%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP149^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:10:53 AM UTC 2026
% Result : Theorem 14.55s 2.38s
% Output : Refutation 14.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP149^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n015.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 20:05:30 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.54/1.09 % (4046762)Will run a generic schedule for satisfiability detection.
% 5.54/1.09 % (4046769)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1667305962:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.54/1.09 % (4046768)% WARNING: option uhcvi not known.
% 5.54/1.09 % (4046767)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4015453376_2999 on theBenchmark for (2999ds/0Mi)
% 5.54/1.09 % (4046768)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=842269677:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.54/1.09 % (4046770)dis+10_1_sil=32000:sp=arity:random_seed=4208757946:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.54/1.09 % (4046771)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1580486405:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.54/1.09 % (4046772)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=511214897:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.54/1.09 % (4046773)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=34817320:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.54/1.09 % (4046768)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.54/1.09 % (4046771)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.54/1.09 % Exception at run slice level
% 5.54/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.54/1.09 % (4046768)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.54/1.09 % (4046770)Instruction limit reached!
% 5.54/1.09 % (4046770)------------------------------
% 5.54/1.09 % (4046770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.09 % (4046770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.09 % (4046770)CaDiCaL version: 2.1.3
% 5.54/1.09 % (4046770)Termination reason: Instruction limit
% 5.54/1.09 % (4046770)Termination phase: Saturation
% 5.54/1.09 % (4046770)Time elapsed: 0.045 s
% 5.54/1.09 % (4046770)Peak memory usage: 12 MB
% 5.54/1.09 % (4046770)Instructions burned: 103 (million)
% 5.54/1.09 % (4046781)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=16849570:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.54/1.09 % (4046771)Instruction limit reached!
% 5.54/1.09 % (4046771)------------------------------
% 5.54/1.09 % (4046771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.09 % (4046771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.09 % (4046771)CaDiCaL version: 2.1.3
% 5.54/1.09 % (4046771)Termination reason: Instruction limit
% 5.54/1.09 % (4046771)Termination phase: Saturation
% 5.54/1.09 % (4046771)Time elapsed: 0.052 s
% 5.54/1.09 % (4046771)Peak memory usage: 13 MB
% 5.54/1.09 % (4046771)Instructions burned: 118 (million)
% 5.54/1.09 % (4046772)Instruction limit reached!
% 5.54/1.09 % (4046772)------------------------------
% 5.54/1.09 % (4046772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.09 % (4046772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.09 % (4046772)CaDiCaL version: 2.1.3
% 5.54/1.09 % (4046772)Termination reason: Instruction limit
% 5.54/1.09 % (4046772)Termination phase: Saturation
% 5.54/1.09 % (4046772)Time elapsed: 0.062 s
% 5.54/1.09 % (4046772)Peak memory usage: 13 MB
% 5.54/1.09 % (4046772)Instructions burned: 131 (million)
% 5.54/1.09 % (4046782)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3035422230:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.54/1.09 % (4046784)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=2614016051:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.54/1.09 % (4046773)Instruction limit reached!
% 5.54/1.09 % (4046773)------------------------------
% 5.54/1.09 % (4046773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.09 % (4046773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.09 % (4046773)CaDiCaL version: 2.1.3
% 5.54/1.09 % (4046773)Termination reason: Instruction limit
% 5.54/1.09 % (4046773)Termination phase: Saturation
% 5.54/1.09 % (4046773)Time elapsed: 0.073 s
% 5.54/1.09 % (4046773)Peak memory usage: 13 MB
% 5.54/1.09 % (4046773)Instructions burned: 159 (million)
% 14.55/2.38 % (4046785)ott-21_1_sil=16000:fs=off:random_seed=2367072501:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046784)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.55/2.38 % (4046788)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1224295465:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 14.55/2.38 % (4046790)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2393428193:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 14.55/2.38 % (4046784)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.55/2.38 % (4046782)Instruction limit reached!
