%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP021^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:22 AM UTC 2026
% Result : Theorem 5.40s 1.13s
% Output : Refutation 5.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP021^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:34:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 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
% 5.40/1.13 % (539042)Will run a generic schedule for satisfiability detection.
% 5.40/1.13 % (539048)% WARNING: option uhcvi not known.
% 5.40/1.13 % (539049)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3189322767:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.40/1.13 % (539048)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3900197932:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.40/1.13 % (539051)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1979387958:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.40/1.13 % (539048)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.40/1.13 % (539051)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.40/1.13 % (539053)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2588356296:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.40/1.13 % (539048)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.40/1.13 % (539052)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=942913781:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.40/1.13 % (539047)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2493258223_2999 on theBenchmark for (2999ds/0Mi)
% 5.40/1.13 % (539050)dis+10_1_sil=32000:sp=arity:random_seed=2052193945:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539061)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1914565663:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539053)Instruction limit reached!
% 5.40/1.13 % (539053)------------------------------
% 5.40/1.13 % (539053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539053)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539053)Termination reason: Instruction limit
% 5.40/1.13 % (539053)Termination phase: Saturation
% 5.40/1.13 % (539053)Time elapsed: 0.068 s
% 5.40/1.13 % (539053)Peak memory usage: 13 MB
% 5.40/1.13 % (539053)Instructions burned: 161 (million)
% 5.40/1.13 % (539063)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=538699096:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.40/1.13 % (539051)Instruction limit reached!
% 5.40/1.13 % (539051)------------------------------
% 5.40/1.13 % (539051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539051)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539051)Termination reason: Instruction limit
% 5.40/1.13 % (539051)Termination phase: Saturation
% 5.40/1.13 % (539051)Time elapsed: 0.075 s
% 5.40/1.13 % (539051)Peak memory usage: 13 MB
% 5.40/1.13 % (539051)Instructions burned: 116 (million)
% 5.40/1.13 % (539050)Instruction limit reached!
% 5.40/1.13 % (539050)------------------------------
% 5.40/1.13 % (539050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539050)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539050)Termination reason: Instruction limit
% 5.40/1.13 % (539050)Termination phase: Saturation
% 5.40/1.13 % (539050)Time elapsed: 0.073 s
% 5.40/1.13 % (539050)Peak memory usage: 13 MB
% 5.40/1.13 % (539050)Instructions burned: 105 (million)
% 5.40/1.13 % (539066)ott-21_1_sil=16000:fs=off:random_seed=1945695535:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.40/1.13 % (539065)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=885524471:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.40/1.13 % (539065)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.40/1.13 % (539065)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.40/1.13 % (539067)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3838882529:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.40/1.13 % (539063)Instruction limit reached!
% 5.40/1.13 % (539063)------------------------------
% 5.40/1.13 % (539063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539063)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539063)Termination reason: Instruction limit
% 5.40/1.13 % (539063)Termination phase: Saturation
% 5.40/1.13 % (539063)Time elapsed: 0.053 s
% 5.40/1.13 % (539063)Peak memory usage: 12 MB
% 5.40/1.13 % (539063)Instructions burned: 131 (million)
% 5.40/1.13 % (539052)Instruction limit reached!
% 5.40/1.13 % (539052)------------------------------
% 5.40/1.13 % (539052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539052)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539052)Termination reason: Instruction limit
% 5.40/1.13 % (539052)Termination phase: Saturation
% 5.40/1.13 % (539052)Time elapsed: 0.121 s
% 5.40/1.13 % (539052)Peak memory usage: 13 MB
% 5.40/1.13 % (539052)Instructions burned: 131 (million)
% 5.40/1.13 % (539071)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4004695737:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539072)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1515392053:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.40/1.13 % (539074)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1500190651:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.40/1.13 % (539066)Instruction limit reached!
% 5.40/1.13 % (539066)------------------------------
% 5.40/1.13 % (539066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539066)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539066)Termination reason: Instruction limit
% 5.40/1.13 % (539066)Termination phase: Saturation
% 5.40/1.13 % (539066)Time elapsed: 0.079 s
% 5.40/1.13 % (539066)Peak memory usage: 13 MB
% 5.40/1.13 % (539066)Instructions burned: 181 (million)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539077)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=1853264428:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 5.40/1.13 % (539077)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.40/1.13 % (539078)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3058030302:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 5.40/1.13 % (539078)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.40/1.13 % (539065)Instruction limit reached!
% 5.40/1.13 % (539065)------------------------------
% 5.40/1.13 % (539065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539065)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539065)Termination reason: Instruction limit
% 5.40/1.13 % (539065)Termination phase: Saturation
% 5.40/1.13 % (539065)Time elapsed: 0.364 s
% 5.40/1.13 % (539065)Peak memory usage: 15 MB
% 5.40/1.13 % (539065)Instructions burned: 684 (million)
% 5.40/1.13 % (539081)fmb+10_1_sil=64000:random_seed=2850685698:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 5.40/1.13 % (539081)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539083)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4060561830:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539085)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3683564639:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539087)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=147035909:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 5.40/1.13 % (539077)Instruction limit reached!
