%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU671^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:32:55 AM UTC 2026
% Result : Theorem 107.62s 15.49s
% Output : Refutation 107.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU671^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:07:39 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.02/0.95 % (3211460)Will run a generic schedule for satisfiability detection.
% 4.02/0.95 % (3211486)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1333787725:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.02/0.95 % (3211483)% WARNING: option uhcvi not known.
% 4.02/0.95 % (3211483)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2597148893:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.02/0.95 % (3211484)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3891194084:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.02/0.95 % (3211482)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=859217305_2999 on theBenchmark for (2999ds/0Mi)
% 4.02/0.95 % (3211487)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2602753970:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.02/0.95 % (3211485)dis+10_1_sil=32000:sp=arity:random_seed=2792482747:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.02/0.95 % (3211488)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=912845495:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.02/0.95 % (3211486)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.02/0.95 % (3211483)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.02/0.95 % (3211486)Instruction limit reached!
% 4.02/0.95 % (3211486)------------------------------
% 4.02/0.95 % (3211486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.02/0.95 % (3211486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/0.95 % (3211486)CaDiCaL version: 2.1.3
% 4.02/0.95 % (3211486)Termination reason: Instruction limit
% 4.02/0.95 % (3211486)Termination phase: Saturation
% 4.02/0.95 % (3211486)Time elapsed: 0.027 s
% 4.02/0.95 % (3211486)Peak memory usage: 13 MB
% 4.02/0.95 % (3211486)Instructions burned: 119 (million)
% 4.02/0.95 % (3211506)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3629722052:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.02/0.95 % (3211483)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.02/0.95 % Exception at run slice level
% 4.02/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.02/0.95 % (3211485)Instruction limit reached!
% 4.02/0.95 % (3211485)------------------------------
% 4.02/0.95 % (3211485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.02/0.95 % (3211485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/0.95 % (3211485)CaDiCaL version: 2.1.3
% 4.02/0.95 % (3211485)Termination reason: Instruction limit
% 4.02/0.95 % (3211485)Termination phase: Saturation
% 4.02/0.95 % (3211485)Time elapsed: 0.045 s
% 4.02/0.95 % (3211485)Peak memory usage: 12 MB
% 4.02/0.95 % (3211485)Instructions burned: 105 (million)
% 4.02/0.95 % Exception at run slice level
% 4.02/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.02/0.95 % (3211512)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3740850786:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.02/0.95 % (3211487)Instruction limit reached!
% 4.02/0.95 % (3211487)------------------------------
% 4.02/0.95 % (3211487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.02/0.95 % (3211487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/0.95 % (3211487)CaDiCaL version: 2.1.3
% 4.02/0.95 % (3211487)Termination reason: Instruction limit
% 4.02/0.95 % (3211487)Termination phase: Saturation
% 4.02/0.95 % (3211487)Time elapsed: 0.056 s
% 4.02/0.95 % (3211487)Peak memory usage: 13 MB
% 4.02/0.95 % (3211487)Instructions burned: 132 (million)
% 4.02/0.95 % (3211520)ott-21_1_sil=16000:fs=off:random_seed=844549743:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.02/0.95 % (3211518)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=2490873500:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.02/0.95 % (3211488)Instruction limit reached!
% 4.02/0.95 % (3211488)------------------------------
% 4.02/0.95 % (3211488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.02/0.95 % (3211488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.78/2.61 % (3211488)CaDiCaL version: 2.1.3
% 15.78/2.61 % (3211488)Termination reason: Instruction limit
% 15.78/2.61 % (3211488)Termination phase: Saturation
% 15.78/2.61 % (3211488)Time elapsed: 0.071 s
% 15.78/2.61 % (3211488)Peak memory usage: 14 MB
% 15.78/2.61 % (3211488)Instructions burned: 160 (million)
% 15.78/2.61 % (3211526)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2000979779:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 15.78/2.61 % (3211518)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 15.78/2.61 % (3211532)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=107629148:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 15.78/2.61 % (3211518)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 15.78/2.61 % (3211520)Instruction limit reached!
% 15.78/2.61 % (3211520)------------------------------
% 15.78/2.61 % (3211520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.78/2.61 % (3211520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.78/2.61 % (3211520)CaDiCaL version: 2.1.3
% 15.78/2.61 % (3211520)Termination reason: Instruction limit
% 15.78/2.61 % (3211520)Termination phase: Saturation
% 15.78/2.61 % (3211520)Time elapsed: 0.046 s
% 15.78/2.61 % (3211520)Peak memory usage: 14 MB
% 15.78/2.61 % (3211520)Instructions burned: 180 (million)
% 15.78/2.61 % (3211512)Instruction limit reached!
% 15.78/2.61 % (3211512)------------------------------
% 15.78/2.61 % (3211512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.78/2.61 % (3211512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.78/2.61 % (3211512)CaDiCaL version: 2.1.3
% 15.78/2.61 % (3211512)Termination reason: Instruction limit
% 15.78/2.61 % (3211512)Termination phase: Saturation
% 15.78/2.61 % (3211512)Time elapsed: 0.059 s
% 15.78/2.61 % (3211512)Peak memory usage: 13 MB
% 15.78/2.61 % (3211512)Instructions burned: 133 (million)
% 15.78/2.61 % (3211545)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2561185316:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 15.78/2.61 % Exception at run slice level
% 15.78/2.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 15.78/2.61 % (3211549)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1385000601:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 15.78/2.61 % (3211556)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=3118688900: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)
% 15.78/2.61 % (3211556)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 15.78/2.61 % Exception at run slice level
% 15.78/2.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 15.78/2.61 % (3211574)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1643175976:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 15.78/2.61 % (3211574)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 15.78/2.61 % (3211526)Instruction limit reached!
% 15.78/2.61 % (3211526)------------------------------
% 15.78/2.61 % (3211526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.78/2.61 % (3211526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.78/2.61 % (3211526)CaDiCaL version: 2.1.3
% 15.78/2.61 % (3211526)Termination reason: Instruction limit
% 15.78/2.61 % (3211526)Termination phase: Saturation
% 15.78/2.61 % (3211526)Time elapsed: 0.245 s
% 15.78/2.61 % (3211526)Peak memory usage: 15 MB
% 15.78/2.61 % (3211526)Instructions burned: 477 (million)
% 15.78/2.61 % (3211603)fmb+10_1_sil=64000:random_seed=2712944585:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 15.78/2.61 % (3211518)Instruction limit reached!
% 15.78/2.61 % (3211518)------------------------------
% 15.78/2.61 % (3211518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.78/2.61 % (3211518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.78/2.61 % (3211518)CaDiCaL version: 2.1.3
% 15.78/2.61 % (3211518)Termination reason: Instruction limit
% 15.78/2.61 % (3211518)Termination phase: Saturation
% 15.78/2.61 % (3211518)Time elapsed: 0.283 s
% 15.78/2.61 % (3211518)Peak memory usage: 15 MB
% 15.78/2.61 % (3211518)Instructions burned: 684 (million)
% 35.72/5.39 % (3211603)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 35.72/5.39 % (3211605)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1631530415:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 35.72/5.39 % Exception at run slice level
% 35.72/5.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.72/5.39 % (3211607)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1270708495:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 35.72/5.39 % Exception at run slice level
% 35.72/5.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.72/5.39 % (3211545)Instruction limit reached!
% 35.72/5.39 % (3211545)------------------------------
% 35.72/5.39 % (3211545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.72/5.39 % (3211545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.72/5.39 % (3211545)CaDiCaL version: 2.1.3
% 35.72/5.39 % (3211545)Termination reason: Instruction limit
% 35.72/5.39 % (3211545)Termination phase: Saturation
% 35.72/5.39 % (3211545)Time elapsed: 0.297 s
% 35.72/5.39 % (3211545)Peak memory usage: 19 MB
% 35.72/5.39 % (3211545)Instructions burned: 1182 (million)
% 35.72/5.39 % (3211609)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3308996644:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 35.72/5.39 % (3211610)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=170342015:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 35.72/5.39 % Exception at run slice level
% 35.72/5.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.72/5.39 % (3211609)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 35.72/5.39 % (3211610)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 35.72/5.39 % (3211556)Instruction limit reached!
% 35.72/5.39 % (3211556)------------------------------
% 35.72/5.39 % (3211556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.72/5.39 % (3211556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.72/5.39 % (3211556)CaDiCaL version: 2.1.3
% 35.72/5.39 % (3211556)Termination reason: Instruction limit
% 35.72/5.39 % (3211556)Termination phase: Saturation
% 35.72/5.39 % (3211556)Time elapsed: 0.295 s
% 35.72/5.39 % (3211556)Peak memory usage: 16 MB
% 35.72/5.39 % (3211556)Instructions burned: 692 (million)
% 35.72/5.39 % (3211610)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 35.72/5.39 % (3211613)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=463657527:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 35.72/5.39 % (3211614)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3872397672:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 35.72/5.39 % Exception at run slice level
% 35.72/5.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.72/5.39 % Exception at run slice level
% 35.72/5.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.72/5.39 % (3211617)ott-2_1_sil=16000:newcnf=on:random_seed=3987649617:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 35.72/5.39 % (3211618)ott+10_1_sil=32000:tgt=ground:random_seed=120938220:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 35.72/5.39 % (3211617)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 35.72/5.39 % (3211574)Instruction limit reached!
% 35.72/5.39 % (3211574)------------------------------
% 35.72/5.39 % (3211574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.72/5.39 % (3211574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.72/5.39 % (3211574)CaDiCaL version: 2.1.3
% 35.72/5.39 % (3211574)Termination reason: Instruction limit
% 35.72/5.39 % (3211574)Termination phase: Saturation
% 35.72/5.39 % (3211574)Time elapsed: 0.435 s
% 35.72/5.39 % (3211574)Peak memory usage: 18 MB
% 35.72/5.39 % (3211574)Instructions burned: 879 (million)
% 35.72/5.39 % (3211621)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3432161508:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 35.72/5.39 % Exception at run slice level
% 35.72/5.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 87.01/12.51 % (3211623)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2687465315:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 87.01/12.51 % (3211623)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 87.01/12.51 % (3211610)Instruction limit reached!