% 14.55/2.38 % (4046782)------------------------------
% 14.55/2.38 % (4046782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046782)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046782)Termination reason: Instruction limit
% 14.55/2.38 % (4046782)Termination phase: Saturation
% 14.55/2.38 % (4046782)Time elapsed: 0.062 s
% 14.55/2.38 % (4046782)Peak memory usage: 13 MB
% 14.55/2.38 % (4046782)Instructions burned: 132 (million)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046793)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1255767935:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 14.55/2.38 % (4046794)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3009395074:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 14.55/2.38 % (4046785)Instruction limit reached!
% 14.55/2.38 % (4046785)------------------------------
% 14.55/2.38 % (4046785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046785)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046785)Termination reason: Instruction limit
% 14.55/2.38 % (4046785)Termination phase: Saturation
% 14.55/2.38 % (4046785)Time elapsed: 0.085 s
% 14.55/2.38 % (4046785)Peak memory usage: 13 MB
% 14.55/2.38 % (4046785)Instructions burned: 180 (million)
% 14.55/2.38 % (4046797)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=457749004: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)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046797)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.55/2.38 % (4046799)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3213532664:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 14.55/2.38 % (4046799)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.55/2.38 % (4046788)Instruction limit reached!
% 14.55/2.38 % (4046788)------------------------------
% 14.55/2.38 % (4046788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046788)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046788)Termination reason: Instruction limit
% 14.55/2.38 % (4046788)Termination phase: Saturation
% 14.55/2.38 % (4046788)Time elapsed: 0.270 s
% 14.55/2.38 % (4046788)Peak memory usage: 14 MB
% 14.55/2.38 % (4046788)Instructions burned: 478 (million)
% 14.55/2.38 % (4046801)fmb+10_1_sil=64000:random_seed=3119856879:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 14.55/2.38 % (4046801)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 14.55/2.38 % (4046784)Instruction limit reached!
% 14.55/2.38 % (4046784)------------------------------
% 14.55/2.38 % (4046784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046784)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046784)Termination reason: Instruction limit
% 14.55/2.38 % (4046784)Termination phase: Saturation
% 14.55/2.38 % (4046784)Time elapsed: 0.339 s
% 14.55/2.38 % (4046784)Peak memory usage: 15 MB
% 14.55/2.38 % (4046784)Instructions burned: 684 (million)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046803)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2381104920:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 14.55/2.38 % (4046804)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1427575294:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046807)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=299611928:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 14.55/2.38 % (4046808)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3648421377:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 14.55/2.38 % (4046807)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.55/2.38 % (4046808)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 14.55/2.38 % (4046808)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.55/2.38 % (4046797)Instruction limit reached!
% 14.55/2.38 % (4046797)------------------------------
% 14.55/2.38 % (4046797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046797)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046797)Termination reason: Instruction limit
% 14.55/2.38 % (4046797)Termination phase: Saturation
% 14.55/2.38 % (4046797)Time elapsed: 0.369 s
% 14.55/2.38 % (4046797)Peak memory usage: 16 MB
% 14.55/2.38 % (4046797)Instructions burned: 694 (million)
% 14.55/2.38 % (4046811)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3496073535:i=6324_2993 on theBenchmark for (2993ds/6324Mi)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046813)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1525028777:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 14.55/2.38 % (4046799)Instruction limit reached!
% 14.55/2.38 % (4046799)------------------------------
% 14.55/2.38 % (4046799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046799)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046799)Termination reason: Instruction limit
% 14.55/2.38 % (4046799)Termination phase: Saturation
% 14.55/2.38 % (4046799)Time elapsed: 0.448 s
% 14.55/2.38 % (4046799)Peak memory usage: 17 MB
% 14.55/2.38 % (4046799)Instructions burned: 879 (million)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046815)ott-2_1_sil=16000:newcnf=on:random_seed=3354970821:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 14.55/2.38 % (4046816)ott+10_1_sil=32000:tgt=ground:random_seed=1938701009:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 14.55/2.38 % (4046815)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.55/2.38 % (4046793)Instruction limit reached!
