%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV174^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:39:06 AM UTC 2026
% Result : Theorem 10.02s 1.81s
% Output : Refutation 10.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV174^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n016.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 15:23:19 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 5.80/1.12 % (479078)Will run a generic schedule for satisfiability detection.
% 5.80/1.12 % (479087)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2509539562:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.80/1.12 % (479087)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.80/1.12 % (479084)% WARNING: option uhcvi not known.
% 5.80/1.12 % (479084)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=83079143:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.80/1.12 % (479083)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=247281414_2999 on theBenchmark for (2999ds/0Mi)
% 5.80/1.12 % (479085)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1442239251:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.80/1.12 % (479086)dis+10_1_sil=32000:sp=arity:random_seed=137147556:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.80/1.12 % (479084)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.80/1.12 % (479084)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.80/1.12 % Exception at run slice level
% 5.80/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.80/1.12 % (479089)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3208903613:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.80/1.12 % (479088)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2296947512:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.80/1.12 % (479095)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2120599146:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.80/1.12 % Exception at run slice level
% 5.80/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.80/1.12 % (479087)Instruction limit reached!
% 5.80/1.12 % (479087)------------------------------
% 5.80/1.12 % (479087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.12 % (479087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.12 % (479087)CaDiCaL version: 2.1.3
% 5.80/1.12 % (479087)Termination reason: Instruction limit
% 5.80/1.12 % (479087)Termination phase: Saturation
% 5.80/1.12 % (479087)Time elapsed: 0.034 s
% 5.80/1.12 % (479087)Peak memory usage: 12 MB
% 5.80/1.12 % (479087)Instructions burned: 120 (million)
% 5.80/1.12 % (479100)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=984977747:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.80/1.12 % (479100)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.80/1.12 % (479100)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.80/1.12 % (479099)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1994364700:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.80/1.12 % (479086)Instruction limit reached!
% 5.80/1.12 % (479086)------------------------------
% 5.80/1.12 % (479086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.12 % (479086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.12 % (479086)CaDiCaL version: 2.1.3
% 5.80/1.12 % (479086)Termination reason: Instruction limit
% 5.80/1.12 % (479086)Termination phase: Saturation
% 5.80/1.12 % (479086)Time elapsed: 0.054 s
% 5.80/1.12 % (479086)Peak memory usage: 12 MB
% 5.80/1.12 % (479086)Instructions burned: 104 (million)
% 5.80/1.12 % (479103)ott-21_1_sil=16000:fs=off:random_seed=2585110642:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 5.80/1.12 % (479088)Instruction limit reached!
% 5.80/1.12 % (479088)------------------------------
% 5.80/1.12 % (479088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.12 % (479088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.12 % (479088)CaDiCaL version: 2.1.3
% 5.80/1.12 % (479088)Termination reason: Instruction limit
% 5.80/1.12 % (479088)Termination phase: Saturation
% 5.80/1.12 % (479088)Time elapsed: 0.070 s
% 5.80/1.12 % (479088)Peak memory usage: 13 MB
% 5.80/1.12 % (479088)Instructions burned: 131 (million)
% 5.80/1.12 % (479105)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3049914369:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 10.02/1.81 % (479089)Instruction limit reached!
% 10.02/1.81 % (479089)------------------------------
% 10.02/1.81 % (479089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479089)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479089)Termination reason: Instruction limit
% 10.02/1.81 % (479089)Termination phase: Saturation
% 10.02/1.81 % (479089)Time elapsed: 0.106 s
% 10.02/1.81 % (479089)Peak memory usage: 12 MB
% 10.02/1.81 % (479089)Instructions burned: 159 (million)
% 10.02/1.81 % (479099)Instruction limit reached!
% 10.02/1.81 % (479099)------------------------------
% 10.02/1.81 % (479099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479099)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479099)Termination reason: Instruction limit
% 10.02/1.81 % (479099)Termination phase: Saturation
% 10.02/1.81 % (479099)Time elapsed: 0.080 s
% 10.02/1.81 % (479099)Peak memory usage: 12 MB
% 10.02/1.81 % (479099)Instructions burned: 132 (million)
% 10.02/1.81 % (479111)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1828737186:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479117)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3628108278:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 10.02/1.81 % (479121)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1297894031:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479103)Instruction limit reached!
% 10.02/1.81 % (479103)------------------------------
% 10.02/1.81 % (479103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479103)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479103)Termination reason: Instruction limit
% 10.02/1.81 % (479103)Termination phase: Saturation
% 10.02/1.81 % (479103)Time elapsed: 0.090 s
% 10.02/1.81 % (479103)Peak memory usage: 12 MB
% 10.02/1.81 % (479103)Instructions burned: 181 (million)
% 10.02/1.81 % (479129)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=132104586: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)
% 10.02/1.81 % (479129)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.02/1.81 % (479133)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1095728741:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 10.02/1.81 % (479133)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.02/1.81 % (479100)Instruction limit reached!
% 10.02/1.81 % (479100)------------------------------
% 10.02/1.81 % (479100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479100)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479100)Termination reason: Instruction limit
% 10.02/1.81 % (479100)Termination phase: Saturation
% 10.02/1.81 % (479100)Time elapsed: 0.180 s
% 10.02/1.81 % (479100)Peak memory usage: 14 MB
% 10.02/1.81 % (479100)Instructions burned: 687 (million)
% 10.02/1.81 % (479158)fmb+10_1_sil=64000:random_seed=1167128601:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 10.02/1.81 % (479158)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479165)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2487731836:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479174)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1064444524:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479183)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=448597584:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 10.02/1.81 % (479183)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.02/1.81 % (479105)Instruction limit reached!
