%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT122^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 07:48:55 AM UTC 2026
% Result : Theorem 17.83s 3.02s
% Output : Refutation 17.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT122^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n019.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 17:58:33 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.28 Running first-order model finding
% 0.24/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.53/1.54 % (1154738)Will run a generic schedule for satisfiability detection.
% 8.53/1.54 % (1154744)% WARNING: option uhcvi not known.
% 8.53/1.54 % (1154749)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1327505104:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 8.53/1.54 % (1154744)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2596339995:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 8.53/1.54 % (1154746)dis+10_1_sil=32000:sp=arity:random_seed=1138865413:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 8.53/1.54 % (1154743)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3195288135_2999 on theBenchmark for (2999ds/0Mi)
% 8.53/1.54 % (1154747)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=732082764:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 8.53/1.54 % (1154748)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2163368680:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 8.53/1.54 % (1154745)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1282544521:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 8.53/1.54 % (1154744)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.53/1.54 % (1154747)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.53/1.54 % (1154749)Instruction limit reached!
% 8.53/1.54 % (1154749)------------------------------
% 8.53/1.54 % (1154749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.53/1.54 % (1154749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/1.54 % (1154749)CaDiCaL version: 2.1.3
% 8.53/1.54 % (1154749)Termination reason: Instruction limit
% 8.53/1.54 % (1154749)Termination phase: Saturation
% 8.53/1.54 % (1154749)Time elapsed: 0.069 s
% 8.53/1.54 % (1154749)Peak memory usage: 14 MB
% 8.53/1.54 % (1154749)Instructions burned: 160 (million)
% 8.53/1.54 % (1154744)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.53/1.54 % Exception at run slice level
% 8.53/1.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.53/1.54 % (1154757)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1167729691:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 8.53/1.54 % (1154746)Instruction limit reached!
% 8.53/1.54 % (1154746)------------------------------
% 8.53/1.54 % (1154746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.53/1.54 % (1154746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/1.54 % (1154746)CaDiCaL version: 2.1.3
% 8.53/1.54 % (1154746)Termination reason: Instruction limit
% 8.53/1.54 % (1154746)Termination phase: Saturation
% 8.53/1.54 % (1154746)Time elapsed: 0.082 s
% 8.53/1.54 % (1154746)Peak memory usage: 12 MB
% 8.53/1.54 % (1154746)Instructions burned: 103 (million)
% 8.53/1.54 % (1154747)Instruction limit reached!
% 8.53/1.54 % (1154747)------------------------------
% 8.53/1.54 % (1154747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.53/1.54 % (1154747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/1.54 % (1154747)CaDiCaL version: 2.1.3
% 8.53/1.54 % (1154747)Termination reason: Instruction limit
% 8.53/1.54 % (1154747)Termination phase: Saturation
% 8.53/1.54 % (1154747)Time elapsed: 0.096 s
% 8.53/1.54 % (1154747)Peak memory usage: 13 MB
% 8.53/1.54 % (1154747)Instructions burned: 116 (million)
% 8.53/1.54 % (1154760)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=2498302830:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 8.53/1.54 % (1154758)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=120716499:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 8.53/1.54 % (1154748)Instruction limit reached!
% 8.53/1.54 % (1154748)------------------------------
% 8.53/1.54 % (1154748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.53/1.54 % (1154748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/1.54 % (1154748)CaDiCaL version: 2.1.3
% 8.53/1.54 % (1154748)Termination reason: Instruction limit
% 8.53/1.54 % (1154748)Termination phase: Saturation
% 8.53/1.54 % (1154748)Time elapsed: 0.106 s
% 8.53/1.54 % (1154748)Peak memory usage: 13 MB
% 8.53/1.54 % (1154748)Instructions burned: 132 (million)
% 17.83/3.02 % (1154760)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.83/3.02 % (1154761)ott-21_1_sil=16000:fs=off:random_seed=1675473055:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 17.83/3.02 % (1154760)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154764)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1328893849:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 17.83/3.02 % (1154766)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2079156579:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 17.83/3.02 % (1154758)Instruction limit reached!
% 17.83/3.02 % (1154758)------------------------------
% 17.83/3.02 % (1154758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154758)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154758)Termination reason: Instruction limit
% 17.83/3.02 % (1154758)Termination phase: Saturation
% 17.83/3.02 % (1154758)Time elapsed: 0.108 s
% 17.83/3.02 % (1154758)Peak memory usage: 13 MB
% 17.83/3.02 % (1154758)Instructions burned: 131 (million)
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154769)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1569157315:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 17.83/3.02 % (1154770)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2905938535:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 17.83/3.02 % (1154761)Instruction limit reached!
% 17.83/3.02 % (1154761)------------------------------
% 17.83/3.02 % (1154761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154761)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154761)Termination reason: Instruction limit
% 17.83/3.02 % (1154761)Termination phase: Saturation
% 17.83/3.02 % (1154761)Time elapsed: 0.144 s
% 17.83/3.02 % (1154761)Peak memory usage: 13 MB
% 17.83/3.02 % (1154761)Instructions burned: 180 (million)
% 17.83/3.02 % (1154773)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=3930811094:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 17.83/3.02 % (1154773)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154775)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3931986922:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 17.83/3.02 % (1154760)Instruction limit reached!
