%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO263^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:49:37 AM UTC 2026
% Result : Theorem 7.04s 1.25s
% Output : Refutation 7.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO263^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:47:52 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 4.43/0.90 % (1486932)Will run a generic schedule for satisfiability detection.
% 4.43/0.90 % (1486949)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3827349089:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 4.43/0.90 % (1486943)% WARNING: option uhcvi not known.
% 4.43/0.90 % (1486944)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1108293942:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 4.43/0.90 % (1486946)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2109731106:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 4.43/0.90 % (1486943)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2029762756:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 4.43/0.90 % (1486945)dis+10_1_sil=32000:sp=arity:random_seed=1733478763:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 4.43/0.90 % (1486946)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.43/0.90 % (1486947)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=243667069:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 4.43/0.90 % (1486943)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.43/0.90 % (1486942)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2203099890_3000 on theBenchmark for (3000ds/0Mi)
% 4.43/0.90 % (1486943)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.43/0.90 % Exception at run slice level
% 4.43/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.43/0.90 % (1486970)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2525755209:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.43/0.90 % Exception at run slice level
% 4.43/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.43/0.90 % (1486949)Instruction limit reached!
% 4.43/0.90 % (1486949)------------------------------
% 4.43/0.90 % (1486949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.43/0.90 % (1486949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/0.90 % (1486949)CaDiCaL version: 2.1.3
% 4.43/0.90 % (1486949)Termination reason: Instruction limit
% 4.43/0.90 % (1486949)Termination phase: Saturation
% 4.43/0.90 % (1486949)Time elapsed: 0.045 s
% 4.43/0.90 % (1486949)Peak memory usage: 12 MB
% 4.43/0.90 % (1486949)Instructions burned: 162 (million)
% 4.43/0.90 % (1486985)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3156822694:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.43/0.90 % (1486989)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=27778640:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.43/0.90 % (1486989)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.43/0.90 % (1486989)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.43/0.90 % (1486945)Instruction limit reached!
% 4.43/0.90 % (1486945)------------------------------
% 4.43/0.90 % (1486945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.43/0.90 % (1486945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/0.90 % (1486945)CaDiCaL version: 2.1.3
% 4.43/0.90 % (1486945)Termination reason: Instruction limit
% 4.43/0.90 % (1486945)Termination phase: Saturation
% 4.43/0.90 % (1486945)Time elapsed: 0.054 s
% 4.43/0.90 % (1486945)Peak memory usage: 12 MB
% 4.43/0.90 % (1486945)Instructions burned: 105 (million)
% 4.43/0.90 % (1486946)Instruction limit reached!
% 4.43/0.90 % (1486946)------------------------------
% 4.43/0.90 % (1486946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.43/0.90 % (1486946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/0.90 % (1486946)CaDiCaL version: 2.1.3
% 4.43/0.90 % (1486946)Termination reason: Instruction limit
% 4.43/0.90 % (1486946)Termination phase: Saturation
% 4.43/0.90 % (1486946)Time elapsed: 0.058 s
% 4.43/0.90 % (1486946)Peak memory usage: 12 MB
% 4.43/0.90 % (1486946)Instructions burned: 117 (million)
% 4.43/0.90 % (1486947)Instruction limit reached!
% 4.43/0.90 % (1486947)------------------------------
% 4.43/0.90 % (1486947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1486947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1486947)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1486947)Termination reason: Instruction limit
% 7.04/1.25 % (1486947)Termination phase: Saturation
% 7.04/1.25 % (1486947)Time elapsed: 0.067 s
% 7.04/1.25 % (1486947)Peak memory usage: 12 MB
% 7.04/1.25 % (1486947)Instructions burned: 132 (million)
% 7.04/1.25 % (1486996)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2317228055:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 7.04/1.25 % (1486995)ott-21_1_sil=16000:fs=off:random_seed=4290354546:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 7.04/1.25 % (1486997)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=274110117:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487001)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=988652576:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 7.04/1.25 % (1486985)Instruction limit reached!
% 7.04/1.25 % (1486985)------------------------------
% 7.04/1.25 % (1486985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1486985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1486985)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1486985)Termination reason: Instruction limit
% 7.04/1.25 % (1486985)Termination phase: Saturation
% 7.04/1.25 % (1486985)Time elapsed: 0.072 s
% 7.04/1.25 % (1486985)Peak memory usage: 13 MB
% 7.04/1.25 % (1486985)Instructions burned: 131 (million)
% 7.04/1.25 % (1487003)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2759170603:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487005)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=1779855100: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)
% 7.04/1.25 % (1487005)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.04/1.25 % (1486995)Instruction limit reached!