% 87.01/12.51 % (3211610)------------------------------
% 87.01/12.51 % (3211610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.01/12.51 % (3211610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.01/12.51 % (3211610)CaDiCaL version: 2.1.3
% 87.01/12.51 % (3211610)Termination reason: Instruction limit
% 87.01/12.51 % (3211610)Termination phase: Saturation
% 87.01/12.51 % (3211610)Time elapsed: 0.370 s
% 87.01/12.51 % (3211610)Peak memory usage: 27 MB
% 87.01/12.51 % (3211610)Instructions burned: 1475 (million)
% 87.01/12.51 % (3211625)dis+21_1_sil=32000:sas=cadical:random_seed=1425922440:i=3773:amm=off_2991 on theBenchmark for (2991ds/3773Mi)
% 87.01/12.51 % (3211617)Instruction limit reached!
% 87.01/12.51 % (3211617)------------------------------
% 87.01/12.51 % (3211617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.01/12.51 % (3211617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.01/12.51 % (3211617)CaDiCaL version: 2.1.3
% 87.01/12.51 % (3211617)Termination reason: Instruction limit
% 87.01/12.51 % (3211617)Termination phase: Saturation
% 87.01/12.51 % (3211617)Time elapsed: 0.423 s
% 87.01/12.51 % (3211617)Peak memory usage: 16 MB
% 87.01/12.51 % (3211617)Instructions burned: 872 (million)
% 87.01/12.51 % (3211627)ott+11_1_sil=16000:gs=on:random_seed=2768038621:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2990 on theBenchmark for (2990ds/2251Mi)
% 87.01/12.51 % (3211627)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 87.01/12.51 % (3211625)Instruction limit reached!
% 87.01/12.51 % (3211625)------------------------------
% 87.01/12.51 % (3211625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.01/12.51 % (3211625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.01/12.51 % (3211625)CaDiCaL version: 2.1.3
% 87.01/12.51 % (3211625)Termination reason: Instruction limit
% 87.01/12.51 % (3211625)Termination phase: Saturation
% 87.01/12.51 % (3211625)Time elapsed: 0.944 s
% 87.01/12.51 % (3211625)Peak memory usage: 24 MB
% 87.01/12.51 % (3211625)Instructions burned: 3778 (million)
% 87.01/12.51 % (3211629)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3525894378:fmbsr=1.6:i=67534_2981 on theBenchmark for (2981ds/67534Mi)
% 87.01/12.51 % Exception at run slice level
% 87.01/12.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 87.01/12.51 % (3211631)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=965383155:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2981 on theBenchmark for (2981ds/4591Mi)
% 87.01/12.51 % (3211627)Instruction limit reached!
% 87.01/12.51 % (3211627)------------------------------
% 87.01/12.51 % (3211627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.01/12.51 % (3211627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.01/12.51 % (3211627)CaDiCaL version: 2.1.3
% 87.01/12.51 % (3211627)Termination reason: Instruction limit
% 87.01/12.51 % (3211627)Termination phase: Saturation
% 87.01/12.51 % (3211627)Time elapsed: 0.934 s
% 87.01/12.51 % (3211627)Peak memory usage: 16 MB
% 87.01/12.51 % (3211627)Instructions burned: 2251 (million)
% 87.01/12.51 % (3211633)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=619502516:i=29340_2980 on theBenchmark for (2980ds/29340Mi)
% 87.01/12.51 % (3211623)Instruction limit reached!
% 87.01/12.51 % (3211623)------------------------------
% 87.01/12.51 % (3211623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.01/12.51 % (3211623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.01/12.51 % (3211623)CaDiCaL version: 2.1.3
% 87.01/12.51 % (3211623)Termination reason: Instruction limit
% 87.01/12.51 % (3211623)Termination phase: Saturation
% 87.01/12.51 % (3211623)Time elapsed: 1.611 s
% 87.01/12.51 % (3211623)Peak memory usage: 22 MB
% 87.01/12.51 % (3211623)Instructions burned: 3513 (million)
% 87.01/12.51 % (3211635)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=3308712263:i=5211_2976 on theBenchmark for (2976ds/5211Mi)
% 107.62/15.49 % (3211618)Instruction limit reached!
% 107.62/15.49 % (3211618)------------------------------
% 107.62/15.49 % (3211618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211618)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211618)Termination reason: Instruction limit
% 107.62/15.49 % (3211618)Termination phase: Saturation
% 107.62/15.49 % (3211618)Time elapsed: 2.228 s
% 107.62/15.49 % (3211618)Peak memory usage: 26 MB
% 107.62/15.49 % (3211618)Instructions burned: 5116 (million)
% 107.62/15.49 % (3211609)Instruction limit reached!
% 107.62/15.49 % (3211609)------------------------------
% 107.62/15.49 % (3211609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211609)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211609)Termination reason: Instruction limit
% 107.62/15.49 % (3211609)Termination phase: Saturation
% 107.62/15.49 % (3211609)Time elapsed: 2.339 s
% 107.62/15.49 % (3211609)Peak memory usage: 26 MB
% 107.62/15.49 % (3211609)Instructions burned: 5133 (million)
% 107.62/15.49 % (3211637)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=446384545:i=5497:nm=2_2972 on theBenchmark for (2972ds/5497Mi)
% 107.62/15.49 % (3211638)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=630941364:fmbsr=2:i=46332_2971 on theBenchmark for (2971ds/46332Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211641)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=947745567:i=14071_2971 on theBenchmark for (2971ds/14071Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211643)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2731917454:i=22565:add=on:rawr=on_2971 on theBenchmark for (2971ds/22565Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211645)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=1199605832:i=8173:av=off_2970 on theBenchmark for (2970ds/8173Mi)
% 107.62/15.49 % (3211631)Instruction limit reached!
% 107.62/15.49 % (3211631)------------------------------
% 107.62/15.49 % (3211631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211631)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211631)Termination reason: Instruction limit
% 107.62/15.49 % (3211631)Termination phase: Saturation
% 107.62/15.49 % (3211631)Time elapsed: 1.089 s
% 107.62/15.49 % (3211631)Peak memory usage: 26 MB
% 107.62/15.49 % (3211631)Instructions burned: 4592 (million)
% 107.62/15.49 % (3211647)dis+10_16:1_sil=16000:random_seed=2187867613:i=9155:fsr=off_2970 on theBenchmark for (2970ds/9155Mi)
% 107.62/15.49 % (3211635)Instruction limit reached!
% 107.62/15.49 % (3211635)------------------------------
% 107.62/15.49 % (3211635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211635)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211635)Termination reason: Instruction limit
% 107.62/15.49 % (3211635)Termination phase: Saturation
% 107.62/15.49 % (3211635)Time elapsed: 2.477 s
% 107.62/15.49 % (3211635)Peak memory usage: 33 MB
% 107.62/15.49 % (3211635)Instructions burned: 5212 (million)
% 107.62/15.49 % (3211649)ott-3_8_sil=64000:random_seed=77165869:i=20139:bs=on_2951 on theBenchmark for (2951ds/20139Mi)
% 107.62/15.49 % (3211647)Instruction limit reached!
% 107.62/15.49 % (3211647)------------------------------
% 107.62/15.49 % (3211647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211647)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211647)Termination reason: Instruction limit
% 107.62/15.49 % (3211647)Termination phase: Saturation
% 107.62/15.49 % (3211647)Time elapsed: 2.196 s
% 107.62/15.49 % (3211647)Peak memory usage: 37 MB
% 107.62/15.49 % (3211647)Instructions burned: 9157 (million)
% 107.62/15.49 % (3211651)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=1553221779:fmbsr=2:i=32576_2948 on theBenchmark for (2948ds/32576Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211653)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=1673744353:i=11404_2948 on theBenchmark for (2948ds/11404Mi)
% 107.62/15.49 % (3211645)Instruction limit reached!
% 107.62/15.49 % (3211645)------------------------------
% 107.62/15.49 % (3211645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211645)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211645)Termination reason: Instruction limit
% 107.62/15.49 % (3211645)Termination phase: Saturation
% 107.62/15.49 % (3211645)Time elapsed: 3.372 s
% 107.62/15.49 % (3211645)Peak memory usage: 27 MB
% 107.62/15.49 % (3211645)Instructions burned: 8173 (million)
% 107.62/15.49 % (3211655)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=1178663310:i=14134_2937 on theBenchmark for (2937ds/14134Mi)
% 107.62/15.49 % (3211655)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 107.62/15.49 % (3211653)Instruction limit reached!
% 107.62/15.49 % (3211653)------------------------------
% 107.62/15.49 % (3211653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211653)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211653)Termination reason: Instruction limit
% 107.62/15.49 % (3211653)Termination phase: Saturation
% 107.62/15.49 % (3211653)Time elapsed: 2.897 s
% 107.62/15.49 % (3211653)Peak memory usage: 50 MB
% 107.62/15.49 % (3211653)Instructions burned: 11404 (million)
% 107.62/15.49 % (3211657)dis+33_16_sil=32000:sac=on:random_seed=1754498663:i=15851:nm=0_2919 on theBenchmark for (2919ds/15851Mi)
% 107.62/15.49 % (3211643)Instruction limit reached!