% 14.55/2.38 % (4046793)------------------------------
% 14.55/2.38 % (4046793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046793)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046793)Termination reason: Instruction limit
% 14.55/2.38 % (4046793)Termination phase: Saturation
% 14.55/2.38 % (4046793)Time elapsed: 0.606 s
% 14.55/2.38 % (4046793)Peak memory usage: 20 MB
% 14.55/2.38 % (4046793)Instructions burned: 1179 (million)
% 14.55/2.38 % (4046819)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4210627408:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 14.55/2.38 % Exception at run slice level
% 14.55/2.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.55/2.38 % (4046821)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2584973271:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 14.55/2.38 % (4046821)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.55/2.38 % (4046815)Instruction limit reached!
% 14.55/2.38 % (4046815)------------------------------
% 14.55/2.38 % (4046815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046815)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046815)Termination reason: Instruction limit
% 14.55/2.38 % (4046815)Termination phase: Saturation
% 14.55/2.38 % (4046815)Time elapsed: 0.401 s
% 14.55/2.38 % (4046815)Peak memory usage: 16 MB
% 14.55/2.38 % (4046815)Instructions burned: 870 (million)
% 14.55/2.38 % (4046823)dis+21_1_sil=32000:sas=cadical:random_seed=583118388:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 14.55/2.38 % (4046808)Instruction limit reached!
% 14.55/2.38 % (4046808)------------------------------
% 14.55/2.38 % (4046808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046808)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046808)Termination reason: Instruction limit
% 14.55/2.38 % (4046808)Termination phase: Saturation
% 14.55/2.38 % (4046808)Time elapsed: 0.738 s
% 14.55/2.38 % (4046808)Peak memory usage: 17 MB
% 14.55/2.38 % (4046808)Instructions burned: 1473 (million)
% 14.55/2.38 % (4046825)ott+11_1_sil=16000:gs=on:random_seed=4207817664:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 14.55/2.38 % (4046825)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.55/2.38 % (4046823) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4046762-4046823"...
% 14.55/2.38 % (4046823)...printing done.
% 14.55/2.38 % (4046823)Refutation found. Thanks to Tanya!
% 14.55/2.38 % SZS status Theorem for theBenchmark
% 14.55/2.38 % SZS output start Proof for theBenchmark
% 14.55/2.38 thf(type_def_5, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 14.55/2.38 thf(type_def_6, type, real: $tType).
% 14.55/2.38 thf(type_def_7, type, set: $tType > $tType).
% 14.55/2.38 thf(type_def_8, type, a: $tType).
% 14.55/2.38 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 14.55/2.38 thf(func_def_0, type, finite_finite: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_2, type, countable: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_4, type, minus: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_5, type, uminus: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_6, type, ord: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_8, type, group_add: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_11, type, ab_group_add: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_12, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_13, type, inner_real_inner: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_16, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_17, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_18, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_19, type, euclid925273238_space: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_20, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_21, type, topolo890362671_space: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_22, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_23, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_24, type, execut510477386_space: !>[X0: $tType]:($o)).
% 14.55/2.38 thf(func_def_25, type, elemen321786957_cball: !>[X0: $tType]:((X0 > real > set @ X0))).
% 14.55/2.38 thf(func_def_26, type, auto_l1112008849e_ivl0: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > set @ real))).
% 14.55/2.38 thf(func_def_27, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 14.55/2.38 thf(func_def_28, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 14.55/2.38 thf(func_def_29, type, zero_zero: !>[X0: $tType]:(X0)).
% 14.55/2.38 thf(func_def_30, type, initia826609931terval: (set @ real > $o)).
% 14.55/2.38 thf(func_def_31, type, inner_780170721_inner: !>[X0: $tType]:((X0 > X0 > real))).
% 14.55/2.38 thf(func_def_32, type, auto_ll_on_invariant: !>[X0: $tType]:(((X0 > X0) > set @ X0 > set @ X0 > $o))).