% 17.83/3.02 % (1154760)------------------------------
% 17.83/3.02 % (1154760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154760)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154760)Termination reason: Instruction limit
% 17.83/3.02 % (1154760)Termination phase: Saturation
% 17.83/3.02 % (1154760)Time elapsed: 0.299 s
% 17.83/3.02 % (1154760)Peak memory usage: 16 MB
% 17.83/3.02 % (1154760)Instructions burned: 684 (million)
% 17.83/3.02 % (1154775)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.83/3.02 % (1154777)fmb+10_1_sil=64000:random_seed=4261399218:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 17.83/3.02 % (1154777)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154779)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1662797984:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 17.83/3.02 % (1154764)Instruction limit reached!
% 17.83/3.02 % (1154764)------------------------------
% 17.83/3.02 % (1154764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154764)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154764)Termination reason: Instruction limit
% 17.83/3.02 % (1154764)Termination phase: Saturation
% 17.83/3.02 % (1154764)Time elapsed: 0.389 s
% 17.83/3.02 % (1154764)Peak memory usage: 14 MB
% 17.83/3.02 % (1154764)Instructions burned: 477 (million)
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154781)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2451095396:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 17.83/3.02 % (1154782)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1980053901:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154782)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.83/3.02 % (1154785)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1602781635:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 17.83/3.02 % (1154785)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 17.83/3.02 % (1154785)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.83/3.02 % (1154773)Instruction limit reached!
% 17.83/3.02 % (1154773)------------------------------
% 17.83/3.02 % (1154773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154773)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154773)Termination reason: Instruction limit
% 17.83/3.02 % (1154773)Termination phase: Saturation
% 17.83/3.02 % (1154773)Time elapsed: 0.590 s
% 17.83/3.02 % (1154773)Peak memory usage: 17 MB
% 17.83/3.02 % (1154773)Instructions burned: 692 (million)
% 17.83/3.02 % (1154787)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=563622983:i=6324_2990 on theBenchmark for (2990ds/6324Mi)
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154789)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3486071473:fmbsr=2.30978:i=2174_2989 on theBenchmark for (2989ds/2174Mi)
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154775)Instruction limit reached!
% 17.83/3.02 % (1154775)------------------------------
% 17.83/3.02 % (1154775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154775)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154775)Termination reason: Instruction limit
% 17.83/3.02 % (1154775)Termination phase: Saturation
% 17.83/3.02 % (1154775)Time elapsed: 0.736 s
% 17.83/3.02 % (1154775)Peak memory usage: 18 MB
% 17.83/3.02 % (1154775)Instructions burned: 879 (million)
% 17.83/3.02 % (1154785)Instruction limit reached!
% 17.83/3.02 % (1154785)------------------------------
% 17.83/3.02 % (1154785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154785)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154785)Termination reason: Instruction limit
% 17.83/3.02 % (1154785)Termination phase: Saturation
% 17.83/3.02 % (1154785)Time elapsed: 0.526 s
% 17.83/3.02 % (1154785)Peak memory usage: 19 MB
% 17.83/3.02 % (1154785)Instructions burned: 1473 (million)
% 17.83/3.02 % (1154792)ott+10_1_sil=32000:tgt=ground:random_seed=516571173:i=5114:av=off_2988 on theBenchmark for (2988ds/5114Mi)
% 17.83/3.02 % (1154791)ott-2_1_sil=16000:newcnf=on:random_seed=1318917213:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2988 on theBenchmark for (2988ds/869Mi)
% 17.83/3.02 % (1154793)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=176464863:i=54282_2988 on theBenchmark for (2988ds/54282Mi)
% 17.83/3.02 % (1154791)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.83/3.02 % Exception at run slice level
% 17.83/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.83/3.02 % (1154797)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3815515036:i=3512:aac=none_2987 on theBenchmark for (2987ds/3512Mi)
% 17.83/3.02 % (1154769)Instruction limit reached!
% 17.83/3.02 % (1154769)------------------------------
% 17.83/3.02 % (1154769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154769)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154769)Termination reason: Instruction limit
% 17.83/3.02 % (1154769)Termination phase: Saturation
% 17.83/3.02 % (1154769)Time elapsed: 0.969 s
% 17.83/3.02 % (1154769)Peak memory usage: 17 MB
% 17.83/3.02 % (1154769)Instructions burned: 1179 (million)
% 17.83/3.02 % (1154799)dis+21_1_sil=32000:sas=cadical:random_seed=4150267000:i=3773:amm=off_2987 on theBenchmark for (2987ds/3773Mi)
% 17.83/3.02 % (1154797)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.83/3.02 % (1154791)Instruction limit reached!
