%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET598^5 : 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 : n007.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 08:23:40 AM UTC 2026
% Result : Theorem 7.45s 1.36s
% Output : Refutation 7.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET598^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 % Computer : n007.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:36:41 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.25 Running first-order model finding
% 0.11/0.25 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
% 4.16/0.97 % (3365833)Will run a generic schedule for satisfiability detection.
% 4.16/0.97 % (3365843)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4036728495:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 4.16/0.97 % (3365842)% WARNING: option uhcvi not known.
% 4.16/0.97 % (3365841)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3534049055_3000 on theBenchmark for (3000ds/0Mi)
% 4.16/0.97 % (3365842)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1660296174:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 4.16/0.97 % (3365844)dis+10_1_sil=32000:sp=arity:random_seed=379940976:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 4.16/0.97 % (3365842)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.16/0.97 % (3365845)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1597854:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 4.16/0.97 % (3365847)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=500603868:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 4.16/0.97 % (3365846)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3802062231:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 4.16/0.97 % Exception at run slice level
% 4.16/0.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.16/0.97 % (3365845)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.16/0.97 % (3365842)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.16/0.97 % (3365862)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3301138760:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.16/0.97 % Exception at run slice level
% 4.16/0.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.16/0.97 % (3365872)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2105457826:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.16/0.97 % (3365844)Instruction limit reached!
% 4.16/0.97 % (3365844)------------------------------
% 4.16/0.97 % (3365844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/0.97 % (3365844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/0.97 % (3365844)CaDiCaL version: 2.1.3
% 4.16/0.97 % (3365844)Termination reason: Instruction limit
% 4.16/0.97 % (3365844)Termination phase: Saturation
% 4.16/0.97 % (3365844)Time elapsed: 0.052 s
% 4.16/0.97 % (3365844)Peak memory usage: 12 MB
% 4.16/0.97 % (3365844)Instructions burned: 105 (million)
% 4.16/0.97 % (3365845)Instruction limit reached!
% 4.16/0.97 % (3365845)------------------------------
% 4.16/0.97 % (3365845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/0.97 % (3365845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/0.97 % (3365845)CaDiCaL version: 2.1.3
% 4.16/0.97 % (3365845)Termination reason: Instruction limit
% 4.16/0.97 % (3365845)Termination phase: Saturation
% 4.16/0.97 % (3365845)Time elapsed: 0.056 s
% 4.16/0.97 % (3365845)Peak memory usage: 12 MB
% 4.16/0.97 % (3365845)Instructions burned: 118 (million)
% 4.16/0.97 % (3365846)Instruction limit reached!
% 4.16/0.97 % (3365846)------------------------------
% 4.16/0.97 % (3365846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/0.97 % (3365846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/0.97 % (3365846)CaDiCaL version: 2.1.3
% 4.16/0.97 % (3365846)Termination reason: Instruction limit
% 4.16/0.97 % (3365846)Termination phase: Saturation
% 4.16/0.97 % (3365846)Time elapsed: 0.064 s
% 4.16/0.97 % (3365846)Peak memory usage: 13 MB
% 4.16/0.97 % (3365846)Instructions burned: 131 (million)
% 4.16/0.97 % (3365889)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=3011299923:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.16/0.97 % (3365889)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.16/0.97 % (3365889)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.16/0.97 % (3365892)ott-21_1_sil=16000:fs=off:random_seed=1277491071:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.16/0.97 % (3365847)Instruction limit reached!
% 7.45/1.36 % (3365847)------------------------------
% 7.45/1.36 % (3365847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365847)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365847)Termination reason: Instruction limit
% 7.45/1.36 % (3365847)Termination phase: Saturation
% 7.45/1.36 % (3365847)Time elapsed: 0.080 s
% 7.45/1.36 % (3365847)Peak memory usage: 13 MB
% 7.45/1.36 % (3365847)Instructions burned: 161 (million)
% 7.45/1.36 % (3365893)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3528044948:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 7.45/1.36 % (3365900)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=49414830:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3365872)Instruction limit reached!
% 7.45/1.36 % (3365872)------------------------------
% 7.45/1.36 % (3365872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365872)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365872)Termination reason: Instruction limit
% 7.45/1.36 % (3365872)Termination phase: Saturation
% 7.45/1.36 % (3365872)Time elapsed: 0.073 s
% 7.45/1.36 % (3365872)Peak memory usage: 13 MB
% 7.45/1.36 % (3365872)Instructions burned: 133 (million)
% 7.45/1.36 % (3365911)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2610779195:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 7.45/1.36 % (3365916)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=473195387:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3365930)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=2578001872: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)
% 7.45/1.36 % (3365930)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.36 % (3365892)Instruction limit reached!
% 7.45/1.36 % (3365892)------------------------------
% 7.45/1.36 % (3365892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365892)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365892)Termination reason: Instruction limit
% 7.45/1.36 % (3365892)Termination phase: Saturation
% 7.45/1.36 % (3365892)Time elapsed: 0.083 s
% 7.45/1.36 % (3365892)Peak memory usage: 12 MB
% 7.45/1.36 % (3365892)Instructions burned: 181 (million)
% 7.45/1.36 % (3365938)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3435607495:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 7.45/1.36 % (3365938)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.36 % (3365893)Instruction limit reached!
% 7.45/1.36 % (3365893)------------------------------
% 7.45/1.36 % (3365893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365893)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365893)Termination reason: Instruction limit
% 7.45/1.36 % (3365893)Termination phase: Saturation
% 7.45/1.36 % (3365893)Time elapsed: 0.237 s
% 7.45/1.36 % (3365893)Peak memory usage: 13 MB
% 7.45/1.36 % (3365893)Instructions burned: 479 (million)
% 7.45/1.36 % (3365973)fmb+10_1_sil=64000:random_seed=705318741:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 7.45/1.36 % (3365973)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3365975)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=367486828:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3365977)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=306536033:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3365889)Instruction limit reached!
% 7.45/1.36 % (3365889)------------------------------
% 7.45/1.36 % (3365889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365889)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365889)Termination reason: Instruction limit
% 7.45/1.36 % (3365889)Termination phase: Saturation
% 7.45/1.36 % (3365889)Time elapsed: 0.327 s
% 7.45/1.36 % (3365889)Peak memory usage: 15 MB
% 7.45/1.36 % (3365889)Instructions burned: 684 (million)
% 7.45/1.36 % (3365979)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1205980037:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 7.45/1.36 % (3365979)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.36 % (3365980)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1361946668:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 7.45/1.36 % (3365980)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.45/1.36 % (3365980)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.45/1.36 % (3365930)Instruction limit reached!
% 7.45/1.36 % (3365930)------------------------------
% 7.45/1.36 % (3365930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365930)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365930)Termination reason: Instruction limit
% 7.45/1.36 % (3365930)Termination phase: Saturation
% 7.45/1.36 % (3365930)Time elapsed: 0.327 s
% 7.45/1.36 % (3365930)Peak memory usage: 16 MB
% 7.45/1.36 % (3365930)Instructions burned: 692 (million)
% 7.45/1.36 % (3365999)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1900260730:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3366013)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=604529507:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3366028)ott-2_1_sil=16000:newcnf=on:random_seed=3209520456:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 7.45/1.36 % (3366028)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.36 % (3365938)Instruction limit reached!
% 7.45/1.36 % (3365938)------------------------------
% 7.45/1.36 % (3365938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365938)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365938)Termination reason: Instruction limit
% 7.45/1.36 % (3365938)Termination phase: Saturation
% 7.45/1.36 % (3365938)Time elapsed: 0.439 s
% 7.45/1.36 % (3365938)Peak memory usage: 17 MB
% 7.45/1.36 % (3365938)Instructions burned: 879 (million)
% 7.45/1.36 % (3366036)ott+10_1_sil=32000:tgt=ground:random_seed=2016138723:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 7.45/1.36 % (3365911)Instruction limit reached!
% 7.45/1.36 % (3365911)------------------------------
% 7.45/1.36 % (3365911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3365911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3365911)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3365911)Termination reason: Instruction limit
% 7.45/1.36 % (3365911)Termination phase: Saturation
% 7.45/1.36 % (3365911)Time elapsed: 0.552 s
% 7.45/1.36 % (3365911)Peak memory usage: 17 MB
% 7.45/1.36 % (3365911)Instructions burned: 1180 (million)
% 7.45/1.36 % (3366038)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2230436504:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 7.45/1.36 % Exception at run slice level
% 7.45/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.36 % (3366040)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2964772883:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 7.45/1.36 % (3366040)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.45/1.36 % (3366028)Instruction limit reached!
