%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP006^3 : 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 : n008.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 08:10:01 AM UTC 2026
% Result : Theorem 6.76s 1.23s
% Output : Refutation 6.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP006^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:23:29 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 4.08/0.98 % (3609040)Will run a generic schedule for satisfiability detection.
% 4.08/0.98 % (3609049)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=944945556:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.08/0.98 % (3609049)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.08/0.98 % (3609046)% WARNING: option uhcvi not known.
% 4.08/0.98 % (3609045)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3512889633_2999 on theBenchmark for (2999ds/0Mi)
% 4.08/0.98 % (3609046)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4007199641:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.08/0.98 % (3609047)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1937018371:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.08/0.98 % (3609048)dis+10_1_sil=32000:sp=arity:random_seed=1040549750:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.08/0.98 % (3609046)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.08/0.98 % Exception at run slice level
% 4.08/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.08/0.98 % (3609046)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.08/0.98 % (3609051)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=487632613:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.08/0.98 % (3609050)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1475087952:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.08/0.98 % (3609057)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3237525260:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.08/0.98 % (3609049)Instruction limit reached!
% 4.08/0.98 % (3609049)------------------------------
% 4.08/0.98 % (3609049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.98 % (3609049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.98 % (3609049)CaDiCaL version: 2.1.3
% 4.08/0.98 % (3609049)Termination reason: Instruction limit
% 4.08/0.98 % (3609049)Termination phase: Saturation
% 4.08/0.98 % (3609049)Time elapsed: 0.036 s
% 4.08/0.98 % (3609049)Peak memory usage: 13 MB
% 4.08/0.98 % (3609049)Instructions burned: 119 (million)
% 4.08/0.98 % Exception at run slice level
% 4.08/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.08/0.98 % (3609061)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=946416008:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.08/0.98 % (3609062)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=3965349647:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.08/0.98 % (3609062)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.08/0.98 % (3609048)Instruction limit reached!
% 4.08/0.98 % (3609048)------------------------------
% 4.08/0.98 % (3609048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.98 % (3609048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.98 % (3609048)CaDiCaL version: 2.1.3
% 4.08/0.98 % (3609048)Termination reason: Instruction limit
% 4.08/0.98 % (3609048)Termination phase: Saturation
% 4.08/0.98 % (3609048)Time elapsed: 0.057 s
% 4.08/0.98 % (3609048)Peak memory usage: 13 MB
% 4.08/0.98 % (3609048)Instructions burned: 103 (million)
% 4.08/0.98 % (3609062)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.08/0.98 % (3609065)ott-21_1_sil=16000:fs=off:random_seed=1286250063:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.08/0.98 % (3609061)Instruction limit reached!
% 4.08/0.98 % (3609061)------------------------------
% 4.08/0.98 % (3609061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.98 % (3609061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.98 % (3609061)CaDiCaL version: 2.1.3
% 4.08/0.98 % (3609061)Termination reason: Instruction limit
% 4.08/0.98 % (3609061)Termination phase: Saturation
% 4.08/0.98 % (3609061)Time elapsed: 0.037 s
% 4.08/0.98 % (3609061)Peak memory usage: 13 MB
% 4.08/0.98 % (3609061)Instructions burned: 133 (million)
% 4.08/0.98 % (3609050)Instruction limit reached!
% 6.76/1.23 % (3609050)------------------------------
% 6.76/1.23 % (3609050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609050)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609050)Termination reason: Instruction limit
% 6.76/1.23 % (3609050)Termination phase: Saturation
% 6.76/1.23 % (3609050)Time elapsed: 0.069 s
% 6.76/1.23 % (3609050)Peak memory usage: 13 MB
% 6.76/1.23 % (3609050)Instructions burned: 133 (million)
% 6.76/1.23 % (3609067)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=720394015:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.76/1.23 % (3609068)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1286365268:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % (3609071)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3153976889:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.76/1.23 % (3609051)Instruction limit reached!
% 6.76/1.23 % (3609051)------------------------------
% 6.76/1.23 % (3609051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609051)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609051)Termination reason: Instruction limit
% 6.76/1.23 % (3609051)Termination phase: Saturation
% 6.76/1.23 % (3609051)Time elapsed: 0.120 s
% 6.76/1.23 % (3609051)Peak memory usage: 13 MB
% 6.76/1.23 % (3609051)Instructions burned: 159 (million)
% 6.76/1.23 % (3609074)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3954721189:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % (3609065)Instruction limit reached!
% 6.76/1.23 % (3609065)------------------------------
% 6.76/1.23 % (3609065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609065)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609065)Termination reason: Instruction limit
% 6.76/1.23 % (3609065)Termination phase: Saturation
% 6.76/1.23 % (3609065)Time elapsed: 0.084 s
% 6.76/1.23 % (3609065)Peak memory usage: 13 MB
% 6.76/1.23 % (3609065)Instructions burned: 181 (million)
% 6.76/1.23 % (3609076)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=3012169241: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)
% 6.76/1.23 % (3609076)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.76/1.23 % (3609077)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3423358566:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 6.76/1.23 % (3609077)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.76/1.23 % (3609067)Instruction limit reached!