% 7.04/1.25 % (1486995)------------------------------
% 7.04/1.25 % (1486995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1486995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1486995)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1486995)Termination reason: Instruction limit
% 7.04/1.25 % (1486995)Termination phase: Saturation
% 7.04/1.25 % (1486995)Time elapsed: 0.087 s
% 7.04/1.25 % (1486995)Peak memory usage: 12 MB
% 7.04/1.25 % (1486995)Instructions burned: 182 (million)
% 7.04/1.25 % (1487007)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2650655990:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 7.04/1.25 % (1487007)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.04/1.25 % (1486989)Instruction limit reached!
% 7.04/1.25 % (1486989)------------------------------
% 7.04/1.25 % (1486989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1486989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1486989)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1486989)Termination reason: Instruction limit
% 7.04/1.25 % (1486989)Termination phase: Saturation
% 7.04/1.25 % (1486989)Time elapsed: 0.178 s
% 7.04/1.25 % (1486989)Peak memory usage: 14 MB
% 7.04/1.25 % (1486989)Instructions burned: 688 (million)
% 7.04/1.25 % (1487009)fmb+10_1_sil=64000:random_seed=4266608389:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 7.04/1.25 % (1487009)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487011)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=86547859:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487013)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1777325761:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487015)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=255888385:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 7.04/1.25 % (1487015)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.04/1.25 % (1486996)Instruction limit reached!
% 7.04/1.25 % (1486996)------------------------------
% 7.04/1.25 % (1486996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1486996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1486996)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1486996)Termination reason: Instruction limit
% 7.04/1.25 % (1486996)Termination phase: Saturation
% 7.04/1.25 % (1486996)Time elapsed: 0.244 s
% 7.04/1.25 % (1486996)Peak memory usage: 14 MB
% 7.04/1.25 % (1486996)Instructions burned: 479 (million)
% 7.04/1.25 % (1487017)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=68290401:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 7.04/1.25 % (1487017)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.04/1.25 % (1487017)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.04/1.25 % (1487005)Instruction limit reached!
% 7.04/1.25 % (1487005)------------------------------
% 7.04/1.25 % (1487005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1487005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1487005)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1487005)Termination reason: Instruction limit
% 7.04/1.25 % (1487005)Termination phase: Saturation
% 7.04/1.25 % (1487005)Time elapsed: 0.317 s
% 7.04/1.25 % (1487005)Peak memory usage: 16 MB
% 7.04/1.25 % (1487005)Instructions burned: 692 (million)
% 7.04/1.25 % (1487019)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1181920116:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487021)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=57116193:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487023)ott-2_1_sil=16000:newcnf=on:random_seed=87779744:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 7.04/1.25 % (1487023)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.04/1.25 % (1487007)Instruction limit reached!
% 7.04/1.25 % (1487007)------------------------------
% 7.04/1.25 % (1487007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1487007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1487007)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1487007)Termination reason: Instruction limit
% 7.04/1.25 % (1487007)Termination phase: Saturation
% 7.04/1.25 % (1487007)Time elapsed: 0.436 s
% 7.04/1.25 % (1487007)Peak memory usage: 15 MB
% 7.04/1.25 % (1487007)Instructions burned: 880 (million)
% 7.04/1.25 % (1487025)ott+10_1_sil=32000:tgt=ground:random_seed=1297448141:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 7.04/1.25 % (1487001)Instruction limit reached!
% 7.04/1.25 % (1487001)------------------------------
% 7.04/1.25 % (1487001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1487001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1487001)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1487001)Termination reason: Instruction limit
% 7.04/1.25 % (1487001)Termination phase: Saturation
% 7.04/1.25 % (1487001)Time elapsed: 0.545 s
% 7.04/1.25 % (1487001)Peak memory usage: 16 MB
% 7.04/1.25 % (1487001)Instructions burned: 1180 (million)
% 7.04/1.25 % (1487027)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=274713683:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 7.04/1.25 % Exception at run slice level
% 7.04/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.04/1.25 % (1487029)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1858101757:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 7.04/1.25 % (1487029)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.04/1.25 % (1487023)Instruction limit reached!
% 7.04/1.25 % (1487023)------------------------------
% 7.04/1.25 % (1487023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1487023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1487023)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1487023)Termination reason: Instruction limit
% 7.04/1.25 % (1487023)Termination phase: Saturation
% 7.04/1.25 % (1487023)Time elapsed: 0.386 s
% 7.04/1.25 % (1487023)Peak memory usage: 14 MB
% 7.04/1.25 % (1487023)Instructions burned: 871 (million)
% 7.04/1.25 % (1487031)dis+21_1_sil=32000:sas=cadical:random_seed=3930917991:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 7.04/1.25 % (1487017)Instruction limit reached!