% 5.40/1.13 % (539077)------------------------------
% 5.40/1.13 % (539077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539077)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539077)Termination reason: Instruction limit
% 5.40/1.13 % (539077)Termination phase: Saturation
% 5.40/1.13 % (539077)Time elapsed: 0.372 s
% 5.40/1.13 % (539077)Peak memory usage: 17 MB
% 5.40/1.13 % (539077)Instructions burned: 693 (million)
% 5.40/1.13 % (539087)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.40/1.13 % (539067)Instruction limit reached!
% 5.40/1.13 % (539067)------------------------------
% 5.40/1.13 % (539067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539067)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539067)Termination reason: Instruction limit
% 5.40/1.13 % (539067)Termination phase: Saturation
% 5.40/1.13 % (539067)Time elapsed: 0.443 s
% 5.40/1.13 % (539067)Peak memory usage: 14 MB
% 5.40/1.13 % (539067)Instructions burned: 477 (million)
% 5.40/1.13 % (539090)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2115786786:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 5.40/1.13 % (539089)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3444829063:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539089)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.40/1.13 % (539089)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.40/1.13 % (539093)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2318837415:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 5.40/1.13 % Exception at run slice level
% 5.40/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.40/1.13 % (539095)ott-2_1_sil=16000:newcnf=on:random_seed=882400868:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 5.40/1.13 % (539095)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.40/1.13 % (539078)Instruction limit reached!
% 5.40/1.13 % (539078)------------------------------
% 5.40/1.13 % (539078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539078)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539078)Termination reason: Instruction limit
% 5.40/1.13 % (539078)Termination phase: Saturation
% 5.40/1.13 % (539078)Time elapsed: 0.625 s
% 5.40/1.13 % (539078)Peak memory usage: 17 MB
% 5.40/1.13 % (539078)Instructions burned: 881 (million)
% 5.40/1.13 % (539072)Instruction limit reached!
% 5.40/1.13 % (539072)------------------------------
% 5.40/1.13 % (539072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539072)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539072)Termination reason: Instruction limit
% 5.40/1.13 % (539072)Termination phase: Saturation
% 5.40/1.13 % (539072)Time elapsed: 0.672 s
% 5.40/1.13 % (539072)Peak memory usage: 17 MB
% 5.40/1.13 % (539072)Instructions burned: 1180 (million)
% 5.40/1.13 % (539097)ott+10_1_sil=32000:tgt=ground:random_seed=2575918350:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 5.40/1.13 % (539048) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-539042-539048"...
% 5.40/1.13 % (539048)...printing done.
% 5.40/1.13 % (539098)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3925937589:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 5.40/1.13 % (539048)Refutation found. Thanks to Tanya!
% 5.40/1.13 % SZS status Theorem for theBenchmark
% 5.40/1.13 % SZS output start Proof for theBenchmark
% 5.40/1.13 thf(type_def_5, type, tyop_2Eextreal_2Eextreal: $tType).
% 5.40/1.13 thf(type_def_6, type, tyop_2Emin_2Ebool: $tType).
% 5.40/1.13 thf(type_def_7, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 5.40/1.13 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 5.40/1.13 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.40/1.13 thf(func_def_1, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 5.40/1.13 thf(func_def_2, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.40/1.13 thf(func_def_3, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 5.40/1.13 thf(func_def_4, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.40/1.13 thf(func_def_5, type, c_2Ebool_2ECOND: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 5.40/1.13 thf(func_def_6, type, c_2Ebool_2EF: $o).
% 5.40/1.13 thf(func_def_7, type, c_2Ebool_2ET: $o).
% 5.40/1.13 thf(func_def_8, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 5.40/1.13 thf(func_def_9, type, c_2Eextreal_2Eextreal__le: (tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > $o)).
% 5.40/1.13 thf(func_def_10, type, c_2Eextreal_2Eextreal__max: (tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal)).
% 5.40/1.13 thf(func_def_11, type, c_2Ebool_2E_7E: ($o > $o)).
% 5.40/1.13 thf(func_def_13, type, vNOT: ($o > $o)).
% 5.40/1.13 thf(func_def_16, type, vAND: ($o > $o > $o)).
% 5.40/1.13 thf(func_def_17, type, vOR: ($o > $o > $o)).
% 5.40/1.13 thf(func_def_18, type, sP0: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_19, type, sP1: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_20, type, sP2: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_21, type, sP3: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_22, type, sP4: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_23, type, sP5: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_24, type, sP6: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_25, type, sP7: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_26, type, sP8: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_27, type, sP9: ($o > $o > $o > $o)).
% 5.40/1.13 thf(func_def_28, type, sK10: !>[X0: $tType]:(((X0 > $o) > X0))).
% 5.40/1.13 thf(func_def_29, type, sK11: !>[X0: $tType]:(((X0 > $o) > X0))).
% 5.40/1.13 thf(func_def_30, type, sK12: tyop_2Eextreal_2Eextreal).
% 5.40/1.13 thf(func_def_31, type, sK13: tyop_2Eextreal_2Eextreal).
% 5.40/1.13 thf(func_def_32, type, sK14: tyop_2Eextreal_2Eextreal).
% 5.40/1.13 thf(func_def_34, type, db0: !>[X0: $tType]:(X0)).
% 5.40/1.13 thf(func_def_35, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.40/1.13 thf(func_def_36, type, db1: !>[X0: $tType]:(X0)).