% 6.76/1.23 % (3609067)------------------------------
% 6.76/1.23 % (3609067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609067)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609067)Termination reason: Instruction limit
% 6.76/1.23 % (3609067)Termination phase: Saturation
% 6.76/1.23 % (3609067)Time elapsed: 0.138 s
% 6.76/1.23 % (3609067)Peak memory usage: 14 MB
% 6.76/1.23 % (3609067)Instructions burned: 481 (million)
% 6.76/1.23 % (3609080)fmb+10_1_sil=64000:random_seed=3870797332:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 6.76/1.23 % (3609080)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % (3609082)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2230003245:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % (3609084)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1272948803:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % (3609086)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2995553544:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 6.76/1.23 % (3609086)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.76/1.23 % (3609062)Instruction limit reached!
% 6.76/1.23 % (3609062)------------------------------
% 6.76/1.23 % (3609062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609062)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609062)Termination reason: Instruction limit
% 6.76/1.23 % (3609062)Termination phase: Saturation
% 6.76/1.23 % (3609062)Time elapsed: 0.330 s
% 6.76/1.23 % (3609062)Peak memory usage: 17 MB
% 6.76/1.23 % (3609062)Instructions burned: 686 (million)
% 6.76/1.23 % (3609088)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2517749896:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 6.76/1.23 % (3609088)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.76/1.23 % (3609088)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.76/1.23 % (3609077)Instruction limit reached!
% 6.76/1.23 % (3609077)------------------------------
% 6.76/1.23 % (3609077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609077)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609077)Termination reason: Instruction limit
% 6.76/1.23 % (3609077)Termination phase: Saturation
% 6.76/1.23 % (3609077)Time elapsed: 0.407 s
% 6.76/1.23 % (3609077)Peak memory usage: 19 MB
% 6.76/1.23 % (3609077)Instructions burned: 880 (million)
% 6.76/1.23 % (3609076)Instruction limit reached!
% 6.76/1.23 % (3609076)------------------------------
% 6.76/1.23 % (3609076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609076)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609076)Termination reason: Instruction limit
% 6.76/1.23 % (3609076)Termination phase: Saturation
% 6.76/1.23 % (3609076)Time elapsed: 0.411 s
% 6.76/1.23 % (3609076)Peak memory usage: 18 MB
% 6.76/1.23 % (3609076)Instructions burned: 692 (million)
% 6.76/1.23 % (3609090)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3661704199:i=6324_2993 on theBenchmark for (2993ds/6324Mi)
% 6.76/1.23 % (3609091)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3058169660:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % (3609094)ott-2_1_sil=16000:newcnf=on:random_seed=2781802737:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 6.76/1.23 % (3609095)ott+10_1_sil=32000:tgt=ground:random_seed=72362540:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.76/1.23 % (3609094)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.76/1.23 % (3609071)Instruction limit reached!
% 6.76/1.23 % (3609071)------------------------------
% 6.76/1.23 % (3609071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609071)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609071)Termination reason: Instruction limit
% 6.76/1.23 % (3609071)Termination phase: Saturation
% 6.76/1.23 % (3609071)Time elapsed: 0.553 s
% 6.76/1.23 % (3609071)Peak memory usage: 19 MB
% 6.76/1.23 % (3609071)Instructions burned: 1180 (million)
% 6.76/1.23 % (3609098)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3747097677:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 6.76/1.23 % Exception at run slice level
% 6.76/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.23 % (3609100)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1497425267:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 6.76/1.23 % (3609100)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.76/1.23 % (3609086) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3609040-3609086"...
% 6.76/1.23 % (3609086)...printing done.
% 6.76/1.23 % (3609086)Refutation found. Thanks to Tanya!
% 6.76/1.23 % SZS status Theorem for theBenchmark
% 6.76/1.23 % SZS output start Proof for theBenchmark
% 6.76/1.23 thf(type_def_5, type, tyop_2Emin_2Ebool: $tType).
% 6.76/1.23 thf(type_def_6, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 6.76/1.23 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 6.76/1.23 thf(type_def_8, type, sK20: $tType).
% 6.76/1.23 thf(type_def_9, type, sK21: $tType).
% 6.76/1.23 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.76/1.23 thf(func_def_1, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 6.76/1.23 thf(func_def_2, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.76/1.23 thf(func_def_3, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 6.76/1.23 thf(func_def_4, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.76/1.23 thf(func_def_5, type, c_2Ebool_2EF: $o).
