%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV095^5 : 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 : n017.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 08:38:59 AM UTC 2026
% Result : Theorem 23.86s 3.74s
% Output : Refutation 23.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV095^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.29 % Computer : n017.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 15:05:22 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.31/0.34 Running first-order model finding
% 0.31/0.34 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
% 7.10/1.57 % (442349)Will run a generic schedule for satisfiability detection.
% 7.10/1.57 % (442355)% WARNING: option uhcvi not known.
% 7.10/1.57 % (442355)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2096410797:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.10/1.57 % (442355)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.10/1.57 % (442355)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.10/1.57 % (442354)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3381483439_2999 on theBenchmark for (2999ds/0Mi)
% 7.10/1.57 % (442356)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=781955523:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.10/1.57 % (442357)dis+10_1_sil=32000:sp=arity:random_seed=2868537418:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.10/1.57 % (442358)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2568585959:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.10/1.57 % (442360)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1158183732:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.10/1.57 % (442359)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2174147240:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.10/1.57 % (442358)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.10/1.57 % Exception at run slice level
% 7.10/1.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.10/1.57 % (442368)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=713400884:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 7.10/1.57 % Exception at run slice level
% 7.10/1.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.10/1.57 % (442370)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2038662862:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 7.10/1.57 % (442357)Instruction limit reached!
% 7.10/1.57 % (442357)------------------------------
% 7.10/1.57 % (442357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.10/1.57 % (442357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.57 % (442357)CaDiCaL version: 2.1.3
% 7.10/1.57 % (442357)Termination reason: Instruction limit
% 7.10/1.57 % (442357)Termination phase: Saturation
% 7.10/1.57 % (442357)Time elapsed: 0.089 s
% 7.10/1.57 % (442357)Peak memory usage: 13 MB
% 7.10/1.57 % (442357)Instructions burned: 104 (million)
% 7.10/1.57 % (442358)Instruction limit reached!
% 7.10/1.57 % (442358)------------------------------
% 7.10/1.57 % (442358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.10/1.57 % (442358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.57 % (442358)CaDiCaL version: 2.1.3
% 7.10/1.57 % (442358)Termination reason: Instruction limit
% 7.10/1.57 % (442358)Termination phase: Saturation
% 7.10/1.57 % (442358)Time elapsed: 0.094 s
% 7.10/1.57 % (442358)Peak memory usage: 14 MB
% 7.10/1.57 % (442358)Instructions burned: 117 (million)
% 7.10/1.57 % (442359)Instruction limit reached!
% 7.10/1.57 % (442359)------------------------------
% 7.10/1.57 % (442359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.10/1.57 % (442359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.57 % (442359)CaDiCaL version: 2.1.3
% 7.10/1.57 % (442359)Termination reason: Instruction limit
% 7.10/1.57 % (442359)Termination phase: Saturation
% 7.10/1.57 % (442359)Time elapsed: 0.107 s
% 7.10/1.57 % (442359)Peak memory usage: 15 MB
% 7.10/1.57 % (442359)Instructions burned: 132 (million)
% 7.10/1.57 % (442372)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=219549355:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 7.10/1.57 % (442372)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.10/1.57 % (442360)Instruction limit reached!
% 7.10/1.57 % (442360)------------------------------
% 7.10/1.57 % (442360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.10/1.57 % (442360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.57 % (442360)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442360)Termination reason: Instruction limit
% 23.86/3.74 % (442360)Termination phase: Saturation
% 23.86/3.74 % (442360)Time elapsed: 0.126 s
% 23.86/3.74 % (442360)Peak memory usage: 14 MB
% 23.86/3.74 % (442360)Instructions burned: 160 (million)
% 23.86/3.74 % (442373)ott-21_1_sil=16000:fs=off:random_seed=3558904605:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 23.86/3.74 % (442372)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 23.86/3.74 % (442374)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3347767354:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 23.86/3.74 % (442377)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1422632027:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442370)Instruction limit reached!
% 23.86/3.74 % (442370)------------------------------
% 23.86/3.74 % (442370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442370)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442370)Termination reason: Instruction limit
% 23.86/3.74 % (442370)Termination phase: Saturation
% 23.86/3.74 % (442370)Time elapsed: 0.107 s
% 23.86/3.74 % (442370)Peak memory usage: 15 MB
% 23.86/3.74 % (442370)Instructions burned: 132 (million)
% 23.86/3.74 % (442380)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1960877958:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 23.86/3.74 % (442381)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2687872527:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442385)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=2508154167:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 23.86/3.74 % (442385)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 23.86/3.74 % (442373)Instruction limit reached!