% 14.55/2.38 thf(func_def_33, type, line_closed_segment: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 14.55/2.38 thf(func_def_34, type, line_open_segment: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 14.55/2.38 thf(func_def_35, type, oDE_au1039603466rapped: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > set @ X0 > $o))).
% 14.55/2.38 thf(func_def_36, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 14.55/2.38 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 14.55/2.38 thf(func_def_38, type, top_top: !>[X0: $tType]:(X0)).
% 14.55/2.38 thf(func_def_39, type, period385816147_orbit: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > $o))).
% 14.55/2.38 thf(func_def_40, type, period1153813292period: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > real))).
% 14.55/2.38 thf(func_def_41, type, period862636932_orbit: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > $o))).
% 14.55/2.38 thf(func_def_42, type, poinca1750768982en_rot: !>[X0: $tType]:((X0 > X0))).
% 14.55/2.38 thf(func_def_43, type, poinca272511729egment: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > X0 > $o))).
% 14.55/2.38 thf(func_def_44, type, reacha1084862253ection: !>[X0: $tType]:(((X0 > X0) > set @ X0 > (X0 > real) > (X0 > bounde2145540817linfun @ X0 @ real) > set @ X0 > $o))).
% 14.55/2.38 thf(func_def_45, type, real_V2000881966t_dist: !>[X0: $tType]:((X0 > X0 > real))).
% 14.55/2.38 thf(func_def_46, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 14.55/2.38 thf(func_def_47, type, set_or331188842AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 14.55/2.38 thf(func_def_48, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 14.55/2.38 thf(func_def_49, type, x: set @ a).
% 14.55/2.38 thf(func_def_50, type, a2: a).
% 14.55/2.38 thf(func_def_51, type, b: a).
% 14.55/2.38 thf(func_def_52, type, d: real).
% 14.55/2.38 thf(func_def_53, type, f: (a > a)).
% 14.55/2.38 thf(func_def_54, type, s: a).
% 14.55/2.38 thf(func_def_55, type, thesis: $o).
% 14.55/2.38 thf(func_def_56, type, x2: a).
% 14.55/2.38 thf(func_def_57, type, z: a).
% 14.55/2.38 thf(func_def_61, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 14.55/2.38 thf(func_def_62, type, vNOT: ($o > $o)).
% 14.55/2.38 thf(func_def_63, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 14.55/2.38 thf(func_def_64, type, db0: !>[X0: $tType]:(X0)).
% 14.55/2.38 thf(func_def_65, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 14.55/2.38 thf(func_def_66, type, vAND: ($o > $o > $o)).
% 14.55/2.38 thf(func_def_67, type, vIMP: ($o > $o > $o)).
% 14.55/2.38 thf(func_def_68, type, db1: !>[X0: $tType]:(X0)).
% 14.55/2.38 thf(func_def_69, type, vOR: ($o > $o > $o)).
% 14.55/2.38 thf(func_def_70, type, db2: !>[X0: $tType]:(X0)).
% 14.55/2.38 thf(func_def_71, type, sP0: (a > a > $o)).
% 14.55/2.38 thf(func_def_72, type, sP1: (real > real > (real > real > $o) > $o)).
% 14.55/2.38 thf(func_def_73, type, sK2: a).
% 14.55/2.38 thf(func_def_74, type, sK3: real).
% 14.55/2.38 thf(func_def_75, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 14.55/2.38 thf(func_def_76, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 14.55/2.38 thf(func_def_77, type, sK6: (real > real > a)).
% 14.55/2.38 thf(func_def_78, type, sK7: (real > real > a)).
% 14.55/2.38 thf(func_def_79, type, sK8: (a > a)).
% 14.55/2.38 thf(func_def_80, type, sK9: (a > a)).
% 14.55/2.38 thf(func_def_81, type, sK10: (real > real > (real > real > $o) > real)).
% 14.55/2.38 thf(func_def_82, type, sK11: (real > real > real > (real > real > $o) > real)).
