%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT141^1 : 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 : n007.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 07:48:57 AM UTC 2026
% Result : Theorem 12.94s 2.80s
% Output : Refutation 12.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT141^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:59:27 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.22 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
% 4.30/1.00 % (3727864)Will run a generic schedule for satisfiability detection.
% 4.30/1.00 % (3727875)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1087214145:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.30/1.00 % (3727870)% WARNING: option uhcvi not known.
% 4.30/1.00 % (3727872)dis+10_1_sil=32000:sp=arity:random_seed=2990800639:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.30/1.00 % (3727869)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2138881327_2999 on theBenchmark for (2999ds/0Mi)
% 4.30/1.00 % (3727871)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=100121948:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.30/1.00 % (3727870)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2990827287:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.30/1.00 % (3727873)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3249647061:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.30/1.00 % (3727874)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1603088006:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.30/1.00 % (3727870)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.30/1.00 % (3727873)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.30/1.00 % (3727875)Instruction limit reached!
% 4.30/1.00 % (3727875)------------------------------
% 4.30/1.00 % (3727875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.30/1.00 % (3727875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.00 % (3727875)CaDiCaL version: 2.1.3
% 4.30/1.00 % (3727875)Termination reason: Instruction limit
% 4.30/1.00 % (3727875)Termination phase: Saturation
% 4.30/1.00 % (3727875)Time elapsed: 0.042 s
% 4.30/1.00 % (3727875)Peak memory usage: 14 MB
% 4.30/1.00 % (3727875)Instructions burned: 161 (million)
% 4.30/1.00 % (3727883)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3623256361:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.30/1.00 % Exception at run slice level
% 4.30/1.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.30/1.00 % (3727870)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.30/1.00 % (3727872)Instruction limit reached!
% 4.30/1.00 % (3727872)------------------------------
% 4.30/1.00 % (3727872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.30/1.00 % (3727872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.00 % (3727872)CaDiCaL version: 2.1.3
% 4.30/1.00 % (3727872)Termination reason: Instruction limit
% 4.30/1.00 % (3727872)Termination phase: Saturation
% 4.30/1.00 % (3727872)Time elapsed: 0.048 s
% 4.30/1.00 % (3727872)Peak memory usage: 12 MB
% 4.30/1.00 % (3727872)Instructions burned: 104 (million)
% 4.30/1.00 % (3727873)Instruction limit reached!
% 4.30/1.00 % (3727873)------------------------------
% 4.30/1.00 % (3727873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.30/1.00 % (3727873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.00 % (3727873)CaDiCaL version: 2.1.3
% 4.30/1.00 % (3727873)Termination reason: Instruction limit
% 4.30/1.00 % (3727873)Termination phase: Saturation
% 4.30/1.00 % (3727873)Time elapsed: 0.054 s
% 4.30/1.00 % (3727873)Peak memory usage: 13 MB
% 4.30/1.00 % (3727873)Instructions burned: 117 (million)
% 4.30/1.00 % (3727874)Instruction limit reached!
% 4.30/1.00 % (3727874)------------------------------
% 4.30/1.00 % (3727874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.30/1.00 % (3727874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.00 % (3727874)CaDiCaL version: 2.1.3
% 4.30/1.00 % (3727874)Termination reason: Instruction limit
% 4.30/1.00 % (3727874)Termination phase: Saturation
% 4.30/1.00 % (3727874)Time elapsed: 0.061 s
% 4.30/1.00 % (3727874)Peak memory usage: 13 MB
% 4.30/1.00 % (3727874)Instructions burned: 132 (million)
% 4.30/1.00 % (3727885)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=531421996:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.30/1.00 % (3727886)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=589054208:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 16.92/2.71 % Exception at run slice level
% 16.92/2.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.92/2.71 % (3727887)ott-21_1_sil=16000:fs=off:random_seed=3690956750:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 16.92/2.71 % (3727888)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2564578594:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 16.92/2.71 % (3727886)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.92/2.71 % (3727891)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2592616050:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 16.92/2.71 % (3727886)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.92/2.71 % (3727887)Instruction limit reached!
% 16.92/2.71 % (3727887)------------------------------
% 16.92/2.71 % (3727887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.92/2.71 % (3727887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.92/2.71 % (3727887)CaDiCaL version: 2.1.3
% 16.92/2.71 % (3727887)Termination reason: Instruction limit
% 16.92/2.71 % (3727887)Termination phase: Saturation
% 16.92/2.71 % (3727887)Time elapsed: 0.046 s
% 16.92/2.71 % (3727887)Peak memory usage: 14 MB
% 16.92/2.71 % (3727887)Instructions burned: 181 (million)
% 16.92/2.71 % (3727885)Instruction limit reached!
% 16.92/2.71 % (3727885)------------------------------
% 16.92/2.71 % (3727885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.92/2.71 % (3727885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.92/2.71 % (3727885)CaDiCaL version: 2.1.3
% 16.92/2.71 % (3727885)Termination reason: Instruction limit
% 16.92/2.71 % (3727885)Termination phase: Saturation
% 16.92/2.71 % (3727885)Time elapsed: 0.061 s
% 16.92/2.71 % (3727885)Peak memory usage: 13 MB
% 16.92/2.71 % (3727885)Instructions burned: 132 (million)
% 16.92/2.71 % (3727895)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3866438994:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 16.92/2.71 % Exception at run slice level
% 16.92/2.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.92/2.71 % (3727896)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3235914687:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 16.92/2.71 % (3727898)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=3141583782: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)
% 16.92/2.71 % (3727898)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.92/2.71 % Exception at run slice level
% 16.92/2.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.92/2.71 % (3727901)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2727908013:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 16.92/2.71 % (3727901)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.92/2.71 % (3727888)Instruction limit reached!