% 23.86/3.74 % (442373)------------------------------
% 23.86/3.74 % (442373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442373)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442373)Termination reason: Instruction limit
% 23.86/3.74 % (442373)Termination phase: Saturation
% 23.86/3.74 % (442373)Time elapsed: 0.148 s
% 23.86/3.74 % (442373)Peak memory usage: 12 MB
% 23.86/3.74 % (442373)Instructions burned: 180 (million)
% 23.86/3.74 % (442387)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1362025304:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 23.86/3.74 % (442387)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 23.86/3.74 % (442374)Instruction limit reached!
% 23.86/3.74 % (442374)------------------------------
% 23.86/3.74 % (442374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442374)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442374)Termination reason: Instruction limit
% 23.86/3.74 % (442374)Termination phase: Saturation
% 23.86/3.74 % (442374)Time elapsed: 0.381 s
% 23.86/3.74 % (442374)Peak memory usage: 14 MB
% 23.86/3.74 % (442374)Instructions burned: 477 (million)
% 23.86/3.74 % (442389)fmb+10_1_sil=64000:random_seed=1023460902:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 23.86/3.74 % (442389)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442391)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2930854889:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442393)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=535156650:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442372)Instruction limit reached!
% 23.86/3.74 % (442372)------------------------------
% 23.86/3.74 % (442372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442372)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442372)Termination reason: Instruction limit
% 23.86/3.74 % (442372)Termination phase: Saturation
% 23.86/3.74 % (442372)Time elapsed: 0.545 s
% 23.86/3.74 % (442372)Peak memory usage: 15 MB
% 23.86/3.74 % (442372)Instructions burned: 685 (million)
% 23.86/3.74 % (442395)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4050055697:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 23.86/3.74 % (442395)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 23.86/3.74 % (442396)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2623250776:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 23.86/3.74 % (442396)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 23.86/3.74 % (442396)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 23.86/3.74 % (442385)Instruction limit reached!
% 23.86/3.74 % (442385)------------------------------
% 23.86/3.74 % (442385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442385)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442385)Termination reason: Instruction limit
% 23.86/3.74 % (442385)Termination phase: Saturation
% 23.86/3.74 % (442385)Time elapsed: 0.553 s
% 23.86/3.74 % (442385)Peak memory usage: 17 MB
% 23.86/3.74 % (442385)Instructions burned: 695 (million)
% 23.86/3.74 % (442399)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1902249209:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442401)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=909267090:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442403)ott-2_1_sil=16000:newcnf=on:random_seed=3212572951:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2990 on theBenchmark for (2990ds/869Mi)
% 23.86/3.74 % (442403)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 23.86/3.74 % (442387)Instruction limit reached!
% 23.86/3.74 % (442387)------------------------------
% 23.86/3.74 % (442387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442387)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442387)Termination reason: Instruction limit
% 23.86/3.74 % (442387)Termination phase: Saturation
% 23.86/3.74 % (442387)Time elapsed: 0.675 s
% 23.86/3.74 % (442387)Peak memory usage: 16 MB
% 23.86/3.74 % (442387)Instructions burned: 880 (million)
% 23.86/3.74 % (442406)ott+10_1_sil=32000:tgt=ground:random_seed=3341819582:i=5114:av=off_2989 on theBenchmark for (2989ds/5114Mi)
% 23.86/3.74 % (442380)Instruction limit reached!
% 23.86/3.74 % (442380)------------------------------
% 23.86/3.74 % (442380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442380)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442380)Termination reason: Instruction limit
% 23.86/3.74 % (442380)Termination phase: Saturation
% 23.86/3.74 % (442380)Time elapsed: 0.900 s
% 23.86/3.74 % (442380)Peak memory usage: 22 MB
% 23.86/3.74 % (442380)Instructions burned: 1180 (million)
% 23.86/3.74 % (442408)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2800462706:i=54282_2988 on theBenchmark for (2988ds/54282Mi)
% 23.86/3.74 % Exception at run slice level
% 23.86/3.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 23.86/3.74 % (442410)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3676979300:i=3512:aac=none_2988 on theBenchmark for (2988ds/3512Mi)
% 23.86/3.74 % (442410)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 23.86/3.74 % (442403)Instruction limit reached!