% 14.55/2.38 thf(func_def_83, type, sK12: (real > real > real > (real > real > $o) > real)).
% 14.55/2.38 thf(func_def_84, type, sK13: ((real > real > $o) > real)).
% 14.55/2.38 thf(func_def_85, type, sK14: ((real > real > $o) > real)).
% 14.55/2.38 thf(func_def_86, type, sK15: ((real > real > $o) > real)).
% 14.55/2.38 thf(func_def_87, type, sK16: !>[X0: $tType]:((X0 > real > X0))).
% 14.55/2.38 thf(func_def_88, type, sK17: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 14.55/2.38 thf(func_def_89, type, sK18: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 14.55/2.38 thf(func_def_90, type, sK19: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 14.55/2.38 thf(func_def_91, type, sK20: (a > real)).
% 14.55/2.38 thf(func_def_92, type, sK21: (a > real)).
% 14.55/2.38 thf(func_def_93, type, sK22: (a > real)).
% 14.55/2.38 thf(func_def_94, type, sK23: (a > real)).
% 14.55/2.38 thf(func_def_95, type, sK24: ((a > a) > set @ a > a)).
% 14.55/2.38 thf(func_def_96, type, sK25: ((a > a) > set @ a > a)).
% 14.55/2.38 thf(func_def_97, type, sK26: (a > real)).
% 14.55/2.38 thf(func_def_98, type, sK27: (a > real)).
% 14.55/2.38 thf(func_def_99, type, sK28: a).
% 14.55/2.38 thf(func_def_100, type, sK29: (real > real > a)).
% 14.55/2.38 thf(func_def_101, type, sK30: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 14.55/2.38 thf(func_def_102, type, sK31: (set @ a > a)).
% 14.55/2.38 thf(func_def_103, type, sK32: (set @ a > a)).
% 14.55/2.38 thf(func_def_104, type, sK33: (a > a > a)).
% 14.55/2.38 thf(func_def_105, type, sK34: !>[X0: $tType]:((X0 > X0))).
% 14.55/2.38 thf(func_def_107, type, sK36: a).
% 14.55/2.38 thf(func_def_108, type, db3: !>[X0: $tType]:(X0)).
% 14.55/2.38 thf(f1,axiom,(
% 14.55/2.38 (ord_less @ real @ zero_zero @ real @ d)),
% 14.55/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_d_I1_J)).
% 14.55/2.38 thf(f2,axiom,(
% 14.55/2.38 (member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))),
% 14.55/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062s_A_092_060in_062_Acball_Ax_Ad_092_060close_062)).
% 14.55/2.38 thf(f6,axiom,(
% 14.55/2.38 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => (ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))),
% 14.55/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062)).
% 14.55/2.38 thf(f9,axiom,(
% 14.55/2.38 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => ((((f @ X0)) != zero_zero @ a) & (member @ a @ X0 @ x) & (ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))))),
% 14.55/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_d_I2_J)).
% 14.55/2.38 thf(f320,conjecture,(
% 14.55/2.38 ? [X0 : real] : (? [X1 : real] : (! [X2 : a] : ((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0)) => (ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) & (ord_less @ real @ zero_zero @ real @ X1)) & (ord_less @ real @ zero_zero @ real @ X0))),
% 14.55/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 14.55/2.38 thf(f321,negated_conjecture,(
% 14.55/2.38 ~ ? [X0 : real] : (? [X1 : real] : (! [X2 : a] : ((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0)) => (ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) & (ord_less @ real @ zero_zero @ real @ X1)) & (ord_less @ real @ zero_zero @ real @ X0))),
% 14.55/2.38 inference(negated_conjecture,[status(cth)],[f320])).
% 14.55/2.38 thf(f322,plain,(
% 14.55/2.38 (ord_less @ real @ zero_zero @ real @ d)),
% 14.55/2.38 inference(rectify,[],[f1])).