% 16.92/2.71 % (3727888)------------------------------
% 16.92/2.71 % (3727888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.92/2.71 % (3727888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.92/2.71 % (3727888)CaDiCaL version: 2.1.3
% 16.92/2.71 % (3727888)Termination reason: Instruction limit
% 16.92/2.71 % (3727888)Termination phase: Saturation
% 16.92/2.71 % (3727888)Time elapsed: 0.251 s
% 16.92/2.71 % (3727888)Peak memory usage: 15 MB
% 16.92/2.71 % (3727888)Instructions burned: 478 (million)
% 16.92/2.71 % (3727903)fmb+10_1_sil=64000:random_seed=2359966172:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 16.92/2.71 % (3727903)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 16.92/2.71 % Exception at run slice level
% 16.92/2.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.92/2.71 % (3727886)Instruction limit reached!
% 16.92/2.71 % (3727886)------------------------------
% 16.92/2.71 % (3727886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.92/2.71 % (3727886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727886)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727886)Termination reason: Instruction limit
% 12.94/2.80 % (3727886)Termination phase: Saturation
% 12.94/2.80 % (3727886)Time elapsed: 0.340 s
% 12.94/2.80 % (3727886)Peak memory usage: 16 MB
% 12.94/2.80 % (3727886)Instructions burned: 685 (million)
% 12.94/2.80 % (3727905)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=730460179:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 12.94/2.80 % (3727906)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3798731212:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 12.94/2.80 % (3727895)Instruction limit reached!
% 12.94/2.80 % (3727895)------------------------------
% 12.94/2.80 % (3727895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727895)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727895)Termination reason: Instruction limit
% 12.94/2.80 % (3727895)Termination phase: Saturation
% 12.94/2.80 % (3727895)Time elapsed: 0.316 s
% 12.94/2.80 % (3727895)Peak memory usage: 19 MB
% 12.94/2.80 % (3727895)Instructions burned: 1181 (million)
% 12.94/2.80 % (3727909)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2715092921:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 12.94/2.80 % (3727909)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 12.94/2.80 % Exception at run slice level
% 12.94/2.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 12.94/2.80 % Exception at run slice level
% 12.94/2.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 12.94/2.80 % (3727911)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2386015645:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 12.94/2.80 % (3727912)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1575975368:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 12.94/2.80 % (3727911)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 12.94/2.80 % (3727911)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 12.94/2.80 % (3727898)Instruction limit reached!
% 12.94/2.80 % (3727898)------------------------------
% 12.94/2.80 % (3727898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727898)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727898)Termination reason: Instruction limit
% 12.94/2.80 % (3727898)Termination phase: Saturation
% 12.94/2.80 % (3727898)Time elapsed: 0.364 s
% 12.94/2.80 % (3727898)Peak memory usage: 19 MB
% 12.94/2.80 % (3727898)Instructions burned: 692 (million)
% 12.94/2.80 % Exception at run slice level
% 12.94/2.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 12.94/2.80 % (3727915)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4059036717:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 12.94/2.80 % (3727916)ott-2_1_sil=16000:newcnf=on:random_seed=2115087099:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 12.94/2.80 % (3727916)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 12.94/2.80 % Exception at run slice level
% 12.94/2.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 12.94/2.80 % (3727919)ott+10_1_sil=32000:tgt=ground:random_seed=3937796418:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 12.94/2.80 % (3727901)Instruction limit reached!
% 12.94/2.80 % (3727901)------------------------------
% 12.94/2.80 % (3727901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727901)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727901)Termination reason: Instruction limit
% 12.94/2.80 % (3727901)Termination phase: Saturation
% 12.94/2.80 % (3727901)Time elapsed: 0.457 s
% 12.94/2.80 % (3727901)Peak memory usage: 19 MB
% 12.94/2.80 % (3727901)Instructions burned: 880 (million)
% 12.94/2.80 % (3727921)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1265702188:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 12.94/2.80 % Exception at run slice level
% 12.94/2.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 12.94/2.80 % (3727923)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3204171401:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 12.94/2.80 % (3727923)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 12.94/2.80 % (3727916)Instruction limit reached!
% 12.94/2.80 % (3727916)------------------------------
% 12.94/2.80 % (3727916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727916)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727916)Termination reason: Instruction limit
% 12.94/2.80 % (3727916)Termination phase: Saturation
% 12.94/2.80 % (3727916)Time elapsed: 0.438 s
% 12.94/2.80 % (3727916)Peak memory usage: 18 MB
% 12.94/2.80 % (3727916)Instructions burned: 869 (million)
% 12.94/2.80 % (3727925)dis+21_1_sil=32000:sas=cadical:random_seed=191246056:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 12.94/2.80 % (3727911)Instruction limit reached!