% 7.04/1.25 % (1487017)------------------------------
% 7.04/1.25 % (1487017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1487017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1487017)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1487017)Termination reason: Instruction limit
% 7.04/1.25 % (1487017)Termination phase: Saturation
% 7.04/1.25 % (1487017)Time elapsed: 0.642 s
% 7.04/1.25 % (1487017)Peak memory usage: 15 MB
% 7.04/1.25 % (1487017)Instructions burned: 1472 (million)
% 7.04/1.25 % (1487033)ott+11_1_sil=16000:gs=on:random_seed=116077152:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2989 on theBenchmark for (2989ds/2251Mi)
% 7.04/1.25 % (1487033)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.04/1.25 % (1487015) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1486932-1487015"...
% 7.04/1.25 % (1487015)...printing done.
% 7.04/1.25 % (1487015)Refutation found. Thanks to Tanya!
% 7.04/1.25 % SZS status Theorem for theBenchmark
% 7.04/1.25 % SZS output start Proof for theBenchmark
% 7.04/1.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 7.04/1.25 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $i > $o)).
% 7.04/1.25 thf(func_def_7, type, sK4: ($i > $o)).
% 7.04/1.25 thf(func_def_8, type, sK5: (($i > $o) > $i)).
% 7.04/1.25 thf(func_def_9, type, vNOT: ($o > $o)).
% 7.04/1.25 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 7.04/1.25 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 7.04/1.25 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 7.04/1.25 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 7.04/1.25 thf(func_def_15, type, sK7: ($i > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_16, type, sK8: ($i > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_17, type, sK9: ($i > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 7.04/1.25 thf(func_def_19, type, sK10: ($i > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_20, type, sK11: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_21, type, sK12: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_22, type, sK13: ($i > $i)).
% 7.04/1.25 thf(func_def_23, type, sK14: ($i > $i)).
% 7.04/1.25 thf(func_def_24, type, sK15: (($i > $o) > $i)).
% 7.04/1.25 thf(func_def_25, type, sK16: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_26, type, sK17: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_27, type, sK18: (($i > $o) > $i)).
% 7.04/1.25 thf(func_def_28, type, sK19: (($i > $o) > $i)).
% 7.04/1.25 thf(func_def_30, type, sK21: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_31, type, sK22: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_32, type, sK23: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_33, type, sK24: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_34, type, sK25: (($i > $o) > $i)).
% 7.04/1.25 thf(func_def_35, type, sK26: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_36, type, sK27: (($i > $o) > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_37, type, sK28: (($i > $o) > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_38, type, sK29: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_39, type, sK30: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_40, type, sK31: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_41, type, sK32: (($i > $i > $o) > ($i > $i) > ($i > $i > $i) > $i)).
% 7.04/1.25 thf(func_def_42, type, sK33: (($i > $i > $i) > ($i > $i) > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_43, type, sK34: (($i > $i > $o) > ($i > $i) > ($i > $i > $i) > $i)).
% 7.04/1.25 thf(func_def_44, type, sK35: (($i > $i > $i) > ($i > $i) > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_45, type, sK36: (($i > $i > $i) > ($i > $i) > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_46, type, sK37: (($i > $i > $o) > ($i > $i) > ($i > $i > $i) > $i)).
% 7.04/1.25 thf(func_def_47, type, sK38: ($i > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_48, type, sK39: ($i > ($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_49, type, sK40: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_50, type, sK41: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_51, type, sK42: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_52, type, sK43: (($i > $o) > $i)).
% 7.04/1.25 thf(func_def_53, type, sK44: (($i > $i > $o) > $i)).
% 7.04/1.25 thf(func_def_54, type, sK45: (($i > $o) > $i)).
% 7.04/1.25 thf(f1,conjecture,(
% 7.04/1.25 ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & (~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X1) | (X3 @ X1)) & ((X4 @ X0) | (X5 @ X0)))),
% 7.04/1.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM125D)).
% 7.04/1.25 thf(f2,negated_conjecture,(
% 7.04/1.25 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & (~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X1) | (X3 @ X1)) & ((X4 @ X0) | (X5 @ X0)))),
% 7.04/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 7.04/1.25 thf(f3,plain,(
% 7.04/1.25 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & (~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X1) | (X3 @ X1)) & ((X4 @ X0) | (X5 @ X0)))),
% 7.04/1.25 inference(rectify,[],[f2])).
% 7.04/1.25 thf(f4,plain,(
% 7.04/1.25 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((((X5 @ X6)) = $true) <=> ~ (((X3 @ X6)) = $true)) & (~ (((X3 @ X2)) = $true) | (((X4 @ X2)) = $true)) & ((((X5 @ X1)) = $true) | (((X3 @ X1)) = $true)) & ((((X4 @ X0)) = $true) | (((X5 @ X0)) = $true)))),
% 7.04/1.25 inference(fool_elimination,[],[f3])).
% 7.04/1.25 thf(f5,plain,(
% 7.04/1.25 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((((X5 @ X6)) = $true) <=> (((X3 @ X6)) != $true)) & ((((X3 @ X2)) != $true) | (((X4 @ X2)) = $true)) & ((((X5 @ X1)) = $true) | (((X3 @ X1)) = $true)) & ((((X4 @ X0)) = $true) | (((X5 @ X0)) = $true)))),
% 7.04/1.25 inference(flattening,[],[f4])).