% 6.76/1.23 thf(func_def_6, type, c_2EquantHeuristics_2EGUESS__EXISTS: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > $o))).
% 6.76/1.23 thf(func_def_7, type, c_2EquantHeuristics_2EGUESS__EXISTS__GAP: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > $o))).
% 6.76/1.23 thf(func_def_8, type, c_2EquantHeuristics_2EGUESS__EXISTS__POINT: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > $o))).
% 6.76/1.23 thf(func_def_9, type, c_2EquantHeuristics_2EGUESS__FORALL: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > $o))).
% 6.76/1.23 thf(func_def_10, type, c_2EquantHeuristics_2EGUESS__FORALL__GAP: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > $o))).
% 6.76/1.23 thf(func_def_11, type, c_2EquantHeuristics_2EGUESS__FORALL__POINT: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > $o))).
% 6.76/1.23 thf(func_def_12, type, c_2Ebool_2ET: $o).
% 6.76/1.23 thf(func_def_13, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 6.76/1.23 thf(func_def_14, type, c_2Ebool_2E_7E: ($o > $o)).
% 6.76/1.23 thf(func_def_16, type, vNOT: ($o > $o)).
% 6.76/1.23 thf(func_def_19, type, vOR: ($o > $o > $o)).
% 6.76/1.23 thf(func_def_20, type, vIMP: ($o > $o > $o)).
% 6.76/1.23 thf(func_def_21, type, sP0: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_22, type, sP1: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_23, type, sP2: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_24, type, sP3: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_25, type, sP4: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_26, type, sP5: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_27, type, sP6: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_28, type, sP7: ($o > $o > $o > $o)).
% 6.76/1.23 thf(func_def_29, type, sK8: !>[X0: $tType]:(((X0 > $o) > X0))).
% 6.76/1.23 thf(func_def_30, type, sK9: !>[X0: $tType]:(((X0 > $o) > X0))).
% 6.76/1.23 thf(func_def_31, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X1))).
% 6.76/1.23 thf(func_def_32, type, sK11: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 6.76/1.23 thf(func_def_33, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X1))).
% 6.76/1.23 thf(func_def_34, type, sK13: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 6.76/1.23 thf(func_def_35, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X0))).
% 6.76/1.23 thf(func_def_36, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X0))).
% 6.76/1.23 thf(func_def_37, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X1))).
% 6.76/1.23 thf(func_def_38, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X0))).
% 6.76/1.23 thf(func_def_39, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X1))).
% 6.76/1.23 thf(func_def_40, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > X0))).
% 6.76/1.23 thf(func_def_41, type, sK22: (sK21 > sK20)).
% 6.76/1.23 thf(func_def_42, type, sK23: (sK20 > $o)).
% 6.76/1.23 thf(func_def_43, type, sK24: (sK20 > $o)).
% 6.76/1.23 thf(func_def_44, type, db0: !>[X0: $tType]:(X0)).
% 6.76/1.23 thf(func_def_45, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.76/1.23 thf(func_def_46, type, db1: !>[X0: $tType]:(X0)).
% 6.76/1.23 thf(func_def_47, type, sK25: !>[X0: $tType]:((X0 > (X0 > sK20 > sK20) > sK20))).
% 6.76/1.23 thf(func_def_48, type, sK26: !>[X0: $tType]:(((X0 > sK21 > sK20) > X0 > sK21))).
% 6.76/1.23 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 6.76/1.23 thf(func_def_50, type, sK27: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > sK21 > sK20) > X1))).
% 6.76/1.23 thf(func_def_51, type, db3: !>[X0: $tType]:(X0)).
% 6.76/1.23 thf(func_def_52, type, sK28: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > sK20 > $o) > X1))).
% 6.76/1.23 thf(func_def_53, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1 > $o) > X0 > X2))).
% 6.76/1.23 thf(func_def_54, type, db5: !>[X0: $tType]:(X0)).
% 6.76/1.23 thf(func_def_55, type, db4: !>[X0: $tType]:(X0)).
% 6.76/1.23 thf(func_def_56, type, sK30: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > sK20 > $o) > sK20))).
% 6.76/1.23 thf(func_def_57, type, sK31: !>[X0: $tType]:(((X0 > $o > sK20 > $o) > X0 > sK20))).
% 6.76/1.23 thf(func_def_58, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1 > $o) > X0 > X1))).
% 6.76/1.23 thf(func_def_59, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2 > X0 > $o) > X1 > X2))).
% 6.76/1.23 thf(func_def_60, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2 > X0 > $o) > X1 > X2))).
% 6.76/1.23 thf(func_def_61, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X1 > X3 > X0 > $o) > X1 > X3))).
% 6.76/1.23 thf(func_def_62, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X1 > X3 > X0 > $o) > X1 > X3))).