% 10.02/1.81 % (479105)------------------------------
% 10.02/1.81 % (479105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479105)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479105)Termination reason: Instruction limit
% 10.02/1.81 % (479105)Termination phase: Saturation
% 10.02/1.81 % (479105)Time elapsed: 0.247 s
% 10.02/1.81 % (479105)Peak memory usage: 14 MB
% 10.02/1.81 % (479105)Instructions burned: 479 (million)
% 10.02/1.81 % (479205)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=329057589:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 10.02/1.81 % (479205)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.02/1.81 % (479205)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.02/1.81 % (479129)Instruction limit reached!
% 10.02/1.81 % (479129)------------------------------
% 10.02/1.81 % (479129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479129)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479129)Termination reason: Instruction limit
% 10.02/1.81 % (479129)Termination phase: Saturation
% 10.02/1.81 % (479129)Time elapsed: 0.328 s
% 10.02/1.81 % (479129)Peak memory usage: 15 MB
% 10.02/1.81 % (479129)Instructions burned: 694 (million)
% 10.02/1.81 % (479237)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=409967512:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479241)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4220155683:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479248)ott-2_1_sil=16000:newcnf=on:random_seed=3654477332:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 10.02/1.81 % (479248)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.02/1.81 % (479133)Instruction limit reached!
% 10.02/1.81 % (479133)------------------------------
% 10.02/1.81 % (479133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479133)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479133)Termination reason: Instruction limit
% 10.02/1.81 % (479133)Termination phase: Saturation
% 10.02/1.81 % (479133)Time elapsed: 0.535 s
% 10.02/1.81 % (479133)Peak memory usage: 16 MB
% 10.02/1.81 % (479133)Instructions burned: 879 (million)
% 10.02/1.81 % (479283)ott+10_1_sil=32000:tgt=ground:random_seed=2910153246:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 10.02/1.81 % (479117)Instruction limit reached!
% 10.02/1.81 % (479117)------------------------------
% 10.02/1.81 % (479117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479117)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479117)Termination reason: Instruction limit
% 10.02/1.81 % (479117)Termination phase: Saturation
% 10.02/1.81 % (479117)Time elapsed: 0.651 s
% 10.02/1.81 % (479117)Peak memory usage: 16 MB
% 10.02/1.81 % (479117)Instructions burned: 1181 (million)
% 10.02/1.81 % (479290)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1432676562:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 10.02/1.81 % Exception at run slice level
% 10.02/1.81 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.02/1.81 % (479295)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2919490830:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 10.02/1.81 % (479295)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.02/1.81 % (479248)Instruction limit reached!
% 10.02/1.81 % (479248)------------------------------
% 10.02/1.81 % (479248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479248)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479248)Termination reason: Instruction limit
% 10.02/1.81 % (479248)Termination phase: Saturation
% 10.02/1.81 % (479248)Time elapsed: 0.708 s
% 10.02/1.81 % (479248)Peak memory usage: 14 MB
% 10.02/1.81 % (479248)Instructions burned: 870 (million)
% 10.02/1.81 % (479313)dis+21_1_sil=32000:sas=cadical:random_seed=1423957809:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 10.02/1.81 % (479205)Instruction limit reached!
% 10.02/1.81 % (479205)------------------------------
% 10.02/1.81 % (479205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.81 % (479205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.81 % (479205)CaDiCaL version: 2.1.3
% 10.02/1.81 % (479205)Termination reason: Instruction limit
% 10.02/1.81 % (479205)Termination phase: Saturation
% 10.02/1.81 % (479205)Time elapsed: 1.059 s
% 10.02/1.81 % (479205)Peak memory usage: 17 MB
% 10.02/1.81 % (479205)Instructions burned: 1472 (million)
% 10.02/1.81 % (479315)ott+11_1_sil=16000:gs=on:random_seed=3174560193:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2985 on theBenchmark for (2985ds/2251Mi)
% 10.02/1.81 % (479315)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.02/1.81 % (479315) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-479078-479315"...
% 10.02/1.81 % (479315)...printing done.
% 10.02/1.81 % (479315)Refutation found. Thanks to Tanya!
% 10.02/1.81 % SZS status Theorem for theBenchmark
% 10.02/1.81 % SZS output start Proof for theBenchmark
% 10.02/1.81 thf(type_def_5, type, a: $tType).
% 10.02/1.81 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 10.02/1.81 thf(func_def_0, type, cP: ((a > $o) > $o)).
% 10.02/1.81 thf(func_def_4, type, sP0: (a > $o)).
% 10.02/1.81 thf(func_def_5, type, sP1: ((a > $o) > (a > $o) > $o)).
% 10.02/1.81 thf(func_def_6, type, sP2: ((a > $o) > $o)).
% 10.02/1.81 thf(func_def_7, type, sP3: $o).
% 10.02/1.81 thf(func_def_8, type, sK4: (a > $o)).
% 10.02/1.81 thf(func_def_9, type, sK5: (a > $o)).
% 10.02/1.81 thf(func_def_10, type, sK6: ((a > $o) > a)).
% 10.02/1.81 thf(func_def_11, type, sK7: ((a > $o) > (a > $o) > a)).
% 10.02/1.81 thf(func_def_12, type, sK8: (a > a > $o)).
% 10.02/1.81 thf(func_def_13, type, sK9: (a > $o)).
% 10.02/1.81 thf(func_def_14, type, sK10: ((a > $o) > a)).
% 10.02/1.81 thf(func_def_15, type, vNOT: ($o > $o)).
% 10.02/1.81 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 10.02/1.81 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 10.02/1.81 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 10.02/1.81 thf(func_def_20, type, sK12: a).
% 10.02/1.81 thf(func_def_21, type, sK13: a).
