%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV066^5 : 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 08:38:57 AM UTC 2026
% Result : Theorem 3.70s 1.03s
% Output : Refutation 3.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV066^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 % Computer : n007.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 15:04:11 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 Running first-order model finding
% 0.10/0.27 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
% 3.43/0.87 % (3477750)Will run a generic schedule for satisfiability detection.
% 3.43/0.87 % (3477759)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1508591768:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.43/0.87 % (3477759)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.43/0.87 % (3477756)% WARNING: option uhcvi not known.
% 3.43/0.87 % (3477755)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=996010700_2999 on theBenchmark for (2999ds/0Mi)
% 3.43/0.87 % (3477756)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1221044394:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.43/0.87 % (3477757)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1574301392:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.43/0.87 % (3477758)dis+10_1_sil=32000:sp=arity:random_seed=2652941595:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.43/0.87 % (3477760)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4276729906:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.43/0.87 % (3477756)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.43/0.87 % (3477761)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2259821816:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.43/0.87 % Exception at run slice level
% 3.43/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.43/0.87 % (3477756)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.43/0.87 % (3477759)Instruction limit reached!
% 3.43/0.87 % (3477759)------------------------------
% 3.43/0.87 % (3477759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.87 % (3477759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.87 % (3477759)CaDiCaL version: 2.1.3
% 3.43/0.87 % (3477759)Termination reason: Instruction limit
% 3.43/0.87 % (3477759)Termination phase: Saturation
% 3.43/0.87 % (3477759)Time elapsed: 0.027 s
% 3.43/0.87 % (3477759)Peak memory usage: 12 MB
% 3.43/0.87 % (3477759)Instructions burned: 117 (million)
% 3.43/0.87 % (3477769)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3068842247:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.43/0.87 % Exception at run slice level
% 3.43/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.43/0.87 % (3477770)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=228969239:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.43/0.87 % (3477772)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=3548354783:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.43/0.87 % (3477772)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.43/0.87 % (3477772)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.43/0.87 % (3477758)Instruction limit reached!
% 3.43/0.87 % (3477758)------------------------------
% 3.43/0.87 % (3477758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.87 % (3477758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.87 % (3477758)CaDiCaL version: 2.1.3
% 3.43/0.87 % (3477758)Termination reason: Instruction limit
% 3.43/0.87 % (3477758)Termination phase: Saturation
% 3.43/0.87 % (3477758)Time elapsed: 0.049 s
% 3.43/0.87 % (3477758)Peak memory usage: 12 MB
% 3.43/0.87 % (3477758)Instructions burned: 105 (million)
% 3.43/0.87 % (3477760)Instruction limit reached!
% 3.43/0.87 % (3477760)------------------------------
% 3.43/0.87 % (3477760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.87 % (3477760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.87 % (3477760)CaDiCaL version: 2.1.3
% 3.43/0.87 % (3477760)Termination reason: Instruction limit
% 3.43/0.87 % (3477760)Termination phase: Saturation
% 3.43/0.87 % (3477760)Time elapsed: 0.060 s
% 3.43/0.87 % (3477760)Peak memory usage: 14 MB
% 3.43/0.87 % (3477760)Instructions burned: 132 (million)
% 3.43/0.87 % (3477770)Instruction limit reached!
% 3.43/0.87 % (3477770)------------------------------
% 3.43/0.87 % (3477770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477770)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477770)Termination reason: Instruction limit
% 3.70/1.03 % (3477770)Termination phase: Saturation
% 3.70/1.03 % (3477770)Time elapsed: 0.034 s
% 3.70/1.03 % (3477770)Peak memory usage: 14 MB
% 3.70/1.03 % (3477770)Instructions burned: 133 (million)
% 3.70/1.03 % (3477781)ott-21_1_sil=16000:fs=off:random_seed=1243198129:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.70/1.03 % (3477789)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3070276887:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477761)Instruction limit reached!