% 6.76/1.23 thf(func_def_63, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.76/1.23 thf(f15,axiom,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X18 : (X0 > X1),X19 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X18 @ X19) <=> ! [X20 : X1] : ((~ (X19 @ X20)) => ? [X21 : X0] : (X20 = ((X18 @ X21))))) & ! [X14 : (X0 > X1),X15 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X14 @ X15) <=> ! [X16 : X1] : ((X15 @ X16) => ? [X17 : X0] : (X16 = ((X14 @ X17))))) & ! [X11 : (X0 > X1),X12 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X11 @ X12) <=> ! [X13 : X0] : (~ (X12 @ (X11 @ X13)))) & ! [X8 : (X0 > X1),X9 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X8 @ X9) <=> ! [X10 : X0] : (X9 @ (X8 @ X10))) & ((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3) <=> ! [X6 : X1] : ((~ (X3 @ X6)) => ? [X7 : X0] : (~ (X3 @ (X2 @ X7))))) & ((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3) <=> ! [X4 : X1] : ((X3 @ X4) => ? [X5 : X0] : (X3 @ (X2 @ X5)))))),
% 6.76/1.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES)).
% 6.76/1.23 thf(f27,conjecture,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X0),X3 : (X0 > $o),X4 : (X0 > $o)] : (! [X5 : X0] : ((X4 @ X5) => (X3 @ X5)) => ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X3) => (c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X4)))),
% 6.76/1.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT)).
% 6.76/1.23 thf(f28,negated_conjecture,(
% 6.76/1.23 ~ ! [X0 : $tType,X1 : $tType,X2 : (X1 > X0),X3 : (X0 > $o),X4 : (X0 > $o)] : (! [X5 : X0] : ((X4 @ X5) => (X3 @ X5)) => ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X3) => (c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X4)))),
% 6.76/1.23 inference(negated_conjecture,[status(cth)],[f27])).
% 6.76/1.23 thf(f55,plain,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X4 : (X0 > X1),X5 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5) <=> ! [X6 : X1] : ((~ (X5 @ X6)) => ? [X7 : X0] : (((X4 @ X7)) = X6))) & ! [X8 : (X0 > X1),X9 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X8 @ X9) <=> ! [X10 : X1] : ((X9 @ X10) => ? [X11 : X0] : (((X8 @ X11)) = X10))) & ! [X12 : (X0 > X1),X13 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X12 @ X13) <=> ! [X14 : X0] : (~ (X13 @ (X12 @ X14)))) & ! [X15 : (X0 > X1),X16 : (X1 > $o)] : ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X15 @ X16) <=> ! [X17 : X0] : (X16 @ (X15 @ X17))) & ((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3) <=> ! [X18 : X1] : ((~ (X3 @ X18)) => ? [X19 : X0] : (~ (X3 @ (X2 @ X19))))) & ((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3) <=> ! [X20 : X1] : ((X3 @ X20) => ? [X21 : X0] : (X3 @ (X2 @ X21)))))),
% 6.76/1.23 inference(rectify,[],[f15])).
% 6.76/1.23 thf(f56,plain,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X4 : (X0 > X1),X5 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))) <=> ! [X6 : X1] : (($true = ((~ (X5 @ X6)))) => ? [X7 : X0] : (((X4 @ X7)) = X6))) & ! [X8 : (X0 > X1),X9 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X8 @ X9))) <=> ! [X10 : X1] : (($true = ((X9 @ X10))) => ? [X11 : X0] : (((X8 @ X11)) = X10))) & ! [X12 : (X0 > X1),X13 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X12 @ X13))) <=> ! [X14 : X0] : ($true = ((~ (X13 @ (X12 @ X14)))))) & ! [X15 : (X0 > X1),X16 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X15 @ X16))) <=> ! [X17 : X0] : ($true = ((X16 @ (X15 @ X17))))) & ((((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) = $true) <=> ! [X18 : X1] : (($true = ((~ (X3 @ X18)))) => ? [X19 : X0] : ($true = ((~ (X3 @ (X2 @ X19))))))) & ((((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) = $true) <=> ! [X20 : X1] : (($true = ((X3 @ X20))) => ? [X21 : X0] : ($true = ((X3 @ (X2 @ X21)))))))),
% 6.76/1.23 inference(fool_elimination,[],[f55])).
% 6.76/1.23 thf(f79,plain,(
% 6.76/1.23 ~ ! [X0 : $tType,X1 : $tType,X2 : (X1 > X0),X3 : (X0 > $o),X4 : (X0 > $o)] : (! [X5 : X0] : ((X4 @ X5) => (X3 @ X5)) => ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X3) => (c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X4)))),
% 6.76/1.23 inference(rectify,[],[f28])).