% 7.45/1.36 % (3366028)------------------------------
% 7.45/1.36 % (3366028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3366028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3366028)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3366028)Termination reason: Instruction limit
% 7.45/1.36 % (3366028)Termination phase: Saturation
% 7.45/1.36 % (3366028)Time elapsed: 0.384 s
% 7.45/1.36 % (3366028)Peak memory usage: 18 MB
% 7.45/1.36 % (3366028)Instructions burned: 869 (million)
% 7.45/1.36 % (3366042)dis+21_1_sil=32000:sas=cadical:random_seed=895391746:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 7.45/1.36 % (3366040) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3365833-3366040"...
% 7.45/1.36 % (3366040)...printing done.
% 7.45/1.36 % (3366040)Refutation found. Thanks to Tanya!
% 7.45/1.36 % SZS status Theorem for theBenchmark
% 7.45/1.36 % SZS output start Proof for theBenchmark
% 7.45/1.36 thf(type_def_5, type, a: $tType).
% 7.45/1.36 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 7.45/1.36 thf(func_def_1, type, vAND: ($o > $o > $o)).
% 7.45/1.36 thf(func_def_2, type, db0: !>[X0: $tType]:(X0)).
% 7.45/1.36 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 7.45/1.36 thf(func_def_6, type, sP0: ((a > $o) > (a > $o) > (a > $o) > $o)).
% 7.45/1.36 thf(func_def_7, type, sK1: ((a > $o) > (a > $o) > (a > $o) > a > $o)).
% 7.45/1.36 thf(func_def_8, type, sK2: ((a > $o) > (a > $o) > (a > $o) > a)).
% 7.45/1.36 thf(func_def_9, type, sK3: ((a > $o) > (a > $o) > a)).
% 7.45/1.36 thf(func_def_10, type, sK4: ((a > $o) > (a > $o) > a)).
% 7.45/1.36 thf(func_def_11, type, sK5: (a > $o)).
% 7.45/1.36 thf(func_def_12, type, sK6: (a > $o)).
% 7.45/1.36 thf(func_def_13, type, sK7: (a > $o)).
% 7.45/1.36 thf(func_def_14, type, sK8: a).
% 7.45/1.36 thf(func_def_15, type, sK9: a).
% 7.45/1.36 thf(func_def_16, type, vNOT: ($o > $o)).
% 7.45/1.36 thf(func_def_18, type, sK11: a).
% 7.45/1.36 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 7.45/1.36 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 7.45/1.36 thf(func_def_21, type, sK12: ((a > $o) > a)).
% 7.45/1.36 thf(func_def_22, type, sK13: ((a > $o) > (a > a > $o) > (a > a > $o) > (a > a > $o) > a)).
% 7.45/1.36 thf(func_def_23, type, sK14: ((a > $o) > a)).
% 7.45/1.36 thf(func_def_24, type, sK15: ((a > $o) > a)).
% 7.45/1.36 thf(func_def_25, type, sK16: ((a > $o) > a)).
% 7.45/1.36 thf(func_def_26, type, sK17: a).
% 7.45/1.36 thf(func_def_27, type, sK18: ((a > a > $o) > (a > a > a) > (a > $o) > (a > a > $o) > (a > $o) > a)).
% 7.45/1.36 thf(f1,conjecture,(
% 7.45/1.36 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((X0 = (^[X3 : a] : ((X2 @ X3) & (X1 @ X3)))) <=> (! [X4 : (a > $o)] : ((! [X3 : a] : ((X4 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X4 @ X3) => (X1 @ X3))) => ! [X3 : a] : ((X4 @ X3) => (X0 @ X3))) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 7.45/1.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_57_pme)).
% 7.45/1.36 thf(f2,negated_conjecture,(
% 7.45/1.36 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((X0 = (^[X3 : a] : ((X2 @ X3) & (X1 @ X3)))) <=> (! [X4 : (a > $o)] : ((! [X3 : a] : ((X4 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X4 @ X3) => (X1 @ X3))) => ! [X3 : a] : ((X4 @ X3) => (X0 @ X3))) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 7.45/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 7.45/1.36 thf(f3,plain,(
% 7.45/1.36 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((X0 = (^[X3 : a] : ((X2 @ X3) & (X1 @ X3)))) <=> (! [X4 : (a > $o)] : ((! [X5 : a] : ((X4 @ X5) => (X2 @ X5)) & ! [X6 : a] : ((X4 @ X6) => (X1 @ X6))) => ! [X7 : a] : ((X4 @ X7) => (X0 @ X7))) & ! [X8 : a] : ((X0 @ X8) => (X2 @ X8)) & ! [X9 : a] : ((X0 @ X9) => (X1 @ X9))))),
% 7.45/1.36 inference(rectify,[],[f2])).
% 7.45/1.36 thf(f4,plain,(
% 7.45/1.36 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0) <=> (! [X4 : (a > $o)] : ((! [X5 : a] : ((((X4 @ X5)) = $true) => (((X2 @ X5)) = $true)) & ! [X6 : a] : ((((X4 @ X6)) = $true) => (((X1 @ X6)) = $true))) => ! [X7 : a] : ((((X4 @ X7)) = $true) => (((X0 @ X7)) = $true))) & ! [X8 : a] : ((((X0 @ X8)) = $true) => (((X2 @ X8)) = $true)) & ! [X9 : a] : ((((X0 @ X9)) = $true) => (((X1 @ X9)) = $true))))),
% 7.45/1.36 inference(fool_elimination,[],[f3])).
% 7.45/1.36 thf(f5,plain,(
% 7.45/1.36 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0) <=> (! [X3 : (a > $o)] : ((! [X4 : a] : (($true = ((X3 @ X4))) => ($true = ((X2 @ X4)))) & ! [X5 : a] : (($true = ((X3 @ X5))) => ($true = ((X1 @ X5))))) => ! [X6 : a] : (($true = ((X3 @ X6))) => ($true = ((X0 @ X6))))) & ! [X7 : a] : ((((X0 @ X7)) = $true) => ($true = ((X2 @ X7)))) & ! [X8 : a] : ((((X0 @ X8)) = $true) => ($true = ((X1 @ X8))))))),
% 7.45/1.36 inference(rectify,[],[f4])).
% 7.45/1.36 thf(f6,plain,(
% 7.45/1.36 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0) <~> (! [X3 : (a > $o)] : (! [X6 : a] : (($true = ((X0 @ X6))) | ($true != ((X3 @ X6)))) | (? [X4 : a] : (($true != ((X2 @ X4))) & ($true = ((X3 @ X4)))) | ? [X5 : a] : (($true != ((X1 @ X5))) & ($true = ((X3 @ X5)))))) & ! [X7 : a] : (($true = ((X2 @ X7))) | (((X0 @ X7)) != $true)) & ! [X8 : a] : (($true = ((X1 @ X8))) | (((X0 @ X8)) != $true))))),
% 7.45/1.36 inference(ennf_transformation,[],[f5])).
% 7.45/1.36 thf(f7,plain,(
% 7.45/1.36 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0) <~> (! [X3 : (a > $o)] : (! [X6 : a] : (($true = ((X0 @ X6))) | ($true != ((X3 @ X6)))) | ? [X4 : a] : (($true != ((X2 @ X4))) & ($true = ((X3 @ X4)))) | ? [X5 : a] : (($true != ((X1 @ X5))) & ($true = ((X3 @ X5))))) & ! [X7 : a] : (($true = ((X2 @ X7))) | (((X0 @ X7)) != $true)) & ! [X8 : a] : (($true = ((X1 @ X8))) | (((X0 @ X8)) != $true))))),
% 7.45/1.36 inference(flattening,[],[f6])).
% 7.45/1.36 thf(f8,definition,(
% 7.45/1.36 ! [X0 : (a > $o),X2 : (a > $o),X1 : (a > $o)] : (($true = ((sP0 @ X1 @ X2 @ X0))) <=> ! [X3 : (a > $o)] : (! [X6 : a] : (($true = ((X0 @ X6))) | ($true != ((X3 @ X6)))) | ? [X4 : a] : (($true != ((X2 @ X4))) & ($true = ((X3 @ X4)))) | ? [X5 : a] : (($true != ((X1 @ X5))) & ($true = ((X3 @ X5))))))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 7.45/1.36 thf(f9,plain,(
% 7.45/1.36 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0) <~> (($true = ((sP0 @ X1 @ X2 @ X0))) & ! [X7 : a] : (($true = ((X2 @ X7))) | (((X0 @ X7)) != $true)) & ! [X8 : a] : (($true = ((X1 @ X8))) | (((X0 @ X8)) != $true))))),
% 7.45/1.36 inference(definition_folding,[],[f7,f8])).