% 10.02/1.81 thf(f1,conjecture,(
% 10.02/1.81 (! [X2 : a,X0 : (a > $o),X3 : (a > $o)] : (((X3 @ X2) & (X0 @ X2) & (cP @ X3) & (cP @ X0)) => (X0 = X3)) & ! [X0 : (a > $o)] : ((cP @ X0) => ? [X1 : a] : (X0 @ X1))) => ? [X4 : (a > $o)] : (! [X7 : (a > $o),X8 : (a > $o)] : ((? [X2 : a] : ((X8 @ X2) & (X7 @ X2)) & (cP @ X8) & (cP @ X7)) => (X7 = X8)) & ! [X2 : a] : ((X4 @ X2) <=> ? [X6 : (a > $o)] : ((X6 @ X2) & (cP @ X6))) & ! [X5 : (a > $o)] : ((cP @ X5) => ? [X2 : a] : (X5 @ X2)))),
% 10.02/1.81 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM555_pme)).
% 10.02/1.81 thf(f2,negated_conjecture,(
% 10.02/1.81 ~((! [X2 : a,X0 : (a > $o),X3 : (a > $o)] : (((X3 @ X2) & (X0 @ X2) & (cP @ X3) & (cP @ X0)) => (X0 = X3)) & ! [X0 : (a > $o)] : ((cP @ X0) => ? [X1 : a] : (X0 @ X1))) => ? [X4 : (a > $o)] : (! [X7 : (a > $o),X8 : (a > $o)] : ((? [X2 : a] : ((X8 @ X2) & (X7 @ X2)) & (cP @ X8) & (cP @ X7)) => (X7 = X8)) & ! [X2 : a] : ((X4 @ X2) <=> ? [X6 : (a > $o)] : ((X6 @ X2) & (cP @ X6))) & ! [X5 : (a > $o)] : ((cP @ X5) => ? [X2 : a] : (X5 @ X2))))),
% 10.02/1.81 inference(negated_conjecture,[status(cth)],[f1])).
% 10.02/1.81 thf(f3,plain,(
% 10.02/1.81 ~((! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : (((X2 @ X0) & (X1 @ X0) & (cP @ X2) & (cP @ X1)) => (X1 = X2)) & ! [X3 : (a > $o)] : ((cP @ X3) => ? [X4 : a] : (X3 @ X4))) => ? [X5 : (a > $o)] : (! [X6 : (a > $o),X7 : (a > $o)] : ((? [X8 : a] : ((X7 @ X8) & (X6 @ X8)) & (cP @ X7) & (cP @ X6)) => (X6 = X7)) & ! [X9 : a] : ((X5 @ X9) <=> ? [X10 : (a > $o)] : ((X10 @ X9) & (cP @ X10))) & ! [X11 : (a > $o)] : ((cP @ X11) => ? [X12 : a] : (X11 @ X12))))),
% 10.02/1.81 inference(rectify,[],[f2])).
% 10.02/1.81 thf(f4,plain,(
% 10.02/1.81 ~((! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : (((((X2 @ X0)) = $true) & (((X1 @ X0)) = $true) & (((cP @ X2)) = $true) & (((cP @ X1)) = $true)) => (X1 = X2)) & ! [X3 : (a > $o)] : ((((cP @ X3)) = $true) => ? [X4 : a] : (((X3 @ X4)) = $true))) => ? [X5 : (a > $o)] : (! [X6 : (a > $o),X7 : (a > $o)] : ((? [X8 : a] : ((((X7 @ X8)) = $true) & (((X6 @ X8)) = $true)) & (((cP @ X7)) = $true) & (((cP @ X6)) = $true)) => (X6 = X7)) & ! [X9 : a] : ((((X5 @ X9)) = $true) <=> ? [X10 : (a > $o)] : ((((X10 @ X9)) = $true) & (((cP @ X10)) = $true))) & ! [X11 : (a > $o)] : ((((cP @ X11)) = $true) => ? [X12 : a] : (((X11 @ X12)) = $true))))),
% 10.02/1.81 inference(fool_elimination,[],[f3])).
% 10.02/1.81 thf(f5,plain,(
% 10.02/1.81 ! [X5 : (a > $o)] : (? [X6 : (a > $o),X7 : (a > $o)] : ((X6 != X7) & (? [X8 : a] : ((((X7 @ X8)) = $true) & (((X6 @ X8)) = $true)) & (((cP @ X7)) = $true) & (((cP @ X6)) = $true))) | ? [X9 : a] : ((((X5 @ X9)) = $true) <~> ? [X10 : (a > $o)] : ((((X10 @ X9)) = $true) & (((cP @ X10)) = $true))) | ? [X11 : (a > $o)] : (! [X12 : a] : (((X11 @ X12)) != $true) & (((cP @ X11)) = $true))) & (! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((X1 = X2) | ((((X2 @ X0)) != $true) | (((X1 @ X0)) != $true) | (((cP @ X2)) != $true) | (((cP @ X1)) != $true))) & ! [X3 : (a > $o)] : (? [X4 : a] : (((X3 @ X4)) = $true) | (((cP @ X3)) != $true)))),
% 10.02/1.81 inference(ennf_transformation,[],[f4])).