% 107.62/15.49 % (3211643)------------------------------
% 107.62/15.49 % (3211643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211643)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211643)Termination reason: Instruction limit
% 107.62/15.49 % (3211643)Termination phase: Saturation
% 107.62/15.49 % (3211643)Time elapsed: 7.565 s
% 107.62/15.49 % (3211643)Peak memory usage: 26 MB
% 107.62/15.49 % (3211643)Instructions burned: 22567 (million)
% 107.62/15.49 % (3211659)dis+4_1024_sil=32000:avsql=on:sp=occurrence:gs=on:avsqc=1:random_seed=3179875848:avsq=on:i=17627:add=on:amm=off_2895 on theBenchmark for (2895ds/17627Mi)
% 107.62/15.49 % (3211657)Instruction limit reached!
% 107.62/15.49 % (3211657)------------------------------
% 107.62/15.49 % (3211657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211657)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211657)Termination reason: Instruction limit
% 107.62/15.49 % (3211657)Termination phase: Saturation
% 107.62/15.49 % (3211657)Time elapsed: 2.994 s
% 107.62/15.49 % (3211657)Peak memory usage: 18 MB
% 107.62/15.49 % (3211657)Instructions burned: 15856 (million)
% 107.62/15.49 % (3211661)ott+10_64_anc=all:sil=128000:sas=cadical:bsr=unit_only:nwc=1:cn=on:random_seed=771010997:s2a=on:i=53295_2889 on theBenchmark for (2889ds/53295Mi)
% 107.62/15.49 % (3211655)Instruction limit reached!
% 107.62/15.49 % (3211655)------------------------------
% 107.62/15.49 % (3211655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211655)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211655)Termination reason: Instruction limit
% 107.62/15.49 % (3211655)Termination phase: Saturation
% 107.62/15.49 % (3211655)Time elapsed: 5.925 s
% 107.62/15.49 % (3211655)Peak memory usage: 40 MB
% 107.62/15.49 % (3211655)Instructions burned: 14136 (million)
% 107.62/15.49 % (3211663)fmb+10_1_sil=32000:sas=cadical:fmbss=16:random_seed=2704983897:i=26857:ins=20_2877 on theBenchmark for (2877ds/26857Mi)
% 107.62/15.49 % (3211649)Instruction limit reached!
% 107.62/15.49 % (3211649)------------------------------
% 107.62/15.49 % (3211649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211649)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211649)Termination reason: Instruction limit
% 107.62/15.49 % (3211649)Termination phase: Saturation
% 107.62/15.49 % (3211649)Time elapsed: 7.401 s
% 107.62/15.49 % (3211649)Peak memory usage: 21 MB
% 107.62/15.49 % (3211649)Instructions burned: 20139 (million)
% 107.62/15.49 % (3211665)ott+10_1_sil=64000:plsq=on:plsqc=4:bsr=unit_only:gs=on:random_seed=2119552968:i=28120:bs=on:fsr=off_2877 on theBenchmark for (2877ds/28120Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211667)fmb+10_1_sil=256000:fmbss=7:random_seed=2900159659:fmbsr=1.6:i=182295_2877 on theBenchmark for (2877ds/182295Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211669)fmb+10_1_sil=128000:fmbss=21:newcnf=on:random_seed=3202009759:i=44625:gsp=on_2876 on theBenchmark for (2876ds/44625Mi)
% 107.62/15.49 % (3211669)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 107.62/15.49 % (3211669)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211671)fmb+10_1_sil=256000:sas=cadical:fmbss=15:random_seed=3670073911:i=160505_2875 on theBenchmark for (2875ds/160505Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211673)fmb+10_1_sil=256000:tgt=full:fmbss=10:random_seed=1914310928:fmbsr=1.3:i=225729_2875 on theBenchmark for (2875ds/225729Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211675)fmb+10_1_sil=256000:tgt=full:sas=cadical:fmbss=10:random_seed=1098048653:fmbsr=2:i=185024:ins=7_2874 on theBenchmark for (2874ds/185024Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211677)fmb+10_1_sas=cadical:si=on:bce=on:rp=on:random_seed=1204830537:rtra=on_2874 on theBenchmark for (2874ds/0Mi)
% 107.62/15.49 % Exception at run slice level
% 107.62/15.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 107.62/15.49 % (3211679)% WARNING: option uhcvi not known.
% 107.62/15.49 % (3211679)dis+11_61:31_drc=ordering:si=on:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=755759893:i=271062:add=off:rtra=on:rawr=on_2873 on theBenchmark for (2873ds/271062Mi)
% 107.62/15.49 % (3211679)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 107.62/15.49 % (3211679)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 107.62/15.49 % (3211633)Instruction limit reached!
% 107.62/15.49 % (3211633)------------------------------
% 107.62/15.49 % (3211633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.49 % (3211633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.49 % (3211633)CaDiCaL version: 2.1.3
% 107.62/15.49 % (3211633)Termination reason: Instruction limit
% 107.62/15.49 % (3211633)Termination phase: Saturation
% 107.62/15.49 % (3211633)Time elapsed: 11.979 s
% 107.62/15.49 % (3211633)Peak memory usage: 60 MB
% 107.62/15.49 % (3211633)Instructions burned: 29340 (million)
% 107.62/15.49 % (3211739)dis+10_161_sil=256000:plsq=on:si=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=104412539:i=176048:add=on:rtra=on:rawr=on_2860 on theBenchmark for (2860ds/176048Mi)
% 107.62/15.49 % (3211483) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3211460-3211483"...
% 107.62/15.49 % (3211483)...printing done.
% 107.62/15.49 % (3211483)Refutation found. Thanks to Tanya!
% 107.62/15.49 % SZS status Theorem for theBenchmark
% 107.62/15.49 % SZS output start Proof for theBenchmark
% 107.62/15.49 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 107.62/15.49 thf(func_def_0, type, in: ($i > $i > $o)).
% 107.62/15.49 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 107.62/15.49 thf(func_def_3, type, setextAx: $o).
% 107.62/15.49 thf(func_def_5, type, emptysetAx: $o).
% 107.62/15.49 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 107.62/15.49 thf(func_def_7, type, setadjoinAx: $o).
% 107.62/15.49 thf(func_def_8, type, powerset: ($i > $i)).
% 107.62/15.49 thf(func_def_9, type, powersetAx: $o).
% 107.62/15.49 thf(func_def_10, type, setunion: ($i > $i)).
% 107.62/15.49 thf(func_def_11, type, setunionAx: $o).
% 107.62/15.49 thf(func_def_13, type, omega0Ax: $o).
% 107.62/15.49 thf(func_def_14, type, omegaSAx: $o).
% 107.62/15.49 thf(func_def_15, type, omegaIndAx: $o).
% 107.62/15.49 thf(func_def_16, type, replAx: $o).
% 107.62/15.49 thf(func_def_17, type, foundationAx: $o).
% 107.62/15.49 thf(func_def_18, type, wellorderingAx: $o).
% 107.62/15.49 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 107.62/15.49 thf(func_def_20, type, descrp: $o).
% 107.62/15.49 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 107.62/15.49 thf(func_def_22, type, dsetconstrI: $o).
% 107.62/15.49 thf(func_def_23, type, dsetconstrEL: $o).
% 107.62/15.49 thf(func_def_24, type, dsetconstrER: $o).
% 107.62/15.49 thf(func_def_25, type, exuE1: $o).
% 107.62/15.49 thf(func_def_26, type, prop2set: ($o > $i)).
% 107.62/15.49 thf(func_def_27, type, prop2setE: $o).
% 107.62/15.49 thf(func_def_28, type, emptysetE: $o).
% 107.62/15.49 thf(func_def_29, type, emptysetimpfalse: $o).
% 107.62/15.49 thf(func_def_30, type, notinemptyset: $o).
% 107.62/15.49 thf(func_def_31, type, exuE3e: $o).
% 107.62/15.49 thf(func_def_32, type, setext: $o).
% 107.62/15.49 thf(func_def_33, type, emptyI: $o).
% 107.62/15.49 thf(func_def_34, type, noeltsimpempty: $o).
% 107.62/15.49 thf(func_def_35, type, setbeta: $o).
% 107.62/15.49 thf(func_def_36, type, nonempty: ($i > $o)).
% 107.62/15.49 thf(func_def_37, type, nonemptyE1: $o).
% 107.62/15.49 thf(func_def_38, type, nonemptyI: $o).
% 107.62/15.49 thf(func_def_39, type, nonemptyI1: $o).
% 107.62/15.49 thf(func_def_40, type, setadjoinIL: $o).
% 107.62/15.49 thf(func_def_41, type, emptyinunitempty: $o).
% 107.62/15.49 thf(func_def_42, type, setadjoinIR: $o).
% 107.62/15.49 thf(func_def_43, type, setadjoinE: $o).
% 107.62/15.49 thf(func_def_44, type, setadjoinOr: $o).
% 107.62/15.49 thf(func_def_45, type, setoftrueEq: $o).
% 107.62/15.49 thf(func_def_46, type, powersetI: $o).
% 107.62/15.49 thf(func_def_47, type, emptyinPowerset: $o).
% 107.62/15.49 thf(func_def_48, type, emptyInPowerset: $o).
% 107.62/15.49 thf(func_def_49, type, powersetE: $o).
% 107.62/15.49 thf(func_def_50, type, setunionI: $o).
% 107.62/15.49 thf(func_def_51, type, setunionE: $o).
% 107.62/15.49 thf(func_def_52, type, subPowSU: $o).
% 107.62/15.49 thf(func_def_53, type, exuE2: $o).
% 107.62/15.49 thf(func_def_54, type, nonemptyImpWitness: $o).
% 107.62/15.49 thf(func_def_55, type, uniqinunit: $o).
% 107.62/15.49 thf(func_def_56, type, notinsingleton: $o).
% 107.62/15.49 thf(func_def_57, type, eqinunit: $o).
% 107.62/15.49 thf(func_def_58, type, singletonsswitch: $o).