% 7.45/1.36 thf(f10,plain,(
% 7.45/1.36 ! [X0 : (a > $o),X2 : (a > $o),X1 : (a > $o)] : ((($true = ((sP0 @ X1 @ X2 @ X0))) | ? [X3 : (a > $o)] : (? [X6 : a] : (($true != ((X0 @ X6))) & ($true = ((X3 @ X6)))) & ! [X4 : a] : (($true = ((X2 @ X4))) | ($true != ((X3 @ X4)))) & ! [X5 : a] : (($true = ((X1 @ X5))) | ($true != ((X3 @ X5)))))) & (! [X3 : (a > $o)] : (! [X6 : a] : (($true = ((X0 @ X6))) | ($true != ((X3 @ X6)))) | ? [X4 : a] : (($true != ((X2 @ X4))) & ($true = ((X3 @ X4)))) | ? [X5 : a] : (($true != ((X1 @ X5))) & ($true = ((X3 @ X5))))) | ($true != ((sP0 @ X1 @ X2 @ X0)))))),
% 7.45/1.36 inference(nnf_transformation,[],[f8])).
% 7.45/1.36 thf(f11,plain,(
% 7.45/1.36 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | ? [X3 : (a > $o)] : (? [X4 : a] : (($true != ((X0 @ X4))) & ($true = ((X3 @ X4)))) & ! [X5 : a] : (($true = ((X1 @ X5))) | ($true != ((X3 @ X5)))) & ! [X6 : a] : (($true = ((X2 @ X6))) | ($true != ((X3 @ X6)))))) & (! [X7 : (a > $o)] : (! [X8 : a] : ((((X0 @ X8)) = $true) | ($true != ((X7 @ X8)))) | ? [X9 : a] : ((((X1 @ X9)) != $true) & ($true = ((X7 @ X9)))) | ? [X10 : a] : (($true != ((X2 @ X10))) & ($true = ((X7 @ X10))))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 7.45/1.36 inference(rectify,[],[f10])).
% 7.45/1.36 thf(f12,plain,(
% 7.45/1.36 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | ((($true != ((X0 @ (sK2 @ X2 @ X1 @ X0)))) & ($true = ((sK1 @ X2 @ X1 @ X0 @ (sK2 @ X2 @ X1 @ X0))))) & ! [X5 : a] : (($true = ((X1 @ X5))) | ($true != ((sK1 @ X2 @ X1 @ X0 @ X5)))) & ! [X6 : a] : (($true = ((X2 @ X6))) | ($true != ((sK1 @ X2 @ X1 @ X0 @ X6)))))) & (! [X7 : (a > $o)] : (! [X8 : a] : ((((X0 @ X8)) = $true) | ($true != ((X7 @ X8)))) | (($true != ((X1 @ (sK3 @ X7 @ X1)))) & ($true = ((X7 @ (sK3 @ X7 @ X1))))) | (($true != ((X2 @ (sK4 @ X7 @ X2)))) & ($true = ((X7 @ (sK4 @ X7 @ X2)))))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 7.45/1.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X10,sK4 @ X7 @ X2),skolemize(X10,sK4 @ X7 @ X2),skolemize(X10,sK4 @ X7 @ X2),skolemize(X10,sK4 @ X7 @ X2)],[f11])).
% 7.45/1.36 thf(f13,plain,(
% 7.45/1.36 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((($true != ((sP0 @ X1 @ X2 @ X0))) | ? [X7 : a] : (($true != ((X2 @ X7))) & (((X0 @ X7)) = $true)) | ? [X8 : a] : (($true != ((X1 @ X8))) & (((X0 @ X8)) = $true))) | ((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) != X0)) & ((($true = ((sP0 @ X1 @ X2 @ X0))) & ! [X7 : a] : (($true = ((X2 @ X7))) | (((X0 @ X7)) != $true)) & ! [X8 : a] : (($true = ((X1 @ X8))) | (((X0 @ X8)) != $true))) | ((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0)))),
% 7.45/1.36 inference(nnf_transformation,[],[f9])).
% 7.45/1.36 thf(f14,plain,(
% 7.45/1.36 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true != ((sP0 @ X1 @ X2 @ X0))) | ? [X7 : a] : (($true != ((X2 @ X7))) & (((X0 @ X7)) = $true)) | ? [X8 : a] : (($true != ((X1 @ X8))) & (((X0 @ X8)) = $true)) | ((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) != X0)) & ((($true = ((sP0 @ X1 @ X2 @ X0))) & ! [X7 : a] : (($true = ((X2 @ X7))) | (((X0 @ X7)) != $true)) & ! [X8 : a] : (($true = ((X1 @ X8))) | (((X0 @ X8)) != $true))) | ((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0)))),
% 7.45/1.36 inference(flattening,[],[f13])).
% 7.45/1.36 thf(f15,plain,(
% 7.45/1.36 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true != ((sP0 @ X1 @ X2 @ X0))) | ? [X3 : a] : ((((X2 @ X3)) != $true) & (((X0 @ X3)) = $true)) | ? [X4 : a] : (($true != ((X1 @ X4))) & ($true = ((X0 @ X4)))) | ((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) != X0)) & ((($true = ((sP0 @ X1 @ X2 @ X0))) & ! [X5 : a] : ((((X2 @ X5)) = $true) | ($true != ((X0 @ X5)))) & ! [X6 : a] : ((((X1 @ X6)) = $true) | ($true != ((X0 @ X6))))) | ((^[Y0 : a]: ((X1 @ Y0) & (X2 @ Y0))) = X0)))),
% 7.45/1.36 inference(rectify,[],[f14])).
% 7.45/1.36 thf(f16,plain,(
% 7.45/1.36 (($true != ((sP0 @ sK6 @ sK7 @ sK5))) | (($true != ((sK7 @ sK8))) & ($true = ((sK5 @ sK8)))) | (($true != ((sK6 @ sK9))) & ($true = ((sK5 @ sK9)))) | (sK5 != (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))) & ((($true = ((sP0 @ sK6 @ sK7 @ sK5))) & ! [X5 : a] : (($true = ((sK7 @ X5))) | ($true != ((sK5 @ X5)))) & ! [X6 : a] : (($true = ((sK6 @ X6))) | ($true != ((sK5 @ X6))))) | (sK5 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0)))))),
% 7.45/1.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8),skolemize(X4,sK9)],[f15])).
% 7.45/1.36 thf(f17,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o),X8 : a,X7 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true != ((X7 @ X8))) | ($true = ((X7 @ (sK3 @ X7 @ X1)))) | ($true = ((X7 @ (sK4 @ X7 @ X2)))) | (((X0 @ X8)) = $true)) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f18,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o),X8 : a,X7 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true != ((X7 @ X8))) | ($true = ((X7 @ (sK3 @ X7 @ X1)))) | ($true != ((X2 @ (sK4 @ X7 @ X2)))) | (((X0 @ X8)) = $true)) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f19,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o),X8 : a,X7 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true != ((X7 @ X8))) | ($true != ((X1 @ (sK3 @ X7 @ X1)))) | ($true = ((X7 @ (sK4 @ X7 @ X2)))) | (((X0 @ X8)) = $true)) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f20,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o),X8 : a,X7 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true != ((X7 @ X8))) | ($true != ((X1 @ (sK3 @ X7 @ X1)))) | ($true != ((X2 @ (sK4 @ X7 @ X2)))) | (((X0 @ X8)) = $true)) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f21,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o),X6 : a] : (($true != ((sK1 @ X2 @ X1 @ X0 @ X6))) | ($true = ((X2 @ X6))) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f22,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o),X5 : a] : (($true != ((sK1 @ X2 @ X1 @ X0 @ X5))) | ($true = ((X1 @ X5))) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f23,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true = ((sK1 @ X2 @ X1 @ X0 @ (sK2 @ X2 @ X1 @ X0)))) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f24,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((X0 @ (sK2 @ X2 @ X1 @ X0)))) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 7.45/1.36 inference(cnf_transformation,[],[f12])).
% 7.45/1.36 thf(f25,plain,(
% 7.45/1.36 ( ! [X6 : a] : (($true = ((sK6 @ X6))) | ($true != ((sK5 @ X6))) | (sK5 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))) )),
% 7.45/1.36 inference(cnf_transformation,[],[f16])).