% 3.70/1.03 % (3477761)------------------------------
% 3.70/1.03 % (3477761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477761)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477761)Termination reason: Instruction limit
% 3.70/1.03 % (3477761)Termination phase: Saturation
% 3.70/1.03 % (3477761)Time elapsed: 0.075 s
% 3.70/1.03 % (3477761)Peak memory usage: 13 MB
% 3.70/1.03 % (3477761)Instructions burned: 161 (million)
% 3.70/1.03 % (3477786)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1859107941:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 3.70/1.03 % (3477798)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3349575331:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.70/1.03 % (3477799)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=190657888:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477811)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=507996153: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)
% 3.70/1.03 % (3477811)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.70/1.03 % (3477781)Instruction limit reached!
% 3.70/1.03 % (3477781)------------------------------
% 3.70/1.03 % (3477781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477781)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477781)Termination reason: Instruction limit
% 3.70/1.03 % (3477781)Termination phase: Saturation
% 3.70/1.03 % (3477781)Time elapsed: 0.080 s
% 3.70/1.03 % (3477781)Peak memory usage: 12 MB
% 3.70/1.03 % (3477781)Instructions burned: 182 (million)
% 3.70/1.03 % (3477834)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3951872698:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.70/1.03 % (3477834)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.70/1.03 % (3477786)Instruction limit reached!
% 3.70/1.03 % (3477786)------------------------------
% 3.70/1.03 % (3477786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477786)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477786)Termination reason: Instruction limit
% 3.70/1.03 % (3477786)Termination phase: Saturation
% 3.70/1.03 % (3477786)Time elapsed: 0.227 s
% 3.70/1.03 % (3477786)Peak memory usage: 14 MB
% 3.70/1.03 % (3477786)Instructions burned: 477 (million)
% 3.70/1.03 % (3477894)fmb+10_1_sil=64000:random_seed=2793349970:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.70/1.03 % (3477894)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477901)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2653038026:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477772)Instruction limit reached!
% 3.70/1.03 % (3477772)------------------------------
% 3.70/1.03 % (3477772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477772)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477772)Termination reason: Instruction limit
% 3.70/1.03 % (3477772)Termination phase: Saturation
% 3.70/1.03 % (3477772)Time elapsed: 0.311 s
% 3.70/1.03 % (3477772)Peak memory usage: 15 MB
% 3.70/1.03 % (3477772)Instructions burned: 685 (million)
% 3.70/1.03 % (3477798)Instruction limit reached!
% 3.70/1.03 % (3477798)------------------------------
% 3.70/1.03 % (3477798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477798)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477798)Termination reason: Instruction limit
% 3.70/1.03 % (3477798)Termination phase: Saturation
% 3.70/1.03 % (3477798)Time elapsed: 0.278 s
% 3.70/1.03 % (3477798)Peak memory usage: 19 MB
% 3.70/1.03 % (3477798)Instructions burned: 1181 (million)
% 3.70/1.03 % (3477909)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1075484326:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477913)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3387030715:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.70/1.03 % (3477913)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.70/1.03 % (3477921)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3260283909:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.70/1.03 % (3477921)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.70/1.03 % (3477921)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.70/1.03 % (3477927)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2888081042:i=6324_2996 on theBenchmark for (2996ds/6324Mi)
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477945)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1133167904:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477953)ott-2_1_sil=16000:newcnf=on:random_seed=110917158:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 3.70/1.03 % (3477953)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.70/1.03 % (3477811)Instruction limit reached!
% 3.70/1.03 % (3477811)------------------------------
% 3.70/1.03 % (3477811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477811)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477811)Termination reason: Instruction limit
% 3.70/1.03 % (3477811)Termination phase: Saturation
% 3.70/1.03 % (3477811)Time elapsed: 0.323 s
% 3.70/1.03 % (3477811)Peak memory usage: 17 MB
% 3.70/1.03 % (3477811)Instructions burned: 694 (million)
% 3.70/1.03 % (3477957)ott+10_1_sil=32000:tgt=ground:random_seed=3935069602:i=5114:av=off_2995 on theBenchmark for (2995ds/5114Mi)
% 3.70/1.03 % (3477834)Instruction limit reached!