% 6.76/1.23 thf(f80,plain,(
% 6.76/1.23 ~ ! [X0 : $tType,X1 : $tType,X2 : (X1 > X0),X3 : (X0 > $o),X4 : (X0 > $o)] : (! [X5 : X0] : ((((X4 @ X5)) = $true) => (((X3 @ X5)) = $true)) => ((((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X3)) = $true) => (((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X4)) = $true)))),
% 6.76/1.23 inference(fool_elimination,[],[f79])).
% 6.76/1.23 thf(f87,plain,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X4 : (X0 > X1),X5 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))) <=> ! [X6 : X1] : (? [X7 : X0] : (((X4 @ X7)) = X6) | ($true != ((~ (X5 @ X6)))))) & ! [X8 : (X0 > X1),X9 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X8 @ X9))) <=> ! [X10 : X1] : (? [X11 : X0] : (((X8 @ X11)) = X10) | ($true != ((X9 @ X10))))) & ! [X12 : (X0 > X1),X13 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X12 @ X13))) <=> ! [X14 : X0] : ($true = ((~ (X13 @ (X12 @ X14)))))) & ! [X15 : (X0 > X1),X16 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X15 @ X16))) <=> ! [X17 : X0] : ($true = ((X16 @ (X15 @ X17))))) & ((((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) = $true) <=> ! [X18 : X1] : (? [X19 : X0] : ($true = ((~ (X3 @ (X2 @ X19))))) | ($true != ((~ (X3 @ X18)))))) & ((((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) = $true) <=> ! [X20 : X1] : (? [X21 : X0] : ($true = ((X3 @ (X2 @ X21)))) | ($true != ((X3 @ X20))))))),
% 6.76/1.23 inference(ennf_transformation,[],[f56])).
% 6.76/1.23 thf(f99,plain,(
% 6.76/1.23 ? [X0 : $tType,X1 : $tType,X2 : (X1 > X0),X3 : (X0 > $o),X4 : (X0 > $o)] : (((((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X4)) != $true) & (((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X3)) = $true)) & ! [X5 : X0] : ((((X3 @ X5)) = $true) | (((X4 @ X5)) != $true)))),
% 6.76/1.23 inference(ennf_transformation,[],[f80])).
% 6.76/1.23 thf(f100,plain,(
% 6.76/1.23 ? [X0 : $tType,X1 : $tType,X2 : (X1 > X0),X3 : (X0 > $o),X4 : (X0 > $o)] : ((((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X4)) != $true) & (((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X0 @ X2 @ X3)) = $true) & ! [X5 : X0] : ((((X3 @ X5)) = $true) | (((X4 @ X5)) != $true)))),
% 6.76/1.23 inference(flattening,[],[f99])).
% 6.76/1.23 thf(f134,plain,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X4 : (X0 > X1),X5 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))) | ? [X6 : X1] : (! [X7 : X0] : (((X4 @ X7)) != X6) & ($true = ((~ (X5 @ X6)))))) & (! [X6 : X1] : (? [X7 : X0] : (((X4 @ X7)) = X6) | ($true != ((~ (X5 @ X6))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))))) & ! [X8 : (X0 > X1),X9 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X8 @ X9))) | ? [X10 : X1] : (! [X11 : X0] : (((X8 @ X11)) != X10) & ($true = ((X9 @ X10))))) & (! [X10 : X1] : (? [X11 : X0] : (((X8 @ X11)) = X10) | ($true != ((X9 @ X10)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X8 @ X9))))) & ! [X12 : (X0 > X1),X13 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X12 @ X13))) | ? [X14 : X0] : ($true != ((~ (X13 @ (X12 @ X14)))))) & (! [X14 : X0] : ($true = ((~ (X13 @ (X12 @ X14))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X12 @ X13))))) & ! [X15 : (X0 > X1),X16 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X15 @ X16))) | ? [X17 : X0] : ($true != ((X16 @ (X15 @ X17))))) & (! [X17 : X0] : ($true = ((X16 @ (X15 @ X17)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X15 @ X16))))) & (((((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) = $true) | ? [X18 : X1] : (! [X19 : X0] : ($true != ((~ (X3 @ (X2 @ X19))))) & ($true = ((~ (X3 @ X18)))))) & (! [X18 : X1] : (? [X19 : X0] : ($true = ((~ (X3 @ (X2 @ X19))))) | ($true != ((~ (X3 @ X18))))) | (((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) != $true))) & (((((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) = $true) | ? [X20 : X1] : (! [X21 : X0] : ($true != ((X3 @ (X2 @ X21)))) & ($true = ((X3 @ X20))))) & (! [X20 : X1] : (? [X21 : X0] : ($true = ((X3 @ (X2 @ X21)))) | ($true != ((X3 @ X20)))) | (((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) != $true))))),
% 6.76/1.23 inference(nnf_transformation,[],[f87])).