% 5.40/1.13 thf(func_def_37, type, sK16: !>[X0: $tType, X1: $tType]:(((X0 > X1 > tyop_2Eextreal_2Eextreal) > X0 > X1))).
% 5.40/1.13 thf(func_def_38, type, sK17: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > tyop_2Eextreal_2Eextreal) > X1))).
% 5.40/1.13 thf(func_def_39, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2 > X0 > $o) > X1 > X2))).
% 5.40/1.13 thf(func_def_40, type, db2: !>[X0: $tType]:(X0)).
% 5.40/1.13 thf(func_def_41, type, db3: !>[X0: $tType]:(X0)).
% 5.40/1.13 thf(func_def_42, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1 > tyop_2Eextreal_2Eextreal) > X0 > X1))).
% 5.40/1.13 thf(func_def_43, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > tyop_2Eextreal_2Eextreal) > X1))).
% 5.40/1.13 thf(f8,axiom,(
% 5.40/1.13 c_2Ebool_2ET),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH)).
% 5.40/1.13 thf(f9,axiom,(
% 5.40/1.13 ! [X0 : $o,X1 : $o] : ((X0 => X1) => ((X1 => X0) => (X0 = X1)))),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX)).
% 5.40/1.13 thf(f17,axiom,(
% 5.40/1.13 ! [X0 : $o] : (((X0 = c_2Ebool_2EF) <=> (~ X0)) & ((c_2Ebool_2EF = X0) <=> (~ X0)) & ((X0 = c_2Ebool_2ET) <=> X0) & ((c_2Ebool_2ET = X0) <=> X0))),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES)).
% 5.40/1.13 thf(f18,axiom,(
% 5.40/1.13 ! [X0 : $tType,X1 : X0,X2 : X0] : ((((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X1 @ X2)) = X2) & (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X1 @ X2)) = X1))),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES)).
% 5.40/1.13 thf(f22,axiom,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : (((c_2Eextreal_2Eextreal__le @ X1 @ X2) & (c_2Eextreal_2Eextreal__le @ X0 @ X1)) => (c_2Eextreal_2Eextreal__le @ X0 @ X2))),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans)).
% 5.40/1.13 thf(f23,axiom,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((c_2Eextreal_2Eextreal__le @ X1 @ X0) | (c_2Eextreal_2Eextreal__le @ X0 @ X1))),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total)).
% 5.40/1.13 thf(f24,axiom,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : (((c_2Eextreal_2Eextreal__max @ X0 @ X1)) = ((c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ (c_2Eextreal_2Eextreal__le @ X0 @ X1) @ X1 @ X0)))),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def)).
% 5.40/1.13 thf(f35,conjecture,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0) <=> ((c_2Eextreal_2Eextreal__le @ X2 @ X0) & (c_2Eextreal_2Eextreal__le @ X1 @ X0)))),
% 5.40/1.13 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le)).
% 5.40/1.13 thf(f36,negated_conjecture,(
% 5.40/1.13 ~ ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0) <=> ((c_2Eextreal_2Eextreal__le @ X2 @ X0) & (c_2Eextreal_2Eextreal__le @ X1 @ X0)))),
% 5.40/1.13 inference(negated_conjecture,[status(cth)],[f35])).
% 5.40/1.13 thf(f51,plain,(
% 5.40/1.13 c_2Ebool_2ET),
% 5.40/1.13 inference(rectify,[],[f8])).
% 5.40/1.13 thf(f52,plain,(
% 5.40/1.13 (c_2Ebool_2ET = $true)),
% 5.40/1.13 inference(fool_elimination,[],[f51])).
% 5.40/1.13 thf(f53,plain,(
% 5.40/1.13 ! [X0 : $o,X1 : $o] : ((X0 => X1) => ((X1 => X0) => (X0 = X1)))),
% 5.40/1.13 inference(rectify,[],[f9])).
% 5.40/1.13 thf(f54,plain,(
% 5.40/1.13 ! [X0 : $o,X1 : $o] : ((($true = X0) => ($true = X1)) => ((($true = X1) => ($true = X0)) => (X0 = X1)))),
% 5.40/1.13 inference(fool_elimination,[],[f53])).
% 5.40/1.13 thf(f67,plain,(
% 5.40/1.13 ! [X0 : $o] : (((X0 = c_2Ebool_2EF) <=> (~ X0)) & ((c_2Ebool_2EF = X0) <=> (~ X0)) & ((X0 = c_2Ebool_2ET) <=> X0) & ((c_2Ebool_2ET = X0) <=> X0))),
% 5.40/1.13 inference(rectify,[],[f17])).
% 5.40/1.13 thf(f68,plain,(
% 5.40/1.13 ! [X0 : $o] : (((c_2Ebool_2EF = X0) <=> (((~ X0)) = $true)) & ((c_2Ebool_2EF = X0) <=> (((~ X0)) = $true)) & ((c_2Ebool_2ET = X0) <=> ($true = X0)) & ((c_2Ebool_2ET = X0) <=> ($true = X0)))),
% 5.40/1.13 inference(fool_elimination,[],[f67])).
% 5.40/1.13 thf(f75,plain,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : (((c_2Eextreal_2Eextreal__le @ X1 @ X2) & (c_2Eextreal_2Eextreal__le @ X0 @ X1)) => (c_2Eextreal_2Eextreal__le @ X0 @ X2))),
% 5.40/1.13 inference(rectify,[],[f22])).