% 3.70/1.03 % (3477834)------------------------------
% 3.70/1.03 % (3477834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477834)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477834)Termination reason: Instruction limit
% 3.70/1.03 % (3477834)Termination phase: Saturation
% 3.70/1.03 % (3477834)Time elapsed: 0.371 s
% 3.70/1.03 % (3477834)Peak memory usage: 15 MB
% 3.70/1.03 % (3477834)Instructions burned: 880 (million)
% 3.70/1.03 % (3477959)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1044636547:i=54282_2994 on theBenchmark for (2994ds/54282Mi)
% 3.70/1.03 % Exception at run slice level
% 3.70/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.70/1.03 % (3477961)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2311248515:i=3512:aac=none_2994 on theBenchmark for (2994ds/3512Mi)
% 3.70/1.03 % (3477961)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.70/1.03 % (3477913) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3477750-3477913"...
% 3.70/1.03 % (3477913)...printing done.
% 3.70/1.03 % (3477913)Refutation found. Thanks to Tanya!
% 3.70/1.03 % SZS status Theorem for theBenchmark
% 3.70/1.03 % SZS output start Proof for theBenchmark
% 3.70/1.03 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.70/1.03 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.70/1.03 thf(func_def_4, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 3.70/1.03 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 3.70/1.03 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 3.70/1.03 thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 3.70/1.03 thf(func_def_8, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 3.70/1.03 thf(func_def_9, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 3.70/1.03 thf(func_def_10, type, vNOT: ($o > $o)).
% 3.70/1.03 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 3.70/1.03 thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 3.70/1.03 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.70/1.03 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 3.70/1.03 thf(func_def_17, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 3.70/1.03 thf(func_def_18, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 3.70/1.03 thf(func_def_19, type, db4: !>[X0: $tType]:(X0)).
% 3.70/1.03 thf(func_def_20, type, db3: !>[X0: $tType]:(X0)).
% 3.70/1.03 thf(f1,conjecture,(
% 3.70/1.03 ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X3 : $i] : ((X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)) & ! [X2 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X2 : ($i > $o),X3 : $i] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 3.70/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120D_pme)).
% 3.70/1.03 thf(f2,negated_conjecture,(
% 3.70/1.03 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X3 : $i] : ((X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)) & ! [X2 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X2 : ($i > $o),X3 : $i] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 3.70/1.03 inference(negated_conjecture,[status(cth)],[f1])).
% 3.70/1.03 thf(f3,plain,(
% 3.70/1.03 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : ($true)) @ (^[X4 : $i] : ($false)) @ X2) | (X1 @ (^[X5 : $i] : ($true)) @ (^[X6 : $i] : ($false)) @ X2)) & ! [X7 : ($i > $o),X8 : ($i > $o),X9 : ($i > $o)] : ((! [X10 : $i] : ((X0 @ X8 @ X9 @ X10) | (X1 @ X8 @ X9 @ X10)) & ! [X11 : $i] : ((X0 @ X7 @ X8 @ X11) | (X1 @ X7 @ X8 @ X11))) => ! [X12 : $i] : ((X0 @ X7 @ X9 @ X12) | (X1 @ X7 @ X9 @ X12))) & ! [X13 : ($i > $o),X14 : $i] : ((X0 @ X13 @ X13 @ X14) | (X1 @ X13 @ X13 @ X14)))),
% 3.70/1.03 inference(rectify,[],[f2])).
% 3.70/1.03 thf(f4,plain,(
% 3.70/1.03 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) & ! [X7 : ($i > $o),X8 : ($i > $o),X9 : ($i > $o)] : ((! [X10 : $i] : ((((X0 @ X8 @ X9 @ X10)) = $true) | (((X1 @ X8 @ X9 @ X10)) = $true)) & ! [X11 : $i] : ((((X0 @ X7 @ X8 @ X11)) = $true) | (((X1 @ X7 @ X8 @ X11)) = $true))) => ! [X12 : $i] : ((((X0 @ X7 @ X9 @ X12)) = $true) | (((X1 @ X7 @ X9 @ X12)) = $true))) & ! [X13 : ($i > $o),X14 : $i] : ((((X0 @ X13 @ X13 @ X14)) = $true) | (((X1 @ X13 @ X13 @ X14)) = $true)))),
% 3.70/1.03 inference(fool_elimination,[],[f3])).