% 10.02/1.81 thf(f6,plain,(
% 10.02/1.81 ! [X5 : (a > $o)] : (? [X6 : (a > $o),X7 : (a > $o)] : ((X6 != X7) & ? [X8 : a] : ((((X7 @ X8)) = $true) & (((X6 @ X8)) = $true)) & (((cP @ X7)) = $true) & (((cP @ X6)) = $true)) | ? [X9 : a] : ((((X5 @ X9)) = $true) <~> ? [X10 : (a > $o)] : ((((X10 @ X9)) = $true) & (((cP @ X10)) = $true))) | ? [X11 : (a > $o)] : (! [X12 : a] : (((X11 @ X12)) != $true) & (((cP @ X11)) = $true))) & ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((X1 = X2) | (((X2 @ X0)) != $true) | (((X1 @ X0)) != $true) | (((cP @ X2)) != $true) | (((cP @ X1)) != $true)) & ! [X3 : (a > $o)] : (? [X4 : a] : (((X3 @ X4)) = $true) | (((cP @ X3)) != $true))),
% 10.02/1.81 inference(flattening,[],[f5])).
% 10.02/1.81 thf(f7,definition,(
% 10.02/1.81 ! [X9 : a] : (($true = ((sP0 @ X9))) <=> ? [X10 : (a > $o)] : ((((X10 @ X9)) = $true) & (((cP @ X10)) = $true)))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 10.02/1.81 thf(f8,definition,(
% 10.02/1.81 ! [X7 : (a > $o),X6 : (a > $o)] : (? [X8 : a] : ((((X7 @ X8)) = $true) & (((X6 @ X8)) = $true)) | ~ ($true = ((sP1 @ X6 @ X7))))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 10.02/1.81 thf(f9,definition,(
% 10.02/1.81 ! [X5 : (a > $o)] : (? [X9 : a] : ((((X5 @ X9)) = $true) <~> ($true = ((sP0 @ X9)))) | ~ ($true = ((sP2 @ X5))))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 10.02/1.81 thf(f10,definition,(
% 10.02/1.81 ? [X6 : (a > $o),X7 : (a > $o)] : ((X6 != X7) & ($true = ((sP1 @ X6 @ X7))) & (((cP @ X7)) = $true) & (((cP @ X6)) = $true)) | ~ ($true = sP3)),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 10.02/1.81 thf(f11,plain,(
% 10.02/1.81 ! [X5 : (a > $o)] : (($true = sP3) | ($true = ((sP2 @ X5))) | ? [X11 : (a > $o)] : (! [X12 : a] : (((X11 @ X12)) != $true) & (((cP @ X11)) = $true))) & ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((X1 = X2) | (((X2 @ X0)) != $true) | (((X1 @ X0)) != $true) | (((cP @ X2)) != $true) | (((cP @ X1)) != $true)) & ! [X3 : (a > $o)] : (? [X4 : a] : (((X3 @ X4)) = $true) | (((cP @ X3)) != $true))),
% 10.02/1.81 inference(definition_folding,[],[f6,f10,f9,f8,f7])).
% 10.02/1.81 thf(f12,plain,(
% 10.02/1.81 ? [X6 : (a > $o),X7 : (a > $o)] : ((X6 != X7) & ($true = ((sP1 @ X6 @ X7))) & (((cP @ X7)) = $true) & (((cP @ X6)) = $true)) | ($true != sP3)),
% 10.02/1.81 inference(nnf_transformation,[],[f10])).
% 10.02/1.81 thf(f13,plain,(
% 10.02/1.81 ? [X0 : (a > $o),X1 : (a > $o)] : ((X0 != X1) & ($true = ((sP1 @ X0 @ X1))) & (((cP @ X1)) = $true) & (((cP @ X0)) = $true)) | ($true != sP3)),
% 10.02/1.81 inference(rectify,[],[f12])).
% 10.02/1.81 thf(f14,plain,(
% 10.02/1.81 ((sK4 != sK5) & ($true = ((sP1 @ sK4 @ sK5))) & ($true = ((cP @ sK5))) & ($true = ((cP @ sK4)))) | ($true != sP3)),
% 10.02/1.81 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f13])).
% 10.02/1.81 thf(f15,plain,(
% 10.02/1.81 ! [X5 : (a > $o)] : (? [X9 : a] : ((($true != ((sP0 @ X9))) | (((X5 @ X9)) != $true)) & (($true = ((sP0 @ X9))) | (((X5 @ X9)) = $true))) | ($true != ((sP2 @ X5))))),
% 10.02/1.81 inference(nnf_transformation,[],[f9])).
% 10.02/1.81 thf(f16,plain,(
% 10.02/1.81 ! [X0 : (a > $o)] : (? [X1 : a] : ((($true != ((sP0 @ X1))) | (((X0 @ X1)) != $true)) & (($true = ((sP0 @ X1))) | (((X0 @ X1)) = $true))) | ($true != ((sP2 @ X0))))),
% 10.02/1.81 inference(rectify,[],[f15])).
% 10.02/1.81 thf(f17,plain,(
% 10.02/1.81 ! [X0 : (a > $o)] : (((($true != ((sP0 @ (sK6 @ X0)))) | ($true != ((X0 @ (sK6 @ X0))))) & (($true = ((sP0 @ (sK6 @ X0)))) | ($true = ((X0 @ (sK6 @ X0)))))) | ($true != ((sP2 @ X0))))),
% 10.02/1.81 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK6 @ X0)],[f16])).
% 10.02/1.81 thf(f18,plain,(
% 10.02/1.81 ! [X7 : (a > $o),X6 : (a > $o)] : (? [X8 : a] : ((((X7 @ X8)) = $true) & (((X6 @ X8)) = $true)) | ($true != ((sP1 @ X6 @ X7))))),
% 10.02/1.81 inference(nnf_transformation,[],[f8])).
% 10.02/1.81 thf(f19,plain,(
% 10.02/1.81 ! [X0 : (a > $o),X1 : (a > $o)] : (? [X2 : a] : ((((X0 @ X2)) = $true) & ($true = ((X1 @ X2)))) | ($true != ((sP1 @ X1 @ X0))))),
% 10.02/1.81 inference(rectify,[],[f18])).