% 7.04/1.25 thf(f6,plain,(
% 7.04/1.25 ? [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : ((((X5 @ X6)) = $true) <~> (((X3 @ X6)) != $true)) | ((((X3 @ X2)) = $true) & (((X4 @ X2)) != $true)) | ((((X5 @ X1)) != $true) & (((X3 @ X1)) != $true)) | ((((X4 @ X0)) != $true) & (((X5 @ X0)) != $true)))),
% 7.04/1.25 inference(ennf_transformation,[],[f5])).
% 7.04/1.25 thf(f7,definition,(
% 7.04/1.25 ! [X0 : $i,X4 : ($i > $o),X5 : ($i > $o)] : (((((X4 @ X0)) != $true) & (((X5 @ X0)) != $true)) | ~ ($true = ((sP0 @ X5 @ X4 @ X0))))),
% 7.04/1.25 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 7.04/1.25 thf(f8,plain,(
% 7.04/1.25 ? [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : ((((X5 @ X6)) = $true) <~> (((X3 @ X6)) != $true)) | ((((X3 @ X2)) = $true) & (((X4 @ X2)) != $true)) | ((((X5 @ X1)) != $true) & (((X3 @ X1)) != $true)) | ($true = ((sP0 @ X5 @ X4 @ X0))))),
% 7.04/1.25 inference(definition_folding,[],[f6,f7])).
% 7.04/1.25 thf(f9,plain,(
% 7.04/1.25 ! [X0 : $i,X4 : ($i > $o),X5 : ($i > $o)] : (((((X4 @ X0)) != $true) & (((X5 @ X0)) != $true)) | ($true != ((sP0 @ X5 @ X4 @ X0))))),
% 7.04/1.25 inference(nnf_transformation,[],[f7])).
% 7.04/1.25 thf(f10,plain,(
% 7.04/1.25 ! [X0 : $i,X1 : ($i > $o),X2 : ($i > $o)] : ((($true != ((X1 @ X0))) & ($true != ((X2 @ X0)))) | ($true != ((sP0 @ X2 @ X1 @ X0))))),
% 7.04/1.25 inference(rectify,[],[f9])).
% 7.04/1.25 thf(f11,plain,(
% 7.04/1.25 ? [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : (((((X3 @ X6)) = $true) | (((X5 @ X6)) != $true)) & ((((X3 @ X6)) != $true) | (((X5 @ X6)) = $true))) | ((((X3 @ X2)) = $true) & (((X4 @ X2)) != $true)) | ((((X5 @ X1)) != $true) & (((X3 @ X1)) != $true)) | ($true = ((sP0 @ X5 @ X4 @ X0))))),
% 7.04/1.25 inference(nnf_transformation,[],[f8])).
% 7.04/1.25 thf(f12,plain,(
% 7.04/1.25 ! [X4 : ($i > $o),X5 : ($i > $o)] : (((($true = ((sK4 @ (sK5 @ X5)))) | ($true != ((X5 @ (sK5 @ X5))))) & (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((X5 @ (sK5 @ X5)))))) | (($true = ((sK4 @ sK3))) & ($true != ((X4 @ sK3)))) | (($true != ((X5 @ sK2))) & ($true != ((sK4 @ sK2)))) | ($true = ((sP0 @ X5 @ X4 @ sK1))))),
% 7.04/1.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X6,sK5 @ X5)],[f11])).
% 7.04/1.25 thf(f14,plain,(
% 7.04/1.25 ( ! [X2 : ($i > $o),X0 : $i,X1 : ($i > $o)] : (($true != ((X1 @ X0))) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 7.04/1.25 inference(cnf_transformation,[],[f10])).
% 7.04/1.25 thf(f15,plain,(
% 7.04/1.25 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true != ((sK4 @ sK2))) | ($true = ((sP0 @ X5 @ X4 @ sK1)))) )),
% 7.04/1.25 inference(cnf_transformation,[],[f12])).
% 7.04/1.25 thf(f16,plain,(
% 7.04/1.25 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true != ((X5 @ sK2))) | ($true = ((sP0 @ X5 @ X4 @ sK1)))) )),
% 7.04/1.25 inference(cnf_transformation,[],[f12])).
% 7.04/1.25 thf(f19,plain,(
% 7.04/1.25 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true = ((sK4 @ (sK5 @ X5)))) | ($true != ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true != ((sK4 @ sK2))) | ($true = ((sP0 @ X5 @ X4 @ sK1)))) )),
% 7.04/1.25 inference(cnf_transformation,[],[f12])).