% 23.86/3.74 % (442403)------------------------------
% 23.86/3.74 % (442403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442403)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442403)Termination reason: Instruction limit
% 23.86/3.74 % (442403)Termination phase: Saturation
% 23.86/3.74 % (442403)Time elapsed: 0.670 s
% 23.86/3.74 % (442403)Peak memory usage: 19 MB
% 23.86/3.74 % (442403)Instructions burned: 869 (million)
% 23.86/3.74 % (442413)dis+21_1_sil=32000:sas=cadical:random_seed=4100257018:i=3773:amm=off_2983 on theBenchmark for (2983ds/3773Mi)
% 23.86/3.74 % (442396)Instruction limit reached!
% 23.86/3.74 % (442396)------------------------------
% 23.86/3.74 % (442396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442396)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442396)Termination reason: Instruction limit
% 23.86/3.74 % (442396)Termination phase: Saturation
% 23.86/3.74 % (442396)Time elapsed: 1.248 s
% 23.86/3.74 % (442396)Peak memory usage: 19 MB
% 23.86/3.74 % (442396)Instructions burned: 1473 (million)
% 23.86/3.74 % (442416)ott+11_1_sil=16000:gs=on:random_seed=197460931:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2980 on theBenchmark for (2980ds/2251Mi)
% 23.86/3.74 % (442416)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 23.86/3.74 % (442395) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-442349-442395"...
% 23.86/3.74 % (442395)...printing done.
% 23.86/3.74 % (442395)Refutation found. Thanks to Tanya!
% 23.86/3.74 % SZS status Theorem for theBenchmark
% 23.86/3.74 % SZS output start Proof for theBenchmark
% 23.86/3.74 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 23.86/3.74 thf(func_def_3, type, sP0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $o)).
% 23.86/3.74 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 23.86/3.74 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 23.86/3.74 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 23.86/3.74 thf(func_def_7, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 23.86/3.74 thf(func_def_8, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 23.86/3.74 thf(func_def_9, type, sK6: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 23.86/3.74 thf(func_def_10, type, sK7: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 23.86/3.74 thf(func_def_11, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 23.86/3.74 thf(func_def_12, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 23.86/3.74 thf(func_def_13, type, vNOT: ($o > $o)).
% 23.86/3.74 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 23.86/3.74 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 23.86/3.74 thf(func_def_18, type, db0: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(func_def_19, type, db4: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(func_def_20, type, db3: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(func_def_22, type, db5: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(func_def_23, type, db7: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(func_def_24, type, db6: !>[X0: $tType]:(X0)).
% 23.86/3.74 thf(f1,conjecture,(
% 23.86/3.74 ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((! [X4 : $i] : ((X0 @ X7 @ X5 @ X4) | (X1 @ X7 @ X5 @ X4)) & ! [X4 : $i] : ((X0 @ X6 @ X7 @ X4) | (X1 @ X6 @ X7 @ X4))) => ! [X4 : $i] : ((X0 @ X6 @ X5 @ X4) | (X1 @ X6 @ X5 @ X4))) & ! [X6 : ($i > $o),X4 : $i] : ((X0 @ X6 @ X6 @ X4) | (X1 @ X6 @ X6 @ X4)) & ! [X2 : ($i > $o),X3 : ($i > $o)] : (! [X4 : $i] : ((X0 @ X2 @ X3 @ X4) | (X1 @ X2 @ X3 @ X4)) => ! [X5 : $i] : ((X2 @ X5) => (X3 @ X5))))),
% 23.86/3.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM122C_pme)).
% 23.86/3.74 thf(f2,negated_conjecture,(
% 23.86/3.74 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((! [X4 : $i] : ((X0 @ X7 @ X5 @ X4) | (X1 @ X7 @ X5 @ X4)) & ! [X4 : $i] : ((X0 @ X6 @ X7 @ X4) | (X1 @ X6 @ X7 @ X4))) => ! [X4 : $i] : ((X0 @ X6 @ X5 @ X4) | (X1 @ X6 @ X5 @ X4))) & ! [X6 : ($i > $o),X4 : $i] : ((X0 @ X6 @ X6 @ X4) | (X1 @ X6 @ X6 @ X4)) & ! [X2 : ($i > $o),X3 : ($i > $o)] : (! [X4 : $i] : ((X0 @ X2 @ X3 @ X4) | (X1 @ X2 @ X3 @ X4)) => ! [X5 : $i] : ((X2 @ X5) => (X3 @ X5))))),
% 23.86/3.74 inference(negated_conjecture,[status(cth)],[f1])).