% 12.94/2.80 % (3727911)------------------------------
% 12.94/2.80 % (3727911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727911)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727911)Termination reason: Instruction limit
% 12.94/2.80 % (3727911)Termination phase: Saturation
% 12.94/2.80 % (3727911)Time elapsed: 0.776 s
% 12.94/2.80 % (3727911)Peak memory usage: 18 MB
% 12.94/2.80 % (3727911)Instructions burned: 1473 (million)
% 12.94/2.80 % (3727927)ott+11_1_sil=16000:gs=on:random_seed=171460700:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2986 on theBenchmark for (2986ds/2251Mi)
% 12.94/2.80 % (3727927)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 12.94/2.80 % (3727909)Instruction limit reached!
% 12.94/2.80 % (3727909)------------------------------
% 12.94/2.80 % (3727909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727909)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727909)Termination reason: Instruction limit
% 12.94/2.80 % (3727909)Termination phase: Saturation
% 12.94/2.80 % (3727909)Time elapsed: 1.308 s
% 12.94/2.80 % (3727909)Peak memory usage: 35 MB
% 12.94/2.80 % (3727909)Instructions burned: 5133 (million)
% 12.94/2.80 % (3727929)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=2956621458:fmbsr=1.6:i=67534_2981 on theBenchmark for (2981ds/67534Mi)
% 12.94/2.80 % Exception at run slice level
% 12.94/2.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 12.94/2.80 % (3727931)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1060150999:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2981 on theBenchmark for (2981ds/4591Mi)
% 12.94/2.80 % (3727923)Instruction limit reached!
% 12.94/2.80 % (3727923)------------------------------
% 12.94/2.80 % (3727923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727923)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727923)Termination reason: Instruction limit
% 12.94/2.80 % (3727923)Termination phase: Saturation
% 12.94/2.80 % (3727923)Time elapsed: 1.669 s
% 12.94/2.80 % (3727923)Peak memory usage: 28 MB
% 12.94/2.80 % (3727923)Instructions burned: 3513 (million)
% 12.94/2.80 % (3727927)Instruction limit reached!
% 12.94/2.80 % (3727927)------------------------------
% 12.94/2.80 % (3727927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.80 % (3727927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.80 % (3727927)CaDiCaL version: 2.1.3
% 12.94/2.80 % (3727927)Termination reason: Instruction limit
% 12.94/2.80 % (3727927)Termination phase: Saturation
% 12.94/2.80 % (3727927)Time elapsed: 1.147 s
% 12.94/2.80 % (3727927)Peak memory usage: 23 MB
% 12.94/2.80 % (3727927)Instructions burned: 2253 (million)
% 12.94/2.80 % (3727934)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=604364996:i=5211_2975 on theBenchmark for (2975ds/5211Mi)
% 12.94/2.80 % (3727933)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=2962870659:i=29340_2975 on theBenchmark for (2975ds/29340Mi)
% 12.94/2.80 % (3727925) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3727864-3727925"...
% 12.94/2.80 % (3727925)...printing done.
% 12.94/2.80 % (3727925)Refutation found. Thanks to Tanya!
% 12.94/2.80 % SZS status Theorem for theBenchmark
% 12.94/2.80 % SZS output start Proof for theBenchmark
% 12.94/2.80 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 12.94/2.80 thf(type_def_6, type, product_unit: $tType).
% 12.94/2.80 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 12.94/2.80 thf(type_def_8, type, set: $tType > $tType).
% 12.94/2.80 thf(type_def_9, type, nat: $tType).
% 12.94/2.80 thf(type_def_10, type, itself: $tType > $tType).
% 12.94/2.80 thf(type_def_11, type, a: $tType).
% 12.94/2.80 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 12.94/2.80 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 12.94/2.80 thf(func_def_1, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 12.94/2.80 thf(func_def_2, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 12.94/2.80 thf(func_def_3, type, bNF_Grp: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0 > X1 > $o))).
% 12.94/2.80 thf(func_def_4, type, bNF_convol: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X0 > X2) > X0 > product_prod @ X1 @ X2))).
% 12.94/2.80 thf(func_def_5, type, bNF_csquare: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ X0 > (X1 > X2) > (X3 > X2) > (X0 > X1) > (X0 > X3) > $o))).
% 12.94/2.80 thf(func_def_6, type, bNF_fstOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X0 @ X1))).
% 12.94/2.80 thf(func_def_7, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1))).
% 12.94/2.80 thf(func_def_8, type, bNF_sndOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 12.94/2.80 thf(func_def_9, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 12.94/2.80 thf(func_def_10, type, basic_BNF_size_prod: !>[X0: $tType, X1: $tType]:(((X0 > nat) > (X1 > nat) > product_prod @ X0 @ X1 > nat))).
% 12.94/2.80 thf(func_def_11, type, basic_pred_fun: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > (X0 > X1) > $o))).
% 12.94/2.80 thf(func_def_12, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 12.94/2.80 thf(func_def_13, type, coinductive_lhd: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 12.94/2.80 thf(func_def_14, type, coinductive_ltl: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 12.94/2.80 thf(func_def_15, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 12.94/2.80 thf(func_def_16, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 12.94/2.80 thf(func_def_17, type, id: !>[X0: $tType]:((X0 > X0))).
% 12.94/2.80 thf(func_def_18, type, fun_reduction_pair: !>[X0: $tType]:((product_prod @ set @ product_prod @ X0 @ X0 @ set @ product_prod @ X0 @ X0 > $o))).