% 107.62/15.49 thf(func_def_59, type, upairsetE: $o).
% 107.62/15.49 thf(func_def_60, type, upairsetIL: $o).
% 107.62/15.49 thf(func_def_61, type, upairsetIR: $o).
% 107.62/15.49 thf(func_def_62, type, emptyE1: $o).
% 107.62/15.49 thf(func_def_63, type, vacuousDall: $o).
% 107.62/15.49 thf(func_def_64, type, quantDeMorgan1: $o).
% 107.62/15.49 thf(func_def_65, type, quantDeMorgan2: $o).
% 107.62/15.49 thf(func_def_66, type, quantDeMorgan3: $o).
% 107.62/15.49 thf(func_def_67, type, quantDeMorgan4: $o).
% 107.62/15.49 thf(func_def_68, type, prop2setI: $o).
% 107.62/15.49 thf(func_def_69, type, set2prop: ($i > $o)).
% 107.62/15.49 thf(func_def_70, type, prop2set2propI: $o).
% 107.62/15.49 thf(func_def_71, type, notdexE: $o).
% 107.62/15.49 thf(func_def_72, type, notdallE: $o).
% 107.62/15.49 thf(func_def_73, type, exuI1: $o).
% 107.62/15.49 thf(func_def_74, type, exuI3: $o).
% 107.62/15.49 thf(func_def_75, type, exuI2: $o).
% 107.62/15.49 thf(func_def_76, type, inCongP: $o).
% 107.62/15.49 thf(func_def_77, type, in__Cong: $o).
% 107.62/15.49 thf(func_def_78, type, exuE3u: $o).
% 107.62/15.49 thf(func_def_79, type, exu__Cong: $o).
% 107.62/15.49 thf(func_def_80, type, emptyset__Cong: $o).
% 107.62/15.49 thf(func_def_81, type, setadjoin__Cong: $o).
% 107.62/15.49 thf(func_def_82, type, powerset__Cong: $o).
% 107.62/15.49 thf(func_def_83, type, setunion__Cong: $o).
% 107.62/15.49 thf(func_def_84, type, omega__Cong: $o).
% 107.62/15.49 thf(func_def_85, type, exuEu: $o).
% 107.62/15.49 thf(func_def_86, type, descr__Cong: $o).
% 107.62/15.49 thf(func_def_87, type, dsetconstr__Cong: $o).
% 107.62/15.49 thf(func_def_88, type, subset: ($i > $i > $o)).
% 107.62/15.49 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 107.62/15.49 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 107.62/15.49 thf(func_def_91, type, subsetI1: $o).
% 107.62/15.49 thf(func_def_92, type, eqimpsubset2: $o).
% 107.62/15.49 thf(func_def_93, type, eqimpsubset1: $o).
% 107.62/15.49 thf(func_def_94, type, subsetI2: $o).
% 107.62/15.49 thf(func_def_95, type, emptysetsubset: $o).
% 107.62/15.49 thf(func_def_96, type, subsetE: $o).
% 107.62/15.49 thf(func_def_97, type, subsetE2: $o).
% 107.62/15.49 thf(func_def_98, type, notsubsetI: $o).
% 107.62/15.49 thf(func_def_99, type, notequalI1: $o).
% 107.62/15.49 thf(func_def_100, type, notequalI2: $o).
% 107.62/15.49 thf(func_def_101, type, subsetRefl: $o).
% 107.62/15.49 thf(func_def_102, type, subsetTrans: $o).
% 107.62/15.49 thf(func_def_103, type, setadjoinSub: $o).
% 107.62/15.49 thf(func_def_104, type, setadjoinSub2: $o).
% 107.62/15.49 thf(func_def_105, type, subset2powerset: $o).
% 107.62/15.49 thf(func_def_106, type, setextsub: $o).
% 107.62/15.49 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 107.62/15.49 thf(func_def_108, type, powersetI1: $o).
% 107.62/15.49 thf(func_def_109, type, powersetE1: $o).
% 107.62/15.49 thf(func_def_110, type, inPowerset: $o).
% 107.62/15.49 thf(func_def_111, type, powersetsubset: $o).
% 107.62/15.49 thf(func_def_112, type, sepInPowerset: $o).
% 107.62/15.49 thf(func_def_113, type, sepSubset: $o).
% 107.62/15.49 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 107.62/15.49 thf(func_def_115, type, binunionIL: $o).
% 107.62/15.49 thf(func_def_116, type, upairset2IR: $o).
% 107.62/15.49 thf(func_def_117, type, binunionIR: $o).
% 107.62/15.49 thf(func_def_118, type, binunionEcases: $o).
% 107.62/15.49 thf(func_def_119, type, binunionE: $o).
% 107.62/15.49 thf(func_def_120, type, binunionLsub: $o).
% 107.62/15.49 thf(func_def_121, type, binunionRsub: $o).
% 107.62/15.49 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 107.62/15.49 thf(func_def_123, type, binintersectI: $o).
% 107.62/15.49 thf(func_def_124, type, binintersectSubset5: $o).
% 107.62/15.49 thf(func_def_125, type, binintersectEL: $o).
% 107.62/15.49 thf(func_def_126, type, binintersectLsub: $o).
% 107.62/15.49 thf(func_def_127, type, binintersectSubset2: $o).
% 107.62/15.49 thf(func_def_128, type, binintersectSubset3: $o).
% 107.62/15.49 thf(func_def_129, type, binintersectER: $o).
% 107.62/15.49 thf(func_def_130, type, disjointsetsI1: $o).
% 107.62/15.49 thf(func_def_131, type, binintersectRsub: $o).
% 107.62/15.49 thf(func_def_132, type, binintersectSubset4: $o).
% 107.62/15.49 thf(func_def_133, type, binintersectSubset1: $o).
% 107.62/15.50 thf(func_def_134, type, bs114d: $o).
% 107.62/15.50 thf(func_def_135, type, regular: ($i > $o)).
% 107.62/15.50 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_137, type, setminusI: $o).
% 107.62/15.50 thf(func_def_138, type, setminusEL: $o).
% 107.62/15.50 thf(func_def_139, type, setminusER: $o).
% 107.62/15.50 thf(func_def_140, type, setminusSubset2: $o).
% 107.62/15.50 thf(func_def_141, type, setminusERneg: $o).
% 107.62/15.50 thf(func_def_142, type, setminusELneg: $o).
% 107.62/15.50 thf(func_def_143, type, setminusILneg: $o).
% 107.62/15.50 thf(func_def_144, type, setminusIRneg: $o).
% 107.62/15.50 thf(func_def_145, type, setminusLsub: $o).
% 107.62/15.50 thf(func_def_146, type, setminusSubset1: $o).
% 107.62/15.50 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_148, type, symdiffE: $o).
% 107.62/15.50 thf(func_def_149, type, symdiffI1: $o).
% 107.62/15.50 thf(func_def_150, type, symdiffI2: $o).
% 107.62/15.50 thf(func_def_151, type, symdiffIneg1: $o).
% 107.62/15.50 thf(func_def_152, type, symdiffIneg2: $o).
% 107.62/15.50 thf(func_def_153, type, iskpair: ($i > $o)).
% 107.62/15.50 thf(func_def_154, type, secondinupair: $o).
% 107.62/15.50 thf(func_def_155, type, setukpairIL: $o).
% 107.62/15.50 thf(func_def_156, type, setukpairIR: $o).
% 107.62/15.50 thf(func_def_157, type, kpairiskpair: $o).
% 107.62/15.50 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_159, type, kpairp: $o).
% 107.62/15.50 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_161, type, singletonsubset: $o).
% 107.62/15.50 thf(func_def_162, type, singletoninpowerset: $o).
% 107.62/15.50 thf(func_def_163, type, singletoninpowunion: $o).
% 107.62/15.50 thf(func_def_164, type, upairset2E: $o).
% 107.62/15.50 thf(func_def_165, type, upairsubunion: $o).
% 107.62/15.50 thf(func_def_166, type, upairinpowunion: $o).
% 107.62/15.50 thf(func_def_167, type, ubforcartprodlem1: $o).
% 107.62/15.50 thf(func_def_168, type, ubforcartprodlem2: $o).
% 107.62/15.50 thf(func_def_169, type, ubforcartprodlem3: $o).
% 107.62/15.50 thf(func_def_170, type, cartprodpairin: $o).
% 107.62/15.50 thf(func_def_171, type, cartprodmempair1: $o).
% 107.62/15.50 thf(func_def_172, type, cartprodmempair: $o).
% 107.62/15.50 thf(func_def_173, type, setunionE2: $o).
% 107.62/15.50 thf(func_def_174, type, setunionsingleton1: $o).
% 107.62/15.50 thf(func_def_175, type, setunionsingleton2: $o).
% 107.62/15.50 thf(func_def_176, type, setunionsingleton: $o).
% 107.62/15.50 thf(func_def_177, type, singleton: ($i > $o)).
% 107.62/15.50 thf(func_def_178, type, singletonprop: $o).
% 107.62/15.50 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 107.62/15.50 thf(func_def_180, type, ex1E1: $o).
% 107.62/15.50 thf(func_def_181, type, ex1I: $o).
% 107.62/15.50 thf(func_def_182, type, ex1I2: $o).
% 107.62/15.50 thf(func_def_183, type, singletonsuniq: $o).
% 107.62/15.50 thf(func_def_184, type, atmost1p: ($i > $o)).
% 107.62/15.50 thf(func_def_185, type, atleast2p: ($i > $o)).
% 107.62/15.50 thf(func_def_186, type, atmost2p: ($i > $o)).
% 107.62/15.50 thf(func_def_187, type, upairsetp: ($i > $o)).
% 107.62/15.50 thf(func_def_188, type, setukpairinjL1: $o).