% 17.83/3.02 % (1154791)------------------------------
% 17.83/3.02 % (1154791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154791)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154791)Termination reason: Instruction limit
% 17.83/3.02 % (1154791)Termination phase: Saturation
% 17.83/3.02 % (1154791)Time elapsed: 0.714 s
% 17.83/3.02 % (1154791)Peak memory usage: 17 MB
% 17.83/3.02 % (1154791)Instructions burned: 870 (million)
% 17.83/3.02 % (1154801)ott+11_1_sil=16000:gs=on:random_seed=4094499847:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2980 on theBenchmark for (2980ds/2251Mi)
% 17.83/3.02 % (1154801)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.83/3.02 % (1154799) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1154738-1154799"...
% 17.83/3.02 % (1154799)...printing done.
% 17.83/3.02 % (1154799)Refutation found. Thanks to Tanya!
% 17.83/3.02 % SZS status Theorem for theBenchmark
% 17.83/3.02 % SZS output start Proof for theBenchmark
% 17.83/3.02 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 17.83/3.02 thf(type_def_6, type, tuple_isomorphism: ($tType * $tType * $tType) > $tType).
% 17.83/3.02 thf(type_def_7, type, code_natural: $tType).
% 17.83/3.02 thf(type_def_8, type, code_term: $tType).
% 17.83/3.02 thf(type_def_9, type, product_unit: $tType).
% 17.83/3.02 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 17.83/3.02 thf(type_def_11, type, extended_enat: $tType).
% 17.83/3.02 thf(type_def_12, type, typerep: $tType).
% 17.83/3.02 thf(type_def_13, type, literal: $tType).
% 17.83/3.02 thf(type_def_14, type, sum_sum: ($tType * $tType) > $tType).
% 17.83/3.02 thf(type_def_15, type, option: $tType > $tType).
% 17.83/3.02 thf(type_def_16, type, set: $tType > $tType).
% 17.83/3.02 thf(type_def_17, type, nat: $tType).
% 17.83/3.02 thf(type_def_18, type, itself: $tType > $tType).
% 17.83/3.02 thf(type_def_19, type, a: $tType).
% 17.83/3.02 thf(type_def_20, type, sTfun: ($tType * $tType) > $tType).
% 17.83/3.02 thf(func_def_0, type, enum: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_1, type, typerep2: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_2, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_3, type, cl_HOL_Oequal: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_4, type, code_term_of: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_5, type, size: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_6, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_7, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_8, type, quickcheck_random: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_9, type, semiring_numeral_div: !>[X0: $tType]:((itself @ X0 > $o))).
% 17.83/3.02 thf(func_def_10, type, code_Suc: (code_natural > code_natural)).
% 17.83/3.02 thf(func_def_11, type, code_case_natural: !>[X0: $tType]:((X0 > (code_natural > X0) > code_natural > X0))).
% 17.83/3.02 thf(func_def_12, type, code_rec_natural: !>[X0: $tType]:((X0 > (code_natural > X0 > X0) > code_natural > X0))).
% 17.83/3.02 thf(func_def_13, type, code_size_natural: (code_natural > nat)).
% 17.83/3.02 thf(func_def_14, type, coindu1529956631erates: !>[X0: $tType]:(((X0 > X0) > X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_15, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_16, type, coindu300403952lexord: !>[X0: $tType]:(((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 17.83/3.02 thf(func_def_17, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_18, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 17.83/3.02 thf(func_def_19, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0))).
% 17.83/3.02 thf(func_def_20, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 17.83/3.02 thf(func_def_21, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o))).
% 17.83/3.02 thf(func_def_22, type, coindu1062782156e_lmap: !>[X0: $tType, X1: $tType]:(((X0 > X1) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1))).
% 17.83/3.02 thf(func_def_23, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 17.83/3.02 thf(func_def_24, type, coindu1047225960le_ltl: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_25, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 17.83/3.02 thf(func_def_26, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 17.83/3.02 thf(func_def_27, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 17.83/3.02 thf(func_def_28, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 17.83/3.02 thf(func_def_29, type, coindu1802687541_ltake: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_30, type, coindu721411036eWhile: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_31, type, coindu847746867e_lzip: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > coindu1593790203_llist @ product_prod @ X0 @ X1))).
% 17.83/3.02 thf(func_def_32, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 17.83/3.02 thf(func_def_33, type, coindu440805660e_enat: !>[X0: $tType]:((X0 > (extended_enat > X0) > extended_enat > X0))).
% 17.83/3.02 thf(func_def_34, type, coinductive_epred: (extended_enat > extended_enat)).
% 17.83/3.02 thf(func_def_35, type, coindu1491768222unfold: !>[X0: $tType]:(((X0 > $o) > (X0 > X0) > X0 > extended_enat))).
% 17.83/3.02 thf(func_def_36, type, semiri577515795es_aux: !>[X0: $tType]:((product_prod @ X0 @ X0 > $o))).
% 17.83/3.02 thf(func_def_37, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 17.83/3.02 thf(func_def_38, type, extended_the_enat: (extended_enat > nat)).