% 12.94/2.80 thf(func_def_19, type, fun_rp_inv_image: !>[X0: $tType, X1: $tType]:((product_prod @ set @ product_prod @ X0 @ X0 @ set @ product_prod @ X0 @ X0 > (X1 > X0) > product_prod @ set @ product_prod @ X1 @ X1 @ set @ product_prod @ X1 @ X1))).
% 12.94/2.80 thf(func_def_20, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_21, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 12.94/2.80 thf(func_def_22, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 12.94/2.80 thf(func_def_23, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 12.94/2.80 thf(func_def_24, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 12.94/2.80 thf(func_def_25, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 12.94/2.80 thf(func_def_26, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 12.94/2.80 thf(func_def_27, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 12.94/2.80 thf(func_def_28, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 12.94/2.80 thf(func_def_29, type, product_rec_set_bool: !>[X0: $tType]:((X0 > X0 > $o > X0 > $o))).
% 12.94/2.80 thf(func_def_30, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 12.94/2.80 thf(func_def_31, type, product_rec_set_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2 > $o))).
% 12.94/2.80 thf(func_def_32, type, product_rec_set_unit: !>[X0: $tType]:((X0 > product_unit > X0 > $o))).
% 12.94/2.80 thf(func_def_33, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 12.94/2.80 thf(func_def_34, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 12.94/2.80 thf(func_def_35, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 12.94/2.80 thf(func_def_36, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 12.94/2.80 thf(func_def_37, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 12.94/2.80 thf(func_def_38, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3))).
% 12.94/2.80 thf(func_def_39, type, type2: !>[X0: $tType]:(itself @ X0)).
% 12.94/2.80 thf(func_def_40, type, iso_tu2017585022assist: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > (X1 > X0) > $o))).
% 12.94/2.80 thf(func_def_41, type, iso_tu2011167877assist: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > (X1 > X0) > X1 > (X0 > X0) > X1 > X0 > $o))).
% 12.94/2.80 thf(func_def_42, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 12.94/2.80 thf(func_def_43, type, relcompp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > $o))).
% 12.94/2.80 thf(func_def_44, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 12.94/2.80 thf(func_def_45, type, same_fst: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 12.94/2.80 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 12.94/2.80 thf(func_def_47, type, xs: coinductive_llist @ a).
% 12.94/2.80 thf(func_def_49, type, vIMP: ($o > $o > $o)).
% 12.94/2.80 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 12.94/2.80 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 12.94/2.80 thf(func_def_52, type, vNOT: ($o > $o)).
% 12.94/2.80 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 12.94/2.80 thf(func_def_54, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 12.94/2.80 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 12.94/2.80 thf(func_def_58, type, db2: !>[X0: $tType]:(X0)).
% 12.94/2.80 thf(func_def_59, type, db3: !>[X0: $tType]:(X0)).
% 12.94/2.80 thf(func_def_60, type, db4: !>[X0: $tType]:(X0)).
% 12.94/2.80 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 12.94/2.80 thf(func_def_62, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 12.94/2.80 thf(func_def_63, type, db5: !>[X0: $tType]:(X0)).
% 12.94/2.80 thf(func_def_64, type, sK0: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1))).
% 12.94/2.80 thf(func_def_65, type, sK1: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0))).
% 12.94/2.80 thf(func_def_66, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X2))).
% 12.94/2.80 thf(func_def_67, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X1))).
% 12.94/2.80 thf(func_def_68, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0))).
% 12.94/2.80 thf(func_def_69, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1))).
% 12.94/2.80 thf(func_def_70, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 12.94/2.80 thf(func_def_71, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 12.94/2.80 thf(func_def_72, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1))).
% 12.94/2.80 thf(func_def_73, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0))).
% 12.94/2.80 thf(func_def_74, type, sK10: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 12.94/2.80 thf(func_def_75, type, sK11: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_76, type, sK12: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 12.94/2.80 thf(func_def_77, type, sK13: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 12.94/2.80 thf(func_def_78, type, sK14: !>[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))).
% 12.94/2.80 thf(func_def_79, type, sK15: !>[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))).
% 12.94/2.80 thf(func_def_80, type, sK16: !>[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))).
% 12.94/2.80 thf(func_def_81, type, sK17: !>[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))).
% 12.94/2.80 thf(func_def_82, type, sK18: !>[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))).
% 12.94/2.80 thf(func_def_83, type, sK19: !>[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))).
% 12.94/2.80 thf(func_def_84, type, sK20: !>[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))).
% 12.94/2.80 thf(func_def_85, type, sK21: !>[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))).
% 12.94/2.80 thf(func_def_86, type, sK22: !>[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))).
% 12.94/2.80 thf(func_def_87, type, sK23: !>[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))).
% 12.94/2.80 thf(func_def_88, type, sK24: !>[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))).
% 12.94/2.80 thf(func_def_89, type, sK25: !>[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))).
% 12.94/2.80 thf(func_def_90, type, sK26: !>[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))).
% 12.94/2.80 thf(func_def_91, type, sK27: !>[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))).
% 12.94/2.80 thf(func_def_92, type, sK28: !>[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))).
% 12.94/2.80 thf(func_def_93, type, sK29: !>[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))).
% 12.94/2.80 thf(func_def_94, type, sK30: !>[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))).
% 12.94/2.80 thf(func_def_95, type, sK31: !>[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))).