% 5.40/1.13 thf(f76,plain,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : (((((c_2Eextreal_2Eextreal__le @ X1 @ X2)) = $true) & (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) = $true)) => (((c_2Eextreal_2Eextreal__le @ X0 @ X2)) = $true))),
% 5.40/1.13 inference(fool_elimination,[],[f75])).
% 5.40/1.13 thf(f77,plain,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((c_2Eextreal_2Eextreal__le @ X1 @ X0) | (c_2Eextreal_2Eextreal__le @ X0 @ X1))),
% 5.40/1.13 inference(rectify,[],[f23])).
% 5.40/1.13 thf(f78,plain,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true) | (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) = $true))),
% 5.40/1.13 inference(fool_elimination,[],[f77])).
% 5.40/1.13 thf(f99,plain,(
% 5.40/1.13 ~ ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0) <=> ((c_2Eextreal_2Eextreal__le @ X2 @ X0) & (c_2Eextreal_2Eextreal__le @ X1 @ X0)))),
% 5.40/1.13 inference(rectify,[],[f36])).
% 5.40/1.13 thf(f100,plain,(
% 5.40/1.13 ~ ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0)) = $true) <=> ((((c_2Eextreal_2Eextreal__le @ X2 @ X0)) = $true) & (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true)))),
% 5.40/1.13 inference(fool_elimination,[],[f99])).
% 5.40/1.13 thf(f102,plain,(
% 5.40/1.13 ! [X0 : $o,X1 : $o] : (((X0 = X1) | (($true != X0) & ($true = X1))) | (($true != X1) & ($true = X0)))),
% 5.40/1.13 inference(ennf_transformation,[],[f54])).
% 5.40/1.13 thf(f103,plain,(
% 5.40/1.13 ! [X0 : $o,X1 : $o] : ((X0 = X1) | (($true != X0) & ($true = X1)) | (($true != X1) & ($true = X0)))),
% 5.40/1.13 inference(flattening,[],[f102])).
% 5.40/1.13 thf(f109,plain,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__le @ X0 @ X2)) = $true) | ((((c_2Eextreal_2Eextreal__le @ X1 @ X2)) != $true) | (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) != $true)))),
% 5.40/1.13 inference(ennf_transformation,[],[f76])).
% 5.40/1.13 thf(f110,plain,(
% 5.40/1.13 ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__le @ X0 @ X2)) = $true) | (((c_2Eextreal_2Eextreal__le @ X1 @ X2)) != $true) | (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) != $true))),
% 5.40/1.13 inference(flattening,[],[f109])).
% 5.40/1.13 thf(f120,plain,(
% 5.40/1.13 ? [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0)) = $true) <~> ((((c_2Eextreal_2Eextreal__le @ X2 @ X0)) = $true) & (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true)))),
% 5.40/1.13 inference(ennf_transformation,[],[f100])).
% 5.40/1.13 thf(f151,plain,(
% 5.40/1.13 ! [X0 : $o] : ((((c_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (c_2Ebool_2EF != X0))) & (((c_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (c_2Ebool_2EF != X0))) & (((c_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (c_2Ebool_2ET != X0))) & (((c_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (c_2Ebool_2ET != X0))))),
% 5.40/1.13 inference(nnf_transformation,[],[f68])).
% 5.40/1.13 thf(f152,plain,(
% 5.40/1.13 ! [X0 : $o] : (((c_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (c_2Ebool_2EF != X0)) & ((c_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (c_2Ebool_2EF != X0)) & ((c_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (c_2Ebool_2ET != X0)) & ((c_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (c_2Ebool_2ET != X0)))),
% 5.40/1.13 inference(flattening,[],[f151])).
% 5.40/1.13 thf(f200,plain,(
% 5.40/1.13 ? [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : ((((((c_2Eextreal_2Eextreal__le @ X2 @ X0)) != $true) | (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) != $true)) | (((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0)) != $true)) & (((((c_2Eextreal_2Eextreal__le @ X2 @ X0)) = $true) & (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true)) | (((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0)) = $true)))),
% 5.40/1.13 inference(nnf_transformation,[],[f120])).
% 5.40/1.13 thf(f201,plain,(
% 5.40/1.13 ? [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal,X2 : tyop_2Eextreal_2Eextreal] : (((((c_2Eextreal_2Eextreal__le @ X2 @ X0)) != $true) | (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) != $true) | (((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0)) != $true)) & (((((c_2Eextreal_2Eextreal__le @ X2 @ X0)) = $true) & (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true)) | (((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ X1 @ X2) @ X0)) = $true)))),
% 5.40/1.13 inference(flattening,[],[f200])).
% 5.40/1.13 thf(f202,plain,(
% 5.40/1.13 (($true != ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | ($true != ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | ($true != ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12)))) & ((($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) & ($true = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12)))) | ($true = ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12))))),
% 5.40/1.13 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f201])).
% 5.40/1.13 thf(f219,plain,(
% 5.40/1.13 (c_2Ebool_2ET = $true)),
% 5.40/1.13 inference(cnf_transformation,[],[f52])).