% 14.55/2.38 thf(f323,plain,(
% 14.55/2.38 (((ord_less @ real @ zero_zero @ real @ d)) = $true)),
% 14.55/2.38 inference(fool_elimination,[],[f322])).
% 14.55/2.38 thf(f324,plain,(
% 14.55/2.38 (member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))),
% 14.55/2.38 inference(rectify,[],[f2])).
% 14.55/2.38 thf(f325,plain,(
% 14.55/2.38 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) = $true)),
% 14.55/2.38 inference(fool_elimination,[],[f324])).
% 14.55/2.38 thf(f328,plain,(
% 14.55/2.38 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => (ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))),
% 14.55/2.38 inference(rectify,[],[f6])).
% 14.55/2.38 thf(f329,plain,(
% 14.55/2.38 ! [X0 : a] : ((((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) = $true) => (((ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true))),
% 14.55/2.38 inference(fool_elimination,[],[f328])).
% 14.55/2.38 thf(f332,plain,(
% 14.55/2.38 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => ((((f @ X0)) != zero_zero @ a) & (member @ a @ X0 @ x) & (ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))))),
% 14.55/2.38 inference(rectify,[],[f9])).
% 14.55/2.38 thf(f333,plain,(
% 14.55/2.38 ! [X0 : a] : ((((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) = $true) => ((((f @ X0)) != zero_zero @ a) & (((member @ a @ X0 @ x)) = $true) & (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true)))),
% 14.55/2.38 inference(fool_elimination,[],[f332])).
% 14.55/2.38 thf(f920,plain,(
% 14.55/2.38 ~ ? [X0 : real] : (? [X1 : real] : (! [X2 : a] : ((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0)) => (ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) & (ord_less @ real @ zero_zero @ real @ X1)) & (ord_less @ real @ zero_zero @ real @ X0))),
% 14.55/2.38 inference(rectify,[],[f321])).
% 14.55/2.38 thf(f921,plain,(
% 14.55/2.38 ~ ? [X0 : real] : (? [X1 : real] : (! [X2 : a] : ((((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0))) = $true) => (((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true)) & (((ord_less @ real @ zero_zero @ real @ X1)) = $true)) & (((ord_less @ real @ zero_zero @ real @ X0)) = $true))),
% 14.55/2.38 inference(fool_elimination,[],[f920])).
% 14.55/2.38 thf(f937,plain,(
% 14.55/2.38 ! [X0 : a] : ((((ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true) | (((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true))),
% 14.55/2.38 inference(ennf_transformation,[],[f329])).
% 14.55/2.38 thf(f938,plain,(
% 14.55/2.38 ! [X0 : a] : (((((f @ X0)) != zero_zero @ a) & (((member @ a @ X0 @ x)) = $true) & (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true)) | (((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true))),
% 14.55/2.38 inference(ennf_transformation,[],[f333])).
% 14.55/2.38 thf(f1223,plain,(
% 14.55/2.38 ! [X0 : real] : (! [X1 : real] : (? [X2 : a] : ((((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) & (((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0))) = $true)) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true)) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true))),
% 14.55/2.38 inference(ennf_transformation,[],[f921])).
% 14.55/2.38 thf(f1252,plain,(
% 14.55/2.38 ! [X0 : real] : (! [X1 : real] : ((($true != ((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ (sK29 @ X1 @ X0)) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) & ($true = ((member @ a @ (sK29 @ X1 @ X0) @ (elemen321786957_cball @ a @ x2 @ X0))))) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true)) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true))),
% 14.55/2.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK4 @ X0 @ X2 @ X1)],[f1223])).
% 14.55/2.38 thf(f1253,plain,(
% 14.55/2.38 (((ord_less @ real @ zero_zero @ real @ d)) = $true)),
% 14.55/2.38 inference(cnf_transformation,[],[f323])).
% 14.55/2.38 thf(f1254,plain,(
% 14.55/2.38 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) = $true)),
% 14.55/2.38 inference(cnf_transformation,[],[f325])).