% 7.04/1.25 thf(f20,plain,(
% 7.04/1.25 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((X5 @ sK2))) | ($true != ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ X5)))) | ($true = ((sP0 @ X5 @ X4 @ sK1)))) )),
% 7.04/1.25 inference(cnf_transformation,[],[f12])).
% 7.04/1.25 thf(f24,definition,(
% 7.04/1.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 7.04/1.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 7.04/1.25 thf(f33,definition,(
% 7.04/1.25 spl6_1 <=> ($true = ((sK4 @ sK2)))),
% 7.04/1.25 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 7.04/1.25 thf(f34,plain,(
% 7.04/1.25 ($true = ((sK4 @ sK2))) | ~spl6_1),
% 7.04/1.25 inference(avatar_component_clause,[],[f33])).
% 7.04/1.25 thf(f35,plain,(
% 7.04/1.25 ($true != ((sK4 @ sK2))) | spl6_1),
% 7.04/1.25 inference(avatar_component_clause,[],[f33])).
% 7.04/1.25 thf(f37,definition,(
% 7.04/1.25 spl6_2 <=> ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((sP0 @ X5 @ X4 @ sK1))) | ($true != ((X4 @ sK3))) | ($true = ((X5 @ (sK5 @ X5)))))),
% 7.04/1.25 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 7.04/1.25 thf(f38,plain,(
% 7.04/1.25 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((sP0 @ X5 @ X4 @ sK1))) | ($true != ((X4 @ sK3))) | ($true = ((X5 @ (sK5 @ X5))))) ) | ~spl6_2),
% 7.04/1.25 inference(avatar_component_clause,[],[f37])).
% 7.04/1.25 thf(f39,plain,(
% 7.04/1.25 ~spl6_1 | spl6_2),
% 7.04/1.25 inference(avatar_split_clause,[],[f15,f37,f33])).
% 7.04/1.25 thf(f46,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != $true) | ($true = ((X0 @ (sK5 @ X0)))) | ($true != ((X1 @ sK3))) | ($true != ((X0 @ sK2))) | ($true = ((sP0 @ X0 @ X1 @ sK1))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 7.04/1.25 inference(constrained_superposition,[],[f16,f24])).
% 7.04/1.25 thf(f47,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != ((X1 @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true != ((X0 @ sK2))) | ($true = ((sP0 @ X0 @ X1 @ sK1))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f46])).
% 7.04/1.25 thf(f58,plain,(
% 7.04/1.25 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true != (((^[Y0 : $i]: (~ (X6 @ Y0))) @ sK2))) | ($true != (((^[Y0 : $i]: (~ (X6 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ X4 @ sK1)))) )),
% 7.04/1.25 inference(primitive_instantiation,[],[f20])).
% 7.04/1.25 thf(f74,plain,(
% 7.04/1.25 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true != ((~ (X6 @ sK2)))) | ($true != ((~ (X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ X4 @ sK1)))) )),
% 7.04/1.25 inference(beta-eta_normalization,[],[f58])).
% 7.04/1.25 thf(f75,plain,(
% 7.04/1.25 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true = ((X6 @ sK2))) | ($true != ((~ (X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ X4 @ sK1)))) )),
% 7.04/1.25 inference(not_proxy_clausification,[],[f74])).
% 7.04/1.25 thf(f76,plain,(
% 7.04/1.25 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true != ((X4 @ sK3))) | ($true = ((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((X6 @ sK2))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ X4 @ sK1)))) )),
% 7.04/1.25 inference(not_proxy_clausification,[],[f75])).
% 7.04/1.25 thf(f140,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((sP0 @ X0 @ (^[Y0 : $i]: ($true)) @ X1)))) )),
% 7.04/1.25 inference(equality_resolution,[],[f14])).
% 7.04/1.25 thf(f254,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($true != ((X0 @ sK2))) | ($true = ((sP0 @ X0 @ (^[Y0 : $i]: ($true)) @ sK1))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 7.04/1.25 inference(equality_resolution,[],[f47])).
% 7.04/1.25 thf(f413,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ sK2))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (X0 @ Y0))) @ (^[Y0 : $i]: ($true)) @ sK1)))) )),
% 7.04/1.25 inference(equality_resolution,[],[f76])).
% 7.04/1.25 thf(f2705,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK2))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f254,f140])).
% 7.04/1.25 thf(f2711,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ sK2)))) )),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f413,f140])).
% 7.04/1.25 thf(f2757,plain,(
% 7.04/1.25 ( ! [X1 : ($i > $o)] : (($true != (((^[Y0 : $i]: (~ (X1 @ Y0))) @ sK2))) | ($true = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) )),
% 7.04/1.25 inference(primitive_instantiation,[],[f2705])).
% 7.04/1.25 thf(f2794,plain,(
% 7.04/1.25 ( ! [X1 : ($i > $o)] : (($true != ((~ (X1 @ sK2)))) | ($true = ((~ (X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) )),
% 7.04/1.25 inference(beta-eta_normalization,[],[f2757])).