% 107.62/15.50 thf(func_def_189, type, kfstsingleton: $o).
% 107.62/15.50 thf(func_def_190, type, theprop: $o).
% 107.62/15.50 thf(func_def_191, type, kfst: ($i > $i)).
% 107.62/15.50 thf(func_def_192, type, kfstpairEq: $o).
% 107.62/15.50 thf(func_def_193, type, cartprodfstin: $o).
% 107.62/15.50 thf(func_def_194, type, setukpairinjL2: $o).
% 107.62/15.50 thf(func_def_195, type, setukpairinjL: $o).
% 107.62/15.50 thf(func_def_196, type, setukpairinjR11: $o).
% 107.62/15.50 thf(func_def_197, type, setukpairinjR12: $o).
% 107.62/15.50 thf(func_def_198, type, setukpairinjR1: $o).
% 107.62/15.50 thf(func_def_199, type, upairequniteq: $o).
% 107.62/15.50 thf(func_def_200, type, setukpairinjR2: $o).
% 107.62/15.50 thf(func_def_201, type, setukpairinjR: $o).
% 107.62/15.50 thf(func_def_202, type, ksndsingleton: $o).
% 107.62/15.50 thf(func_def_203, type, ksnd: ($i > $i)).
% 107.62/15.50 thf(func_def_204, type, ksndpairEq: $o).
% 107.62/15.50 thf(func_def_205, type, kpairsurjEq: $o).
% 107.62/15.50 thf(func_def_206, type, cartprodsndin: $o).
% 107.62/15.50 thf(func_def_207, type, cartprodpairmemEL: $o).
% 107.62/15.50 thf(func_def_208, type, cartprodpairmemER: $o).
% 107.62/15.50 thf(func_def_209, type, cartprodmempaircEq: $o).
% 107.62/15.50 thf(func_def_210, type, cartprodfstpairEq: $o).
% 107.62/15.50 thf(func_def_211, type, cartprodsndpairEq: $o).
% 107.62/15.50 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 107.62/15.50 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 107.62/15.50 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_215, type, dpsetconstrI: $o).
% 107.62/15.50 thf(func_def_216, type, dpsetconstrSub: $o).
% 107.62/15.50 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 107.62/15.50 thf(func_def_218, type, dpsetconstrERa: $o).
% 107.62/15.50 thf(func_def_219, type, dpsetconstrEL1: $o).
% 107.62/15.50 thf(func_def_220, type, dpsetconstrEL2: $o).
% 107.62/15.50 thf(func_def_221, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 107.62/15.50 thf(func_def_222, type, vAND: ($o > $o > $o)).
% 107.62/15.50 thf(func_def_223, type, db1: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_224, type, db0: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_225, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 107.62/15.50 thf(func_def_226, type, vIMP: ($o > $o > $o)).
% 107.62/15.50 thf(func_def_227, type, db2: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_228, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 107.62/15.50 thf(func_def_229, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 107.62/15.50 thf(func_def_230, type, vIFF: ($o > $o > $o)).
% 107.62/15.50 thf(func_def_231, type, vNOT: ($o > $o)).
% 107.62/15.50 thf(func_def_232, type, vOR: ($o > $o > $o)).
% 107.62/15.50 thf(func_def_233, type, db4: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_234, type, db3: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_237, type, db5: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_240, type, sK2: ($i > $i > $o)).
% 107.62/15.50 thf(func_def_243, type, db7: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_244, type, db6: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_245, type, db8: !>[X0: $tType]:(X0)).
% 107.62/15.50 thf(func_def_246, type, sK5: ($i > $i)).
% 107.62/15.50 thf(func_def_247, type, sK6: ($i > $i)).
% 107.62/15.50 thf(func_def_248, type, sK7: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_249, type, sK8: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_250, type, sK9: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_251, type, sK10: ($i > $i > ($i > $o) > $i)).
% 107.62/15.50 thf(func_def_252, type, sK11: ($i > ($i > $o) > $i)).
% 107.62/15.50 thf(func_def_253, type, sK12: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_254, type, sK13: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_255, type, sK14: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_256, type, sK15: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_257, type, sK16: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_258, type, sK17: ($i > $i > $i > $i)).
% 107.62/15.50 thf(func_def_259, type, sK18: ($i > $i > $i > $i)).
% 107.62/15.50 thf(func_def_260, type, sK19: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_261, type, sK20: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_262, type, sK21: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_263, type, sK22: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 107.62/15.50 thf(func_def_264, type, sK23: ($i > $i > ($i > $o) > ($i > $o) > $i)).
% 107.62/15.50 thf(func_def_265, type, sK24: (($i > $o) > ($i > $o) > $i)).
% 107.62/15.50 thf(func_def_266, type, sK25: (($i > $o) > ($i > $o) > $i)).
% 107.62/15.50 thf(func_def_267, type, sK26: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_268, type, sK27: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_269, type, sK28: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_270, type, sK29: (($i > $o) > ($i > $o) > $i)).
% 107.62/15.50 thf(func_def_271, type, sK30: (($i > $o) > ($i > $o) > $i)).
% 107.62/15.50 thf(func_def_272, type, sK31: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_273, type, sK32: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_274, type, sK33: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_275, type, sK34: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_276, type, sK35: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_277, type, sK36: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_278, type, sK37: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_279, type, sK38: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_280, type, sK39: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_281, type, sK40: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_282, type, sK41: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_283, type, sK42: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_284, type, sK43: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_285, type, sK44: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_286, type, sK45: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_287, type, sK46: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_288, type, sK47: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_289, type, sK48: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_290, type, sK49: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_291, type, sK50: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_292, type, sK51: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_293, type, sK52: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_294, type, sK53: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_295, type, sK54: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_296, type, sK55: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_297, type, sK56: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_298, type, sK57: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_299, type, sK58: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_300, type, sK59: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_301, type, sK60: ($i > $i)).
% 107.62/15.50 thf(func_def_302, type, sK61: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_303, type, sK62: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_304, type, sK63: ($i > $o > $i > $i)).
% 107.62/15.50 thf(func_def_305, type, sK64: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_306, type, sK65: ($i > $i)).
% 107.62/15.50 thf(func_def_307, type, sK66: ($i > $i)).
% 107.62/15.50 thf(func_def_308, type, sK67: ($i > $i)).
% 107.62/15.50 thf(func_def_309, type, sK68: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_310, type, sK69: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_311, type, sK70: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_312, type, sK71: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_313, type, sK72: (($i > $o) > $i)).
% 107.62/15.50 thf(func_def_314, type, sK73: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_315, type, sK74: (($i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_316, type, sK75: ($i > $i)).
% 107.62/15.50 thf(func_def_317, type, sK76: ($i > $i > $i > $i)).
% 107.62/15.50 thf(func_def_318, type, sK77: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_319, type, sK78: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_320, type, sK79: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_321, type, sK80: ($i > $i)).
% 107.62/15.50 thf(func_def_322, type, sK81: ($i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_323, type, sK82: ($i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_324, type, sK83: ($i > $i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_325, type, sK84: ($i > ($i > $i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_326, type, sK85: ($i > $i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_327, type, sK86: ($i > $i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_328, type, sK87: ($i > $i)).
% 107.62/15.50 thf(func_def_329, type, sK88: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_330, type, sK89: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_331, type, sK90: ($i > $i > $i)).
% 107.62/15.50 thf(func_def_337, type, sK96: ($i > $i > $i > $i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_338, type, sK97: ($i > $i > $i > ($i > $i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_339, type, sK98: ($i > $i > $i > $i > ($i > $i > $o) > $i)).
% 107.62/15.50 thf(func_def_340, type, sK99: ($i > $i > $i > ($i > $i > $o) > $i > $i)).
% 107.62/15.50 thf(func_def_341, type, sK100: (($i > $i > $i) > $i)).
% 107.62/15.50 thf(func_def_342, type, sK101: (($i > $i > $i) > $i)).
% 107.62/15.50 thf(f187,axiom,(
% 107.62/15.50 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : ($i > $i > $o)] : ((dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : ((X3 = ((kpair @ X4 @ X5))) & (X2 @ X4 @ X5) & (in @ X5 @ X1)) & (in @ X4 @ X0))))))))),
% 107.62/15.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr)).
% 107.62/15.50 thf(f191,axiom,(
% 107.62/15.50 (dpsetconstrERa = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (X2 @ X3 @ X4)))))),
% 107.62/15.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa)).
% 107.62/15.50 thf(f192,axiom,(
% 107.62/15.50 (dpsetconstrEL1 = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X3 @ X0)))),
% 107.62/15.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1)).
% 107.62/15.50 thf(f193,axiom,(
% 107.62/15.50 (dpsetconstrEL2 = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X4 @ X1)))),
% 107.62/15.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2)).
% 107.62/15.50 thf(f194,conjecture,(
% 107.62/15.50 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (X2 @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.62/15.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER)).
% 107.62/15.50 thf(f195,negated_conjecture,(
% 107.62/15.50 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (X2 @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.62/15.50 inference(negated_conjecture,[status(cth)],[f194])).
% 107.62/15.50 thf(f544,plain,(
% 107.62/15.50 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : ($i > $i > $o)] : ((dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : ((X3 = ((kpair @ X4 @ X5))) & (X2 @ X4 @ X5) & (in @ X5 @ X1)) & (in @ X4 @ X0))))))))),
% 107.62/15.50 inference(rectify,[],[f187])).
% 107.62/15.50 thf(f545,plain,(
% 107.62/15.50 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 107.62/15.50 inference(fool_elimination,[],[f544])).
% 107.62/15.50 thf(f552,plain,(
% 107.62/15.50 (dpsetconstrERa = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (X2 @ X3 @ X4)))))),
% 107.62/15.50 inference(rectify,[],[f191])).