% 17.83/3.02 thf(func_def_39, type, zero_zero: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_40, type, size_bool: ($o > nat)).
% 17.83/3.02 thf(func_def_41, type, default_default: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_42, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 17.83/3.02 thf(func_def_43, type, rec_nat: !>[X0: $tType]:((X0 > (nat > X0 > X0) > nat > X0))).
% 17.83/3.02 thf(func_def_44, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 17.83/3.02 thf(func_def_45, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 17.83/3.02 thf(func_def_46, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 17.83/3.02 thf(func_def_47, type, product_Unity: product_unit).
% 17.83/3.02 thf(func_def_48, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 17.83/3.02 thf(func_def_49, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 17.83/3.02 thf(func_def_50, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 17.83/3.02 thf(func_def_51, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 17.83/3.02 thf(func_def_52, type, product_case_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 17.83/3.02 thf(func_def_53, type, product_size_unit: (product_unit > nat)).
% 17.83/3.02 thf(func_def_54, type, type2: !>[X0: $tType]:(itself @ X0)).
% 17.83/3.02 thf(func_def_55, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 17.83/3.02 thf(func_def_56, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 17.83/3.02 thf(func_def_57, type, xs: coindu1593790203_llist @ a).
% 17.83/3.02 thf(func_def_61, type, vNOT: ($o > $o)).
% 17.83/3.02 thf(func_def_62, type, vAND: ($o > $o > $o)).
% 17.83/3.02 thf(func_def_63, type, vOR: ($o > $o > $o)).
% 17.83/3.02 thf(func_def_64, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 17.83/3.02 thf(func_def_65, type, db0: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_66, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 17.83/3.02 thf(func_def_67, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 17.83/3.02 thf(func_def_68, type, db1: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_69, type, vIMP: ($o > $o > $o)).
% 17.83/3.02 thf(func_def_70, type, db2: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_71, type, db3: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_72, type, db4: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_73, type, db5: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_74, type, db6: !>[X0: $tType]:(X0)).
% 17.83/3.02 thf(func_def_75, type, sP0: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > $o))).
% 17.83/3.02 thf(func_def_76, type, sP1: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 17.83/3.02 thf(func_def_77, type, sP2: ((extended_enat > extended_enat > $o) > $o)).
% 17.83/3.02 thf(func_def_78, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_79, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 17.83/3.02 thf(func_def_80, type, sK5: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 17.83/3.02 thf(func_def_81, type, sK6: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_82, type, sK7: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_83, type, sK8: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_84, type, sK9: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_85, type, sK10: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_86, type, sK11: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 17.83/3.02 thf(func_def_87, type, sK12: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 17.83/3.02 thf(func_def_88, type, sK13: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 17.83/3.02 thf(func_def_89, type, sK14: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_90, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 17.83/3.02 thf(func_def_91, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 17.83/3.02 thf(func_def_92, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 17.83/3.02 thf(func_def_93, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 17.83/3.02 thf(func_def_94, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 17.83/3.02 thf(func_def_95, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 17.83/3.02 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 17.83/3.02 thf(func_def_97, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 17.83/3.02 thf(func_def_98, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 17.83/3.02 thf(func_def_99, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 17.83/3.02 thf(func_def_100, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 17.83/3.02 thf(func_def_101, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 17.83/3.02 thf(func_def_102, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 17.83/3.02 thf(func_def_103, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 17.83/3.02 thf(func_def_104, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 17.83/3.02 thf(func_def_105, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 17.83/3.02 thf(func_def_106, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 17.83/3.02 thf(func_def_107, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 17.83/3.02 thf(func_def_108, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 17.83/3.02 thf(func_def_109, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 17.83/3.02 thf(func_def_110, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 17.83/3.02 thf(func_def_111, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 17.83/3.02 thf(func_def_112, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 17.83/3.02 thf(func_def_113, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 17.83/3.02 thf(func_def_114, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 17.83/3.02 thf(func_def_115, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 17.83/3.02 thf(func_def_116, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 17.83/3.02 thf(func_def_117, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_118, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 17.83/3.02 thf(func_def_119, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 17.83/3.02 thf(func_def_120, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 17.83/3.02 thf(func_def_121, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_122, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 17.83/3.02 thf(func_def_123, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 17.83/3.02 thf(func_def_124, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 17.83/3.02 thf(func_def_125, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 17.83/3.02 thf(func_def_126, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_127, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 17.83/3.02 thf(func_def_128, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 17.83/3.02 thf(func_def_129, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 17.83/3.02 thf(func_def_130, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 17.83/3.02 thf(func_def_131, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 17.83/3.02 thf(func_def_132, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_133, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 17.83/3.02 thf(func_def_134, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 17.83/3.02 thf(func_def_135, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 17.83/3.02 thf(func_def_136, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 17.83/3.02 thf(func_def_137, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 17.83/3.02 thf(func_def_138, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 17.83/3.02 thf(func_def_139, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_140, type, sK65: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 17.83/3.02 thf(func_def_141, type, sK66: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 17.83/3.02 thf(func_def_142, type, sK67: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 17.83/3.02 thf(func_def_143, type, sK68: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_144, type, sK69: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_145, type, sK70: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_146, type, sK71: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_147, type, sK72: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_148, type, sK73: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_149, type, sK74: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_150, type, sK75: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_151, type, sK76: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_152, type, sK77: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_153, type, sK78: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_154, type, sK79: ((code_natural > $o) > code_natural)).