% 7.45/1.36 thf(f26,plain,(
% 7.45/1.36 ( ! [X5 : a] : (($true = ((sK7 @ X5))) | ($true != ((sK5 @ X5))) | (sK5 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))) )),
% 7.45/1.36 inference(cnf_transformation,[],[f16])).
% 7.45/1.36 thf(f27,plain,(
% 7.45/1.36 ($true = ((sP0 @ sK6 @ sK7 @ sK5))) | (sK5 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))),
% 7.45/1.36 inference(cnf_transformation,[],[f16])).
% 7.45/1.36 thf(f28,plain,(
% 7.45/1.36 ($true != ((sP0 @ sK6 @ sK7 @ sK5))) | ($true = ((sK5 @ sK8))) | ($true = ((sK5 @ sK9))) | (sK5 != (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))),
% 7.45/1.36 inference(cnf_transformation,[],[f16])).
% 7.45/1.36 thf(f29,plain,(
% 7.45/1.36 ($true != ((sP0 @ sK6 @ sK7 @ sK5))) | ($true = ((sK5 @ sK8))) | ($true != ((sK6 @ sK9))) | (sK5 != (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))),
% 7.45/1.36 inference(cnf_transformation,[],[f16])).
% 7.45/1.36 thf(f30,plain,(
% 7.45/1.36 ($true != ((sP0 @ sK6 @ sK7 @ sK5))) | ($true != ((sK7 @ sK8))) | ($true = ((sK5 @ sK9))) | (sK5 != (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))),
% 7.45/1.36 inference(cnf_transformation,[],[f16])).
% 7.45/1.36 thf(f31,plain,(
% 7.45/1.36 ($true != ((sP0 @ sK6 @ sK7 @ sK5))) | ($true != ((sK7 @ sK8))) | ($true != ((sK6 @ sK9))) | (sK5 != (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))),
% 7.45/1.36 inference(cnf_transformation,[],[f16])).
% 7.45/1.36 thf(f33,definition,(
% 7.45/1.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 7.45/1.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 7.45/1.36 thf(f35,definition,(
% 7.45/1.36 spl10_1 <=> (sK5 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition])).
% 7.45/1.36 thf(f36,plain,(
% 7.45/1.36 (sK5 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0)))) | ~spl10_1),
% 7.45/1.36 inference(avatar_component_clause,[],[f35])).
% 7.45/1.36 thf(f38,definition,(
% 7.45/1.36 spl10_2 <=> ! [X6 : a] : (($true = ((sK6 @ X6))) | ($true != ((sK5 @ X6))))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition])).
% 7.45/1.36 thf(f39,plain,(
% 7.45/1.36 ( ! [X6 : a] : (($true != ((sK5 @ X6))) | ($true = ((sK6 @ X6)))) ) | ~spl10_2),
% 7.45/1.36 inference(avatar_component_clause,[],[f38])).
% 7.45/1.36 thf(f40,plain,(
% 7.45/1.36 spl10_1 | spl10_2),
% 7.45/1.36 inference(avatar_split_clause,[],[f25,f38,f35])).
% 7.45/1.36 thf(f42,definition,(
% 7.45/1.36 spl10_3 <=> ! [X5 : a] : (($true = ((sK7 @ X5))) | ($true != ((sK5 @ X5))))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition])).
% 7.45/1.36 thf(f43,plain,(
% 7.45/1.36 ( ! [X5 : a] : (($true != ((sK5 @ X5))) | ($true = ((sK7 @ X5)))) ) | ~spl10_3),
% 7.45/1.36 inference(avatar_component_clause,[],[f42])).
% 7.45/1.36 thf(f44,plain,(
% 7.45/1.36 spl10_1 | spl10_3),
% 7.45/1.36 inference(avatar_split_clause,[],[f26,f42,f35])).
% 7.45/1.36 thf(f46,definition,(
% 7.45/1.36 spl10_4 <=> ($true = ((sP0 @ sK6 @ sK7 @ sK5)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition])).
% 7.45/1.36 thf(f47,plain,(
% 7.45/1.36 ($true = ((sP0 @ sK6 @ sK7 @ sK5))) | ~spl10_4),
% 7.45/1.36 inference(avatar_component_clause,[],[f46])).
% 7.45/1.36 thf(f48,plain,(
% 7.45/1.36 spl10_1 | spl10_4),
% 7.45/1.36 inference(avatar_split_clause,[],[f27,f46,f35])).
% 7.45/1.36 thf(f49,plain,(
% 7.45/1.36 (sK5 != (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0)))) | spl10_1),
% 7.45/1.36 inference(avatar_component_clause,[],[f35])).
% 7.45/1.36 thf(f51,definition,(
% 7.45/1.36 spl10_5 <=> ($true = ((sK5 @ sK9)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition])).
% 7.45/1.36 thf(f52,plain,(
% 7.45/1.36 ($true = ((sK5 @ sK9))) | ~spl10_5),
% 7.45/1.36 inference(avatar_component_clause,[],[f51])).
% 7.45/1.36 thf(f54,definition,(
% 7.45/1.36 spl10_6 <=> ($true = ((sK5 @ sK8)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition])).
% 7.45/1.36 thf(f55,plain,(
% 7.45/1.36 ($true = ((sK5 @ sK8))) | ~spl10_6),
% 7.45/1.36 inference(avatar_component_clause,[],[f54])).
% 7.45/1.36 thf(f56,plain,(
% 7.45/1.36 ($true != ((sP0 @ sK6 @ sK7 @ sK5))) | spl10_4),
% 7.45/1.36 inference(avatar_component_clause,[],[f46])).
% 7.45/1.36 thf(f57,plain,(
% 7.45/1.36 ~spl10_1 | spl10_5 | spl10_6 | ~spl10_4),
% 7.45/1.36 inference(avatar_split_clause,[],[f28,f46,f54,f51,f35])).
% 7.45/1.36 thf(f59,definition,(
% 7.45/1.36 spl10_7 <=> ($true = ((sK6 @ sK9)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition])).
% 7.45/1.36 thf(f60,plain,(
% 7.45/1.36 ($true != ((sK6 @ sK9))) | spl10_7),
% 7.45/1.36 inference(avatar_component_clause,[],[f59])).
% 7.45/1.36 thf(f61,plain,(
% 7.45/1.36 ~spl10_1 | ~spl10_7 | spl10_6 | ~spl10_4),
% 7.45/1.36 inference(avatar_split_clause,[],[f29,f46,f54,f59,f35])).
% 7.45/1.36 thf(f63,definition,(
% 7.45/1.36 spl10_8 <=> ($true = ((sK7 @ sK8)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition])).
% 7.45/1.36 thf(f64,plain,(
% 7.45/1.36 ($true != ((sK7 @ sK8))) | spl10_8),
% 7.45/1.36 inference(avatar_component_clause,[],[f63])).
% 7.45/1.36 thf(f65,plain,(
% 7.45/1.36 ~spl10_1 | spl10_5 | ~spl10_8 | ~spl10_4),
% 7.45/1.36 inference(avatar_split_clause,[],[f30,f46,f63,f51,f35])).
% 7.45/1.36 thf(f66,plain,(
% 7.45/1.36 ~spl10_1 | ~spl10_7 | ~spl10_8 | ~spl10_4),
% 7.45/1.36 inference(avatar_split_clause,[],[f31,f46,f63,f59,f35])).
% 7.45/1.36 thf(f94,plain,(
% 7.45/1.36 ( ! [X1 : a] : ((((sK5 @ X1)) = (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ X1)))) ) | ~spl10_1),
% 7.45/1.36 inference(argument_congruence,[],[f36])).
% 7.45/1.36 thf(f95,plain,(
% 7.45/1.36 ( ! [X1 : a] : (($true = ((sK5 @ X1))) | ($false = (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ X1)))) ) | ~spl10_1),
% 7.45/1.36 inference(iff_proxy_clausification,[],[f94])).
% 7.45/1.36 thf(f96,plain,(
% 7.45/1.36 ( ! [X1 : a] : (($false = ((sK5 @ X1))) | ($true = (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ X1)))) ) | ~spl10_1),
% 7.45/1.36 inference(iff_proxy_clausification,[],[f94])).
% 7.45/1.36 thf(f97,plain,(
% 7.45/1.36 ( ! [X1 : a] : (($false = ((sK5 @ X1))) | ($true = (((sK6 @ X1) & (sK7 @ X1))))) ) | ~spl10_1),
% 7.45/1.36 inference(beta-eta_normalization,[],[f96])).