% 7.04/1.25 thf(f2795,plain,(
% 7.04/1.25 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ sK2))) | ($true = ((~ (X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) )),
% 7.04/1.25 inference(not_proxy_clausification,[],[f2794])).
% 7.04/1.25 thf(f2796,plain,(
% 7.04/1.25 ( ! [X1 : ($i > $o)] : (($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($false = ((X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($true = ((X1 @ sK2)))) )),
% 7.04/1.25 inference(not_proxy_clausification,[],[f2795])).
% 7.04/1.25 thf(f5408,definition,(
% 7.04/1.25 spl6_14 <=> ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))),
% 7.04/1.25 introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition])).
% 7.04/1.25 thf(f5410,plain,(
% 7.04/1.25 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_14),
% 7.04/1.25 inference(avatar_component_clause,[],[f5408])).
% 7.04/1.25 thf(f6817,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != $true) | ($true = ((sP0 @ X0 @ X1 @ sK1))) | ($true != ((X1 @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 7.04/1.25 inference(constrained_superposition,[],[f38,f24])).
% 7.04/1.25 thf(f6871,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != ((X1 @ sK3))) | ($true = ((sP0 @ X0 @ X1 @ sK1))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f6817])).
% 7.04/1.25 thf(f6939,plain,(
% 7.04/1.25 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((X4 @ sK3))) | ($true != ((X5 @ (sK5 @ X5)))) | ($true = ((sK4 @ (sK5 @ X5)))) | ($true = ((sP0 @ X5 @ X4 @ sK1)))) ) | ~spl6_1),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f19,f34])).
% 7.04/1.25 thf(f6992,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ X0)))) | ($true = ((sP0 @ X0 @ (^[Y0 : $i]: ($true)) @ sK1)))) ) | ~spl6_1),
% 7.04/1.25 inference(equality_resolution,[],[f6939])).
% 7.04/1.25 thf(f7064,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_1),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f6992,f140])).
% 7.04/1.25 thf(f7074,plain,(
% 7.04/1.25 ( ! [X1 : ($i > $o)] : (($true != (((^[Y0 : $i]: (~ (X1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) ) | ~spl6_1),
% 7.04/1.25 inference(primitive_instantiation,[],[f7064])).
% 7.04/1.25 thf(f7189,plain,(
% 7.04/1.25 ( ! [X1 : ($i > $o)] : (($true != ((~ (X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) ) | ~spl6_1),
% 7.04/1.25 inference(beta-eta_normalization,[],[f7074])).
% 7.04/1.25 thf(f7190,plain,(
% 7.04/1.25 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) ) | ~spl6_1),
% 7.04/1.25 inference(not_proxy_clausification,[],[f7189])).
% 7.04/1.25 thf(f7847,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((sP0 @ X0 @ (^[Y0 : $i]: ($true)) @ sK1))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 7.04/1.25 inference(equality_resolution,[],[f6871])).
% 7.04/1.25 thf(f7925,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f7847,f140])).
% 7.04/1.25 thf(f8900,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = $false) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0)) ) | (~spl6_1 | ~spl6_2)),
% 7.04/1.25 inference(constrained_superposition,[],[f7925,f7190])).
% 7.04/1.25 thf(f9275,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0)) ) | (~spl6_1 | ~spl6_2)),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f8900])).
% 7.04/1.25 thf(f9276,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0)) ) | (~spl6_1 | ~spl6_2)),
% 7.04/1.25 inference(beta-eta_normalization,[],[f9275])).
% 7.04/1.25 thf(f10075,definition,(
% 7.04/1.25 spl6_21 <=> ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0))),
% 7.04/1.25 introduced(definition,[new_symbols(definition,[spl6_21])],[avatar_definition])).
% 7.04/1.25 thf(f10076,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0) | ($true = ((X0 @ (sK5 @ X0))))) ) | ~spl6_21),
% 7.04/1.25 inference(avatar_component_clause,[],[f10075])).
% 7.04/1.25 thf(f10077,plain,(
% 7.04/1.25 spl6_14 | spl6_21 | ~spl6_1 | ~spl6_2),
% 7.04/1.25 inference(avatar_split_clause,[],[f9276,f37,f33,f10075,f5408])).
% 7.04/1.25 thf(f10148,plain,(
% 7.04/1.25 ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_21),
% 7.04/1.25 inference(equality_resolution,[],[f10076])).
% 7.04/1.25 thf(f10149,plain,(
% 7.04/1.25 ($true = ((~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) | ~spl6_21),
% 7.04/1.25 inference(beta-eta_normalization,[],[f10148])).
% 7.04/1.25 thf(f10150,plain,(
% 7.04/1.25 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_21),
% 7.04/1.25 inference(not_proxy_clausification,[],[f10149])).