% 17.83/3.02 thf(func_def_155, type, sK80: (code_natural > code_natural)).
% 17.83/3.02 thf(func_def_156, type, sK81: (product_prod @ code_natural @ code_natural > code_natural)).
% 17.83/3.02 thf(func_def_157, type, sK82: (product_prod @ code_natural @ code_natural > code_natural)).
% 17.83/3.02 thf(func_def_158, type, sK83: (product_prod @ code_natural @ code_natural > code_natural)).
% 17.83/3.02 thf(func_def_159, type, sK84: !>[X0: $tType]:(((code_natural > X0) > (code_natural > X0) > code_natural))).
% 17.83/3.02 thf(func_def_160, type, sK85: ((code_natural > code_natural > $o) > code_natural)).
% 17.83/3.02 thf(func_def_161, type, sK86: ((code_natural > code_natural > $o) > code_natural)).
% 17.83/3.02 thf(func_def_162, type, sK87: ((code_natural > code_natural > $o) > code_natural)).
% 17.83/3.02 thf(func_def_163, type, sK88: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_164, type, sK89: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_165, type, sK90: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_166, type, sK91: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_167, type, sK92: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0))).
% 17.83/3.02 thf(func_def_168, type, sK93: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_169, type, sK94: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_170, type, sK95: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_171, type, sK96: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_172, type, sK97: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_173, type, sK98: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X0))).
% 17.83/3.02 thf(func_def_174, type, sK99: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_175, type, sK100: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X1))).
% 17.83/3.02 thf(func_def_176, type, sK101: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X1))).
% 17.83/3.02 thf(func_def_177, type, sK102: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 17.83/3.02 thf(func_def_178, type, sK103: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o) > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_179, type, sK104: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o) > coindu1593790203_llist @ X1))).
% 17.83/3.02 thf(func_def_180, type, sK105: ((extended_enat > extended_enat > $o) > extended_enat)).
% 17.83/3.02 thf(func_def_181, type, sK106: ((extended_enat > extended_enat > $o) > extended_enat)).
% 17.83/3.02 thf(func_def_182, type, sK107: ((extended_enat > extended_enat > $o) > extended_enat)).
% 17.83/3.02 thf(func_def_183, type, sK108: ((extended_enat > extended_enat > $o) > extended_enat)).
% 17.83/3.02 thf(func_def_184, type, sK109: ((extended_enat > extended_enat > $o) > extended_enat)).
% 17.83/3.02 thf(func_def_185, type, sK110: ((extended_enat > extended_enat > $o) > extended_enat)).
% 17.83/3.02 thf(func_def_186, type, sK111: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_187, type, sK112: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_188, type, sK113: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_189, type, sK114: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 17.83/3.02 thf(func_def_190, type, sK115: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 17.83/3.02 thf(func_def_191, type, sK116: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 17.83/3.02 thf(func_def_192, type, sK117: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > X0 > (X1 > X0) > coindu1593790203_llist @ X1))).
% 17.83/3.02 thf(func_def_193, type, sK118: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X1 > (X1 > X0) > X1))).
% 17.83/3.02 thf(f24,axiom,(
% 17.83/3.02 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0] : (((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ zero_zero @ nat)) = X1)),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_lnth__0)).
% 17.83/3.02 thf(f39,axiom,(
% 17.83/3.02 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((X1 != coindu1598213697e_LNil @ X0) => (X1 = ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)))))),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_llist_Oexhaust__sel)).
% 17.83/3.02 thf(f75,axiom,(
% 17.83/3.02 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0] : (((coindu1046438764le_lhd @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2))) = X1)),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_lhd__LCons)).
% 17.83/3.02 thf(f79,axiom,(
% 17.83/3.02 ! [X0 : $tType] : (coindu335574135_lnull @ X0 = (^[X1 : coindu1593790203_llist @ X0] : ((X1 = coindu1598213697e_LNil @ X0))))),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_lnull__def)).
% 17.83/3.02 thf(f132,axiom,(
% 17.83/3.02 ! [X0 : $tType,X1 : X0,X2 : (code_natural > X0),X3 : code_natural] : (((code_case_natural @ X0 @ X1 @ X2 @ (code_Suc @ X3))) = ((X2 @ X3)))),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_natural_Osimps_I5_J)).
% 17.83/3.02 thf(f135,axiom,(
% 17.83/3.02 ! [X0 : code_natural,X1 : code_natural] : ((((code_Suc @ X0)) = ((code_Suc @ X1))) = (X0 = X1))),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_natural_Oinject)).