% 14.55/2.38 thf(f1258,plain,(
% 14.55/2.38 ( ! [X0 : a] : ((((ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true) | (((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true)) )),
% 14.55/2.38 inference(cnf_transformation,[],[f937])).
% 14.55/2.38 thf(f1261,plain,(
% 14.55/2.38 ( ! [X0 : a] : ((((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true) | (((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true)) )),
% 14.55/2.38 inference(cnf_transformation,[],[f938])).
% 14.55/2.38 thf(f1611,plain,(
% 14.55/2.38 ( ! [X0 : real,X1 : real] : (($true = ((member @ a @ (sK29 @ X1 @ X0) @ (elemen321786957_cball @ a @ x2 @ X0)))) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 14.55/2.38 inference(cnf_transformation,[],[f1252])).
% 14.55/2.38 thf(f1612,plain,(
% 14.55/2.38 ( ! [X0 : real,X1 : real] : (($true != ((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ (sK29 @ X1 @ X0)) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 14.55/2.38 inference(cnf_transformation,[],[f1252])).
% 14.55/2.38 thf(f1614,definition,(
% 14.55/2.38 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 14.55/2.38 introduced(theory,[fool_exhaustiveness_axiom])).
% 14.55/2.38 thf(f2024,plain,(
% 14.55/2.38 ( ! [X0 : real,X1 : real] : (($true != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true) | ($false = ((ord_less_eq @ real @ X0 @ (inner_780170721_inner @ a @ (f @ (sK29 @ X0 @ X1)) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))))) )),
% 14.55/2.38 inference(constrained_superposition,[],[f1612,f1614])).
% 14.55/2.38 thf(f2025,plain,(
% 14.55/2.38 ( ! [X0 : real,X1 : real] : (($false = ((ord_less_eq @ real @ X0 @ (inner_780170721_inner @ a @ (f @ (sK29 @ X0 @ X1)) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 14.55/2.38 inference(trivial_inequality_removal,[],[f2024])).
% 14.55/2.38 thf(f11520,plain,(
% 14.55/2.38 ( ! [X0 : real] : (($true = $false) | ($true != ((member @ a @ (sK29 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d)))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | ($true != ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))))) )),
% 14.55/2.38 inference(constrained_superposition,[],[f1258,f2025])).
% 14.55/2.38 thf(f11542,plain,(
% 14.55/2.38 ( ! [X0 : real] : (($true != ((member @ a @ (sK29 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d)))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | ($true != ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))))) )),
% 14.55/2.38 inference(trivial_inequality_removal,[],[f11520])).
% 14.55/2.38 thf(f11544,definition,(
% 14.55/2.38 spl35_278 <=> ! [X0 : real] : ((((ord_less @ real @ zero_zero @ real @ X0)) != $true) | ($true != ((member @ a @ (sK29 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d)))))),
% 14.55/2.38 introduced(definition,[new_symbols(definition,[spl35_278])],[avatar_definition])).
% 14.55/2.38 thf(f11545,plain,(
% 14.55/2.38 ( ! [X0 : real] : (($true != ((member @ a @ (sK29 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d)))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) ) | ~spl35_278),
% 14.55/2.38 inference(avatar_component_clause,[],[f11544])).
% 14.55/2.38 thf(f11547,definition,(
% 14.55/2.38 spl35_279 <=> ($true = ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))))),
% 14.55/2.38 introduced(definition,[new_symbols(definition,[spl35_279])],[avatar_definition])).
% 14.55/2.38 thf(f11548,plain,(
% 14.55/2.38 ($true = ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | ~spl35_279),
% 14.55/2.38 inference(avatar_component_clause,[],[f11547])).
% 14.55/2.38 thf(f11549,plain,(
% 14.55/2.38 ($true != ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | spl35_279),
% 14.55/2.38 inference(avatar_component_clause,[],[f11547])).
% 14.55/2.38 thf(f11553,plain,(
% 14.55/2.38 ~spl35_279 | spl35_278),
% 14.55/2.38 inference(avatar_split_clause,[],[f11542,f11544,f11547])).