% 7.45/1.36 thf(f98,plain,(
% 7.45/1.36 ( ! [X1 : a] : (($false = ((sK5 @ X1))) | ($true = ((sK7 @ X1)))) ) | ~spl10_1),
% 7.45/1.36 inference(and_proxy_clausification,[],[f97])).
% 7.45/1.36 thf(f99,plain,(
% 7.45/1.36 ( ! [X1 : a] : (($false = ((sK5 @ X1))) | ($true = ((sK6 @ X1)))) ) | ~spl10_1),
% 7.45/1.36 inference(and_proxy_clausification,[],[f97])).
% 7.45/1.36 thf(f100,plain,(
% 7.45/1.36 ( ! [X1 : a] : (($true = ((sK5 @ X1))) | ($false = (((sK6 @ X1) & (sK7 @ X1))))) ) | ~spl10_1),
% 7.45/1.36 inference(beta-eta_normalization,[],[f95])).
% 7.45/1.36 thf(f101,plain,(
% 7.45/1.36 ( ! [X1 : a] : (($true = ((sK5 @ X1))) | ($false = ((sK7 @ X1))) | ($false = ((sK6 @ X1)))) ) | ~spl10_1),
% 7.45/1.36 inference(and_proxy_clausification,[],[f100])).
% 7.45/1.36 thf(f169,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X3 : (a > $o),X0 : a,X1 : (a > $o)] : ((((sK3 @ (= @ X0) @ X1)) = X0) | ($true != ((sP0 @ X2 @ X1 @ X3))) | ($true = ((X0 = (sK4 @ (= @ X0) @ X2)))) | ($true = ((X3 @ X0)))) )),
% 7.45/1.36 inference(leibniz_equality_elimination,[],[f17])).
% 7.45/1.36 thf(f174,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X3 : (a > $o),X0 : a,X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X3))) | (((sK3 @ (= @ X0) @ X1)) = X0) | (((sK4 @ (= @ X0) @ X2)) = X0) | ($true = ((X3 @ X0)))) )),
% 7.45/1.36 inference(equality_proxy_clausification,[],[f169])).
% 7.45/1.36 thf(f180,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X3 : (a > $o),X0 : a,X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X3))) | (((sK3 @ (= @ X0) @ X1)) = X0) | ($true != ((X2 @ (sK4 @ (= @ X0) @ X2)))) | ($true = ((X3 @ X0)))) )),
% 7.45/1.36 inference(leibniz_equality_elimination,[],[f18])).
% 7.45/1.36 thf(f198,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X3 : (a > $o),X0 : a,X1 : (a > $o)] : (($true != ((sP0 @ X1 @ X2 @ X3))) | (((sK4 @ (= @ X0) @ X1)) = X0) | ($true != ((X2 @ (sK3 @ (= @ X0) @ X2)))) | ($true = ((X3 @ X0)))) )),
% 7.45/1.36 inference(leibniz_equality_elimination,[],[f19])).
% 7.45/1.36 thf(f205,plain,(
% 7.45/1.36 ($true = $false) | ($true = ((sK7 @ sK8))) | (~spl10_1 | ~spl10_6)),
% 7.45/1.36 inference(constrained_superposition,[],[f98,f55])).
% 7.45/1.36 thf(f212,plain,(
% 7.45/1.36 ($true = ((sK7 @ sK8))) | (~spl10_1 | ~spl10_6)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f205])).
% 7.45/1.36 thf(f217,plain,(
% 7.45/1.36 $false | (~spl10_1 | ~spl10_6 | spl10_8)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f212,f64])).
% 7.45/1.36 thf(f218,plain,(
% 7.45/1.36 ~spl10_1 | ~spl10_6 | spl10_8),
% 7.45/1.36 inference(avatar_contradiction_clause,[],[f217])).
% 7.45/1.36 thf(f228,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != $true) | ($true = ((X1 @ (sK2 @ X0 @ X1 @ X2)))) | ($true = ((sP0 @ X0 @ X1 @ X2))) | ($true = ((sP0 @ X0 @ X1 @ X2)))) )),
% 7.45/1.36 inference(constrained_superposition,[],[f22,f23])).
% 7.45/1.36 thf(f229,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != $true) | ($true = ((X0 @ (sK2 @ X0 @ X1 @ X2)))) | ($true = ((sP0 @ X0 @ X1 @ X2))) | ($true = ((sP0 @ X0 @ X1 @ X2)))) )),
% 7.45/1.36 inference(constrained_superposition,[],[f21,f23])).
% 7.45/1.36 thf(f230,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != $true) | ($true = ((X0 @ (sK2 @ X0 @ X1 @ X2)))) | ($true = ((sP0 @ X0 @ X1 @ X2)))) )),
% 7.45/1.36 inference(duplicate_literal_removal,[],[f229])).
% 7.45/1.36 thf(f231,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true = ((X0 @ (sK2 @ X0 @ X1 @ X2)))) | ($true = ((sP0 @ X0 @ X1 @ X2)))) )),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f230])).
% 7.45/1.36 thf(f232,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != $true) | ($true = ((X1 @ (sK2 @ X0 @ X1 @ X2)))) | ($true = ((sP0 @ X0 @ X1 @ X2)))) )),
% 7.45/1.36 inference(duplicate_literal_removal,[],[f228])).
% 7.45/1.36 thf(f233,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true = ((X1 @ (sK2 @ X0 @ X1 @ X2)))) | ($true = ((sP0 @ X0 @ X1 @ X2)))) )),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f232])).
% 7.45/1.36 thf(f278,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X3 : a,X0 : (a > a),X1 : (a > $o)] : (($true != $true) | ($true = ((sP0 @ X1 @ X2 @ (^[Y0 : a]: (sK5 @ (X0 @ Y0)))))) | ($false = ((sK7 @ X3))) | ($false = ((sK6 @ X3))) | (((X0 @ (sK2 @ X1 @ X2 @ (^[Y0 : a]: (sK5 @ (X0 @ Y0)))))) != X3)) ) | ~spl10_1),
% 7.45/1.36 inference(constrained_superposition,[],[f24,f101])).
% 7.45/1.36 thf(f285,plain,(
% 7.45/1.36 ( ! [X2 : (a > $o),X3 : a,X0 : (a > a),X1 : (a > $o)] : (($true = ((sP0 @ X1 @ X2 @ (^[Y0 : a]: (sK5 @ (X0 @ Y0)))))) | ($false = ((sK7 @ X3))) | ($false = ((sK6 @ X3))) | (((X0 @ (sK2 @ X1 @ X2 @ (^[Y0 : a]: (sK5 @ (X0 @ Y0)))))) != X3)) ) | ~spl10_1),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f278])).
% 7.45/1.36 thf(f366,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != $true) | ($false = ((sK7 @ X0))) | ($false = ((sK6 @ X0))) | ((((^[Y0 : a]: (Y0)) @ (sK2 @ sK6 @ sK7 @ (^[Y0 : a]: (sK5 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) != X0)) ) | (~spl10_1 | spl10_4)),
% 7.45/1.36 inference(constrained_superposition,[],[f56,f285])).
% 7.45/1.36 thf(f368,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($false = ((sK7 @ X0))) | ($false = ((sK6 @ X0))) | ((((^[Y0 : a]: (Y0)) @ (sK2 @ sK6 @ sK7 @ (^[Y0 : a]: (sK5 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) != X0)) ) | (~spl10_1 | spl10_4)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f366])).
% 7.45/1.36 thf(f369,plain,(
% 7.45/1.36 ( ! [X0 : a] : ((((sK2 @ sK6 @ sK7 @ sK5)) != X0) | ($false = ((sK6 @ X0))) | ($false = ((sK7 @ X0)))) ) | (~spl10_1 | spl10_4)),
% 7.45/1.36 inference(beta-eta_normalization,[],[f368])).
% 7.45/1.36 thf(f484,plain,(
% 7.45/1.36 ($false = ((sK6 @ (sK2 @ sK6 @ sK7 @ sK5)))) | ($false = ((sK7 @ (sK2 @ sK6 @ sK7 @ sK5)))) | (~spl10_1 | spl10_4)),
% 7.45/1.36 inference(equality_resolution,[],[f369])).
% 7.45/1.36 thf(f486,definition,(
% 7.45/1.36 spl10_14 <=> ($false = ((sK7 @ (sK2 @ sK6 @ sK7 @ sK5))))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition])).