% 5.40/1.13 thf(f220,plain,(
% 5.40/1.13 ( ! [X0 : $o,X1 : $o] : ((X0 = X1) | ($true = X1) | ($true = X0)) )),
% 5.40/1.13 inference(cnf_transformation,[],[f103])).
% 5.40/1.13 thf(f256,plain,(
% 5.40/1.13 ( ! [X0 : $o] : ((c_2Ebool_2EF = X0) | (((~ X0)) != $true)) )),
% 5.40/1.13 inference(cnf_transformation,[],[f152])).
% 5.40/1.13 thf(f257,plain,(
% 5.40/1.13 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X1 @ X2)) = X1)) )),
% 5.40/1.13 inference(cnf_transformation,[],[f18])).
% 5.40/1.13 thf(f258,plain,(
% 5.40/1.13 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X1 @ X2)) = X2)) )),
% 5.40/1.13 inference(cnf_transformation,[],[f18])).
% 5.40/1.13 thf(f275,plain,(
% 5.40/1.13 ( ! [X2 : tyop_2Eextreal_2Eextreal,X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__le @ X1 @ X2)) != $true) | (((c_2Eextreal_2Eextreal__le @ X0 @ X2)) = $true) | (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) != $true)) )),
% 5.40/1.13 inference(cnf_transformation,[],[f110])).
% 5.40/1.13 thf(f276,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true) | (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) = $true)) )),
% 5.40/1.13 inference(cnf_transformation,[],[f78])).
% 5.40/1.13 thf(f277,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__max @ X0 @ X1)) = ((c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ (c_2Eextreal_2Eextreal__le @ X0 @ X1) @ X1 @ X0)))) )),
% 5.40/1.13 inference(cnf_transformation,[],[f24])).
% 5.40/1.13 thf(f376,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | ($true = ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12)))),
% 5.40/1.13 inference(cnf_transformation,[],[f202])).
% 5.40/1.13 thf(f377,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | ($true = ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12)))),
% 5.40/1.13 inference(cnf_transformation,[],[f202])).
% 5.40/1.13 thf(f378,plain,(
% 5.40/1.13 ($true != ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | ($true != ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | ($true != ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12)))),
% 5.40/1.13 inference(cnf_transformation,[],[f202])).
% 5.40/1.13 thf(f379,definition,(
% 5.40/1.13 ($true != $false)),
% 5.40/1.13 introduced(theory,[fool_distinctness_axiom])).
% 5.40/1.13 thf(f398,plain,(
% 5.40/1.13 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ $true @ X1 @ X2)) = X1)) )),
% 5.40/1.13 inference(definition_unfolding,[],[f257,f219])).
% 5.40/1.13 thf(f636,plain,(
% 5.40/1.13 ( ! [X0 : $o] : ((c_2Ebool_2EF = $false) | (((~ X0)) != $true) | ($true = X0)) )),
% 5.40/1.13 inference(iff_proxy_clausification,[],[f256])).
% 5.40/1.13 thf(f637,plain,(
% 5.40/1.13 ( ! [X0 : $o] : ((c_2Ebool_2EF = $false) | ($true = X0) | ($true = X0)) )),
% 5.40/1.13 inference(not_proxy_clausification,[],[f636])).
% 5.40/1.13 thf(f638,plain,(
% 5.40/1.13 ( ! [X0 : $o] : ((c_2Ebool_2EF = $false) | ($true = X0)) )),
% 5.40/1.13 inference(duplicate_literal_removal,[],[f637])).
% 5.40/1.13 thf(f660,plain,(
% 5.40/1.13 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true = X0) | ($false = X1)) )),
% 5.40/1.13 inference(iff_proxy_clausification,[],[f220])).
% 5.40/1.13 thf(f663,plain,(
% 5.40/1.13 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($false = X1)) )),
% 5.40/1.13 inference(duplicate_literal_removal,[],[f660])).
% 5.40/1.13 thf(f669,definition,(
% 5.40/1.13 spl15_1 <=> ($true = ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12)))),
% 5.40/1.13 introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition])).
% 5.40/1.13 thf(f670,plain,(
% 5.40/1.13 ($true != ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12))) | spl15_1),
% 5.40/1.13 inference(avatar_component_clause,[],[f669])).
% 5.40/1.13 thf(f671,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ (c_2Eextreal_2Eextreal__max @ sK13 @ sK14) @ sK12))) | ~spl15_1),
% 5.40/1.13 inference(avatar_component_clause,[],[f669])).
% 5.40/1.13 thf(f673,definition,(
% 5.40/1.13 spl15_2 <=> ($true = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12)))),
% 5.40/1.13 introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition])).
% 5.40/1.13 thf(f674,plain,(
% 5.40/1.13 ($true != ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | spl15_2),
% 5.40/1.13 inference(avatar_component_clause,[],[f673])).
% 5.40/1.13 thf(f675,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | ~spl15_2),
% 5.40/1.13 inference(avatar_component_clause,[],[f673])).
% 5.40/1.13 thf(f676,plain,(
% 5.40/1.13 spl15_1 | spl15_2),
% 5.40/1.13 inference(avatar_split_clause,[],[f376,f673,f669])).
% 5.40/1.13 thf(f678,definition,(
% 5.40/1.13 spl15_3 <=> ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12)))),
% 5.40/1.13 introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition])).