% 3.70/1.03 thf(f5,plain,(
% 3.70/1.03 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((! [X6 : $i] : (($true = ((X0 @ X4 @ X5 @ X6))) | ($true = ((X1 @ X4 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X3 @ X4 @ X7))) | ($true = ((X1 @ X3 @ X4 @ X7))))) => ! [X8 : $i] : (($true = ((X0 @ X3 @ X5 @ X8))) | ($true = ((X1 @ X3 @ X5 @ X8))))) & ! [X9 : ($i > $o),X10 : $i] : (($true = ((X0 @ X9 @ X9 @ X10))) | ($true = ((X1 @ X9 @ X9 @ X10)))))),
% 3.70/1.03 inference(rectify,[],[f4])).
% 3.70/1.03 thf(f6,plain,(
% 3.70/1.03 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (? [X8 : $i] : (($true != ((X0 @ X3 @ X5 @ X8))) & ($true != ((X1 @ X3 @ X5 @ X8)))) & (! [X6 : $i] : (($true = ((X0 @ X4 @ X5 @ X6))) | ($true = ((X1 @ X4 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X3 @ X4 @ X7))) | ($true = ((X1 @ X3 @ X4 @ X7)))))) | ? [X9 : ($i > $o),X10 : $i] : (($true != ((X0 @ X9 @ X9 @ X10))) & ($true != ((X1 @ X9 @ X9 @ X10)))))),
% 3.70/1.03 inference(ennf_transformation,[],[f5])).
% 3.70/1.03 thf(f7,plain,(
% 3.70/1.03 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (? [X8 : $i] : (($true != ((X0 @ X3 @ X5 @ X8))) & ($true != ((X1 @ X3 @ X5 @ X8)))) & ! [X6 : $i] : (($true = ((X0 @ X4 @ X5 @ X6))) | ($true = ((X1 @ X4 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X3 @ X4 @ X7))) | ($true = ((X1 @ X3 @ X4 @ X7))))) | ? [X9 : ($i > $o),X10 : $i] : (($true != ((X0 @ X9 @ X9 @ X10))) & ($true != ((X1 @ X9 @ X9 @ X10)))))),
% 3.70/1.03 inference(flattening,[],[f6])).
% 3.70/1.03 thf(f8,plain,(
% 3.70/1.03 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : (($true != ((X0 @ X3 @ X5 @ X6))) & ($true != ((X1 @ X3 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X4 @ X5 @ X7))) | ($true = ((X1 @ X4 @ X5 @ X7)))) & ! [X8 : $i] : (($true = ((X0 @ X3 @ X4 @ X8))) | ($true = ((X1 @ X3 @ X4 @ X8))))) | ? [X9 : ($i > $o),X10 : $i] : (($true != ((X0 @ X9 @ X9 @ X10))) & ($true != ((X1 @ X9 @ X9 @ X10)))))),
% 3.70/1.03 inference(rectify,[],[f7])).
% 3.70/1.03 thf(f9,plain,(
% 3.70/1.03 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) | ((($true != ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) & ! [X7 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)))) & ! [X8 : $i] : (($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))))) | (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) & ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))))),
% 3.70/1.03 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0)],[f8])).
% 3.70/1.03 thf(f10,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(cnf_transformation,[],[f9])).
% 3.70/1.03 thf(f12,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(cnf_transformation,[],[f9])).
% 3.70/1.03 thf(f14,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(cnf_transformation,[],[f9])).
% 3.70/1.03 thf(f19,definition,(
% 3.70/1.03 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.70/1.03 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.70/1.03 thf(f33,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X0 @ (sK0 @ X0 @ X1) @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($false = ((X0 @ (sK4 @ X0 @ X1) @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1))))) )),
% 3.70/1.03 inference(constrained_superposition,[],[f14,f19])).