% 7.45/1.36 thf(f487,plain,(
% 7.45/1.36 ($false = ((sK7 @ (sK2 @ sK6 @ sK7 @ sK5)))) | ~spl10_14),
% 7.45/1.36 inference(avatar_component_clause,[],[f486])).
% 7.45/1.36 thf(f489,definition,(
% 7.45/1.36 spl10_15 <=> ($false = ((sK6 @ (sK2 @ sK6 @ sK7 @ sK5))))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition])).
% 7.45/1.36 thf(f490,plain,(
% 7.45/1.36 ($false = ((sK6 @ (sK2 @ sK6 @ sK7 @ sK5)))) | ~spl10_15),
% 7.45/1.36 inference(avatar_component_clause,[],[f489])).
% 7.45/1.36 thf(f491,plain,(
% 7.45/1.36 spl10_14 | spl10_15 | ~spl10_1 | spl10_4),
% 7.45/1.36 inference(avatar_split_clause,[],[f484,f46,f35,f489,f486])).
% 7.45/1.36 thf(f605,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true = $false) | ($true = ((sP0 @ X0 @ (^[Y0 : a]: (sK7 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) | (sK6 != X0) | (sK5 != X1)) ) | ~spl10_14),
% 7.45/1.36 inference(constrained_superposition,[],[f487,f233])).
% 7.45/1.36 thf(f636,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true = ((sP0 @ X0 @ (^[Y0 : a]: (sK7 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) | (sK6 != X0) | (sK5 != X1)) ) | ~spl10_14),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f605])).
% 7.45/1.36 thf(f637,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : (a > $o)] : ((sK6 != X0) | ($true = ((sP0 @ X0 @ sK7 @ X1))) | (sK5 != X1)) ) | ~spl10_14),
% 7.45/1.36 inference(beta-eta_normalization,[],[f636])).
% 7.45/1.36 thf(f1477,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o)] : ((sK5 != X0) | ($true = ((sP0 @ sK6 @ sK7 @ X0)))) ) | ~spl10_14),
% 7.45/1.36 inference(equality_resolution,[],[f637])).
% 7.45/1.36 thf(f1487,plain,(
% 7.45/1.36 ($true = ((sP0 @ sK6 @ sK7 @ sK5))) | ~spl10_14),
% 7.45/1.36 inference(equality_resolution,[],[f1477])).
% 7.45/1.36 thf(f1490,plain,(
% 7.45/1.36 $false | (spl10_4 | ~spl10_14)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f1487,f56])).
% 7.45/1.36 thf(f1491,plain,(
% 7.45/1.36 spl10_4 | ~spl10_14),
% 7.45/1.36 inference(avatar_contradiction_clause,[],[f1490])).
% 7.45/1.36 thf(f1575,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true = $false) | ($true = ((sP0 @ (^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X0 @ X1))) | (sK7 != X0) | (sK5 != X1)) ) | ~spl10_15),
% 7.45/1.36 inference(constrained_superposition,[],[f231,f490])).
% 7.45/1.36 thf(f1589,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true = ((sP0 @ (^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X0 @ X1))) | (sK7 != X0) | (sK5 != X1)) ) | ~spl10_15),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f1575])).
% 7.45/1.36 thf(f1590,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : (a > $o)] : ((sK7 != X0) | ($true = ((sP0 @ sK6 @ X0 @ X1))) | (sK5 != X1)) ) | ~spl10_15),
% 7.45/1.36 inference(beta-eta_normalization,[],[f1589])).
% 7.45/1.36 thf(f1655,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o)] : ((sK5 != X0) | ($true = ((sP0 @ sK6 @ sK7 @ X0)))) ) | ~spl10_15),
% 7.45/1.36 inference(equality_resolution,[],[f1590])).
% 7.45/1.36 thf(f1659,plain,(
% 7.45/1.36 ($true = ((sP0 @ sK6 @ sK7 @ sK5))) | ~spl10_15),
% 7.45/1.36 inference(equality_resolution,[],[f1655])).
% 7.45/1.36 thf(f1662,plain,(
% 7.45/1.36 $false | (spl10_4 | ~spl10_15)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f1659,f56])).
% 7.45/1.36 thf(f1663,plain,(
% 7.45/1.36 spl10_4 | ~spl10_15),
% 7.45/1.36 inference(avatar_contradiction_clause,[],[f1662])).
% 7.45/1.36 thf(f1721,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | ($true != ((X0 @ X1))) | ($true != ((sK7 @ (sK3 @ X0 @ sK7)))) | ($true != ((sK6 @ (sK4 @ X0 @ sK6)))) | ($true = ((sK5 @ X1)))) ) | ~spl10_4),
% 7.45/1.36 inference(constrained_superposition,[],[f20,f47])).
% 7.45/1.36 thf(f1722,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != $true) | (((sK3 @ (= @ X0) @ sK7)) = X0) | (((sK4 @ (= @ X0) @ sK6)) = X0) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(constrained_superposition,[],[f174,f47])).
% 7.45/1.36 thf(f1723,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != $true) | (((sK3 @ (= @ X0) @ sK7)) = X0) | ($true != ((sK6 @ (sK4 @ (= @ X0) @ sK6)))) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(constrained_superposition,[],[f180,f47])).
% 7.45/1.36 thf(f1724,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != $true) | (((sK4 @ (= @ X0) @ sK6)) = X0) | ($true != ((sK7 @ (sK3 @ (= @ X0) @ sK7)))) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(constrained_superposition,[],[f198,f47])).
% 7.45/1.36 thf(f1725,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != ((sK7 @ (sK3 @ (= @ X0) @ sK7)))) | (((sK4 @ (= @ X0) @ sK6)) = X0) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f1724])).
% 7.45/1.36 thf(f1726,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != ((sK6 @ (sK4 @ (= @ X0) @ sK6)))) | (((sK3 @ (= @ X0) @ sK7)) = X0) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f1723])).
% 7.45/1.36 thf(f1727,plain,(
% 7.45/1.36 ( ! [X0 : a] : ((((sK4 @ (= @ X0) @ sK6)) = X0) | (((sK3 @ (= @ X0) @ sK7)) = X0) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f1722])).
% 7.45/1.36 thf(f1728,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : a] : (($true != ((sK7 @ (sK3 @ X0 @ sK7)))) | ($true != ((X0 @ X1))) | ($true != ((sK6 @ (sK4 @ X0 @ sK6)))) | ($true = ((sK5 @ X1)))) ) | ~spl10_4),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f1721])).
% 7.45/1.36 thf(f1750,plain,(
% 7.45/1.36 ($true = $false) | ($true = ((sK6 @ sK9))) | (~spl10_1 | ~spl10_5)),
% 7.45/1.36 inference(constrained_superposition,[],[f99,f52])).
% 7.45/1.36 thf(f1770,plain,(
% 7.45/1.36 ($true = ((sK6 @ sK9))) | (~spl10_1 | ~spl10_5)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f1750])).
% 7.45/1.36 thf(f1778,plain,(
% 7.45/1.36 $false | (~spl10_1 | ~spl10_5 | spl10_7)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f1770,f60])).
% 7.45/1.36 thf(f1779,plain,(
% 7.45/1.36 ~spl10_1 | ~spl10_5 | spl10_7),
% 7.45/1.36 inference(avatar_contradiction_clause,[],[f1778])).
% 7.45/1.36 thf(f1855,plain,(
% 7.45/1.36 (((sK5 @ sK17)) != (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ sK17))) | spl10_1),
% 7.45/1.36 inference(negative_extensionality,[],[f49])).
% 7.45/1.36 thf(f1856,plain,(
% 7.45/1.36 ($true = ((sK5 @ sK17))) | ($true = (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ sK17))) | spl10_1),
% 7.45/1.36 inference(xor_proxy_clausification,[],[f1855])).
% 7.45/1.36 thf(f1857,plain,(
% 7.45/1.36 ($false = ((sK5 @ sK17))) | ($false = (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ sK17))) | spl10_1),
% 7.45/1.36 inference(xor_proxy_clausification,[],[f1855])).
% 7.45/1.36 thf(f1858,plain,(
% 7.45/1.36 ($false = ((sK5 @ sK17))) | ($false = (((sK6 @ sK17) & (sK7 @ sK17)))) | spl10_1),
% 7.45/1.36 inference(beta-eta_normalization,[],[f1857])).
% 7.45/1.36 thf(f1859,plain,(
% 7.45/1.36 ($false = ((sK5 @ sK17))) | ($false = ((sK7 @ sK17))) | ($false = ((sK6 @ sK17))) | spl10_1),
% 7.45/1.36 inference(and_proxy_clausification,[],[f1858])).