% 23.86/3.74 thf(f3,plain,(
% 23.86/3.74 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5)) & ! [X6 : $i] : ((X0 @ X2 @ X3 @ X6) | (X1 @ X2 @ X3 @ X6))) => ! [X7 : $i] : ((X0 @ X2 @ X4 @ X7) | (X1 @ X2 @ X4 @ X7))) & ! [X8 : ($i > $o),X9 : $i] : ((X0 @ X8 @ X8 @ X9) | (X1 @ X8 @ X8 @ X9)) & ! [X10 : ($i > $o),X11 : ($i > $o)] : (! [X12 : $i] : ((X0 @ X10 @ X11 @ X12) | (X1 @ X10 @ X11 @ X12)) => ! [X13 : $i] : ((X10 @ X13) => (X11 @ X13))))),
% 23.86/3.74 inference(rectify,[],[f2])).
% 23.86/3.74 thf(f4,plain,(
% 23.86/3.74 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((! [X5 : $i] : ((((X0 @ X3 @ X4 @ X5)) = $true) | (((X1 @ X3 @ X4 @ X5)) = $true)) & ! [X6 : $i] : ((((X0 @ X2 @ X3 @ X6)) = $true) | (((X1 @ X2 @ X3 @ X6)) = $true))) => ! [X7 : $i] : ((((X0 @ X2 @ X4 @ X7)) = $true) | (((X1 @ X2 @ X4 @ X7)) = $true))) & ! [X8 : ($i > $o),X9 : $i] : ((((X0 @ X8 @ X8 @ X9)) = $true) | (((X1 @ X8 @ X8 @ X9)) = $true)) & ! [X10 : ($i > $o),X11 : ($i > $o)] : (! [X12 : $i] : ((((X0 @ X10 @ X11 @ X12)) = $true) | (((X1 @ X10 @ X11 @ X12)) = $true)) => ! [X13 : $i] : ((((X10 @ X13)) = $true) => (((X11 @ X13)) = $true))))),
% 23.86/3.74 inference(fool_elimination,[],[f3])).
% 23.86/3.74 thf(f5,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (? [X7 : $i] : ((((X0 @ X2 @ X4 @ X7)) != $true) & (((X1 @ X2 @ X4 @ X7)) != $true)) & (! [X5 : $i] : ((((X0 @ X3 @ X4 @ X5)) = $true) | (((X1 @ X3 @ X4 @ X5)) = $true)) & ! [X6 : $i] : ((((X0 @ X2 @ X3 @ X6)) = $true) | (((X1 @ X2 @ X3 @ X6)) = $true)))) | ? [X8 : ($i > $o),X9 : $i] : ((((X0 @ X8 @ X8 @ X9)) != $true) & (((X1 @ X8 @ X8 @ X9)) != $true)) | ? [X10 : ($i > $o),X11 : ($i > $o)] : (? [X13 : $i] : ((((X11 @ X13)) != $true) & (((X10 @ X13)) = $true)) & ! [X12 : $i] : ((((X0 @ X10 @ X11 @ X12)) = $true) | (((X1 @ X10 @ X11 @ X12)) = $true))))),
% 23.86/3.74 inference(ennf_transformation,[],[f4])).
% 23.86/3.74 thf(f6,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (? [X7 : $i] : ((((X0 @ X2 @ X4 @ X7)) != $true) & (((X1 @ X2 @ X4 @ X7)) != $true)) & ! [X5 : $i] : ((((X0 @ X3 @ X4 @ X5)) = $true) | (((X1 @ X3 @ X4 @ X5)) = $true)) & ! [X6 : $i] : ((((X0 @ X2 @ X3 @ X6)) = $true) | (((X1 @ X2 @ X3 @ X6)) = $true))) | ? [X8 : ($i > $o),X9 : $i] : ((((X0 @ X8 @ X8 @ X9)) != $true) & (((X1 @ X8 @ X8 @ X9)) != $true)) | ? [X10 : ($i > $o),X11 : ($i > $o)] : (? [X13 : $i] : ((((X11 @ X13)) != $true) & (((X10 @ X13)) = $true)) & ! [X12 : $i] : ((((X0 @ X10 @ X11 @ X12)) = $true) | (((X1 @ X10 @ X11 @ X12)) = $true))))),
% 23.86/3.74 inference(flattening,[],[f5])).