% 3.70/1.03 thf(f36,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X0 @ (sK0 @ X0 @ X1) @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($false = ((X0 @ (sK4 @ X0 @ X1) @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1))))) )),
% 3.70/1.03 inference(trivial_inequality_removal,[],[f33])).
% 3.70/1.03 thf(f86,definition,(
% 3.70/1.03 spl6_2 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 3.70/1.03 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 3.70/1.03 thf(f87,plain,(
% 3.70/1.03 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_2),
% 3.70/1.03 inference(avatar_component_clause,[],[f86])).
% 3.70/1.03 thf(f88,plain,(
% 3.70/1.03 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_2),
% 3.70/1.03 inference(avatar_component_clause,[],[f86])).
% 3.70/1.03 thf(f115,plain,(
% 3.70/1.03 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_2),
% 3.70/1.03 inference(argument_congruence,[],[f88])).
% 3.70/1.03 thf(f117,plain,(
% 3.70/1.03 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X1))) | ($true = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_2),
% 3.70/1.03 inference(iff_proxy_clausification,[],[f115])).
% 3.70/1.03 thf(f118,plain,(
% 3.70/1.03 ($true = $false) | ($true = $false) | ~spl6_2),
% 3.70/1.03 inference(beta-eta_normalization,[],[f117])).
% 3.70/1.03 thf(f119,plain,(
% 3.70/1.03 ($true = $false) | ~spl6_2),
% 3.70/1.03 inference(duplicate_literal_removal,[],[f118])).
% 3.70/1.03 thf(f120,plain,(
% 3.70/1.03 $false | ~spl6_2),
% 3.70/1.03 inference(trivial_inequality_removal,[],[f119])).
% 3.70/1.03 thf(f121,plain,(
% 3.70/1.03 ~spl6_2),
% 3.70/1.03 inference(avatar_contradiction_clause,[],[f120])).
% 3.70/1.03 thf(f159,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(primitive_instantiation,[],[f10])).
% 3.70/1.03 thf(f187,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(beta-eta_normalization,[],[f159])).
% 3.70/1.03 thf(f188,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f187])).
% 3.70/1.03 thf(f189,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f188])).
% 3.70/1.03 thf(f190,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f189])).
% 3.70/1.03 thf(f191,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(trivial_inequality_removal,[],[f190])).
% 3.70/1.03 thf(f192,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_2),
% 3.70/1.03 inference(forward_subsumption_resolution,[],[f191,f87])).
% 3.70/1.03 thf(f231,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(primitive_instantiation,[],[f12])).
% 3.70/1.03 thf(f259,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(beta-eta_normalization,[],[f231])).
% 3.70/1.03 thf(f260,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f259])).
% 3.70/1.03 thf(f261,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f260])).
% 3.70/1.03 thf(f262,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f261])).
% 3.70/1.03 thf(f263,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 3.70/1.03 inference(trivial_inequality_removal,[],[f262])).
% 3.70/1.03 thf(f264,plain,(
% 3.70/1.03 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_2),
% 3.70/1.03 inference(forward_subsumption_resolution,[],[f263,f87])).
% 3.70/1.03 thf(f1228,plain,(
% 3.70/1.03 ( ! [X2 : $i,X8 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK0 @ (^[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))))))) @ X8))) | (((sK0 @ (^[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)))))))))) ) | spl6_2),
% 3.70/1.03 inference(primitive_instantiation,[],[f192])).
% 3.70/1.03 thf(f1443,plain,(
% 3.70/1.03 ($true = $false) | ($true = $false) | (((sK0 @ (^[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))))))))) | spl6_2),
% 3.70/1.03 inference(beta-eta_normalization,[],[f1228])).
% 3.70/1.03 thf(f1444,plain,(
% 3.70/1.03 ($true = $false) | (((sK0 @ (^[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))))))))) | spl6_2),
% 3.70/1.03 inference(duplicate_literal_removal,[],[f1443])).
% 3.70/1.03 thf(f1445,plain,(
% 3.70/1.03 (((sK0 @ (^[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))))))))) | spl6_2),
% 3.70/1.03 inference(trivial_inequality_removal,[],[f1444])).