% 6.76/1.23 thf(f135,plain,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X4 : (X0 > X1),X5 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))) | ? [X6 : X1] : (! [X7 : X0] : (((X4 @ X7)) != X6) & ($true = ((~ (X5 @ X6)))))) & (! [X6 : X1] : (? [X7 : X0] : (((X4 @ X7)) = X6) | ($true != ((~ (X5 @ X6))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))))) & ! [X8 : (X0 > X1),X9 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X8 @ X9))) | ? [X10 : X1] : (! [X11 : X0] : (((X8 @ X11)) != X10) & ($true = ((X9 @ X10))))) & (! [X10 : X1] : (? [X11 : X0] : (((X8 @ X11)) = X10) | ($true != ((X9 @ X10)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X8 @ X9))))) & ! [X12 : (X0 > X1),X13 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X12 @ X13))) | ? [X14 : X0] : ($true != ((~ (X13 @ (X12 @ X14)))))) & (! [X14 : X0] : ($true = ((~ (X13 @ (X12 @ X14))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X12 @ X13))))) & ! [X15 : (X0 > X1),X16 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X15 @ X16))) | ? [X17 : X0] : ($true != ((X16 @ (X15 @ X17))))) & (! [X17 : X0] : ($true = ((X16 @ (X15 @ X17)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X15 @ X16))))) & ((((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) = $true) | ? [X18 : X1] : (! [X19 : X0] : ($true != ((~ (X3 @ (X2 @ X19))))) & ($true = ((~ (X3 @ X18)))))) & (! [X18 : X1] : (? [X19 : X0] : ($true = ((~ (X3 @ (X2 @ X19))))) | ($true != ((~ (X3 @ X18))))) | (((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) != $true)) & ((((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) = $true) | ? [X20 : X1] : (! [X21 : X0] : ($true != ((X3 @ (X2 @ X21)))) & ($true = ((X3 @ X20))))) & (! [X20 : X1] : (? [X21 : X0] : ($true = ((X3 @ (X2 @ X21)))) | ($true != ((X3 @ X20)))) | (((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) != $true)))),
% 6.76/1.23 inference(flattening,[],[f134])).
% 6.76/1.23 thf(f136,plain,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X4 : (X0 > X1),X5 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))) | ? [X6 : X1] : (! [X7 : X0] : (((X4 @ X7)) != X6) & ($true = ((~ (X5 @ X6)))))) & (! [X8 : X1] : (? [X9 : X0] : (((X4 @ X9)) = X8) | ($true != ((~ (X5 @ X8))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))))) & ! [X10 : (X0 > X1),X11 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X10 @ X11))) | ? [X12 : X1] : (! [X13 : X0] : (((X10 @ X13)) != X12) & ($true = ((X11 @ X12))))) & (! [X14 : X1] : (? [X15 : X0] : (((X10 @ X15)) = X14) | ($true != ((X11 @ X14)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X10 @ X11))))) & ! [X16 : (X0 > X1),X17 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17))) | ? [X18 : X0] : ($true != ((~ (X17 @ (X16 @ X18)))))) & (! [X19 : X0] : ($true = ((~ (X17 @ (X16 @ X19))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17))))) & ! [X20 : (X0 > X1),X21 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X20 @ X21))) | ? [X22 : X0] : ($true != ((X21 @ (X20 @ X22))))) & (! [X23 : X0] : ($true = ((X21 @ (X20 @ X23)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X20 @ X21))))) & ((((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) = $true) | ? [X24 : X1] : (! [X25 : X0] : ($true != ((~ (X3 @ (X2 @ X25))))) & ($true = ((~ (X3 @ X24)))))) & (! [X26 : X1] : (? [X27 : X0] : ($true = ((~ (X3 @ (X2 @ X27))))) | ($true != ((~ (X3 @ X26))))) | (((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) != $true)) & ((((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) = $true) | ? [X28 : X1] : (! [X29 : X0] : ($true != ((X3 @ (X2 @ X29)))) & ($true = ((X3 @ X28))))) & (! [X30 : X1] : (? [X31 : X0] : ($true = ((X3 @ (X2 @ X31)))) | ($true != ((X3 @ X30)))) | (((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) != $true)))),
% 6.76/1.23 inference(rectify,[],[f135])).