% 17.83/3.02 thf(f201,axiom,(
% 17.83/3.02 ! [X0 : $tType,X1 : X0] : (((product_case_unit @ X0 @ X1 @ product_Unity)) = X1)),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_old_Ounit_Ocase)).
% 17.83/3.02 thf(f328,axiom,(
% 17.83/3.02 ~(coindu335574135_lnull @ a @ xs)),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 17.83/3.02 thf(f329,conjecture,(
% 17.83/3.02 (((coindu1046438764le_lhd @ a @ xs)) = ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 17.83/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 17.83/3.02 thf(f330,negated_conjecture,(
% 17.83/3.02 ~ (((coindu1046438764le_lhd @ a @ xs)) = ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 17.83/3.02 inference(negated_conjecture,[status(cth)],[f329])).
% 17.83/3.02 thf(f426,plain,(
% 17.83/3.02 ! [X0 : $tType] : (coindu335574135_lnull @ X0 = (^[Y0 : coindu1593790203_llist @ X0]: (coindu1598213697e_LNil @ X0 = Y0)))),
% 17.83/3.02 inference(fool_elimination,[],[f79])).
% 17.83/3.02 thf(f496,plain,(
% 17.83/3.02 ! [X0 : code_natural,X1 : code_natural] : ((((code_Suc @ X0) = (code_Suc @ X1))) = ((X0 = X1)))),
% 17.83/3.02 inference(fool_elimination,[],[f135])).
% 17.83/3.02 thf(f807,plain,(
% 17.83/3.02 ~(coindu335574135_lnull @ a @ xs)),
% 17.83/3.02 inference(rectify,[],[f328])).
% 17.83/3.02 thf(f808,plain,(
% 17.83/3.02 ~ (((coindu335574135_lnull @ a @ xs)) = $true)),
% 17.83/3.02 inference(fool_elimination,[],[f807])).
% 17.83/3.02 thf(f858,plain,(
% 17.83/3.02 (((coindu335574135_lnull @ a @ xs)) != $true)),
% 17.83/3.02 inference(flattening,[],[f808])).
% 17.83/3.02 thf(f859,plain,(
% 17.83/3.02 (((coindu1046438764le_lhd @ a @ xs)) != ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 17.83/3.02 inference(flattening,[],[f330])).
% 17.83/3.02 thf(f888,plain,(
% 17.83/3.02 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((X1 = ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)))) | (coindu1598213697e_LNil @ X0 = X1))),
% 17.83/3.02 inference(ennf_transformation,[],[f39])).
% 17.83/3.02 thf(f1143,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : X0] : ((((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ zero_zero @ nat)) = X1)) )),
% 17.83/3.02 inference(cnf_transformation,[],[f24])).
% 17.83/3.02 thf(f1162,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1))) = X1) | (coindu1598213697e_LNil @ X0 = X1)) )),
% 17.83/3.02 inference(cnf_transformation,[],[f888])).
% 17.83/3.02 thf(f1199,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : X0] : ((((coindu1046438764le_lhd @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2))) = X1)) )),
% 17.83/3.02 inference(cnf_transformation,[],[f75])).
% 17.83/3.02 thf(f1203,plain,(
% 17.83/3.02 ( ! [X0 : $tType] : ((coindu335574135_lnull @ X0 = (^[Y0 : coindu1593790203_llist @ X0]: (coindu1598213697e_LNil @ X0 = Y0)))) )),
% 17.83/3.02 inference(cnf_transformation,[],[f426])).
% 17.83/3.02 thf(f1280,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X2 : (code_natural > X0),X3 : code_natural,X1 : X0] : ((((code_case_natural @ X0 @ X1 @ X2 @ (code_Suc @ X3))) = ((X2 @ X3)))) )),
% 17.83/3.02 inference(cnf_transformation,[],[f132])).
% 17.83/3.02 thf(f1283,plain,(
% 17.83/3.02 ( ! [X0 : code_natural,X1 : code_natural] : (((((code_Suc @ X0) = (code_Suc @ X1))) = ((X0 = X1)))) )),
% 17.83/3.02 inference(cnf_transformation,[],[f496])).
% 17.83/3.02 thf(f1372,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X1 : X0] : ((((product_case_unit @ X0 @ X1 @ product_Unity)) = X1)) )),
% 17.83/3.02 inference(cnf_transformation,[],[f201])).
% 17.83/3.02 thf(f1524,plain,(
% 17.83/3.02 (((coindu335574135_lnull @ a @ xs)) != $true)),
% 17.83/3.02 inference(cnf_transformation,[],[f858])).
% 17.83/3.02 thf(f1525,plain,(
% 17.83/3.02 (((coindu1046438764le_lhd @ a @ xs)) != ((coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 17.83/3.02 inference(cnf_transformation,[],[f859])).
% 17.83/3.02 thf(f1639,plain,(
% 17.83/3.02 ($true != (((^[Y0 : coindu1593790203_llist @ a]: (coindu1598213697e_LNil @ a = Y0)) @ xs)))),
% 17.83/3.02 inference(definition_unfolding,[],[f1524,f1203])).