% 14.55/2.38 thf(f13750,plain,(
% 14.55/2.38 ($true != $true) | (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | spl35_279),
% 14.55/2.38 inference(constrained_superposition,[],[f11549,f1261])).
% 14.55/2.38 thf(f13756,plain,(
% 14.55/2.38 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | spl35_279),
% 14.55/2.38 inference(trivial_inequality_removal,[],[f13750])).
% 14.55/2.38 thf(f13785,plain,(
% 14.55/2.38 $false | spl35_279),
% 14.55/2.38 inference(forward_subsumption_resolution,[],[f13756,f1254])).
% 14.55/2.38 thf(f13786,plain,(
% 14.55/2.38 spl35_279),
% 14.55/2.38 inference(avatar_contradiction_clause,[],[f13785])).
% 14.55/2.38 thf(f14016,plain,(
% 14.55/2.38 ($true != $true) | (((ord_less @ real @ zero_zero @ real @ d)) != $true) | ($true != ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | (((ord_less @ real @ zero_zero @ real @ d)) != $true) | ~spl35_278),
% 14.55/2.38 inference(constrained_superposition,[],[f11545,f1611])).
% 14.55/2.38 thf(f14021,plain,(
% 14.55/2.38 ($true != $true) | (((ord_less @ real @ zero_zero @ real @ d)) != $true) | ($true != ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | ~spl35_278),
% 14.55/2.38 inference(duplicate_literal_removal,[],[f14016])).
% 14.55/2.38 thf(f14022,plain,(
% 14.55/2.38 (((ord_less @ real @ zero_zero @ real @ d)) != $true) | ($true != ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | ~spl35_278),
% 14.55/2.38 inference(trivial_inequality_removal,[],[f14021])).
% 14.55/2.38 thf(f14028,plain,(
% 14.55/2.38 ($true != ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))) | ~spl35_278),
% 14.55/2.38 inference(forward_subsumption_resolution,[],[f14022,f1253])).
% 14.55/2.38 thf(f14029,plain,(
% 14.55/2.38 $false | (~spl35_278 | ~spl35_279)),
% 14.55/2.38 inference(forward_subsumption_resolution,[],[f14028,f11548])).
% 14.55/2.38 thf(f14030,plain,(
% 14.55/2.38 ~spl35_278 | ~spl35_279),
% 14.55/2.38 inference(avatar_contradiction_clause,[],[f14029])).
% 14.55/2.38 cnf(s631, plain, spl35_278 | ~spl35_279, inference(sat_conversion,[],[f11553])).
% 14.55/2.38 cnf(s748, plain, spl35_279, inference(sat_conversion,[],[f13786])).
% 14.55/2.38 cnf(s755, plain, ~spl35_278 | ~spl35_279, inference(sat_conversion,[],[f14030])).
% 14.55/2.38 cnf(s756, plain, ~spl35_278, inference(rat,[],[s755,s748])).
% 14.55/2.38 cnf(s838, plain, $false, inference(rat,[],[s631,s748,s756])).
% 14.55/2.38 thf(f14031,plain,(
% 14.55/2.38 $false),
% 14.55/2.38 inference(avatar_sat_refutation,[],[s838])).
% 14.55/2.38 % SZS output end Proof for theBenchmark
% 14.55/2.38 % (4046823)------------------------------
% 14.55/2.38 % (4046823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.55/2.38 % (4046823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.55/2.38 % (4046823)CaDiCaL version: 2.1.3
% 14.55/2.38 % (4046823)Termination reason: Refutation
% 14.55/2.38 % (4046823)Time elapsed: 0.992 s
% 14.55/2.38 % (4046823)Peak memory usage: 21 MB
% 14.55/2.38 % (4046823)Instructions burned: 1989 (million)
% 14.55/2.38 % (4046762)Success in time 2.147 s
% 14.55/2.38 % Vampire exiting
%------------------------------------------------------------------------------