% 10.02/1.81 thf(f20,plain,(
% 10.02/1.81 ! [X0 : (a > $o),X1 : (a > $o)] : ((($true = ((X0 @ (sK7 @ X1 @ X0)))) & ($true = ((X1 @ (sK7 @ X1 @ X0))))) | ($true != ((sP1 @ X1 @ X0))))),
% 10.02/1.81 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK6 @ X0)],[f19])).
% 10.02/1.81 thf(f24,plain,(
% 10.02/1.81 ! [X0 : (a > $o)] : (($true = sP3) | ($true = ((sP2 @ X0))) | ? [X1 : (a > $o)] : (! [X2 : a] : ($true != ((X1 @ X2))) & (((cP @ X1)) = $true))) & ! [X3 : a,X4 : (a > $o),X5 : (a > $o)] : ((X4 = X5) | ($true != ((X5 @ X3))) | ($true != ((X4 @ X3))) | (((cP @ X5)) != $true) | ($true != ((cP @ X4)))) & ! [X6 : (a > $o)] : (? [X7 : a] : ($true = ((X6 @ X7))) | (((cP @ X6)) != $true))),
% 10.02/1.81 inference(rectify,[],[f11])).
% 10.02/1.81 thf(f25,plain,(
% 10.02/1.81 ! [X0 : (a > $o)] : (($true = sP3) | ($true = ((sP2 @ X0))) | (! [X2 : a] : ($true != ((sK9 @ X2))) & ($true = ((cP @ sK9))))) & ! [X3 : a,X4 : (a > $o),X5 : (a > $o)] : ((X4 = X5) | ($true != ((X5 @ X3))) | ($true != ((X4 @ X3))) | (((cP @ X5)) != $true) | ($true != ((cP @ X4)))) & ! [X6 : (a > $o)] : (($true = ((X6 @ (sK10 @ X6)))) | (((cP @ X6)) != $true))),
% 10.02/1.81 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,vAPP]),skolemize(X1,sK9),skolemize(X1,sK6 @ X0)],[f24])).
% 10.02/1.81 thf(f26,plain,(
% 10.02/1.81 ($true = ((cP @ sK4))) | ($true != sP3)),
% 10.02/1.81 inference(cnf_transformation,[],[f14])).
% 10.02/1.81 thf(f27,plain,(
% 10.02/1.81 ($true = ((cP @ sK5))) | ($true != sP3)),
% 10.02/1.81 inference(cnf_transformation,[],[f14])).
% 10.02/1.81 thf(f28,plain,(
% 10.02/1.81 ($true = ((sP1 @ sK4 @ sK5))) | ($true != sP3)),
% 10.02/1.81 inference(cnf_transformation,[],[f14])).
% 10.02/1.81 thf(f29,plain,(
% 10.02/1.81 (sK4 != sK5) | ($true != sP3)),
% 10.02/1.81 inference(cnf_transformation,[],[f14])).
% 10.02/1.81 thf(f30,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o)] : (($true != ((sP2 @ X0))) | ($true = ((X0 @ (sK6 @ X0)))) | ($true = ((sP0 @ (sK6 @ X0))))) )),
% 10.02/1.81 inference(cnf_transformation,[],[f17])).
% 10.02/1.81 thf(f31,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o)] : (($true != ((sP0 @ (sK6 @ X0)))) | ($true != ((X0 @ (sK6 @ X0)))) | ($true != ((sP2 @ X0)))) )),
% 10.02/1.81 inference(cnf_transformation,[],[f17])).
% 10.02/1.81 thf(f32,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP1 @ X1 @ X0))) | ($true = ((X1 @ (sK7 @ X1 @ X0))))) )),
% 10.02/1.81 inference(cnf_transformation,[],[f20])).
% 10.02/1.81 thf(f33,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP1 @ X1 @ X0))) | ($true = ((X0 @ (sK7 @ X1 @ X0))))) )),
% 10.02/1.81 inference(cnf_transformation,[],[f20])).
% 10.02/1.81 thf(f37,plain,(
% 10.02/1.81 ( ! [X6 : (a > $o)] : ((((cP @ X6)) != $true) | ($true = ((X6 @ (sK10 @ X6))))) )),
% 10.02/1.81 inference(cnf_transformation,[],[f25])).
% 10.02/1.81 thf(f38,plain,(
% 10.02/1.81 ( ! [X3 : a,X4 : (a > $o),X5 : (a > $o)] : (($true != ((cP @ X4))) | ($true != ((X5 @ X3))) | ($true != ((X4 @ X3))) | (((cP @ X5)) != $true) | (X4 = X5)) )),
% 10.02/1.81 inference(cnf_transformation,[],[f25])).
% 10.02/1.81 thf(f39,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o)] : (($true = sP3) | ($true = ((sP2 @ X0))) | ($true = ((cP @ sK9)))) )),
% 10.02/1.81 inference(cnf_transformation,[],[f25])).
% 10.02/1.81 thf(f40,plain,(
% 10.02/1.81 ( ! [X2 : a,X0 : (a > $o)] : (($true = sP3) | ($true = ((sP2 @ X0))) | ($true != ((sK9 @ X2)))) )),
% 10.02/1.81 inference(cnf_transformation,[],[f25])).
% 10.02/1.81 thf(f42,definition,(
% 10.02/1.81 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 10.02/1.81 introduced(theory,[fool_exhaustiveness_axiom])).
% 10.02/1.81 thf(f44,definition,(
% 10.02/1.81 spl11_1 <=> ($true = ((cP @ sK9)))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition])).