% 5.40/1.13 thf(f679,plain,(
% 5.40/1.13 ($true != ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | spl15_3),
% 5.40/1.13 inference(avatar_component_clause,[],[f678])).
% 5.40/1.13 thf(f680,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | ~spl15_3),
% 5.40/1.13 inference(avatar_component_clause,[],[f678])).
% 5.40/1.13 thf(f681,plain,(
% 5.40/1.13 spl15_1 | spl15_3),
% 5.40/1.13 inference(avatar_split_clause,[],[f377,f678,f669])).
% 5.40/1.13 thf(f682,plain,(
% 5.40/1.13 ~spl15_1 | ~spl15_2 | ~spl15_3),
% 5.40/1.13 inference(avatar_split_clause,[],[f378,f678,f673,f669])).
% 5.40/1.13 thf(f684,definition,(
% 5.40/1.13 spl15_4 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 5.40/1.13 introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition])).
% 5.40/1.13 thf(f685,plain,(
% 5.40/1.13 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl15_4),
% 5.40/1.13 inference(avatar_component_clause,[],[f684])).
% 5.40/1.13 thf(f693,definition,(
% 5.40/1.13 spl15_6 <=> ! [X0 : $o] : ($true = X0)),
% 5.40/1.13 introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition])).
% 5.40/1.13 thf(f694,plain,(
% 5.40/1.13 ( ! [X0 : $o] : (($true = X0)) ) | ~spl15_6),
% 5.40/1.13 inference(avatar_component_clause,[],[f693])).
% 5.40/1.13 thf(f713,definition,(
% 5.40/1.13 spl15_8 <=> (c_2Ebool_2EF = $false)),
% 5.40/1.13 introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition])).
% 5.40/1.13 thf(f715,plain,(
% 5.40/1.13 (c_2Ebool_2EF = $false) | ~spl15_8),
% 5.40/1.13 inference(avatar_component_clause,[],[f713])).
% 5.40/1.13 thf(f719,plain,(
% 5.40/1.13 spl15_6 | spl15_8),
% 5.40/1.13 inference(avatar_split_clause,[],[f638,f713,f693])).
% 5.40/1.13 thf(f726,plain,(
% 5.40/1.13 spl15_4 | spl15_6),
% 5.40/1.13 inference(avatar_split_clause,[],[f663,f693,f684])).
% 5.40/1.13 thf(f965,plain,(
% 5.40/1.13 $false | ~spl15_6),
% 5.40/1.13 inference(backward_subsumption_resolution,[],[f379,f694])).
% 5.40/1.13 thf(f1004,plain,(
% 5.40/1.13 ~spl15_6),
% 5.40/1.13 inference(avatar_contradiction_clause,[],[f965])).
% 5.40/1.13 thf(f1563,plain,(
% 5.40/1.13 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ $false @ X1 @ X2)) = X2)) ) | ~spl15_8),
% 5.40/1.13 inference(forward_demodulation,[],[f258,f715])).
% 5.40/1.13 thf(f3596,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal] : (($true != $true) | ($true = ((c_2Eextreal_2Eextreal__le @ X0 @ sK12))) | ($true != ((c_2Eextreal_2Eextreal__le @ X0 @ sK13)))) ) | ~spl15_2),
% 5.40/1.13 inference(constrained_superposition,[],[f275,f675])).
% 5.40/1.13 thf(f3597,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal] : (($true != $true) | ($true = ((c_2Eextreal_2Eextreal__le @ X0 @ sK12))) | ($true != ((c_2Eextreal_2Eextreal__le @ X0 @ sK14)))) ) | ~spl15_3),
% 5.40/1.13 inference(constrained_superposition,[],[f275,f680])).
% 5.40/1.13 thf(f3605,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal] : (($true != ((c_2Eextreal_2Eextreal__le @ X0 @ sK14))) | ($true = ((c_2Eextreal_2Eextreal__le @ X0 @ sK12)))) ) | ~spl15_3),
% 5.40/1.13 inference(trivial_inequality_removal,[],[f3597])).
% 5.40/1.13 thf(f3606,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal] : (($true != ((c_2Eextreal_2Eextreal__le @ X0 @ sK13))) | ($true = ((c_2Eextreal_2Eextreal__le @ X0 @ sK12)))) ) | ~spl15_2),
% 5.40/1.13 inference(trivial_inequality_removal,[],[f3596])).
% 5.40/1.13 thf(f3608,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal] : (($true != $true) | ($true = ((c_2Eextreal_2Eextreal__le @ X0 @ sK12))) | ($false = ((c_2Eextreal_2Eextreal__le @ X0 @ sK14)))) ) | (~spl15_3 | ~spl15_4)),
% 5.40/1.13 inference(constrained_superposition,[],[f3605,f685])).
% 5.40/1.13 thf(f3613,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal] : (($false = ((c_2Eextreal_2Eextreal__le @ X0 @ sK14))) | ($true = ((c_2Eextreal_2Eextreal__le @ X0 @ sK12)))) ) | (~spl15_3 | ~spl15_4)),
% 5.40/1.13 inference(trivial_inequality_removal,[],[f3608])).
% 5.40/1.13 thf(f3614,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__max @ X0 @ X1)) = ((c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $true @ X1 @ X0))) | (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) = $false)) ) | ~spl15_4),
% 5.40/1.13 inference(constrained_superposition,[],[f277,f685])).