% 17.83/3.02 thf(f1654,plain,(
% 17.83/3.02 ($true != ((coindu1598213697e_LNil @ a = xs)))),
% 17.83/3.02 inference(beta-eta_normalization,[],[f1639])).
% 17.83/3.02 thf(f1655,plain,(
% 17.83/3.02 (xs != coindu1598213697e_LNil @ a)),
% 17.83/3.02 inference(equality_proxy_clausification,[],[f1654])).
% 17.83/3.02 thf(f1922,plain,(
% 17.83/3.02 ( ! [X0 : code_natural,X1 : code_natural] : (($true = (((code_Suc @ X0) = (code_Suc @ X1)))) | (((X0 = X1)) = $false)) )),
% 17.83/3.02 inference(iff_proxy_clausification,[],[f1283])).
% 17.83/3.02 thf(f1926,plain,(
% 17.83/3.02 ( ! [X0 : code_natural,X1 : code_natural] : ((((code_Suc @ X0)) = ((code_Suc @ X1))) | (((X0 = X1)) = $false)) )),
% 17.83/3.02 inference(equality_proxy_clausification,[],[f1922])).
% 17.83/3.02 thf(f1927,plain,(
% 17.83/3.02 ( ! [X0 : code_natural,X1 : code_natural] : ((((code_Suc @ X0)) = ((code_Suc @ X1))) | (X0 != X1)) )),
% 17.83/3.02 inference(equality_proxy_clausification,[],[f1926])).
% 17.83/3.02 thf(f10623,plain,(
% 17.83/3.02 ( ! [X1 : $tType,X2 : X1,X3 : (code_natural > X1),X0 : code_natural,X4 : code_natural] : ((((X3 @ X4)) = ((code_case_natural @ X1 @ X2 @ X3 @ (code_Suc @ X0)))) | (X0 != X4)) )),
% 17.83/3.02 inference(constrained_superposition,[],[f1280,f1927])).
% 17.83/3.02 thf(f10785,plain,(
% 17.83/3.02 ( ! [X1 : $tType,X3 : (code_natural > X1),X0 : code_natural,X4 : code_natural] : ((((X3 @ X4)) = ((X3 @ X0))) | (X0 != X4)) )),
% 17.83/3.02 inference(forward_demodulation,[],[f10623,f1280])).
% 17.83/3.02 thf(f11408,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X2 : code_natural,X3 : X0,X1 : (code_natural > X0),X4 : code_natural] : (((((^[Y0 : code_natural]: (product_case_unit @ X0 @ (X1 @ Y0) @ ((^[Y1 : code_natural]: (product_Unity)) @ Y0))) @ X2)) = X3) | (X2 != X4) | (((X1 @ X4)) != X3)) )),
% 17.83/3.02 inference(constrained_superposition,[],[f1372,f10785])).
% 17.83/3.02 thf(f11711,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X2 : code_natural,X3 : X0,X1 : (code_natural > X0),X4 : code_natural] : ((((product_case_unit @ X0 @ (X1 @ X2) @ product_Unity)) = X3) | (X2 != X4) | (((X1 @ X4)) != X3)) )),
% 17.83/3.02 inference(beta-eta_normalization,[],[f11408])).
% 17.83/3.02 thf(f12271,plain,(
% 17.83/3.02 ( ! [X0 : $tType,X2 : code_natural,X3 : X0,X1 : (code_natural > X0),X4 : code_natural] : ((((X1 @ X2)) = X3) | (X2 != X4) | (((X1 @ X4)) != X3)) )),
% 17.83/3.02 inference(forward_demodulation,[],[f11711,f1372])).
% 17.83/3.02 thf(f19442,plain,(
% 17.83/3.02 ( ! [X2 : code_natural,X0 : coindu1593790203_llist @ a,X1 : code_natural] : ((((coindu1046438764le_lhd @ a @ X0)) != ((coindu749330388e_lnth @ a @ X0 @ zero_zero @ nat))) | (X1 != X2) | ((((^[Y0 : code_natural]: (xs)) @ X2)) != X0)) )),
% 17.83/3.02 inference(constrained_superposition,[],[f1525,f12271])).
% 17.83/3.02 thf(f20947,plain,(
% 17.83/3.02 ( ! [X2 : code_natural,X0 : coindu1593790203_llist @ a,X1 : code_natural] : ((((coindu1046438764le_lhd @ a @ X0)) != ((coindu749330388e_lnth @ a @ X0 @ zero_zero @ nat))) | (X1 != X2) | (xs != X0)) )),
% 17.83/3.02 inference(beta-eta_normalization,[],[f19442])).
% 17.83/3.02 thf(f22037,definition,(
% 17.83/3.02 spl119_182 <=> ! [X4 : code_natural,X5 : code_natural] : (X4 != X5)),
% 17.83/3.02 introduced(definition,[new_symbols(definition,[spl119_182])],[avatar_definition])).