% 10.02/1.81 thf(f46,plain,(
% 10.02/1.81 ($true = ((cP @ sK9))) | ~spl11_1),
% 10.02/1.81 inference(avatar_component_clause,[],[f44])).
% 10.02/1.81 thf(f48,definition,(
% 10.02/1.81 spl11_2 <=> ! [X0 : (a > $o)] : ($true = ((sP2 @ X0)))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition])).
% 10.02/1.81 thf(f49,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o)] : (($true = ((sP2 @ X0)))) ) | ~spl11_2),
% 10.02/1.81 inference(avatar_component_clause,[],[f48])).
% 10.02/1.81 thf(f51,definition,(
% 10.02/1.81 spl11_3 <=> ($true = sP3)),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition])).
% 10.02/1.81 thf(f54,plain,(
% 10.02/1.81 spl11_1 | spl11_2 | spl11_3),
% 10.02/1.81 inference(avatar_split_clause,[],[f39,f51,f48,f44])).
% 10.02/1.81 thf(f56,definition,(
% 10.02/1.81 spl11_4 <=> ! [X2 : a] : ($true != ((sK9 @ X2)))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition])).
% 10.02/1.81 thf(f57,plain,(
% 10.02/1.81 ( ! [X2 : a] : (($true != ((sK9 @ X2)))) ) | ~spl11_4),
% 10.02/1.81 inference(avatar_component_clause,[],[f56])).
% 10.02/1.81 thf(f58,plain,(
% 10.02/1.81 spl11_4 | spl11_2 | spl11_3),
% 10.02/1.81 inference(avatar_split_clause,[],[f40,f51,f48,f56])).
% 10.02/1.81 thf(f60,definition,(
% 10.02/1.81 spl11_5 <=> ($true = ((cP @ sK4)))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition])).
% 10.02/1.81 thf(f62,plain,(
% 10.02/1.81 ($true = ((cP @ sK4))) | ~spl11_5),
% 10.02/1.81 inference(avatar_component_clause,[],[f60])).
% 10.02/1.81 thf(f63,plain,(
% 10.02/1.81 ~spl11_3 | spl11_5),
% 10.02/1.81 inference(avatar_split_clause,[],[f26,f60,f51])).
% 10.02/1.81 thf(f65,definition,(
% 10.02/1.81 spl11_6 <=> ($true = ((cP @ sK5)))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition])).
% 10.02/1.81 thf(f67,plain,(
% 10.02/1.81 ($true = ((cP @ sK5))) | ~spl11_6),
% 10.02/1.81 inference(avatar_component_clause,[],[f65])).
% 10.02/1.81 thf(f68,plain,(
% 10.02/1.81 ~spl11_3 | spl11_6),
% 10.02/1.81 inference(avatar_split_clause,[],[f27,f65,f51])).
% 10.02/1.81 thf(f70,definition,(
% 10.02/1.81 spl11_7 <=> ($true = ((sP1 @ sK4 @ sK5)))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition])).
% 10.02/1.81 thf(f72,plain,(
% 10.02/1.81 ($true = ((sP1 @ sK4 @ sK5))) | ~spl11_7),
% 10.02/1.81 inference(avatar_component_clause,[],[f70])).
% 10.02/1.81 thf(f73,plain,(
% 10.02/1.81 ~spl11_3 | spl11_7),
% 10.02/1.81 inference(avatar_split_clause,[],[f28,f70,f51])).
% 10.02/1.81 thf(f75,definition,(
% 10.02/1.81 spl11_8 <=> (sK4 = sK5)),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition])).
% 10.02/1.81 thf(f78,plain,(
% 10.02/1.81 ~spl11_3 | ~spl11_8),
% 10.02/1.81 inference(avatar_split_clause,[],[f29,f75,f51])).
% 10.02/1.81 thf(f330,definition,(
% 10.02/1.81 spl11_9 <=> ($true = ((sP0 @ (sK6 @ sP0))))),
% 10.02/1.81 introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition])).
% 10.02/1.81 thf(f331,plain,(
% 10.02/1.81 ($true != ((sP0 @ (sK6 @ sP0)))) | spl11_9),
% 10.02/1.81 inference(avatar_component_clause,[],[f330])).
% 10.02/1.81 thf(f332,plain,(
% 10.02/1.81 ($true = ((sP0 @ (sK6 @ sP0)))) | ~spl11_9),
% 10.02/1.81 inference(avatar_component_clause,[],[f330])).
% 10.02/1.81 thf(f372,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((X0 @ (sK6 @ X0)))) | ($true = ((sP0 @ (sK6 @ X0))))) ) | ~spl11_2),
% 10.02/1.81 inference(constrained_superposition,[],[f30,f49])).
% 10.02/1.81 thf(f374,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o)] : (($true = ((X0 @ (sK6 @ X0)))) | ($true = ((sP0 @ (sK6 @ X0))))) ) | ~spl11_2),
% 10.02/1.81 inference(trivial_inequality_removal,[],[f372])).
% 10.02/1.81 thf(f408,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | (((X0 @ X1)) != $true) | ($true != ((sK4 @ X1))) | (((cP @ X0)) != $true) | (sK4 = X0)) ) | ~spl11_5),
% 10.02/1.81 inference(constrained_superposition,[],[f38,f62])).
% 10.02/1.81 thf(f413,plain,(
% 10.02/1.81 ( ! [X0 : (a > $o),X1 : a] : ((((cP @ X0)) != $true) | ($true != ((sK4 @ X1))) | (((X0 @ X1)) != $true) | (sK4 = X0)) ) | ~spl11_5),
% 10.02/1.81 inference(trivial_inequality_removal,[],[f408])).