% 23.86/3.74 thf(f7,definition,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (? [X7 : $i] : ((((X0 @ X2 @ X4 @ X7)) != $true) & (((X1 @ X2 @ X4 @ X7)) != $true)) & ! [X5 : $i] : ((((X0 @ X3 @ X4 @ X5)) = $true) | (((X1 @ X3 @ X4 @ X5)) = $true)) & ! [X6 : $i] : ((((X0 @ X2 @ X3 @ X6)) = $true) | (((X1 @ X2 @ X3 @ X6)) = $true))) | ~ ($true = ((sP0 @ X1 @ X0))))),
% 23.86/3.74 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 23.86/3.74 thf(f8,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((sP0 @ X1 @ X0))) | ? [X8 : ($i > $o),X9 : $i] : ((((X0 @ X8 @ X8 @ X9)) != $true) & (((X1 @ X8 @ X8 @ X9)) != $true)) | ? [X10 : ($i > $o),X11 : ($i > $o)] : (? [X13 : $i] : ((((X11 @ X13)) != $true) & (((X10 @ X13)) = $true)) & ! [X12 : $i] : ((((X0 @ X10 @ X11 @ X12)) = $true) | (((X1 @ X10 @ X11 @ X12)) = $true))))),
% 23.86/3.74 inference(definition_folding,[],[f6,f7])).
% 23.86/3.74 thf(f9,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (? [X7 : $i] : ((((X0 @ X2 @ X4 @ X7)) != $true) & (((X1 @ X2 @ X4 @ X7)) != $true)) & ! [X5 : $i] : ((((X0 @ X3 @ X4 @ X5)) = $true) | (((X1 @ X3 @ X4 @ X5)) = $true)) & ! [X6 : $i] : ((((X0 @ X2 @ X3 @ X6)) = $true) | (((X1 @ X2 @ X3 @ X6)) = $true))) | ($true != ((sP0 @ X1 @ X0))))),
% 23.86/3.74 inference(nnf_transformation,[],[f7])).
% 23.86/3.74 thf(f10,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (? [X5 : $i] : (($true != ((X0 @ X2 @ X4 @ X5))) & ($true != ((X1 @ X2 @ X4 @ X5)))) & ! [X6 : $i] : (($true = ((X0 @ X3 @ X4 @ X6))) | ($true = ((X1 @ X3 @ X4 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X2 @ X3 @ X7))) | ($true = ((X1 @ X2 @ X3 @ X7))))) | ($true != ((sP0 @ X1 @ X0))))),
% 23.86/3.74 inference(rectify,[],[f9])).
% 23.86/3.74 thf(f11,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (((($true != ((X0 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) & ($true != ((X1 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0))))) & ! [X6 : $i] : (($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X6))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))))) | ($true != ((sP0 @ X1 @ X0))))),
% 23.86/3.74 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X5,sK4 @ X1 @ X0),skolemize(X5,sK4 @ X1 @ X0),skolemize(X5,sK4 @ X1 @ X0),skolemize(X5,sK4 @ X1 @ X0)],[f10])).
% 23.86/3.74 thf(f12,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((sP0 @ X1 @ X0))) | ? [X2 : ($i > $o),X3 : $i] : (($true != ((X0 @ X2 @ X2 @ X3))) & ($true != ((X1 @ X2 @ X2 @ X3)))) | ? [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : (($true != ((X5 @ X6))) & ($true = ((X4 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X4 @ X5 @ X7))) | ($true = ((X1 @ X4 @ X5 @ X7))))))),
% 23.86/3.74 inference(rectify,[],[f8])).
% 23.86/3.74 thf(f13,plain,(
% 23.86/3.74 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((sP0 @ X1 @ X0))) | (($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)))) & ($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0))))) | ((($true != ((sK8 @ X1 @ X0 @ (sK9 @ X1 @ X0)))) & ($true = ((sK7 @ X1 @ X0 @ (sK9 @ X1 @ X0))))) & ! [X7 : $i] : (($true = ((X0 @ (sK7 @ X1 @ X0) @ (sK8 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK7 @ X1 @ X0) @ (sK8 @ X1 @ X0) @ X7))))))),
% 23.86/3.74 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X5,sK4 @ X1 @ X0),skolemize(X5,sK4 @ X1 @ X0),skolemize(X5,sK4 @ X1 @ X0),skolemize(X5,sK4 @ X1 @ X0),skolemize(X5,sK4 @ X1 @ X0)],[f12])).