% 107.62/15.50 thf(f553,plain,(
% 107.62/15.50 (dpsetconstrERa = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (Y1 @ Y0 @ Y4))))))))))))))))),
% 107.62/15.50 inference(fool_elimination,[],[f552])).
% 107.62/15.50 thf(f554,plain,(
% 107.62/15.50 (dpsetconstrEL1 = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X3 @ X0)))),
% 107.62/15.50 inference(rectify,[],[f192])).
% 107.62/15.50 thf(f555,plain,(
% 107.62/15.50 (dpsetconstrEL1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ (dpsetconstr @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y1 @ Y4))))))))))))))),
% 107.62/15.50 inference(fool_elimination,[],[f554])).
% 107.62/15.50 thf(f556,plain,(
% 107.62/15.50 (dpsetconstrEL2 = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X4 @ X1)))),
% 107.62/15.50 inference(rectify,[],[f193])).
% 107.62/15.50 thf(f557,plain,(
% 107.62/15.50 (dpsetconstrEL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ (dpsetconstr @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y0 @ Y3))))))))))))))),
% 107.62/15.50 inference(fool_elimination,[],[f556])).
% 107.62/15.50 thf(f558,plain,(
% 107.62/15.50 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (X2 @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.62/15.50 inference(rectify,[],[f195])).
% 107.62/15.50 thf(f559,plain,(
% 107.62/15.50 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : (($true = ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) => (((X2 @ X3 @ X4)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.62/15.50 inference(fool_elimination,[],[f558])).
% 107.62/15.50 thf(f560,plain,(
% 107.62/15.50 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((((X2 @ X3 @ X4)) != $true) & ($true = ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))))) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 107.62/15.50 inference(ennf_transformation,[],[f559])).
% 107.62/15.50 thf(f561,plain,(
% 107.62/15.50 ? [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((((X2 @ X3 @ X4)) != $true) & ($true = ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))))) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 107.62/15.50 inference(flattening,[],[f560])).
% 107.62/15.50 thf(f562,plain,(
% 107.62/15.50 (($true != ((sK2 @ sK3 @ sK4))) & ($true = ((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))))))) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 107.62/15.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f561])).
% 107.62/15.50 thf(f749,plain,(
% 107.62/15.50 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 107.62/15.50 inference(cnf_transformation,[],[f545])).
% 107.62/15.50 thf(f753,plain,(
% 107.62/15.50 (dpsetconstrERa = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (Y1 @ Y0 @ Y4))))))))))))))))),
% 107.62/15.50 inference(cnf_transformation,[],[f553])).
% 107.62/15.50 thf(f754,plain,(
% 107.62/15.50 (dpsetconstrEL1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ (dpsetconstr @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y1 @ Y4))))))))))))))),
% 107.62/15.50 inference(cnf_transformation,[],[f555])).
% 107.62/15.50 thf(f755,plain,(
% 107.62/15.50 (dpsetconstrEL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ (dpsetconstr @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y0 @ Y3))))))))))))))),
% 107.62/15.50 inference(cnf_transformation,[],[f557])).
% 107.62/15.50 thf(f940,plain,(
% 107.62/15.50 (dpsetconstrERa = $true)),
% 107.62/15.50 inference(cnf_transformation,[],[f562])).
% 107.62/15.50 thf(f941,plain,(
% 107.62/15.50 (dpsetconstrEL1 = $true)),
% 107.62/15.50 inference(cnf_transformation,[],[f562])).
% 107.62/15.50 thf(f942,plain,(
% 107.62/15.50 (dpsetconstrEL2 = $true)),
% 107.62/15.50 inference(cnf_transformation,[],[f562])).
% 107.62/15.50 thf(f943,plain,(
% 107.62/15.50 ($true = ((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))))))),
% 107.62/15.50 inference(cnf_transformation,[],[f562])).
% 107.62/15.50 thf(f944,plain,(
% 107.62/15.50 ($true != ((sK2 @ sK3 @ sK4)))),
% 107.62/15.50 inference(cnf_transformation,[],[f562])).
% 107.62/15.50 thf(f946,definition,(
% 107.62/15.50 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 107.62/15.50 introduced(theory,[fool_exhaustiveness_axiom])).
% 107.62/15.50 thf(f1132,plain,(
% 107.62/15.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y0 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y5 @ Y6) @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y5) & (?? @ $i @ (^[Y10 : $i]: (((in @ Y10 @ Y6) & (Y7 @ Y9 @ Y10)) & ((kpair @ Y9 @ Y10) = Y8)))))))))))))) @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (Y1 @ Y0 @ Y4))))))))))))))))),
% 107.62/15.50 inference(definition_unfolding,[],[f753,f940,f749])).
% 107.62/15.50 thf(f1133,plain,(
% 107.62/15.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y5 @ Y6) @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y5) & (?? @ $i @ (^[Y10 : $i]: (((in @ Y10 @ Y6) & (Y7 @ Y9 @ Y10)) & ((kpair @ Y9 @ Y10) = Y8)))))))))))))) @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y1 @ Y4))))))))))))))),
% 107.62/15.50 inference(definition_unfolding,[],[f754,f941,f749])).
% 107.62/15.50 thf(f1134,plain,(
% 107.62/15.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y5 @ Y6) @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y5) & (?? @ $i @ (^[Y10 : $i]: (((in @ Y10 @ Y6) & (Y7 @ Y9 @ Y10)) & ((kpair @ Y9 @ Y10) = Y8)))))))))))))) @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y0 @ Y3))))))))))))))),
% 107.62/15.50 inference(definition_unfolding,[],[f755,f942,f749])).
% 107.62/15.50 thf(f1135,plain,(
% 107.62/15.50 ($true = ((in @ (kpair @ sK3 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))) @ sK0 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))))))),
% 107.62/15.50 inference(definition_unfolding,[],[f943,f749])).
% 107.62/15.50 thf(f1136,plain,(
% 107.62/15.50 ($true = ((in @ (kpair @ sK3 @ sK4) @ (dsetconstr @ (cartprod @ sK0 @ sK1) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (sK2 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0))))))))))))),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1135])).
% 107.62/15.50 thf(f1137,plain,(
% 107.62/15.50 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y5 @ Y6) @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y5) & (?? @ $i @ (^[Y10 : $i]: (((in @ Y10 @ Y6) & (Y7 @ Y9 @ Y10)) & ((kpair @ Y9 @ Y10) = Y8)))))))))))))) @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y0 @ Y3))))))))))) @ X1)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1134])).
% 107.62/15.50 thf(f1138,plain,(
% 107.62/15.50 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ X1) @ (dsetconstr @ (cartprod @ Y3 @ Y2) @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (?? @ $i @ (^[Y6 : $i]: (((in @ Y6 @ Y2) & (Y1 @ Y5 @ Y6)) & ((kpair @ Y5 @ Y6) = Y4)))))))))) => (in @ X1 @ Y2))))))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1137])).
% 107.62/15.50 thf(f1139,plain,(
% 107.62/15.50 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ X1) @ (dsetconstr @ (cartprod @ Y3 @ Y2) @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (?? @ $i @ (^[Y6 : $i]: (((in @ Y6 @ Y2) & (Y1 @ Y5 @ Y6)) & ((kpair @ Y5 @ Y6) = Y4)))))))))) => (in @ X1 @ Y2))))))))) @ X2)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1138])).
% 107.62/15.50 thf(f1140,plain,(
% 107.62/15.50 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y2 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y0 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))) => (in @ X1 @ Y1))))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1139])).
% 107.62/15.50 thf(f1141,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y2 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y0 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))) => (in @ X1 @ Y1))))))) @ X3)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1140])).
% 107.62/15.50 thf(f1142,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y1 @ Y0) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ Y0) & (X3 @ Y3 @ Y4)) & ((kpair @ Y3 @ Y4) = Y2)))))))))) => (in @ X1 @ Y0))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1141])).
% 107.62/15.50 thf(f1143,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y1 @ Y0) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ Y0) & (X3 @ Y3 @ Y4)) & ((kpair @ Y3 @ Y4) = Y2)))))))))) => (in @ X1 @ Y0))))) @ X4)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1142])).
% 107.62/15.50 thf(f1144,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y0 @ X4) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X4) & (X3 @ Y2 @ Y3)) & ((kpair @ Y2 @ Y3) = Y1)))))))))) => (in @ X1 @ X4))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1143])).
% 107.62/15.50 thf(f1145,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y0 @ X4) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X4) & (X3 @ Y2 @ Y3)) & ((kpair @ Y2 @ Y3) = Y1)))))))))) => (in @ X1 @ X4))) @ X5)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1144])).
% 107.62/15.50 thf(f1146,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = (((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ X5 @ X4) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X5) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X4) & (X3 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))) => (in @ X1 @ X4))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1145])).
% 107.62/15.50 thf(f1147,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ X5 @ X4) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X5) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X4) & (X3 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))))) | ($true = ((in @ X1 @ X4)))) )),
% 107.62/15.50 inference(imp_proxy_clausification,[],[f1146])).
% 107.62/15.50 thf(f1148,plain,(
% 107.62/15.50 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y0) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y5 @ Y6) @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y5) & (?? @ $i @ (^[Y10 : $i]: (((in @ Y10 @ Y6) & (Y7 @ Y9 @ Y10)) & ((kpair @ Y9 @ Y10) = Y8)))))))))))))) @ Y4 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (in @ Y1 @ Y4))))))))))) @ X1)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1133])).
% 107.62/15.50 thf(f1149,plain,(
% 107.62/15.50 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ X1) @ (dsetconstr @ (cartprod @ Y3 @ Y2) @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (?? @ $i @ (^[Y6 : $i]: (((in @ Y6 @ Y2) & (Y1 @ Y5 @ Y6)) & ((kpair @ Y5 @ Y6) = Y4)))))))))) => (in @ Y0 @ Y3))))))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1148])).