% 10.02/1.81 thf(f437,plain,(
% 10.02/1.81 ($true != $true) | ($true != $true) | ($true != ((sP2 @ sP0))) | ~spl11_9),
% 10.02/1.81 inference(constrained_superposition,[],[f31,f332])).
% 10.02/1.81 thf(f438,plain,(
% 10.02/1.81 ($true != $true) | ($true != ((sP2 @ sP0))) | ~spl11_9),
% 10.02/1.81 inference(duplicate_literal_removal,[],[f437])).
% 10.02/1.81 thf(f439,plain,(
% 10.02/1.81 ($true != ((sP2 @ sP0))) | ~spl11_9),
% 10.02/1.81 inference(trivial_inequality_removal,[],[f438])).
% 10.02/1.81 thf(f443,plain,(
% 10.02/1.81 ($true != $true) | (~spl11_2 | ~spl11_9)),
% 10.02/1.81 inference(forward_demodulation,[],[f439,f49])).
% 10.02/1.81 thf(f444,plain,(
% 10.02/1.81 $false | (~spl11_2 | ~spl11_9)),
% 10.02/1.81 inference(trivial_inequality_removal,[],[f443])).
% 10.02/1.81 thf(f445,plain,(
% 10.02/1.81 ~spl11_2 | ~spl11_9),
% 10.02/1.81 inference(avatar_contradiction_clause,[],[f444])).
% 10.02/1.81 thf(f447,plain,(
% 10.02/1.81 ($true != $true) | ($true = ((sK5 @ (sK7 @ sK4 @ sK5)))) | ~spl11_7),
% 10.02/1.81 inference(constrained_superposition,[],[f33,f72])).
% 10.02/1.81 thf(f448,plain,(
% 10.02/1.81 ($true != $true) | ($true = ((sK4 @ (sK7 @ sK4 @ sK5)))) | ~spl11_7),
% 10.02/1.81 inference(constrained_superposition,[],[f32,f72])).
% 10.02/1.81 thf(f451,plain,(
% 10.02/1.81 ($true = ((sK4 @ (sK7 @ sK4 @ sK5)))) | ~spl11_7),
% 10.02/1.81 inference(trivial_inequality_removal,[],[f448])).
% 10.02/1.81 thf(f452,plain,(
% 10.02/1.81 ($true = ((sK5 @ (sK7 @ sK4 @ sK5)))) | ~spl11_7),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f447])).
% 10.02/1.82 thf(f455,plain,(
% 10.02/1.82 ($true != $true) | ($false = ((sP0 @ (sK6 @ sP0)))) | spl11_9),
% 10.02/1.82 inference(constrained_superposition,[],[f331,f42])).
% 10.02/1.82 thf(f459,plain,(
% 10.02/1.82 ($false = ((sP0 @ (sK6 @ sP0)))) | spl11_9),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f455])).
% 10.02/1.82 thf(f479,plain,(
% 10.02/1.82 ($true != $true) | ($true = ((sP0 @ (sK6 @ (^[Y0 : a]: (sP0 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | (~spl11_2 | spl11_9)),
% 10.02/1.82 inference(constrained_superposition,[],[f331,f374])).
% 10.02/1.82 thf(f516,plain,(
% 10.02/1.82 ($true = ((sP0 @ (sK6 @ (^[Y0 : a]: (sP0 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | (~spl11_2 | spl11_9)),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f479])).
% 10.02/1.82 thf(f517,plain,(
% 10.02/1.82 ($true = ((sP0 @ (sK6 @ sP0)))) | (~spl11_2 | spl11_9)),
% 10.02/1.82 inference(beta-eta_normalization,[],[f516])).
% 10.02/1.82 thf(f545,plain,(
% 10.02/1.82 ($true = $false) | (~spl11_2 | spl11_9)),
% 10.02/1.82 inference(forward_demodulation,[],[f517,f459])).
% 10.02/1.82 thf(f546,plain,(
% 10.02/1.82 $false | (~spl11_2 | spl11_9)),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f545])).
% 10.02/1.82 thf(f547,plain,(
% 10.02/1.82 ~spl11_2 | spl11_9),
% 10.02/1.82 inference(avatar_contradiction_clause,[],[f546])).
% 10.02/1.82 thf(f550,plain,(
% 10.02/1.82 ( ! [X0 : a] : (($true != $true) | ($false = ((sK9 @ X0)))) ) | ~spl11_4),
% 10.02/1.82 inference(constrained_superposition,[],[f57,f42])).
% 10.02/1.82 thf(f553,plain,(
% 10.02/1.82 ( ! [X0 : a] : (($false = ((sK9 @ X0)))) ) | ~spl11_4),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f550])).
% 10.02/1.82 thf(f557,plain,(
% 10.02/1.82 ($true != $true) | ($true = ((sK9 @ (sK10 @ sK9)))) | ~spl11_1),
% 10.02/1.82 inference(constrained_superposition,[],[f37,f46])).
% 10.02/1.82 thf(f560,plain,(
% 10.02/1.82 ($true = ((sK9 @ (sK10 @ sK9)))) | ~spl11_1),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f557])).
% 10.02/1.82 thf(f564,plain,(
% 10.02/1.82 ($true = $false) | (~spl11_1 | ~spl11_4)),
% 10.02/1.82 inference(forward_demodulation,[],[f560,f553])).
% 10.02/1.82 thf(f565,plain,(
% 10.02/1.82 $false | (~spl11_1 | ~spl11_4)),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f564])).
% 10.02/1.82 thf(f566,plain,(
% 10.02/1.82 ~spl11_1 | ~spl11_4),
% 10.02/1.82 inference(avatar_contradiction_clause,[],[f565])).