% 23.86/3.74 thf(f14,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != ((sP0 @ X1 @ X0))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)))) )),
% 23.86/3.74 inference(cnf_transformation,[],[f11])).
% 23.86/3.74 thf(f15,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true != ((sP0 @ X1 @ X0))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X6))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X6)))) )),
% 23.86/3.74 inference(cnf_transformation,[],[f11])).
% 23.86/3.74 thf(f16,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((sP0 @ X1 @ X0))) | ($true != ((X1 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0))))) )),
% 23.86/3.74 inference(cnf_transformation,[],[f11])).
% 23.86/3.74 thf(f18,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)))) | ($true = ((sP0 @ X1 @ X0))) | ($true = ((X0 @ (sK7 @ X1 @ X0) @ (sK8 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK7 @ X1 @ X0) @ (sK8 @ X1 @ X0) @ X7)))) )),
% 23.86/3.74 inference(cnf_transformation,[],[f13])).
% 23.86/3.74 thf(f19,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)))) | ($true = ((sP0 @ X1 @ X0))) | ($true = ((sK7 @ X1 @ X0 @ (sK9 @ X1 @ X0))))) )),
% 23.86/3.74 inference(cnf_transformation,[],[f13])).
% 23.86/3.74 thf(f20,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((sK8 @ X1 @ X0 @ (sK9 @ X1 @ X0)))) | ($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)))) | ($true = ((sP0 @ X1 @ X0)))) )),
% 23.86/3.74 inference(cnf_transformation,[],[f13])).
% 23.86/3.74 thf(f25,definition,(
% 23.86/3.74 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 23.86/3.74 introduced(theory,[fool_exhaustiveness_axiom])).
% 23.86/3.74 thf(f33,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 23.86/3.74 inference(primitive_instantiation,[],[f19])).
% 23.86/3.74 thf(f50,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 23.86/3.74 inference(beta-eta_normalization,[],[f33])).
% 23.86/3.74 thf(f51,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 23.86/3.74 inference(equality_proxy_clausification,[],[f50])).
% 23.86/3.74 thf(f52,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f51])).
% 23.86/3.74 thf(f54,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != $true) | ($true != ((X0 @ (sK5 @ X0 @ X1) @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1)))) | ($true = ((sP0 @ X0 @ X1))) | ($false = ((sK8 @ X0 @ X1 @ (sK9 @ X0 @ X1))))) )),
% 23.86/3.74 inference(constrained_superposition,[],[f20,f25])).
% 23.86/3.74 thf(f55,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X0 @ (sK5 @ X0 @ X1) @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1)))) | ($true = ((sP0 @ X0 @ X1))) | ($false = ((sK8 @ X0 @ X1 @ (sK9 @ X0 @ X1))))) )),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f54])).
% 23.86/3.74 thf(f91,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7)))) )),
% 23.86/3.74 inference(primitive_instantiation,[],[f18])).
% 23.86/3.74 thf(f118,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 23.86/3.74 inference(beta-eta_normalization,[],[f91])).
% 23.86/3.74 thf(f119,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 23.86/3.74 inference(equality_proxy_clausification,[],[f118])).
% 23.86/3.74 thf(f120,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 23.86/3.74 inference(equality_proxy_clausification,[],[f119])).
% 23.86/3.74 thf(f121,plain,(
% 23.86/3.74 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f120])).
% 23.86/3.74 thf(f183,plain,(
% 23.86/3.74 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != $true) | ($true = ((X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1) @ X2))) | ($true = ((X1 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1) @ X2))) | ($false = ((sP0 @ X0 @ X1)))) )),
% 23.86/3.74 inference(constrained_superposition,[],[f15,f25])).
% 23.86/3.74 thf(f184,plain,(
% 23.86/3.74 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X1 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1) @ X2))) | ($true = ((X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1) @ X2))) | ($false = ((sP0 @ X0 @ X1)))) )),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f183])).