% 5.40/1.13 thf(f3619,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__max @ X0 @ X1)) = ((c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $true @ X1 @ X0))) | (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true)) )),
% 5.40/1.13 inference(constrained_superposition,[],[f277,f276])).
% 5.40/1.13 thf(f3670,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__max @ X0 @ X1)) = X1) | (((c_2Eextreal_2Eextreal__le @ X1 @ X0)) = $true)) )),
% 5.40/1.13 inference(forward_demodulation,[],[f3619,f398])).
% 5.40/1.13 thf(f3675,plain,(
% 5.40/1.13 ( ! [X0 : tyop_2Eextreal_2Eextreal,X1 : tyop_2Eextreal_2Eextreal] : ((((c_2Eextreal_2Eextreal__max @ X0 @ X1)) = X1) | (((c_2Eextreal_2Eextreal__le @ X0 @ X1)) = $false)) ) | ~spl15_4),
% 5.40/1.13 inference(forward_demodulation,[],[f3614,f398])).
% 5.40/1.13 thf(f9343,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK13))) | ~spl15_1),
% 5.40/1.13 inference(constrained_superposition,[],[f671,f3670])).
% 5.40/1.13 thf(f9354,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | (~spl15_1 | ~spl15_2)),
% 5.40/1.13 inference(forward_subsumption_resolution,[],[f9343,f3606])).
% 5.40/1.13 thf(f9355,plain,(
% 5.40/1.13 $false | (~spl15_1 | ~spl15_2 | spl15_3)),
% 5.40/1.13 inference(forward_subsumption_resolution,[],[f9354,f679])).
% 5.40/1.13 thf(f9356,plain,(
% 5.40/1.13 ~spl15_1 | ~spl15_2 | spl15_3),
% 5.40/1.13 inference(avatar_contradiction_clause,[],[f9355])).
% 5.40/1.13 thf(f10091,plain,(
% 5.40/1.13 ($true != ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | ($false = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK14))) | (spl15_1 | ~spl15_4)),
% 5.40/1.13 inference(constrained_superposition,[],[f670,f3675])).
% 5.40/1.13 thf(f10108,plain,(
% 5.40/1.13 ($false = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK14))) | (spl15_1 | ~spl15_3 | ~spl15_4)),
% 5.40/1.13 inference(forward_subsumption_resolution,[],[f10091,f680])).
% 5.40/1.13 thf(f10110,definition,(
% 5.40/1.13 spl15_501 <=> ($false = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK14)))),
% 5.40/1.13 introduced(definition,[new_symbols(definition,[spl15_501])],[avatar_definition])).
% 5.40/1.13 thf(f10111,plain,(
% 5.40/1.13 ($false != ((c_2Eextreal_2Eextreal__le @ sK13 @ sK14))) | spl15_501),
% 5.40/1.13 inference(avatar_component_clause,[],[f10110])).
% 5.40/1.13 thf(f10112,plain,(
% 5.40/1.13 ($false = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK14))) | ~spl15_501),
% 5.40/1.13 inference(avatar_component_clause,[],[f10110])).
% 5.40/1.13 thf(f10114,plain,(
% 5.40/1.13 spl15_501 | spl15_1 | ~spl15_3 | ~spl15_4),
% 5.40/1.13 inference(avatar_split_clause,[],[f10108,f684,f678,f669,f10110])).
% 5.40/1.13 thf(f12338,plain,(
% 5.40/1.13 (((c_2Eextreal_2Eextreal__max @ sK13 @ sK14)) = ((c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $false @ sK14 @ sK13))) | ~spl15_501),
% 5.40/1.13 inference(constrained_superposition,[],[f277,f10112])).
% 5.40/1.13 thf(f12357,plain,(
% 5.40/1.13 (sK13 = ((c_2Eextreal_2Eextreal__max @ sK13 @ sK14))) | (~spl15_8 | ~spl15_501)),
% 5.40/1.13 inference(forward_demodulation,[],[f12338,f1563])).
% 5.40/1.13 thf(f13218,plain,(
% 5.40/1.13 ($true != ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | (spl15_1 | ~spl15_8 | ~spl15_501)),
% 5.40/1.13 inference(constrained_superposition,[],[f670,f12357])).
% 5.40/1.13 thf(f13241,plain,(
% 5.40/1.13 $false | (spl15_1 | ~spl15_2 | ~spl15_8 | ~spl15_501)),
% 5.40/1.13 inference(forward_subsumption_resolution,[],[f13218,f675])).
% 5.40/1.13 thf(f13242,plain,(
% 5.40/1.13 spl15_1 | ~spl15_2 | ~spl15_8 | ~spl15_501),
% 5.40/1.13 inference(avatar_contradiction_clause,[],[f13241])).
% 5.40/1.13 thf(f13250,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | (~spl15_1 | ~spl15_8 | ~spl15_501)),
% 5.40/1.13 inference(forward_demodulation,[],[f671,f12357])).
% 5.40/1.13 thf(f13261,plain,(
% 5.40/1.13 spl15_2 | ~spl15_1 | ~spl15_8 | ~spl15_501),
% 5.40/1.13 inference(avatar_split_clause,[],[f13250,f10110,f713,f669,f673])).