% 12.94/2.80 thf(func_def_96, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 12.94/2.80 thf(func_def_97, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 12.94/2.80 thf(func_def_98, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 12.94/2.80 thf(func_def_99, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_100, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 12.94/2.80 thf(func_def_101, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 12.94/2.80 thf(func_def_102, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_103, 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 > X0))).
% 12.94/2.80 thf(func_def_104, type, sK40: !>[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))).
% 12.94/2.80 thf(func_def_105, type, sK41: !>[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))).
% 12.94/2.80 thf(func_def_106, type, sK42: !>[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))).
% 12.94/2.80 thf(func_def_107, type, sK43: !>[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))).
% 12.94/2.80 thf(func_def_108, type, sK44: !>[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))).
% 12.94/2.80 thf(func_def_109, type, sK45: !>[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))).
% 12.94/2.80 thf(func_def_110, type, sK46: !>[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))).
% 12.94/2.80 thf(func_def_111, type, sK47: !>[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))).
% 12.94/2.80 thf(func_def_112, type, sK48: !>[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))).
% 12.94/2.80 thf(func_def_113, type, sK49: !>[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))).
% 12.94/2.80 thf(func_def_114, type, sK50: !>[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))).
% 12.94/2.80 thf(func_def_115, type, sK51: !>[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))).
% 12.94/2.80 thf(func_def_116, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 12.94/2.80 thf(func_def_117, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 12.94/2.80 thf(func_def_118, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 12.94/2.80 thf(func_def_119, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 12.94/2.80 thf(func_def_120, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 12.94/2.80 thf(func_def_121, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 12.94/2.80 thf(func_def_122, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 12.94/2.80 thf(func_def_123, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 12.94/2.80 thf(func_def_124, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 12.94/2.80 thf(func_def_125, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 12.94/2.80 thf(func_def_126, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 12.94/2.80 thf(func_def_127, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 12.94/2.80 thf(func_def_128, type, sK64: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 12.94/2.80 thf(func_def_129, type, sK65: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_130, type, sK66: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 12.94/2.80 thf(func_def_131, type, sK67: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 12.94/2.80 thf(func_def_132, type, sK68: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_133, type, sK69: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 12.94/2.80 thf(func_def_134, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2))).
% 12.94/2.80 thf(func_def_135, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1))).
% 12.94/2.80 thf(func_def_136, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0))).
% 12.94/2.80 thf(func_def_137, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2))).
% 12.94/2.80 thf(func_def_138, type, sK74: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0))).
% 12.94/2.80 thf(func_def_139, type, sK75: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1))).
% 12.94/2.80 thf(func_def_140, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 12.94/2.80 thf(func_def_141, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 12.94/2.80 thf(func_def_142, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X2))).
% 12.94/2.80 thf(func_def_143, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X1))).
% 12.94/2.80 thf(func_def_144, type, sK80: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 12.94/2.80 thf(func_def_145, type, sK81: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 12.94/2.80 thf(func_def_146, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X1) > product_prod @ X1 @ X2 > X0))).
% 12.94/2.80 thf(func_def_147, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X1) > product_prod @ X1 @ X2 > X2))).
% 12.94/2.80 thf(func_def_148, type, sK84: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > $o) > (X1 > $o) > X1))).
% 12.94/2.80 thf(func_def_149, type, sK85: !>[X0: $tType]:(((X0 > X0) > (X0 > X0) > X0 > X0))).
% 12.94/2.80 thf(func_def_150, type, sK86: !>[X0: $tType]:(((X0 > X0) > (X0 > X0) > X0 > X0))).
% 12.94/2.80 thf(func_def_151, type, sK87: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_152, type, sK88: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_153, type, sK89: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_154, type, sK90: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_155, type, sK91: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_156, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_157, type, sK93: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_158, type, sK94: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 12.94/2.80 thf(func_def_159, type, sK95: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.80 thf(func_def_160, type, sK96: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > (X1 > X0) > X1))).
% 12.94/2.80 thf(func_def_161, type, sK97: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.80 thf(func_def_162, type, sK98: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.80 thf(func_def_163, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.80 thf(func_def_164, type, sK100: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.80 thf(func_def_165, type, sK101: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.80 thf(func_def_166, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.80 thf(func_def_167, type, sK103: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.81 thf(func_def_168, type, sK104: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_169, type, sK105: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_170, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.81 thf(func_def_171, type, sK107: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_172, type, sK108: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_173, type, sK109: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.81 thf(func_def_174, type, sK110: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_175, type, sK111: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_176, type, sK112: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.81 thf(func_def_177, type, sK113: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_178, type, sK114: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_179, type, sK115: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.81 thf(func_def_180, type, sK116: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_181, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_182, type, sK118: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.81 thf(func_def_183, type, sK119: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_184, type, sK120: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_185, type, sK121: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X0 > X0))).
% 12.94/2.81 thf(func_def_186, type, sK122: !>[X0: $tType, X1: $tType]:((((X1 > X1) > X0 > X0) > X0))).
% 12.94/2.81 thf(func_def_187, type, sK123: !>[X0: $tType, X1: $tType]:(((X0 > X1) > ((X1 > X1) > X0 > X0) > X0))).
% 12.94/2.81 thf(func_def_188, type, sK124: !>[X0: $tType, X1: $tType]:((((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_189, type, sK125: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ((X0 > X0) > X1 > X1) > X1))).