% 6.76/1.23 thf(f137,plain,(
% 6.76/1.23 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o)] : (! [X4 : (X0 > X1),X5 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))) | (! [X7 : X0] : (((X4 @ X7)) != ((sK10 @ X0 @ X1 @ X5 @ X4))) & ($true = ((~ (X5 @ (sK10 @ X0 @ X1 @ X5 @ X4))))))) & (! [X8 : X1] : ((((X4 @ (sK11 @ X0 @ X1 @ X8 @ X4))) = X8) | ($true != ((~ (X5 @ X8))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X0 @ X1 @ X4 @ X5))))) & ! [X10 : (X0 > X1),X11 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X10 @ X11))) | (! [X13 : X0] : (((X10 @ X13)) != ((sK12 @ X0 @ X1 @ X11 @ X10))) & ($true = ((X11 @ (sK12 @ X0 @ X1 @ X11 @ X10)))))) & (! [X14 : X1] : ((((X10 @ (sK13 @ X0 @ X1 @ X14 @ X10))) = X14) | ($true != ((X11 @ X14)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X0 @ X1 @ X10 @ X11))))) & ! [X16 : (X0 > X1),X17 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17))) | ($true != ((~ (X17 @ (X16 @ (sK14 @ X0 @ X1 @ X17 @ X16))))))) & (! [X19 : X0] : ($true = ((~ (X17 @ (X16 @ X19))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17))))) & ! [X20 : (X0 > X1),X21 : (X1 > $o)] : ((($true = ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X20 @ X21))) | ($true != ((X21 @ (X20 @ (sK15 @ X0 @ X1 @ X21 @ X20)))))) & (! [X23 : X0] : ($true = ((X21 @ (X20 @ X23)))) | ($true != ((c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X0 @ X1 @ X20 @ X21))))) & ((((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) = $true) | (! [X25 : X0] : ($true != ((~ (X3 @ (X2 @ X25))))) & ($true = ((~ (X3 @ (sK16 @ X0 @ X1 @ X3 @ X2))))))) & (! [X26 : X1] : (($true = ((~ (X3 @ (X2 @ (sK17 @ X0 @ X1 @ X3 @ X2)))))) | ($true != ((~ (X3 @ X26))))) | (((c_2EquantHeuristics_2EGUESS__FORALL @ X0 @ X1 @ X2 @ X3)) != $true)) & ((((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) = $true) | (! [X29 : X0] : ($true != ((X3 @ (X2 @ X29)))) & ($true = ((X3 @ (sK18 @ X0 @ X1 @ X3 @ X2)))))) & (! [X30 : X1] : (($true = ((X3 @ (X2 @ (sK19 @ X0 @ X1 @ X3 @ X2))))) | ($true != ((X3 @ X30)))) | (((c_2EquantHeuristics_2EGUESS__EXISTS @ X0 @ X1 @ X2 @ X3)) != $true)))),
% 6.76/1.23 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1),skolemize(X2,sK8 @ X0 @ X1)],[f136])).
% 6.76/1.23 thf(f172,plain,(
% 6.76/1.23 ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ sK21 @ sK20 @ sK22 @ sK24))) & ($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ sK21 @ sK20 @ sK22 @ sK23))) & ! [X5 : sK20] : (($true = ((sK23 @ X5))) | ($true != ((sK24 @ X5))))),
% 6.76/1.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24)],[f100])).
% 6.76/1.23 thf(f240,plain,(
% 6.76/1.23 ( ! [X1 : $tType,X0 : $tType,X19 : X0,X16 : (X0 > X1),X17 : (X1 > $o)] : (($true = ((~ (X17 @ (X16 @ X19))))) | ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17)))) )),
% 6.76/1.23 inference(cnf_transformation,[],[f137])).
% 6.76/1.23 thf(f241,plain,(
% 6.76/1.23 ( ! [X1 : $tType,X0 : $tType,X16 : (X0 > X1),X17 : (X1 > $o)] : (($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17))) | ($true != ((~ (X17 @ (X16 @ (sK14 @ X0 @ X1 @ X17 @ X16))))))) )),
% 6.76/1.23 inference(cnf_transformation,[],[f137])).
% 6.76/1.23 thf(f331,plain,(
% 6.76/1.23 ( ! [X5 : sK20] : (($true != ((sK24 @ X5))) | ($true = ((sK23 @ X5)))) )),
% 6.76/1.23 inference(cnf_transformation,[],[f172])).
% 6.76/1.23 thf(f332,plain,(
% 6.76/1.23 ($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ sK21 @ sK20 @ sK22 @ sK23)))),
% 6.76/1.23 inference(cnf_transformation,[],[f172])).
% 6.76/1.23 thf(f333,plain,(
% 6.76/1.23 ($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ sK21 @ sK20 @ sK22 @ sK24)))),
% 6.76/1.23 inference(cnf_transformation,[],[f172])).
% 6.76/1.23 thf(f568,plain,(
% 6.76/1.23 ( ! [X1 : $tType,X0 : $tType,X19 : X0,X16 : (X0 > X1),X17 : (X1 > $o)] : (($true != ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17))) | (((X17 @ (X16 @ X19))) = $false)) )),
% 6.76/1.23 inference(not_proxy_clausification,[],[f240])).
% 6.76/1.23 thf(f569,plain,(
% 6.76/1.23 ( ! [X1 : $tType,X0 : $tType,X16 : (X0 > X1),X17 : (X1 > $o)] : (($true = ((X17 @ (X16 @ (sK14 @ X0 @ X1 @ X17 @ X16))))) | ($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X0 @ X1 @ X16 @ X17)))) )),
% 6.76/1.23 inference(not_proxy_clausification,[],[f241])).