% 10.02/1.82 thf(f677,plain,(
% 10.02/1.82 ( ! [X0 : a] : (($true != $true) | ($true != ((sK4 @ X0))) | ($true != ((sK5 @ X0))) | (sK4 = sK5)) ) | (~spl11_5 | ~spl11_6)),
% 10.02/1.82 inference(constrained_superposition,[],[f413,f67])).
% 10.02/1.82 thf(f687,plain,(
% 10.02/1.82 ( ! [X0 : a] : (($true != ((sK4 @ X0))) | ($true != ((sK5 @ X0))) | (sK4 = sK5)) ) | (~spl11_5 | ~spl11_6)),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f677])).
% 10.02/1.82 thf(f690,definition,(
% 10.02/1.82 spl11_23 <=> ! [X0 : a] : (($true != ((sK4 @ X0))) | ($true != ((sK5 @ X0))))),
% 10.02/1.82 introduced(definition,[new_symbols(definition,[spl11_23])],[avatar_definition])).
% 10.02/1.82 thf(f691,plain,(
% 10.02/1.82 ( ! [X0 : a] : (($true != ((sK5 @ X0))) | ($true != ((sK4 @ X0)))) ) | ~spl11_23),
% 10.02/1.82 inference(avatar_component_clause,[],[f690])).
% 10.02/1.82 thf(f692,plain,(
% 10.02/1.82 spl11_8 | spl11_23 | ~spl11_5 | ~spl11_6),
% 10.02/1.82 inference(avatar_split_clause,[],[f687,f65,f60,f690,f75])).
% 10.02/1.82 thf(f980,plain,(
% 10.02/1.82 ($true != $true) | ($true != ((sK4 @ (sK7 @ sK4 @ sK5)))) | (~spl11_7 | ~spl11_23)),
% 10.02/1.82 inference(constrained_superposition,[],[f691,f452])).
% 10.02/1.82 thf(f991,plain,(
% 10.02/1.82 ($true != ((sK4 @ (sK7 @ sK4 @ sK5)))) | (~spl11_7 | ~spl11_23)),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f980])).
% 10.02/1.82 thf(f992,plain,(
% 10.02/1.82 ($true != $true) | (~spl11_7 | ~spl11_23)),
% 10.02/1.82 inference(forward_demodulation,[],[f991,f451])).
% 10.02/1.82 thf(f993,plain,(
% 10.02/1.82 $false | (~spl11_7 | ~spl11_23)),
% 10.02/1.82 inference(trivial_inequality_removal,[],[f992])).
% 10.02/1.82 thf(f994,plain,(
% 10.02/1.82 ~spl11_7 | ~spl11_23),
% 10.02/1.82 inference(avatar_contradiction_clause,[],[f993])).
% 10.02/1.82 cnf(s4, plain, spl11_1 | spl11_2 | spl11_3, inference(sat_conversion,[],[f54])).
% 10.02/1.82 cnf(s6, plain, spl11_2 | spl11_3 | spl11_4, inference(sat_conversion,[],[f58])).
% 10.02/1.82 cnf(s15, plain, ~spl11_3 | spl11_5, inference(sat_conversion,[],[f63])).
% 10.02/1.82 cnf(s17, plain, ~spl11_3 | spl11_6, inference(sat_conversion,[],[f68])).
% 10.02/1.82 cnf(s19, plain, ~spl11_3 | spl11_7, inference(sat_conversion,[],[f73])).
% 10.02/1.82 cnf(s21, plain, ~spl11_3 | ~spl11_8, inference(sat_conversion,[],[f78])).
% 10.02/1.82 cnf(s103, plain, ~spl11_2 | ~spl11_9, inference(sat_conversion,[],[f445])).
% 10.02/1.82 cnf(s119, plain, ~spl11_2 | spl11_9, inference(sat_conversion,[],[f547])).
% 10.02/1.82 cnf(s135, plain, ~spl11_1 | ~spl11_4, inference(sat_conversion,[],[f566])).
% 10.02/1.82 cnf(s177, plain, ~spl11_5 | ~spl11_6 | spl11_8 | spl11_23, inference(sat_conversion,[],[f692])).
% 10.02/1.82 cnf(s238, plain, ~spl11_7 | ~spl11_23, inference(sat_conversion,[],[f994])).
% 10.02/1.82 cnf(s239, plain, ~spl11_3, inference(rat,[],[s177,s238,s15,s17,s19,s21])).
% 10.02/1.82 cnf(s240, plain, ~spl11_2, inference(rat,[],[s103,s119])).
% 10.02/1.82 cnf(s241, plain, spl11_1, inference(rat,[],[s4,s239,s240])).
% 10.02/1.82 cnf(s242, plain, spl11_4, inference(rat,[],[s6,s239,s240])).
% 10.02/1.82 cnf(s243, plain, $false, inference(rat,[],[s135,s242,s241])).
% 10.02/1.82 thf(f995,plain,(
% 10.02/1.82 $false),
% 10.02/1.82 inference(avatar_sat_refutation,[],[s243])).
% 10.02/1.82 % SZS output end Proof for theBenchmark
% 10.02/1.82 % (479315)------------------------------
% 10.02/1.82 % (479315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.02/1.82 % (479315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.02/1.82 % (479315)CaDiCaL version: 2.1.3
% 10.02/1.82 % (479315)Termination reason: Refutation
% 10.02/1.82 % (479315)Time elapsed: 0.073 s
% 10.02/1.82 % (479315)Peak memory usage: 14 MB
% 10.02/1.82 % (479315)Instructions burned: 87 (million)
% 10.02/1.82 % (479078)Success in time 1.575 s
% 10.02/1.82 % Vampire exiting
%------------------------------------------------------------------------------