% 107.62/15.50 thf(f1150,plain,(
% 107.62/15.50 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ X1) @ (dsetconstr @ (cartprod @ Y3 @ Y2) @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (?? @ $i @ (^[Y6 : $i]: (((in @ Y6 @ Y2) & (Y1 @ Y5 @ Y6)) & ((kpair @ Y5 @ Y6) = Y4)))))))))) => (in @ Y0 @ Y3))))))))) @ X2)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1149])).
% 107.62/15.50 thf(f1151,plain,(
% 107.62/15.50 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y2 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y0 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))) => (in @ X2 @ Y2))))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1150])).
% 107.62/15.50 thf(f1152,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y2 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y0 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))) => (in @ X2 @ Y2))))))) @ X3)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1151])).
% 107.62/15.50 thf(f1153,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y1 @ Y0) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ Y0) & (X3 @ Y3 @ Y4)) & ((kpair @ Y3 @ Y4) = Y2)))))))))) => (in @ X2 @ Y1))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1152])).
% 107.62/15.50 thf(f1154,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y1 @ Y0) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ Y0) & (X3 @ Y3 @ Y4)) & ((kpair @ Y3 @ Y4) = Y2)))))))))) => (in @ X2 @ Y1))))) @ X4)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1153])).
% 107.62/15.50 thf(f1155,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y0 @ X4) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X4) & (X3 @ Y2 @ Y3)) & ((kpair @ Y2 @ Y3) = Y1)))))))))) => (in @ X2 @ Y0))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1154])).
% 107.62/15.50 thf(f1156,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ Y0 @ X4) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X4) & (X3 @ Y2 @ Y3)) & ((kpair @ Y2 @ Y3) = Y1)))))))))) => (in @ X2 @ Y0))) @ X5)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1155])).
% 107.62/15.50 thf(f1157,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = (((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ X5 @ X4) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X5) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X4) & (X3 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))) => (in @ X2 @ X5))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1156])).
% 107.62/15.50 thf(f1158,plain,(
% 107.62/15.50 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ (kpair @ X2 @ X1) @ (dsetconstr @ (cartprod @ X5 @ X4) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X5) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X4) & (X3 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))))) | ($true = ((in @ X2 @ X5)))) )),
% 107.62/15.50 inference(imp_proxy_clausification,[],[f1157])).
% 107.62/15.50 thf(f1159,plain,(
% 107.62/15.50 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y0 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y5 @ Y6) @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y5) & (?? @ $i @ (^[Y10 : $i]: (((in @ Y10 @ Y6) & (Y7 @ Y9 @ Y10)) & ((kpair @ Y9 @ Y10) = Y8)))))))))))))) @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (Y1 @ Y0 @ Y4))))))))))))) @ X1)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1132])).
% 107.62/15.50 thf(f1160,plain,(
% 107.62/15.50 ( ! [X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ X1 @ Y3) @ (dsetconstr @ (cartprod @ Y2 @ Y1) @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (?? @ $i @ (^[Y6 : $i]: (((in @ Y6 @ Y1) & (Y0 @ Y5 @ Y6)) & ((kpair @ Y5 @ Y6) = Y4)))))))))) => (Y0 @ X1 @ Y3))))))))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1159])).
% 107.62/15.50 thf(f1161,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ X1 @ Y3) @ (dsetconstr @ (cartprod @ Y2 @ Y1) @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (?? @ $i @ (^[Y6 : $i]: (((in @ Y6 @ Y1) & (Y0 @ Y5 @ Y6)) & ((kpair @ Y5 @ Y6) = Y4)))))))))) => (Y0 @ X1 @ Y3))))))))))) @ X2)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1160])).
% 107.62/15.50 thf(f1162,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ X1 @ Y2) @ (dsetconstr @ (cartprod @ Y1 @ Y0) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (X2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))) => (X2 @ X1 @ Y2))))))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1161])).
% 107.62/15.50 thf(f1163,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ X1 @ Y2) @ (dsetconstr @ (cartprod @ Y1 @ Y0) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (X2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))) => (X2 @ X1 @ Y2))))))))) @ X3)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1162])).
% 107.62/15.50 thf(f1164,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((in @ (kpair @ X1 @ Y1) @ (dsetconstr @ (cartprod @ Y0 @ X3) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ X3) & (X2 @ Y3 @ Y4)) & ((kpair @ Y3 @ Y4) = Y2)))))))))) => (X2 @ X1 @ Y1))))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1163])).
% 107.62/15.50 thf(f1165,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((in @ (kpair @ X1 @ Y1) @ (dsetconstr @ (cartprod @ Y0 @ X3) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ X3) & (X2 @ Y3 @ Y4)) & ((kpair @ Y3 @ Y4) = Y2)))))))))) => (X2 @ X1 @ Y1))))))) @ X4)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1164])).
% 107.62/15.50 thf(f1166,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i] : (($true = (((in @ X1 @ X4) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((in @ (kpair @ X1 @ Y0) @ (dsetconstr @ (cartprod @ X4 @ X3) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X4) & (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X3) & (X2 @ Y2 @ Y3)) & ((kpair @ Y2 @ Y3) = Y1)))))))))) => (X2 @ X1 @ Y0))))))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1165])).
% 107.62/15.50 thf(f1167,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((in @ (kpair @ X1 @ Y0) @ (dsetconstr @ (cartprod @ X4 @ X3) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X4) & (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X3) & (X2 @ Y2 @ Y3)) & ((kpair @ Y2 @ Y3) = Y1)))))))))) => (X2 @ X1 @ Y0)))))))) )),
% 107.62/15.50 inference(imp_proxy_clausification,[],[f1166])).
% 107.62/15.50 thf(f1168,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ X4))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X3) => ((in @ (kpair @ X1 @ Y0) @ (dsetconstr @ (cartprod @ X4 @ X3) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X4) & (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X3) & (X2 @ Y2 @ Y3)) & ((kpair @ Y2 @ Y3) = Y1)))))))))) => (X2 @ X1 @ Y0)))) @ X5)))) )),
% 107.62/15.50 inference(pi_proxy_clausification,[],[f1167])).
% 107.62/15.50 thf(f1169,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ X4))) | ($true = (((in @ X5 @ X3) => ((in @ (kpair @ X1 @ X5) @ (dsetconstr @ (cartprod @ X4 @ X3) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X4) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X3) & (X2 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))) => (X2 @ X1 @ X5)))))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f1168])).
% 107.62/15.50 thf(f1170,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ X4))) | ($false = ((in @ X5 @ X3))) | ($true = (((in @ (kpair @ X1 @ X5) @ (dsetconstr @ (cartprod @ X4 @ X3) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X4) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X3) & (X2 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))) => (X2 @ X1 @ X5))))) )),
% 107.62/15.50 inference(imp_proxy_clausification,[],[f1169])).
% 107.62/15.50 thf(f1171,plain,(
% 107.62/15.50 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ (kpair @ X1 @ X5) @ (dsetconstr @ (cartprod @ X4 @ X3) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X4) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X3) & (X2 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))))) | ($false = ((in @ X5 @ X3))) | ($false = ((in @ X1 @ X4))) | ($true = ((X2 @ X1 @ X5)))) )),
% 107.62/15.50 inference(imp_proxy_clausification,[],[f1170])).
% 107.62/15.50 thf(f3137,definition,(
% 107.62/15.50 spl91_4 <=> ! [X4 : $o] : (($false = X4) | ($true = X4))),
% 107.62/15.50 introduced(definition,[new_symbols(definition,[spl91_4])],[avatar_definition])).
% 107.62/15.50 thf(f3138,plain,(
% 107.62/15.50 ( ! [X4 : $o] : (($true = X4) | ($false = X4)) ) | ~spl91_4),
% 107.62/15.50 inference(avatar_component_clause,[],[f3137])).
% 107.62/15.50 thf(f3209,plain,(
% 107.62/15.50 spl91_4),
% 107.62/15.50 inference(avatar_split_clause,[],[f946,f3137])).
% 107.62/15.50 thf(f3211,plain,(
% 107.62/15.50 ($true != $true) | ($false = ((sK2 @ sK3 @ sK4))) | ~spl91_4),
% 107.62/15.50 inference(constrained_superposition,[],[f944,f3138])).
% 107.62/15.50 thf(f3213,plain,(
% 107.62/15.50 ($false = ((sK2 @ sK3 @ sK4))) | ~spl91_4),
% 107.62/15.50 inference(trivial_inequality_removal,[],[f3211])).
% 107.62/15.50 thf(f6095,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (($false = $true) | ($true = ((in @ sK4 @ sK1))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) )),
% 107.62/15.50 inference(constrained_superposition,[],[f1147,f1136])).
% 107.62/15.50 thf(f6119,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (($true = ((in @ sK4 @ sK1))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) )),
% 107.62/15.50 inference(trivial_inequality_removal,[],[f6095])).
% 107.62/15.50 thf(f6135,definition,(
% 107.62/15.50 spl91_24 <=> ! [X0 : ($i > $i > $i)] : ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))),
% 107.62/15.50 introduced(definition,[new_symbols(definition,[spl91_24])],[avatar_definition])).
% 107.62/15.50 thf(f6136,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) ) | ~spl91_24),
% 107.62/15.50 inference(avatar_component_clause,[],[f6135])).
% 107.62/15.50 thf(f6138,definition,(
% 107.62/15.50 spl91_25 <=> ($true = ((in @ sK4 @ sK1)))),
% 107.62/15.50 introduced(definition,[new_symbols(definition,[spl91_25])],[avatar_definition])).
% 107.62/15.50 thf(f6140,plain,(
% 107.62/15.50 ($true = ((in @ sK4 @ sK1))) | ~spl91_25),
% 107.62/15.50 inference(avatar_component_clause,[],[f6138])).