% 6.76/1.23 thf(f6461,plain,(
% 6.76/1.23 ( ! [X0 : sK21] : (($true != $true) | ($false = ((sK23 @ (sK22 @ X0))))) )),
% 6.76/1.23 inference(constrained_superposition,[],[f568,f332])).
% 6.76/1.23 thf(f6463,plain,(
% 6.76/1.23 ( ! [X0 : sK21] : (($false = ((sK23 @ (sK22 @ X0))))) )),
% 6.76/1.23 inference(trivial_inequality_removal,[],[f6461])).
% 6.76/1.23 thf(f14733,plain,(
% 6.76/1.23 ( ! [X1 : $tType,X3 : $tType,X2 : (X1 > sK20),X0 : sK20,X4 : (X3 > X1)] : (($true != $true) | ($true = ((sK23 @ X0))) | ($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X3 @ X1 @ X4 @ (^[Y0 : X1]: (sK24 @ (X2 @ Y0)))))) | (((X2 @ (X4 @ (sK14 @ X3 @ X1 @ (^[Y0 : X1]: (sK24 @ (X2 @ Y0))) @ X4)))) != X0)) )),
% 6.76/1.23 inference(constrained_superposition,[],[f331,f569])).
% 6.76/1.23 thf(f14774,plain,(
% 6.76/1.23 ( ! [X1 : $tType,X3 : $tType,X2 : (X1 > sK20),X0 : sK20,X4 : (X3 > X1)] : (($true = ((sK23 @ X0))) | ($true = ((c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X3 @ X1 @ X4 @ (^[Y0 : X1]: (sK24 @ (X2 @ Y0)))))) | (((X2 @ (X4 @ (sK14 @ X3 @ X1 @ (^[Y0 : X1]: (sK24 @ (X2 @ Y0))) @ X4)))) != X0)) )),
% 6.76/1.23 inference(trivial_inequality_removal,[],[f14733])).
% 6.76/1.23 thf(f19363,plain,(
% 6.76/1.23 ( ! [X0 : sK20] : (($true != $true) | ($true = ((sK23 @ X0))) | ((((^[Y0 : sK20]: (Y0)) @ (sK22 @ (sK14 @ sK21 @ sK20 @ (^[Y0 : sK20]: (sK24 @ ((^[Y1 : sK20]: (Y1)) @ Y0))) @ sK22)))) != X0)) )),
% 6.76/1.23 inference(constrained_superposition,[],[f333,f14774])).
% 6.76/1.23 thf(f19381,plain,(
% 6.76/1.23 ( ! [X0 : sK20] : (($true = ((sK23 @ X0))) | ((((^[Y0 : sK20]: (Y0)) @ (sK22 @ (sK14 @ sK21 @ sK20 @ (^[Y0 : sK20]: (sK24 @ ((^[Y1 : sK20]: (Y1)) @ Y0))) @ sK22)))) != X0)) )),
% 6.76/1.23 inference(trivial_inequality_removal,[],[f19363])).
% 6.76/1.23 thf(f19382,plain,(
% 6.76/1.23 ( ! [X0 : sK20] : ((((sK22 @ (sK14 @ sK21 @ sK20 @ sK24 @ sK22))) != X0) | ($true = ((sK23 @ X0)))) )),
% 6.76/1.23 inference(beta-eta_normalization,[],[f19381])).
% 6.76/1.23 thf(f19434,plain,(
% 6.76/1.23 ($true = ((sK23 @ (sK22 @ (sK14 @ sK21 @ sK20 @ sK24 @ sK22)))))),
% 6.76/1.23 inference(equality_resolution,[],[f19382])).
% 6.76/1.23 thf(f19435,plain,(
% 6.76/1.23 ($true = $false)),
% 6.76/1.23 inference(forward_demodulation,[],[f19434,f6463])).
% 6.76/1.23 thf(f19436,plain,(
% 6.76/1.23 $false),
% 6.76/1.23 inference(trivial_inequality_removal,[],[f19435])).
% 6.76/1.23 % SZS output end Proof for theBenchmark
% 6.76/1.23 % (3609086)------------------------------
% 6.76/1.23 % (3609086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.23 % (3609086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.23 % (3609086)CaDiCaL version: 2.1.3
% 6.76/1.23 % (3609086)Termination reason: Refutation
% 6.76/1.23 % (3609086)Time elapsed: 0.643 s
% 6.76/1.23 % (3609086)Peak memory usage: 21 MB
% 6.76/1.23 % (3609086)Instructions burned: 2055 (million)
% 6.76/1.23 % (3609040)Success in time 0.991 s
% 6.76/1.23 % Vampire exiting
%------------------------------------------------------------------------------