% 23.86/3.74 thf(f265,plain,(
% 23.86/3.74 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1))) | ($false = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1))))) )),
% 23.86/3.74 inference(primitive_instantiation,[],[f55])).
% 23.86/3.74 thf(f297,plain,(
% 23.86/3.74 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1))) | ($false = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1))))) )),
% 23.86/3.74 inference(beta-eta_normalization,[],[f265])).
% 23.86/3.74 thf(f298,plain,(
% 23.86/3.74 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o)] : ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1))) | ($false = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1))))) )),
% 23.86/3.74 inference(equality_proxy_clausification,[],[f297])).
% 23.86/3.74 thf(f299,plain,(
% 23.86/3.74 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($false = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1 @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1)))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X1)))) )),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f298])).
% 23.86/3.74 thf(f1386,plain,(
% 23.86/3.74 ( ! [X7 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X7))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) )),
% 23.86/3.74 inference(primitive_instantiation,[],[f121])).
% 23.86/3.74 thf(f1524,plain,(
% 23.86/3.74 ($true = $false) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))),
% 23.86/3.74 inference(beta-eta_normalization,[],[f1386])).
% 23.86/3.74 thf(f1525,plain,(
% 23.86/3.74 ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f1524])).
% 23.86/3.74 thf(f3960,definition,(
% 23.86/3.74 spl10_1 <=> (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))),
% 23.86/3.74 introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition])).
% 23.86/3.74 thf(f3962,plain,(
% 23.86/3.74 (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_1),
% 23.86/3.74 inference(avatar_component_clause,[],[f3960])).
% 23.86/3.74 thf(f3964,definition,(
% 23.86/3.74 spl10_2 <=> ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))),
% 23.86/3.74 introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition])).
% 23.86/3.74 thf(f3965,plain,(
% 23.86/3.74 ($true != ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl10_2),
% 23.86/3.74 inference(avatar_component_clause,[],[f3964])).
% 23.86/3.74 thf(f3966,plain,(
% 23.86/3.74 ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 23.86/3.74 inference(avatar_component_clause,[],[f3964])).
% 23.86/3.74 thf(f3967,plain,(
% 23.86/3.74 spl10_1 | spl10_2),
% 23.86/3.74 inference(avatar_split_clause,[],[f1525,f3964,f3960])).
% 23.86/3.74 thf(f4101,plain,(
% 23.86/3.74 ( ! [X0 : $i] : (($true != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)))) ) | ~spl10_2),
% 23.86/3.74 inference(constrained_superposition,[],[f14,f3966])).
% 23.86/3.74 thf(f4103,plain,(
% 23.86/3.74 ($true != $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ~spl10_2),
% 23.86/3.74 inference(constrained_superposition,[],[f16,f3966])).
% 23.86/3.74 thf(f4149,plain,(
% 23.86/3.74 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ~spl10_2),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f4103])).
% 23.86/3.74 thf(f4150,plain,(
% 23.86/3.74 ($true != (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ~spl10_2),
% 23.86/3.74 inference(beta-eta_normalization,[],[f4149])).
% 23.86/3.74 thf(f4151,plain,(
% 23.86/3.74 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 23.86/3.74 inference(equality_proxy_clausification,[],[f4150])).
% 23.86/3.74 thf(f4154,plain,(
% 23.86/3.74 ( ! [X0 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)))) ) | ~spl10_2),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f4101])).
% 23.86/3.74 thf(f4155,plain,(
% 23.86/3.74 ($true = (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = $false) | ~spl10_2),
% 23.86/3.74 inference(beta-eta_normalization,[],[f4154])).
% 23.86/3.74 thf(f4156,plain,(
% 23.86/3.74 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = $false) | ~spl10_2),
% 23.86/3.74 inference(equality_proxy_clausification,[],[f4155])).
% 23.86/3.74 thf(f4157,plain,(
% 23.86/3.74 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f4156])).
% 23.86/3.74 thf(f4775,plain,(
% 23.86/3.74 ( ! [X0 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0))) | ($false = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) ) | ~spl10_2),
% 23.86/3.74 inference(constrained_superposition,[],[f184,f4157])).
% 23.86/3.74 thf(f5113,plain,(
% 23.86/3.74 ($true = (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = $false) | ($false = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 23.86/3.74 inference(beta-eta_normalization,[],[f4775])).
% 23.86/3.74 thf(f5114,plain,(
% 23.86/3.74 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = $false) | ($false = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 23.86/3.74 inference(equality_proxy_clausification,[],[f5113])).