% 107.62/15.50 thf(f6142,plain,(
% 107.62/15.50 spl91_24 | spl91_25),
% 107.62/15.50 inference(avatar_split_clause,[],[f6119,f6138,f6135])).
% 107.62/15.50 thf(f6158,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (($false = $true) | ($true = ((in @ sK3 @ sK0))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) )),
% 107.62/15.50 inference(constrained_superposition,[],[f1158,f1136])).
% 107.62/15.50 thf(f6182,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (($true = ((in @ sK3 @ sK0))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) )),
% 107.62/15.50 inference(trivial_inequality_removal,[],[f6158])).
% 107.62/15.50 thf(f6198,definition,(
% 107.62/15.50 spl91_26 <=> ($true = ((in @ sK3 @ sK0)))),
% 107.62/15.50 introduced(definition,[new_symbols(definition,[spl91_26])],[avatar_definition])).
% 107.62/15.50 thf(f6200,plain,(
% 107.62/15.50 ($true = ((in @ sK3 @ sK0))) | ~spl91_26),
% 107.62/15.50 inference(avatar_component_clause,[],[f6198])).
% 107.62/15.50 thf(f6202,plain,(
% 107.62/15.50 spl91_24 | spl91_26),
% 107.62/15.50 inference(avatar_split_clause,[],[f6182,f6198,f6135])).
% 107.62/15.50 thf(f6210,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (($false = $true) | ($false = ((in @ sK4 @ sK1))) | ($false = ((in @ sK3 @ sK0))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ sK3 @ sK4))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) )),
% 107.62/15.50 inference(constrained_superposition,[],[f1171,f1136])).
% 107.62/15.50 thf(f6239,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (($false = ((in @ sK4 @ sK1))) | ($false = ((in @ sK3 @ sK0))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ sK3 @ sK4))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) )),
% 107.62/15.50 inference(trivial_inequality_removal,[],[f6210])).
% 107.62/15.50 thf(f6240,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (($false = ((in @ sK4 @ sK1))) | ($false = ((in @ sK3 @ sK0))) | ($true = ((sK2 @ (X0 @ sK3 @ sK4) @ sK4))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0)))) )),
% 107.62/15.50 inference(beta-eta_normalization,[],[f6239])).
% 107.62/15.50 thf(f6256,definition,(
% 107.62/15.50 spl91_27 <=> ! [X0 : ($i > $i > $i)] : (($true = ((sK2 @ (X0 @ sK3 @ sK4) @ sK4))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0))))),
% 107.62/15.50 introduced(definition,[new_symbols(definition,[spl91_27])],[avatar_definition])).
% 107.62/15.50 thf(f6257,plain,(
% 107.62/15.50 ( ! [X0 : ($i > $i > $i)] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1)))))) != (^[Y0 : $i]: (X0))) | ($true = ((sK2 @ (X0 @ sK3 @ sK4) @ sK4)))) ) | ~spl91_27),
% 107.62/15.50 inference(avatar_component_clause,[],[f6256])).
% 107.62/15.50 thf(f6259,definition,(
% 107.62/15.50 spl91_28 <=> ($false = ((in @ sK3 @ sK0)))),
% 107.62/15.50 introduced(definition,[new_symbols(definition,[spl91_28])],[avatar_definition])).
% 107.62/15.50 thf(f6261,plain,(
% 107.62/15.50 ($false = ((in @ sK3 @ sK0))) | ~spl91_28),
% 107.62/15.50 inference(avatar_component_clause,[],[f6259])).
% 107.62/15.50 thf(f6263,definition,(
% 107.62/15.50 spl91_29 <=> ($false = ((in @ sK4 @ sK1)))),
% 107.62/15.50 introduced(definition,[new_symbols(definition,[spl91_29])],[avatar_definition])).
% 107.62/15.50 thf(f6265,plain,(
% 107.62/15.50 ($false = ((in @ sK4 @ sK1))) | ~spl91_29),
% 107.62/15.50 inference(avatar_component_clause,[],[f6263])).
% 107.62/15.50 thf(f6267,plain,(
% 107.62/15.50 spl91_27 | spl91_28 | spl91_29),
% 107.62/15.50 inference(avatar_split_clause,[],[f6240,f6263,f6259,f6256])).
% 107.62/15.50 thf(f9709,plain,(
% 107.62/15.50 $false | ~spl91_24),
% 107.62/15.50 inference(equality_resolution,[],[f6136])).
% 107.62/15.50 thf(f9710,plain,(
% 107.62/15.50 ~spl91_24),
% 107.62/15.50 inference(avatar_contradiction_clause,[],[f9709])).
% 107.62/15.50 thf(f207592,plain,(
% 107.62/15.50 ($true = ((sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ sK3 @ sK4) @ sK4))) | ~spl91_27),
% 107.62/15.50 inference(equality_resolution,[],[f6257])).
% 107.62/15.50 thf(f207593,plain,(
% 107.62/15.50 ($true = ((sK2 @ sK3 @ sK4))) | ~spl91_27),
% 107.62/15.50 inference(beta-eta_normalization,[],[f207592])).
% 107.62/15.50 thf(f207595,plain,(
% 107.62/15.50 ($false = $true) | (~spl91_4 | ~spl91_27)),
% 107.62/15.50 inference(forward_demodulation,[],[f207593,f3213])).
% 107.62/15.50 thf(f207596,plain,(
% 107.62/15.50 $false | (~spl91_4 | ~spl91_27)),
% 107.62/15.50 inference(trivial_inequality_removal,[],[f207595])).
% 107.62/15.50 thf(f207597,plain,(
% 107.62/15.50 ~spl91_4 | ~spl91_27),
% 107.62/15.50 inference(avatar_contradiction_clause,[],[f207596])).
% 107.62/15.50 thf(f207638,plain,(
% 107.62/15.50 ($false = $true) | (~spl91_26 | ~spl91_28)),
% 107.62/15.50 inference(constrained_superposition,[],[f6261,f6200])).
% 107.62/15.50 thf(f207730,plain,(
% 107.62/15.50 $false | (~spl91_26 | ~spl91_28)),
% 107.62/15.50 inference(trivial_inequality_removal,[],[f207638])).
% 107.62/15.50 thf(f207731,plain,(
% 107.62/15.50 ~spl91_26 | ~spl91_28),
% 107.62/15.50 inference(avatar_contradiction_clause,[],[f207730])).
% 107.62/15.50 thf(f207976,plain,(
% 107.62/15.50 ($false = $true) | (~spl91_25 | ~spl91_29)),
% 107.62/15.50 inference(constrained_superposition,[],[f6265,f6140])).
% 107.62/15.50 thf(f208068,plain,(
% 107.62/15.50 $false | (~spl91_25 | ~spl91_29)),
% 107.62/15.50 inference(trivial_inequality_removal,[],[f207976])).
% 107.62/15.50 thf(f208069,plain,(
% 107.62/15.50 ~spl91_25 | ~spl91_29),
% 107.62/15.50 inference(avatar_contradiction_clause,[],[f208068])).
% 107.62/15.50 cnf(s22, plain, spl91_4, inference(sat_conversion,[],[f3209])).
% 107.62/15.50 cnf(s31, plain, spl91_24 | spl91_25, inference(sat_conversion,[],[f6142])).
% 107.62/15.50 cnf(s33, plain, spl91_24 | spl91_26, inference(sat_conversion,[],[f6202])).
% 107.62/15.50 cnf(s35, plain, spl91_27 | spl91_28 | spl91_29, inference(sat_conversion,[],[f6267])).
% 107.62/15.50 cnf(s99, plain, ~spl91_24, inference(sat_conversion,[],[f9710])).
% 107.62/15.50 cnf(s693, plain, ~spl91_4 | ~spl91_27, inference(sat_conversion,[],[f207597])).
% 107.62/15.50 cnf(s695, plain, ~spl91_26 | ~spl91_28, inference(sat_conversion,[],[f207731])).
% 107.62/15.50 cnf(s697, plain, ~spl91_25 | ~spl91_29, inference(sat_conversion,[],[f208069])).
% 107.62/15.50 cnf(s783, plain, spl91_26, inference(rat,[],[s33,s99])).
% 107.62/15.50 cnf(s784, plain, ~spl91_28, inference(rat,[],[s695,s783])).
% 107.62/15.50 cnf(s785, plain, spl91_25, inference(rat,[],[s31,s99])).
% 107.62/15.50 cnf(s786, plain, ~spl91_29, inference(rat,[],[s697,s785])).
% 107.62/15.50 cnf(s787, plain, spl91_27, inference(rat,[],[s35,s784,s786])).
% 107.62/15.50 cnf(s788, plain, ~spl91_4, inference(rat,[],[s693,s787])).
% 107.62/15.50 cnf(s789, plain, $false, inference(rat,[],[s22,s788])).
% 107.62/15.50 thf(f208128,plain,(
% 107.62/15.50 $false),
% 107.62/15.50 inference(avatar_sat_refutation,[],[s789])).
% 107.62/15.50 % SZS output end Proof for theBenchmark
% 107.62/15.50 % (3211483)------------------------------
% 107.62/15.50 % (3211483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 107.62/15.50 % (3211483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 107.62/15.50 % (3211483)CaDiCaL version: 2.1.3
% 107.62/15.50 % (3211483)Termination reason: Refutation
% 107.62/15.50 % (3211483)Time elapsed: 15.200 s
% 107.62/15.50 % (3211483)Peak memory usage: 71 MB
% 107.62/15.50 % (3211483)Instructions burned: 33185 (million)
% 107.62/15.50 % (3211460)Success in time 15.263 s
% 107.62/15.50 % Vampire exiting
%------------------------------------------------------------------------------