% 7.45/1.36 thf(f1860,plain,(
% 7.45/1.36 ($true = ((sK5 @ sK17))) | ($true = (((sK6 @ sK17) & (sK7 @ sK17)))) | spl10_1),
% 7.45/1.36 inference(beta-eta_normalization,[],[f1856])).
% 7.45/1.36 thf(f1861,plain,(
% 7.45/1.36 ($true = ((sK5 @ sK17))) | ($true = ((sK7 @ sK17))) | spl10_1),
% 7.45/1.36 inference(and_proxy_clausification,[],[f1860])).
% 7.45/1.36 thf(f1862,plain,(
% 7.45/1.36 ($true = ((sK5 @ sK17))) | ($true = ((sK6 @ sK17))) | spl10_1),
% 7.45/1.36 inference(and_proxy_clausification,[],[f1860])).
% 7.45/1.36 thf(f1864,definition,(
% 7.45/1.36 spl10_29 <=> ($false = ((sK6 @ sK17)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_29])],[avatar_definition])).
% 7.45/1.36 thf(f1865,plain,(
% 7.45/1.36 ($false = ((sK6 @ sK17))) | ~spl10_29),
% 7.45/1.36 inference(avatar_component_clause,[],[f1864])).
% 7.45/1.36 thf(f1867,definition,(
% 7.45/1.36 spl10_30 <=> ($false = ((sK7 @ sK17)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_30])],[avatar_definition])).
% 7.45/1.36 thf(f1868,plain,(
% 7.45/1.36 ($false = ((sK7 @ sK17))) | ~spl10_30),
% 7.45/1.36 inference(avatar_component_clause,[],[f1867])).
% 7.45/1.36 thf(f1870,definition,(
% 7.45/1.36 spl10_31 <=> ($false = ((sK5 @ sK17)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_31])],[avatar_definition])).
% 7.45/1.36 thf(f1871,plain,(
% 7.45/1.36 ($false = ((sK5 @ sK17))) | ~spl10_31),
% 7.45/1.36 inference(avatar_component_clause,[],[f1870])).
% 7.45/1.36 thf(f1872,plain,(
% 7.45/1.36 spl10_29 | spl10_30 | spl10_31 | spl10_1),
% 7.45/1.36 inference(avatar_split_clause,[],[f1859,f35,f1870,f1867,f1864])).
% 7.45/1.36 thf(f1873,plain,(
% 7.45/1.36 ($true = ((sK6 @ sK17))) | (spl10_1 | ~spl10_2)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f1862,f39])).
% 7.45/1.36 thf(f1874,plain,(
% 7.45/1.36 ($true = ((sK7 @ sK17))) | (spl10_1 | ~spl10_3)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f1861,f43])).
% 7.45/1.36 thf(f2011,plain,(
% 7.45/1.36 ($true = $false) | (spl10_1 | ~spl10_2 | ~spl10_29)),
% 7.45/1.36 inference(forward_demodulation,[],[f1873,f1865])).
% 7.45/1.36 thf(f2012,plain,(
% 7.45/1.36 $false | (spl10_1 | ~spl10_2 | ~spl10_29)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f2011])).
% 7.45/1.36 thf(f2013,plain,(
% 7.45/1.36 spl10_1 | ~spl10_2 | ~spl10_29),
% 7.45/1.36 inference(avatar_contradiction_clause,[],[f2012])).
% 7.45/1.36 thf(f2014,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | ($true != ((X0 @ X1))) | ($true != ((sK6 @ (sK4 @ X0 @ sK6)))) | ($true = ((sK5 @ X1))) | ($false = ((sK7 @ (sK3 @ X0 @ sK7))))) ) | ~spl10_4),
% 7.45/1.36 inference(constrained_superposition,[],[f1728,f33])).
% 7.45/1.36 thf(f2026,plain,(
% 7.45/1.36 ( ! [X0 : (a > $o),X1 : a] : (($true != ((sK6 @ (sK4 @ X0 @ sK6)))) | ($true != ((X0 @ X1))) | ($true = ((sK5 @ X1))) | ($false = ((sK7 @ (sK3 @ X0 @ sK7))))) ) | ~spl10_4),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f2014])).
% 7.45/1.36 thf(f2113,plain,(
% 7.45/1.36 ($true = $false) | (spl10_1 | ~spl10_3 | ~spl10_30)),
% 7.45/1.36 inference(forward_demodulation,[],[f1874,f1868])).
% 7.45/1.36 thf(f2114,plain,(
% 7.45/1.36 $false | (spl10_1 | ~spl10_3 | ~spl10_30)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f2113])).
% 7.45/1.36 thf(f2115,plain,(
% 7.45/1.36 spl10_1 | ~spl10_3 | ~spl10_30),
% 7.45/1.36 inference(avatar_contradiction_clause,[],[f2114])).
% 7.45/1.36 thf(f2223,definition,(
% 7.45/1.36 spl10_35 <=> ! [X0 : a] : (($true = ((sK5 @ X0))) | (sK17 != X0))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_35])],[avatar_definition])).
% 7.45/1.36 thf(f2224,plain,(
% 7.45/1.36 ( ! [X0 : a] : ((sK17 != X0) | ($true = ((sK5 @ X0)))) ) | ~spl10_35),
% 7.45/1.36 inference(avatar_component_clause,[],[f2223])).
% 7.45/1.36 thf(f3271,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != ((sK6 @ X0))) | (((sK3 @ (= @ X0) @ sK7)) = X0) | ($true = ((sK5 @ X0))) | (((sK3 @ (= @ X0) @ sK7)) = X0) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(constrained_superposition,[],[f1726,f1727])).
% 7.45/1.36 thf(f3285,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != ((sK6 @ X0))) | (((sK3 @ (= @ X0) @ sK7)) = X0) | ($true = ((sK5 @ X0)))) ) | ~spl10_4),
% 7.45/1.36 inference(duplicate_literal_removal,[],[f3271])).
% 7.45/1.36 thf(f4485,plain,(
% 7.45/1.36 ($true != $true) | (sK17 = ((sK3 @ (= @ sK17) @ sK7))) | ($true = ((sK5 @ sK17))) | (spl10_1 | ~spl10_2 | ~spl10_4)),
% 7.45/1.36 inference(constrained_superposition,[],[f3285,f1873])).
% 7.45/1.36 thf(f4486,plain,(
% 7.45/1.36 (sK17 = ((sK3 @ (= @ sK17) @ sK7))) | ($true = ((sK5 @ sK17))) | (spl10_1 | ~spl10_2 | ~spl10_4)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f4485])).
% 7.45/1.36 thf(f4500,plain,(
% 7.45/1.36 ($true = $false) | (sK17 = ((sK3 @ (= @ sK17) @ sK7))) | (spl10_1 | ~spl10_2 | ~spl10_4 | ~spl10_31)),
% 7.45/1.36 inference(forward_demodulation,[],[f4486,f1871])).
% 7.45/1.36 thf(f4501,plain,(
% 7.45/1.36 (sK17 = ((sK3 @ (= @ sK17) @ sK7))) | (spl10_1 | ~spl10_2 | ~spl10_4 | ~spl10_31)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f4500])).
% 7.45/1.36 thf(f4737,plain,(
% 7.45/1.36 ($true != ((sK7 @ sK17))) | (sK17 = ((sK4 @ (= @ sK17) @ sK6))) | ($true = ((sK5 @ sK17))) | (spl10_1 | ~spl10_2 | ~spl10_4 | ~spl10_31)),
% 7.45/1.36 inference(constrained_superposition,[],[f1725,f4501])).
% 7.45/1.36 thf(f4744,plain,(
% 7.45/1.36 (sK17 = ((sK4 @ (= @ sK17) @ sK6))) | ($true = ((sK5 @ sK17))) | (spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f4737,f1874])).
% 7.45/1.36 thf(f4749,plain,(
% 7.45/1.36 ($true = $false) | (sK17 = ((sK4 @ (= @ sK17) @ sK6))) | (spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31)),
% 7.45/1.36 inference(forward_demodulation,[],[f4744,f1871])).
% 7.45/1.36 thf(f4750,plain,(
% 7.45/1.36 (sK17 = ((sK4 @ (= @ sK17) @ sK6))) | (spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f4749])).