% 7.04/1.25 thf(f10160,plain,(
% 7.04/1.25 ($true = $false) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | (~spl6_1 | ~spl6_21)),
% 7.04/1.25 inference(constrained_superposition,[],[f10150,f7190])).
% 7.04/1.25 thf(f10231,plain,(
% 7.04/1.25 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | (~spl6_1 | ~spl6_21)),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f10160])).
% 7.04/1.25 thf(f10232,plain,(
% 7.04/1.25 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (~spl6_1 | ~spl6_21)),
% 7.04/1.25 inference(beta-eta_normalization,[],[f10231])).
% 7.04/1.25 thf(f10241,plain,(
% 7.04/1.25 ($true = $false) | (~spl6_1 | ~spl6_21)),
% 7.04/1.25 inference(forward_demodulation,[],[f10232,f10150])).
% 7.04/1.25 thf(f10242,plain,(
% 7.04/1.25 $false | (~spl6_1 | ~spl6_21)),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f10241])).
% 7.04/1.25 thf(f10243,plain,(
% 7.04/1.25 ~spl6_1 | ~spl6_21),
% 7.04/1.25 inference(avatar_contradiction_clause,[],[f10242])).
% 7.04/1.25 thf(f16094,definition,(
% 7.04/1.25 spl6_27 <=> ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))),
% 7.04/1.25 introduced(definition,[new_symbols(definition,[spl6_27])],[avatar_definition])).
% 7.04/1.25 thf(f16095,plain,(
% 7.04/1.25 ($false != ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | spl6_27),
% 7.04/1.25 inference(avatar_component_clause,[],[f16094])).
% 7.04/1.25 thf(f16096,plain,(
% 7.04/1.25 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_27),
% 7.04/1.25 inference(avatar_component_clause,[],[f16094])).
% 7.04/1.25 thf(f16126,plain,(
% 7.04/1.25 ($true = $false) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ~spl6_27),
% 7.04/1.25 inference(constrained_superposition,[],[f2711,f16096])).
% 7.04/1.25 thf(f16152,plain,(
% 7.04/1.25 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ~spl6_27),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f16126])).
% 7.04/1.25 thf(f16153,plain,(
% 7.04/1.25 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ($true = ((sK4 @ sK2))) | ~spl6_27),
% 7.04/1.25 inference(beta-eta_normalization,[],[f16152])).
% 7.04/1.25 thf(f16196,plain,(
% 7.04/1.25 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (spl6_1 | ~spl6_27)),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f16153,f35])).
% 7.04/1.25 thf(f16198,plain,(
% 7.04/1.25 ($true = $false) | (spl6_1 | ~spl6_27)),
% 7.04/1.25 inference(forward_demodulation,[],[f16196,f16096])).
% 7.04/1.25 thf(f16199,plain,(
% 7.04/1.25 $false | (spl6_1 | ~spl6_27)),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f16198])).
% 7.04/1.25 thf(f16200,plain,(
% 7.04/1.25 spl6_1 | ~spl6_27),
% 7.04/1.25 inference(avatar_contradiction_clause,[],[f16199])).
% 7.04/1.25 thf(f16213,plain,(
% 7.04/1.25 ($false != $false) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | spl6_27),
% 7.04/1.25 inference(constrained_superposition,[],[f16095,f2796])).
% 7.04/1.25 thf(f16246,plain,(
% 7.04/1.25 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | spl6_27),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f16213])).
% 7.04/1.25 thf(f16247,plain,(
% 7.04/1.25 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ($true = ((sK4 @ sK2))) | spl6_27),
% 7.04/1.25 inference(beta-eta_normalization,[],[f16246])).
% 7.04/1.25 thf(f16255,plain,(
% 7.04/1.25 ($true = ((sK4 @ sK2))) | spl6_27),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f16247,f16095])).
% 7.04/1.25 thf(f16256,plain,(
% 7.04/1.25 $false | (spl6_1 | spl6_27)),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f16255,f35])).
% 7.04/1.25 thf(f16257,plain,(
% 7.04/1.25 spl6_1 | spl6_27),
% 7.04/1.25 inference(avatar_contradiction_clause,[],[f16256])).
% 7.04/1.25 thf(f17860,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ X0 @ sK1))) | ($true != ((X0 @ sK3))) | ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) ) | (~spl6_2 | ~spl6_14)),
% 7.04/1.25 inference(constrained_superposition,[],[f38,f5410])).
% 7.04/1.25 thf(f17955,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ X0 @ sK1))) | ($true != ((X0 @ sK3))) | ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) ) | (~spl6_2 | ~spl6_14)),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f17860])).
% 7.04/1.25 thf(f17956,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ X0 @ sK1))) | ($true != ((X0 @ sK3))) | ($true = ((~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))))) ) | (~spl6_2 | ~spl6_14)),
% 7.04/1.25 inference(beta-eta_normalization,[],[f17955])).