% 12.94/2.81 thf(func_def_190, type, sK126: !>[X0: $tType]:(((X0 > X0) > X0))).
% 12.94/2.81 thf(func_def_191, type, sK127: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 12.94/2.81 thf(func_def_192, type, sK128: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 12.94/2.81 thf(func_def_193, type, sK129: !>[X0: $tType]:(((X0 > X0) > X0))).
% 12.94/2.81 thf(func_def_195, type, sK131: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 12.94/2.81 thf(func_def_196, type, sK132: !>[X0: $tType]:(X0)).
% 12.94/2.81 thf(func_def_197, type, sK133: !>[X0: $tType]:(X0)).
% 12.94/2.81 thf(func_def_198, type, sK134: !>[X0: $tType]:(((X0 > $o) > X0))).
% 12.94/2.81 thf(func_def_199, type, sK135: !>[X0: $tType]:(((X0 > $o) > X0))).
% 12.94/2.81 thf(f5,axiom,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X0 > X2 > X1),X4 : X0,X5 : X2] : (((product_case_prod @ X0 @ X2 @ X1 @ X3 @ (product_Pair @ X0 @ X2 @ X4 @ X5))) = ((X3 @ X4 @ X5)))),
% 12.94/2.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_case__prod__conv)).
% 12.94/2.81 thf(f12,axiom,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (comp @ X2 @ X1 @ X0 = (^[X3 : (X2 > X1), X4 : (X0 > X2), X5 : X0] : ((X3 @ (X4 @ X5)))))),
% 12.94/2.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_comp__apply)).
% 12.94/2.81 thf(f21,axiom,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType] : (product_map_prod @ X3 @ X2 @ X0 @ X1 = (^[X4 : (X3 > X2), X5 : (X0 > X1)] : ((product_case_prod @ X3 @ X0 @ product_prod @ X2 @ X1 @ (^[X6 : X3, X7 : X0] : ((product_Pair @ X2 @ X1 @ (X4 @ X6) @ (X5 @ X7))))))))),
% 12.94/2.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_map__prod__def)).
% 12.94/2.81 thf(f56,axiom,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : X0,X4 : (X0 > X1),X5 : (X0 > X0)] : ((X2 @ X3) => (((coindu1441602521_llist @ X0 @ X1 @ X2 @ X4 @ X5 @ X3)) = coinductive_LNil @ X1))),
% 12.94/2.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_unfold__llist_Octr_I1_J)).
% 12.94/2.81 thf(f64,axiom,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType] : (product_snd @ X1 @ X0 = ((product_case_prod @ X1 @ X0 @ X0 @ (^[X2 : X1, X3 : X0] : (X3)))))),
% 12.94/2.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_snd__def)).
% 12.94/2.81 thf(f270,conjecture,(
% 12.94/2.81 (((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[X0 : coinductive_llist @ a, X1 : coinductive_llist @ a] : ((X0 != coinductive_LNil @ a) => ((X1 != coinductive_LNil @ a) => (((coinductive_lhd @ a @ X0)) != ((coinductive_lhd @ a @ X1))))))) @ (comp @ coinductive_llist @ a @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_lhd @ a @ product_snd @ coinductive_llist @ a @ coinductive_llist @ a) @ (product_map_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_ltl @ a @ coinductive_ltl @ a) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))) = coinductive_LNil @ a)),
% 12.94/2.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 12.94/2.81 thf(f271,negated_conjecture,(
% 12.94/2.81 ~ (((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[X0 : coinductive_llist @ a, X1 : coinductive_llist @ a] : ((X0 != coinductive_LNil @ a) => ((X1 != coinductive_LNil @ a) => (((coinductive_lhd @ a @ X0)) != ((coinductive_lhd @ a @ X1))))))) @ (comp @ coinductive_llist @ a @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_lhd @ a @ product_snd @ coinductive_llist @ a @ coinductive_llist @ a) @ (product_map_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_ltl @ a @ coinductive_ltl @ a) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))) = coinductive_LNil @ a)),
% 12.94/2.81 inference(negated_conjecture,[status(cth)],[f270])).
% 12.94/2.81 thf(f286,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (comp @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1]: ((^[Y1 : X0 > X2]: ((^[Y2 : X0]: (Y0 @ (Y1 @ Y2))))))))),
% 12.94/2.81 inference(fool_elimination,[],[f12])).
% 12.94/2.81 thf(f301,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType] : (product_map_prod @ X3 @ X2 @ X0 @ X1 = (^[X4 : (X3 > X2), X5 : (X0 > X1)] : ((product_case_prod @ X3 @ X0 @ product_prod @ X2 @ X1 @ (^[X6 : X3, X7 : X0] : ((product_Pair @ X2 @ X1 @ (X4 @ X6) @ (X5 @ X7))))))))),
% 12.94/2.81 inference(rectify,[],[f21])).
% 12.94/2.81 thf(f302,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType] : (product_map_prod @ X3 @ X2 @ X0 @ X1 = (^[Y0 : X3 > X2]: ((^[Y1 : X0 > X1]: (product_case_prod @ X3 @ X0 @ product_prod @ X2 @ X1 @ (^[Y2 : X3]: ((^[Y3 : X0]: (product_Pair @ X2 @ X1 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))),
% 12.94/2.81 inference(fool_elimination,[],[f301])).