% 23.86/3.74 thf(f5115,plain,(
% 23.86/3.74 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($false = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f5114])).
% 23.86/3.74 thf(f5186,plain,(
% 23.86/3.74 ($false = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 23.86/3.74 inference(forward_subsumption_resolution,[],[f5115,f4151])).
% 23.86/3.74 thf(f5204,plain,(
% 23.86/3.74 ($true = $false) | ~spl10_2),
% 23.86/3.74 inference(constrained_superposition,[],[f5186,f3966])).
% 23.86/3.74 thf(f5284,plain,(
% 23.86/3.74 $false | ~spl10_2),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f5204])).
% 23.86/3.74 thf(f5285,plain,(
% 23.86/3.74 ~spl10_2),
% 23.86/3.74 inference(avatar_contradiction_clause,[],[f5284])).
% 23.86/3.74 thf(f5512,plain,(
% 23.86/3.74 ( ! [X1 : $i] : ((((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ X1)) = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ X1)))) ) | ~spl10_1),
% 23.86/3.74 inference(argument_congruence,[],[f3962])).
% 23.86/3.74 thf(f5521,plain,(
% 23.86/3.74 ( ! [X1 : $i] : (($true = ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ X1))) | ($false = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ X1)))) ) | ~spl10_1),
% 23.86/3.74 inference(iff_proxy_clausification,[],[f5512])).
% 23.86/3.74 thf(f5783,plain,(
% 23.86/3.74 ($true = $false) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($false = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ~spl10_1),
% 23.86/3.74 inference(constrained_superposition,[],[f299,f5521])).
% 23.86/3.74 thf(f5805,plain,(
% 23.86/3.74 ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($false = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ~spl10_1),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f5783])).
% 23.86/3.74 thf(f5849,plain,(
% 23.86/3.74 ($false = ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | (~spl10_1 | spl10_2)),
% 23.86/3.74 inference(forward_subsumption_resolution,[],[f5805,f3965])).
% 23.86/3.74 thf(f6070,plain,(
% 23.86/3.74 ($true = $false) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | (~spl10_1 | spl10_2)),
% 23.86/3.74 inference(constrained_superposition,[],[f5849,f52])).
% 23.86/3.74 thf(f6191,plain,(
% 23.86/3.74 ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | (~spl10_1 | spl10_2)),
% 23.86/3.74 inference(trivial_inequality_removal,[],[f6070])).
% 23.86/3.74 thf(f6243,plain,(
% 23.86/3.74 $false | (~spl10_1 | spl10_2)),
% 23.86/3.74 inference(forward_subsumption_resolution,[],[f6191,f3965])).
% 23.86/3.74 thf(f6244,plain,(
% 23.86/3.74 ~spl10_1 | spl10_2),
% 23.86/3.74 inference(avatar_contradiction_clause,[],[f6243])).
% 23.86/3.74 cnf(s1, plain, spl10_1 | spl10_2, inference(sat_conversion,[],[f3967])).
% 23.86/3.74 cnf(s3, plain, ~spl10_2, inference(sat_conversion,[],[f5285])).
% 23.86/3.74 cnf(s7, plain, ~spl10_1 | spl10_2, inference(sat_conversion,[],[f6244])).
% 23.86/3.74 cnf(s8, plain, ~spl10_1, inference(rat,[],[s7,s3])).
% 23.86/3.74 cnf(s9, plain, $false, inference(rat,[],[s1,s3,s8])).
% 23.86/3.74 thf(f6245,plain,(
% 23.86/3.74 $false),
% 23.86/3.74 inference(avatar_sat_refutation,[],[s9])).
% 23.86/3.74 % SZS output end Proof for theBenchmark
% 23.86/3.74 % (442395)------------------------------
% 23.86/3.74 % (442395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.74 % (442395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.74 % (442395)CaDiCaL version: 2.1.3
% 23.86/3.74 % (442395)Termination reason: Refutation
% 23.86/3.74 % (442395)Time elapsed: 2.640 s
% 23.86/3.74 % (442395)Peak memory usage: 21 MB
% 23.86/3.74 % (442395)Instructions burned: 3419 (million)
% 23.86/3.74 % (442349)Success in time 3.38 s
% 23.86/3.74 % Vampire exiting
%------------------------------------------------------------------------------