% 17.83/3.02 thf(f22038,plain,(
% 17.83/3.02 ( ! [X4 : code_natural,X5 : code_natural] : ((X4 != X5)) ) | ~spl119_182),
% 17.83/3.02 inference(avatar_component_clause,[],[f22037])).
% 17.83/3.02 thf(f22140,definition,(
% 17.83/3.02 spl119_192 <=> ! [X0 : coindu1593790203_llist @ a] : ((((coindu1046438764le_lhd @ a @ X0)) != ((coindu749330388e_lnth @ a @ X0 @ zero_zero @ nat))) | (xs != X0))),
% 17.83/3.02 introduced(definition,[new_symbols(definition,[spl119_192])],[avatar_definition])).
% 17.83/3.02 thf(f22141,plain,(
% 17.83/3.02 ( ! [X0 : coindu1593790203_llist @ a] : ((((coindu1046438764le_lhd @ a @ X0)) != ((coindu749330388e_lnth @ a @ X0 @ zero_zero @ nat))) | (xs != X0)) ) | ~spl119_192),
% 17.83/3.02 inference(avatar_component_clause,[],[f22140])).
% 17.83/3.02 thf(f22142,plain,(
% 17.83/3.02 spl119_182 | spl119_192),
% 17.83/3.02 inference(avatar_split_clause,[],[f20947,f22140,f22037])).
% 17.83/3.02 thf(f22703,plain,(
% 17.83/3.02 $false | ~spl119_182),
% 17.83/3.02 inference(flex-flex_simplification,[],[f22038])).
% 17.83/3.02 thf(f22704,plain,(
% 17.83/3.02 ~spl119_182),
% 17.83/3.02 inference(avatar_contradiction_clause,[],[f22703])).
% 17.83/3.02 thf(f22745,plain,(
% 17.83/3.02 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((((coindu1046438764le_lhd @ a @ (coindu1121789889_LCons @ a @ X0 @ X1))) != X0) | (xs != ((coindu1121789889_LCons @ a @ X0 @ X1)))) ) | ~spl119_192),
% 17.83/3.02 inference(constrained_superposition,[],[f22141,f1143])).
% 17.83/3.02 thf(f22758,plain,(
% 17.83/3.02 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((xs != ((coindu1121789889_LCons @ a @ X0 @ X1)))) ) | ~spl119_192),
% 17.83/3.02 inference(forward_subsumption_resolution,[],[f22745,f1199])).
% 17.83/3.02 thf(f22803,plain,(
% 17.83/3.02 ( ! [X0 : coindu1593790203_llist @ a] : ((coindu1598213697e_LNil @ a = X0) | (xs != X0)) ) | ~spl119_192),
% 17.83/3.02 inference(constrained_superposition,[],[f22758,f1162])).
% 17.83/3.02 thf(f22818,plain,(
% 17.83/3.02 ( ! [X0 : coindu1593790203_llist @ a] : ((xs != X0) | (xs != X0)) ) | ~spl119_192),
% 17.83/3.02 inference(constrained_superposition,[],[f1655,f22803])).
% 17.83/3.02 thf(f22905,plain,(
% 17.83/3.02 ( ! [X0 : coindu1593790203_llist @ a] : ((xs != X0)) ) | ~spl119_192),
% 17.83/3.02 inference(duplicate_literal_removal,[],[f22818])).
% 17.83/3.02 thf(f22986,plain,(
% 17.83/3.02 $false | ~spl119_192),
% 17.83/3.02 inference(equality_resolution,[],[f22905])).
% 17.83/3.02 thf(f22987,plain,(
% 17.83/3.02 ~spl119_192),
% 17.83/3.02 inference(avatar_contradiction_clause,[],[f22986])).
% 17.83/3.02 cnf(s947, plain, spl119_182 | spl119_192, inference(sat_conversion,[],[f22142])).
% 17.83/3.02 cnf(s1159, plain, ~spl119_182, inference(sat_conversion,[],[f22704])).
% 17.83/3.02 cnf(s1168, plain, ~spl119_192, inference(sat_conversion,[],[f22987])).
% 17.83/3.02 cnf(s1277, plain, $false, inference(rat,[],[s947,s1168,s1159])).
% 17.83/3.02 thf(f22989,plain,(
% 17.83/3.02 $false),
% 17.83/3.02 inference(avatar_sat_refutation,[],[s1277])).
% 17.83/3.02 % SZS output end Proof for theBenchmark
% 17.83/3.02 % (1154799)------------------------------
% 17.83/3.02 % (1154799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.83/3.02 % (1154799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.83/3.02 % (1154799)CaDiCaL version: 2.1.3
% 17.83/3.02 % (1154799)Termination reason: Refutation
% 17.83/3.02 % (1154799)Time elapsed: 1.401 s
% 17.83/3.02 % (1154799)Peak memory usage: 20 MB
% 17.83/3.02 % (1154799)Instructions burned: 1677 (million)
% 17.83/3.02 % (1154738)Success in time 2.724 s
% 17.83/3.02 % Vampire exiting
%------------------------------------------------------------------------------