% 7.45/1.36 thf(f4756,definition,(
% 7.45/1.36 spl10_72 <=> (sK17 = ((sK4 @ (= @ sK17) @ sK6)))),
% 7.45/1.36 introduced(definition,[new_symbols(definition,[spl10_72])],[avatar_definition])).
% 7.45/1.36 thf(f4757,plain,(
% 7.45/1.36 (sK17 = ((sK4 @ (= @ sK17) @ sK6))) | ~spl10_72),
% 7.45/1.36 inference(avatar_component_clause,[],[f4756])).
% 7.45/1.36 thf(f4759,plain,(
% 7.45/1.36 spl10_72 | spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31),
% 7.45/1.36 inference(avatar_split_clause,[],[f4750,f1870,f46,f42,f38,f35,f4756])).
% 7.45/1.36 thf(f4760,plain,(
% 7.45/1.36 ($true = ((sK5 @ sK17))) | ~spl10_35),
% 7.45/1.36 inference(equality_resolution,[],[f2224])).
% 7.45/1.36 thf(f4761,plain,(
% 7.45/1.36 ($true = $false) | (~spl10_31 | ~spl10_35)),
% 7.45/1.36 inference(forward_demodulation,[],[f4760,f1871])).
% 7.45/1.36 thf(f4762,plain,(
% 7.45/1.36 $false | (~spl10_31 | ~spl10_35)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f4761])).
% 7.45/1.36 thf(f4763,plain,(
% 7.45/1.36 ~spl10_31 | ~spl10_35),
% 7.45/1.36 inference(avatar_contradiction_clause,[],[f4762])).
% 7.45/1.36 thf(f4792,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != ((sK6 @ sK17))) | ($true != ((sK17 = X0))) | ($true = ((sK5 @ X0))) | ($false = ((sK7 @ (sK3 @ (= @ sK17) @ sK7))))) ) | (~spl10_4 | ~spl10_72)),
% 7.45/1.36 inference(constrained_superposition,[],[f2026,f4757])).
% 7.45/1.36 thf(f4797,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true != ((sK6 @ sK17))) | (sK17 != X0) | ($true = ((sK5 @ X0))) | ($false = ((sK7 @ (sK3 @ (= @ sK17) @ sK7))))) ) | (~spl10_4 | ~spl10_72)),
% 7.45/1.36 inference(equality_proxy_clausification,[],[f4792])).
% 7.45/1.36 thf(f4800,plain,(
% 7.45/1.36 ( ! [X0 : a] : ((sK17 != X0) | ($true = ((sK5 @ X0))) | ($false = ((sK7 @ (sK3 @ (= @ sK17) @ sK7))))) ) | (spl10_1 | ~spl10_2 | ~spl10_4 | ~spl10_72)),
% 7.45/1.36 inference(forward_subsumption_resolution,[],[f4797,f1873])).
% 7.45/1.36 thf(f4802,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($false = ((sK7 @ sK17))) | (sK17 != X0) | ($true = ((sK5 @ X0)))) ) | (spl10_1 | ~spl10_2 | ~spl10_4 | ~spl10_31 | ~spl10_72)),
% 7.45/1.36 inference(forward_demodulation,[],[f4800,f4501])).
% 7.45/1.36 thf(f4803,plain,(
% 7.45/1.36 ( ! [X0 : a] : (($true = $false) | (sK17 != X0) | ($true = ((sK5 @ X0)))) ) | (spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31 | ~spl10_72)),
% 7.45/1.36 inference(forward_demodulation,[],[f4802,f1874])).
% 7.45/1.36 thf(f4804,plain,(
% 7.45/1.36 ( ! [X0 : a] : ((sK17 != X0) | ($true = ((sK5 @ X0)))) ) | (spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31 | ~spl10_72)),
% 7.45/1.36 inference(trivial_inequality_removal,[],[f4803])).
% 7.45/1.36 thf(f4805,plain,(
% 7.45/1.36 spl10_35 | spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31 | ~spl10_72),
% 7.45/1.36 inference(avatar_split_clause,[],[f4804,f4756,f1870,f46,f42,f38,f35,f2223])).
% 7.45/1.36 cnf(s1, plain, spl10_1 | spl10_2, inference(sat_conversion,[],[f40])).
% 7.45/1.36 cnf(s2, plain, spl10_1 | spl10_3, inference(sat_conversion,[],[f44])).
% 7.45/1.36 cnf(s3, plain, spl10_1 | spl10_4, inference(sat_conversion,[],[f48])).
% 7.45/1.36 cnf(s4, plain, ~spl10_1 | ~spl10_4 | spl10_5 | spl10_6, inference(sat_conversion,[],[f57])).
% 7.45/1.36 cnf(s5, plain, ~spl10_1 | ~spl10_4 | spl10_6 | ~spl10_7, inference(sat_conversion,[],[f61])).
% 7.45/1.36 cnf(s6, plain, ~spl10_1 | ~spl10_4 | spl10_5 | ~spl10_8, inference(sat_conversion,[],[f65])).
% 7.45/1.36 cnf(s7, plain, ~spl10_1 | ~spl10_4 | ~spl10_7 | ~spl10_8, inference(sat_conversion,[],[f66])).
% 7.45/1.36 cnf(s14, plain, ~spl10_1 | ~spl10_6 | spl10_8, inference(sat_conversion,[],[f218])).
% 7.45/1.36 cnf(s23, plain, ~spl10_1 | spl10_4 | spl10_14 | spl10_15, inference(sat_conversion,[],[f491])).
% 7.45/1.36 cnf(s43, plain, spl10_4 | ~spl10_14, inference(sat_conversion,[],[f1491])).
% 7.45/1.36 cnf(s44, plain, spl10_4 | ~spl10_15, inference(sat_conversion,[],[f1663])).
% 7.45/1.36 cnf(s46, plain, ~spl10_1 | ~spl10_5 | spl10_7, inference(sat_conversion,[],[f1779])).
% 7.45/1.36 cnf(s55, plain, spl10_1 | spl10_29 | spl10_30 | spl10_31, inference(sat_conversion,[],[f1872])).
% 7.45/1.36 cnf(s57, plain, spl10_1 | ~spl10_2 | ~spl10_29, inference(sat_conversion,[],[f2013])).
% 7.45/1.36 cnf(s58, plain, spl10_1 | ~spl10_3 | ~spl10_30, inference(sat_conversion,[],[f2115])).
% 7.45/1.36 cnf(s122, plain, spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31 | spl10_72, inference(sat_conversion,[],[f4759])).
% 7.45/1.36 cnf(s123, plain, ~spl10_31 | ~spl10_35, inference(sat_conversion,[],[f4763])).
% 7.45/1.36 cnf(s127, plain, spl10_1 | ~spl10_2 | ~spl10_3 | ~spl10_4 | ~spl10_31 | spl10_35 | ~spl10_72, inference(sat_conversion,[],[f4805])).
% 7.45/1.36 cnf(s131, plain, spl10_1, inference(rat,[],[s127,s122,s123,s55,s57,s58,s1,s2,s3])).
% 7.45/1.36 cnf(s132, plain, spl10_4, inference(rat,[],[s23,s43,s44,s131])).
% 7.45/1.36 cnf(s136, plain, spl10_5, inference(rat,[],[s14,s4,s6,s131,s132])).
% 7.45/1.36 cnf(s137, plain, spl10_7, inference(rat,[],[s46,s131,s136])).
% 7.45/1.36 cnf(s138, plain, ~spl10_8, inference(rat,[],[s7,s132,s131,s137])).
% 7.45/1.36 cnf(s139, plain, spl10_6, inference(rat,[],[s5,s132,s131,s137])).
% 7.45/1.36 cnf(s140, plain, $false, inference(rat,[],[s14,s131,s138,s139])).
% 7.45/1.36 thf(f4806,plain,(
% 7.45/1.36 $false),
% 7.45/1.36 inference(avatar_sat_refutation,[],[s140])).
% 7.45/1.36 % SZS output end Proof for theBenchmark
% 7.45/1.36 % (3366040)------------------------------
% 7.45/1.36 % (3366040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.36 % (3366040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.36 % (3366040)CaDiCaL version: 2.1.3
% 7.45/1.36 % (3366040)Termination reason: Refutation
% 7.45/1.36 % (3366040)Time elapsed: 0.363 s
% 7.45/1.36 % (3366040)Peak memory usage: 16 MB
% 7.45/1.36 % (3366040)Instructions burned: 768 (million)
% 7.45/1.36 % (3365833)Success in time 1.102 s
% 7.45/1.36 % Vampire exiting
%------------------------------------------------------------------------------