% 12.94/2.81 thf(f324,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : X0,X4 : (X0 > X1),X5 : (X0 > X0)] : ((X2 @ X3) => (((coindu1441602521_llist @ X0 @ X1 @ X2 @ X4 @ X5 @ X3)) = coinductive_LNil @ X1))),
% 12.94/2.81 inference(rectify,[],[f56])).
% 12.94/2.81 thf(f325,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : X0,X4 : (X0 > X1),X5 : (X0 > X0)] : ((((X2 @ X3)) = $true) => (((coindu1441602521_llist @ X0 @ X1 @ X2 @ X4 @ X5 @ X3)) = coinductive_LNil @ X1))),
% 12.94/2.81 inference(fool_elimination,[],[f324])).
% 12.94/2.81 thf(f338,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType] : (product_snd @ X1 @ X0 = ((product_case_prod @ X1 @ X0 @ X0 @ (^[X2 : X1, X3 : X0] : (X3)))))),
% 12.94/2.81 inference(rectify,[],[f64])).
% 12.94/2.81 thf(f339,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType] : (product_snd @ X1 @ X0 = ((product_case_prod @ X1 @ X0 @ X0 @ (^[Y0 : X1]: ((^[Y1 : X0]: (Y1)))))))),
% 12.94/2.81 inference(fool_elimination,[],[f338])).
% 12.94/2.81 thf(f579,plain,(
% 12.94/2.81 ~ (((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[X0 : coinductive_llist @ a, X1 : coinductive_llist @ a] : ((X0 != coinductive_LNil @ a) => ((X1 != coinductive_LNil @ a) => (((coinductive_lhd @ a @ X0)) != ((coinductive_lhd @ a @ X1))))))) @ (comp @ coinductive_llist @ a @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_lhd @ a @ product_snd @ coinductive_llist @ a @ coinductive_llist @ a) @ (product_map_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_ltl @ a @ coinductive_ltl @ a) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))) = coinductive_LNil @ a)),
% 12.94/2.81 inference(rectify,[],[f271])).
% 12.94/2.81 thf(f580,plain,(
% 12.94/2.81 ~ (coinductive_LNil @ a = ((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1))))))))) @ (comp @ coinductive_llist @ a @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_lhd @ a @ product_snd @ coinductive_llist @ a @ coinductive_llist @ a) @ (product_map_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_ltl @ a @ coinductive_ltl @ a) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))))),
% 12.94/2.81 inference(fool_elimination,[],[f579])).
% 12.94/2.81 thf(f590,plain,(
% 12.94/2.81 (coinductive_LNil @ a != ((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1))))))))) @ (comp @ coinductive_llist @ a @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_lhd @ a @ product_snd @ coinductive_llist @ a @ coinductive_llist @ a) @ (product_map_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_ltl @ a @ coinductive_ltl @ a) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))))),
% 12.94/2.81 inference(flattening,[],[f580])).
% 12.94/2.81 thf(f620,plain,(
% 12.94/2.81 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : X0,X4 : (X0 > X1),X5 : (X0 > X0)] : ((((coindu1441602521_llist @ X0 @ X1 @ X2 @ X4 @ X5 @ X3)) = coinductive_LNil @ X1) | (((X2 @ X3)) != $true))),
% 12.94/2.81 inference(ennf_transformation,[],[f325])).
% 12.94/2.81 thf(f764,plain,(
% 12.94/2.81 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X0 > X2 > X1),X4 : X0,X5 : X2] : ((((product_case_prod @ X0 @ X2 @ X1 @ X3 @ (product_Pair @ X0 @ X2 @ X4 @ X5))) = ((X3 @ X4 @ X5)))) )),
% 12.94/2.81 inference(cnf_transformation,[],[f5])).
% 12.94/2.81 thf(f772,plain,(
% 12.94/2.81 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((comp @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1]: ((^[Y1 : X0 > X2]: ((^[Y2 : X0]: (Y0 @ (Y1 @ Y2))))))))) )),
% 12.94/2.81 inference(cnf_transformation,[],[f286])).
% 12.94/2.81 thf(f785,plain,(
% 12.94/2.81 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : ((product_map_prod @ X3 @ X2 @ X0 @ X1 = (^[Y0 : X3 > X2]: ((^[Y1 : X0 > X1]: (product_case_prod @ X3 @ X0 @ product_prod @ X2 @ X1 @ (^[Y2 : X3]: ((^[Y3 : X0]: (product_Pair @ X2 @ X1 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))) )),
% 12.94/2.81 inference(cnf_transformation,[],[f302])).
% 12.94/2.81 thf(f821,plain,(
% 12.94/2.81 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : X0,X4 : (X0 > X1),X5 : (X0 > X0)] : ((((coindu1441602521_llist @ X0 @ X1 @ X2 @ X4 @ X5 @ X3)) = coinductive_LNil @ X1) | (((X2 @ X3)) != $true)) )),
% 12.94/2.81 inference(cnf_transformation,[],[f620])).
% 12.94/2.81 thf(f831,plain,(
% 12.94/2.81 ( ! [X1 : $tType,X0 : $tType] : ((product_snd @ X1 @ X0 = ((product_case_prod @ X1 @ X0 @ X0 @ (^[Y0 : X1]: ((^[Y1 : X0]: (Y1)))))))) )),
% 12.94/2.81 inference(cnf_transformation,[],[f339])).