% 7.04/1.25 thf(f17957,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ X0 @ sK1))) | ($true != ((X0 @ sK3))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) ) | (~spl6_2 | ~spl6_14)),
% 7.04/1.25 inference(not_proxy_clausification,[],[f17956])).
% 7.04/1.25 thf(f17982,plain,(
% 7.04/1.25 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK3))) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ X0 @ sK1)))) ) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f17957,f16095])).
% 7.04/1.25 thf(f21451,plain,(
% 7.04/1.25 ($true != (((^[Y0 : $i]: ($true)) @ sK3))) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ (^[Y0 : $i]: ($true)) @ sK1))) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 7.04/1.25 inference(primitive_instantiation,[],[f17982])).
% 7.04/1.25 thf(f21686,plain,(
% 7.04/1.25 ($true != $true) | ($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ (^[Y0 : $i]: ($true)) @ sK1))) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 7.04/1.25 inference(beta-eta_normalization,[],[f21451])).
% 7.04/1.25 thf(f21687,plain,(
% 7.04/1.25 ($true = ((sP0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ (^[Y0 : $i]: ($true)) @ sK1))) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f21686])).
% 7.04/1.25 thf(f21705,plain,(
% 7.04/1.25 $false | (~spl6_2 | ~spl6_14 | spl6_27)),
% 7.04/1.25 inference(forward_subsumption_resolution,[],[f21687,f140])).
% 7.04/1.25 thf(f21706,plain,(
% 7.04/1.25 ~spl6_2 | ~spl6_14 | spl6_27),
% 7.04/1.25 inference(avatar_contradiction_clause,[],[f21705])).
% 7.04/1.25 thf(f21711,plain,(
% 7.04/1.25 ($true = $false) | (~spl6_14 | ~spl6_27)),
% 7.04/1.25 inference(constrained_superposition,[],[f16096,f5410])).
% 7.04/1.25 thf(f21837,plain,(
% 7.04/1.25 $false | (~spl6_14 | ~spl6_27)),
% 7.04/1.25 inference(trivial_inequality_removal,[],[f21711])).
% 7.04/1.25 thf(f21838,plain,(
% 7.04/1.25 ~spl6_14 | ~spl6_27),
% 7.04/1.25 inference(avatar_contradiction_clause,[],[f21837])).
% 7.04/1.25 cnf(s1, plain, ~spl6_1 | spl6_2, inference(sat_conversion,[],[f39])).
% 7.04/1.25 cnf(s15, plain, ~spl6_1 | ~spl6_2 | spl6_14 | spl6_21, inference(sat_conversion,[],[f10077])).
% 7.04/1.25 cnf(s17, plain, ~spl6_1 | ~spl6_21, inference(sat_conversion,[],[f10243])).
% 7.04/1.25 cnf(s22, plain, spl6_1 | ~spl6_27, inference(sat_conversion,[],[f16200])).
% 7.04/1.25 cnf(s24, plain, spl6_1 | spl6_27, inference(sat_conversion,[],[f16257])).
% 7.04/1.25 cnf(s36, plain, ~spl6_2 | ~spl6_14 | spl6_27, inference(sat_conversion,[],[f21706])).
% 7.04/1.25 cnf(s38, plain, ~spl6_14 | ~spl6_27, inference(sat_conversion,[],[f21838])).
% 7.04/1.25 cnf(s43, plain, spl6_1, inference(rat,[],[s22,s24])).
% 7.04/1.25 cnf(s45, plain, ~spl6_21, inference(rat,[],[s17,s43])).
% 7.04/1.25 cnf(s46, plain, spl6_2, inference(rat,[],[s1,s43])).
% 7.04/1.25 cnf(s47, plain, spl6_14, inference(rat,[],[s15,s45,s43,s46])).
% 7.04/1.25 cnf(s48, plain, ~spl6_27, inference(rat,[],[s38,s47])).
% 7.04/1.25 cnf(s49, plain, $false, inference(rat,[],[s36,s46,s48,s47])).
% 7.04/1.25 thf(f21840,plain,(
% 7.04/1.25 $false),
% 7.04/1.25 inference(avatar_sat_refutation,[],[s49])).
% 7.04/1.25 % SZS output end Proof for theBenchmark
% 7.04/1.25 % (1487015)------------------------------
% 7.04/1.25 % (1487015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.04/1.25 % (1487015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.04/1.25 % (1487015)CaDiCaL version: 2.1.3
% 7.04/1.25 % (1487015)Termination reason: Refutation
% 7.04/1.25 % (1487015)Time elapsed: 0.748 s
% 7.04/1.25 % (1487015)Peak memory usage: 18 MB
% 7.04/1.25 % (1487015)Instructions burned: 3167 (million)
% 7.04/1.25 % (1486932)Success in time 1.041 s
% 7.04/1.25 % Vampire exiting
%------------------------------------------------------------------------------