% 3.70/1.03 thf(f1743,plain,(
% 3.70/1.03 ( ! [X2 : $i,X7 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($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))))))) @ X7))) | (((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)))))))))) ) | spl6_2),
% 3.70/1.03 inference(primitive_instantiation,[],[f264])).
% 3.70/1.03 thf(f1978,plain,(
% 3.70/1.03 ($true = $false) | ($true = $false) | (((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))))))))) | spl6_2),
% 3.70/1.03 inference(beta-eta_normalization,[],[f1743])).
% 3.70/1.03 thf(f1979,plain,(
% 3.70/1.03 ($true = $false) | (((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))))))))) | spl6_2),
% 3.70/1.03 inference(duplicate_literal_removal,[],[f1978])).
% 3.70/1.03 thf(f1980,plain,(
% 3.70/1.03 (((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))))))))) | spl6_2),
% 3.70/1.03 inference(trivial_inequality_removal,[],[f1979])).
% 3.70/1.03 thf(f2009,plain,(
% 3.70/1.03 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 3.70/1.03 inference(forward_demodulation,[],[f1980,f1445])).
% 3.70/1.03 thf(f3188,plain,(
% 3.70/1.03 ( ! [X0 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK0 @ (^[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 = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | ($false = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ (^[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))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))))) ) | spl6_2),
% 3.70/1.03 inference(constrained_superposition,[],[f36,f2009])).
% 3.70/1.03 thf(f3204,plain,(
% 3.70/1.03 ($true != (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = $false) | ($false = (((sK4 @ (^[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)))))))))) | spl6_2),
% 3.70/1.03 inference(beta-eta_normalization,[],[f3188])).
% 3.70/1.03 thf(f3205,plain,(
% 3.70/1.03 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = $false) | ($false = (((sK4 @ (^[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)))))))))) | spl6_2),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f3204])).
% 3.70/1.03 thf(f3206,plain,(
% 3.70/1.03 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = $false) | ($false = (((sK4 @ (^[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)))))))))) | spl6_2),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f3205])).
% 3.70/1.03 thf(f3207,plain,(
% 3.70/1.03 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = $false) | (((sK4 @ (^[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))))))))) | spl6_2),
% 3.70/1.03 inference(equality_proxy_clausification,[],[f3206])).
% 3.70/1.03 thf(f3208,plain,(
% 3.70/1.03 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 3.70/1.03 inference(trivial_inequality_removal,[],[f3207])).
% 3.70/1.03 thf(f3216,plain,(
% 3.70/1.03 $false | spl6_2),
% 3.70/1.03 inference(forward_subsumption_resolution,[],[f3208,f87])).
% 3.70/1.03 thf(f3217,plain,(
% 3.70/1.03 spl6_2),
% 3.70/1.03 inference(avatar_contradiction_clause,[],[f3216])).
% 3.70/1.03 cnf(s2, plain, ~spl6_2, inference(sat_conversion,[],[f121])).
% 3.70/1.03 cnf(s4, plain, spl6_2, inference(sat_conversion,[],[f3217])).
% 3.70/1.03 cnf(s5, plain, $false, inference(rat,[],[s2,s4])).
% 3.70/1.03 thf(f3218,plain,(
% 3.70/1.03 $false),
% 3.70/1.03 inference(avatar_sat_refutation,[],[s5])).
% 3.70/1.03 % SZS output end Proof for theBenchmark
% 3.70/1.03 % (3477913)------------------------------
% 3.70/1.03 % (3477913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.70/1.03 % (3477913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.03 % (3477913)CaDiCaL version: 2.1.3
% 3.70/1.03 % (3477913)Termination reason: Refutation
% 3.70/1.03 % (3477913)Time elapsed: 0.338 s
% 3.70/1.03 % (3477913)Peak memory usage: 15 MB
% 3.70/1.03 % (3477913)Instructions burned: 769 (million)
% 3.70/1.03 % (3477750)Success in time 0.749 s
% 3.70/1.03 % Vampire exiting
%------------------------------------------------------------------------------