% 5.40/1.13 thf(f13290,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | ($false = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK14))) | (~spl15_1 | ~spl15_4)),
% 5.40/1.13 inference(constrained_superposition,[],[f671,f3675])).
% 5.40/1.13 thf(f22492,plain,(
% 5.40/1.13 ($false != $false) | ($true = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | (~spl15_3 | ~spl15_4 | spl15_501)),
% 5.40/1.13 inference(constrained_superposition,[],[f10111,f3613])).
% 5.40/1.13 thf(f22493,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK13 @ sK12))) | (~spl15_3 | ~spl15_4 | spl15_501)),
% 5.40/1.13 inference(trivial_inequality_removal,[],[f22492])).
% 5.40/1.13 thf(f22524,plain,(
% 5.40/1.13 $false | (spl15_2 | ~spl15_3 | ~spl15_4 | spl15_501)),
% 5.40/1.13 inference(forward_subsumption_resolution,[],[f22493,f674])).
% 5.40/1.13 thf(f22525,plain,(
% 5.40/1.13 spl15_2 | ~spl15_3 | ~spl15_4 | spl15_501),
% 5.40/1.13 inference(avatar_contradiction_clause,[],[f22524])).
% 5.40/1.13 thf(f22557,plain,(
% 5.40/1.13 ($true = ((c_2Eextreal_2Eextreal__le @ sK14 @ sK12))) | (~spl15_1 | ~spl15_4 | spl15_501)),
% 5.40/1.13 inference(forward_subsumption_resolution,[],[f13290,f10111])).
% 5.40/1.13 thf(f22560,plain,(
% 5.40/1.13 spl15_3 | ~spl15_1 | ~spl15_4 | spl15_501),
% 5.40/1.13 inference(avatar_split_clause,[],[f22557,f10110,f684,f669,f678])).
% 5.40/1.13 cnf(s1, plain, spl15_1 | spl15_2, inference(sat_conversion,[],[f676])).
% 5.40/1.13 cnf(s2, plain, spl15_1 | spl15_3, inference(sat_conversion,[],[f681])).
% 5.40/1.13 cnf(s3, plain, ~spl15_1 | ~spl15_2 | ~spl15_3, inference(sat_conversion,[],[f682])).
% 5.40/1.13 cnf(s24, plain, spl15_6 | spl15_8, inference(sat_conversion,[],[f719])).
% 5.40/1.13 cnf(s38, plain, spl15_4 | spl15_6, inference(sat_conversion,[],[f726])).
% 5.40/1.13 cnf(s74, plain, ~spl15_6, inference(sat_conversion,[],[f1004])).
% 5.40/1.13 cnf(s1014, plain, ~spl15_1 | ~spl15_2 | spl15_3, inference(sat_conversion,[],[f9356])).
% 5.40/1.13 cnf(s1086, plain, spl15_1 | ~spl15_3 | ~spl15_4 | spl15_501, inference(sat_conversion,[],[f10114])).
% 5.40/1.13 cnf(s1529, plain, spl15_1 | ~spl15_2 | ~spl15_8 | ~spl15_501, inference(sat_conversion,[],[f13242])).
% 5.40/1.13 cnf(s1531, plain, ~spl15_1 | spl15_2 | ~spl15_8 | ~spl15_501, inference(sat_conversion,[],[f13261])).
% 5.40/1.13 cnf(s2537, plain, spl15_2 | ~spl15_3 | ~spl15_4 | spl15_501, inference(sat_conversion,[],[f22525])).
% 5.40/1.13 cnf(s2549, plain, ~spl15_1 | spl15_3 | ~spl15_4 | spl15_501, inference(sat_conversion,[],[f22560])).
% 5.40/1.13 cnf(s2873, plain, spl15_4, inference(rat,[],[s38,s74])).
% 5.40/1.13 cnf(s3146, plain, spl15_8, inference(rat,[],[s24,s74])).
% 5.40/1.13 cnf(s3161, plain, spl15_1, inference(rat,[],[s1086,s1529,s1,s2,s2873,s3146])).
% 5.40/1.13 cnf(s3166, plain, spl15_2, inference(rat,[],[s2537,s2549,s1531,s2873,s3161,s3146])).
% 5.40/1.13 cnf(s3167, plain, spl15_3, inference(rat,[],[s1014,s3161,s3166])).
% 5.40/1.13 cnf(s3174, plain, $false, inference(rat,[],[s3,s3161,s3167,s3166])).
% 5.40/1.13 thf(f22561,plain,(
% 5.40/1.13 $false),
% 5.40/1.13 inference(avatar_sat_refutation,[],[s3174])).
% 5.40/1.13 % SZS output end Proof for theBenchmark
% 5.40/1.13 % (539048)------------------------------
% 5.40/1.13 % (539048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.40/1.13 % (539048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/1.13 % (539048)CaDiCaL version: 2.1.3
% 5.40/1.13 % (539048)Termination reason: Refutation
% 5.40/1.13 % (539048)Time elapsed: 0.861 s
% 5.40/1.13 % (539048)Peak memory usage: 22 MB
% 5.40/1.13 % (539048)Instructions burned: 1538 (million)
% 5.40/1.13 % (539042)Success in time 0.898 s
% 5.40/1.13 % Vampire exiting
%------------------------------------------------------------------------------