (~spl106_5 | ~spl106_8)),
% 10.16/1.85 inference(forward_subsumption_resolution,[],[f32000,f1034])).
% 10.16/1.85 thf(f32002,plain,(
% 10.16/1.85 ~spl106_5 | ~spl106_8),
% 10.16/1.85 inference(avatar_contradiction_clause,[],[f32001])).
% 10.16/1.85 thf(f32091,plain,(
% 10.16/1.85 ($true != $true) | (n1 = zero_zero_nat) | spl106_8),
% 10.16/1.85 inference(constrained_superposition,[],[f16975,f4582])).
% 10.16/1.85 thf(f32167,plain,(
% 10.16/1.85 (n1 = zero_zero_nat) | spl106_8),
% 10.16/1.85 inference(trivial_inequality_removal,[],[f32091])).
% 10.16/1.85 thf(f32169,plain,(
% 10.16/1.85 $false | spl106_8),
% 10.16/1.85 inference(forward_subsumption_resolution,[],[f32167,f2859])).
% 10.16/1.85 thf(f32170,plain,(
% 10.16/1.85 spl106_8),
% 10.16/1.85 inference(avatar_contradiction_clause,[],[f32169])).
% 10.16/1.85 cnf(s3, plain, spl106_4 | spl106_5, inference(sat_conversion,[],[f11349])).
% 10.16/1.85 cnf(s65, plain, ~spl106_4, inference(sat_conversion,[],[f31565])).
% 10.16/1.85 cnf(s68, plain, ~spl106_5 | ~spl106_8, inference(sat_conversion,[],[f32002])).
% 10.16/1.85 cnf(s69, plain, spl106_8, inference(sat_conversion,[],[f32170])).
% 10.16/1.85 cnf(s70, plain, ~spl106_5, inference(rat,[],[s68,s69])).
% 10.16/1.85 cnf(s77, plain, $false, inference(rat,[],[s3,s70,s65])).
% 10.16/1.85 thf(f32171,plain,(
% 10.16/1.85 $false),
% 10.16/1.85 inference(avatar_sat_refutation,[],[s77])).
% 10.16/1.85 % SZS output end Proof for theBenchmark
% 10.16/1.85 % (2565363)------------------------------
% 10.16/1.85 % (2565363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.16/1.85 % (2565363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/1.85 % (2565363)CaDiCaL version: 2.1.3
% 10.16/1.85 % (2565363)Termination reason: Refutation
% 10.16/1.85 % (2565363)Time elapsed: 1.131 s
% 10.16/1.85 % (2565363)Peak memory usage: 28 MB
% 10.16/1.85 % (2565363)Instructions burned: 4392 (million)
% 10.16/1.85 % (2565319)Success in time 1.63 s
% 10.16/1.85 % Vampire exiting
%------------------------------------------------------------------------------