% 12.94/2.81 thf(f1056,plain,(
% 12.94/2.81 (coinductive_LNil @ a != ((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1))))))))) @ (comp @ coinductive_llist @ a @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_lhd @ a @ product_snd @ coinductive_llist @ a @ coinductive_llist @ a) @ (product_map_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_ltl @ a @ coinductive_ltl @ a) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))))),
% 12.94/2.81 inference(cnf_transformation,[],[f590])).
% 12.94/2.81 thf(f1227,plain,(
% 12.94/2.81 (coinductive_LNil @ a != ((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1))))))))) @ ((^[Y0 : coinductive_llist @ a > a]: ((^[Y1 : product_prod @ coinductive_llist @ a @ coinductive_llist @ a > coinductive_llist @ a]: ((^[Y2 : product_prod @ coinductive_llist @ a @ coinductive_llist @ a]: (Y0 @ (Y1 @ Y2))))))) @ coinductive_lhd @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: (Y1)))))) @ ((^[Y0 : coinductive_llist @ a > coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a > coinductive_llist @ a]: (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ (^[Y2 : coinductive_llist @ a]: ((^[Y3 : coinductive_llist @ a]: (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ (Y0 @ Y2) @ (Y1 @ Y3))))))))) @ coinductive_ltl @ a @ coinductive_ltl @ a) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))))),
% 12.94/2.81 inference(definition_unfolding,[],[f1056,f772,f831,f785])).
% 12.94/2.81 thf(f1257,plain,(
% 12.94/2.81 (coinductive_LNil @ a != ((coindu1441602521_llist @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1))))))))) @ (^[Y0 : product_prod @ coinductive_llist @ a @ coinductive_llist @ a]: (coinductive_lhd @ a @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ a @ (^[Y1 : coinductive_llist @ a]: ((^[Y2 : coinductive_llist @ a]: (Y2)))) @ Y0))) @ (product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ product_prod @ coinductive_llist @ a @ coinductive_llist @ a @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ (coinductive_ltl @ a @ Y0) @ (coinductive_ltl @ a @ Y1)))))) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))))),
% 12.94/2.81 inference(beta-eta_normalization,[],[f1227])).
% 12.94/2.81 thf(f26538,plain,(
% 12.94/2.81 (coinductive_LNil @ a != coinductive_LNil @ a) | ($true != ((product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1)))))))) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))))),
% 12.94/2.81 inference(constrained_superposition,[],[f1257,f821])).
% 12.94/2.81 thf(f26539,plain,(
% 12.94/2.81 ($true != ((product_case_prod @ coinductive_llist @ a @ coinductive_llist @ a @ $o @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1)))))))) @ (product_Pair @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_LNil @ a @ xs))))),
% 12.94/2.81 inference(trivial_inequality_removal,[],[f26538])).
% 12.94/2.81 thf(f26554,plain,(
% 12.94/2.81 ($true != (((^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: ((~ (coinductive_LNil @ a = Y0)) => ((~ (coinductive_LNil @ a = Y1)) => (~ ((coinductive_lhd @ a @ Y0) = (coinductive_lhd @ a @ Y1)))))))) @ coinductive_LNil @ a @ xs)))),
% 12.94/2.81 inference(forward_demodulation,[],[f26539,f764])).
% 12.94/2.81 thf(f26555,plain,(
% 12.94/2.81 ($true != (((~ (coinductive_LNil @ a = coinductive_LNil @ a)) => ((~ (coinductive_LNil @ a = xs)) => (~ ((coinductive_lhd @ a @ coinductive_LNil @ a) = (coinductive_lhd @ a @ xs)))))))),
% 12.94/2.81 inference(beta-eta_normalization,[],[f26554])).
% 12.94/2.81 thf(f26557,plain,(
% 12.94/2.81 ($true = ((~ (coinductive_LNil @ a = coinductive_LNil @ a))))),
% 12.94/2.81 inference(imp_proxy_clausification,[],[f26555])).
% 12.94/2.81 thf(f26558,plain,(
% 12.94/2.81 ($false = ((coinductive_LNil @ a = coinductive_LNil @ a)))),
% 12.94/2.81 inference(not_proxy_clausification,[],[f26557])).
% 12.94/2.81 thf(f26559,plain,(
% 12.94/2.81 (coinductive_LNil @ a != coinductive_LNil @ a)),
% 12.94/2.81 inference(equality_proxy_clausification,[],[f26558])).
% 12.94/2.81 thf(f26560,plain,(
% 12.94/2.81 $false),
% 12.94/2.81 inference(trivial_inequality_removal,[],[f26559])).
% 12.94/2.81 % SZS output end Proof for theBenchmark
% 12.94/2.81 % (3727925)------------------------------
% 12.94/2.81 % (3727925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.94/2.81 % (3727925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.94/2.81 % (3727925)CaDiCaL version: 2.1.3
% 12.94/2.81 % (3727925)Termination reason: Refutation
% 12.94/2.81 % (3727925)Time elapsed: 1.515 s
% 12.94/2.81 % (3727925)Peak memory usage: 25 MB
% 12.94/2.81 % (3727925)Instructions burned: 3363 (million)
% 12.94/2.81 % (3727864)Success in time 2.583 s
% 12.94/2.81 % Vampire exiting
%------------------------------------------------------------------------------