%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU562^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:30:05 AM UTC 2026
% Result : Theorem 1.03s 0.54s
% Output : Refutation 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU562^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n013.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 13:49:36 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.34 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.03/0.54 % (2145854)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.03/0.54 % (2145859)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1812627685:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.03/0.54 % (2145865)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.03/0.54 % (2145865)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.03/0.54 % (2145860)lrs+10_16_si=on:nwc=1.5:random_seed=947806641:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.03/0.54 % (2145861)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1101238693:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.03/0.54 % (2145864)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3479532347:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.03/0.54 % (2145863)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2259314756:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.03/0.54 % (2145862)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=613021956:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 1.03/0.54 % (2145865)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2346368221:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.03/0.54 % (2145861)Instruction limit reached!
% 1.03/0.54 % (2145861)------------------------------
% 1.03/0.54 % (2145861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145861)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145861)Termination reason: Instruction limit
% 1.03/0.54 % (2145861)Termination phase: shuffling
% 1.03/0.54 % (2145861)Time elapsed: 0.003 s
% 1.03/0.54 % (2145861)Peak memory usage: 9 MB
% 1.03/0.54 % (2145861)Instructions burned: 3 (million)
% 1.03/0.54 % (2145860)Instruction limit reached!
% 1.03/0.54 % (2145860)------------------------------
% 1.03/0.54 % (2145860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145860)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145860)Termination reason: Instruction limit
% 1.03/0.54 % (2145860)Termination phase: Property scanning
% 1.03/0.54 % (2145860)Time elapsed: 0.016 s
% 1.03/0.54 % (2145860)Peak memory usage: 10 MB
% 1.03/0.54 % (2145860)Instructions burned: 19 (million)
% 1.03/0.54 % (2145863)Instruction limit reached!
% 1.03/0.54 % (2145863)------------------------------
% 1.03/0.54 % (2145863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145863)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145863)Termination reason: Instruction limit
% 1.03/0.54 % (2145863)Termination phase: Property scanning
% 1.03/0.54 % (2145863)Time elapsed: 0.022 s
% 1.03/0.54 % (2145863)Peak memory usage: 11 MB
% 1.03/0.54 % (2145863)Instructions burned: 24 (million)
% 1.03/0.54 % (2145859)Instruction limit reached!
% 1.03/0.54 % (2145859)------------------------------
% 1.03/0.54 % (2145859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145859)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145859)Termination reason: Instruction limit
% 1.03/0.54 % (2145859)Termination phase: Saturation
% 1.03/0.54 % (2145859)Time elapsed: 0.039 s
% 1.03/0.54 % (2145859)Peak memory usage: 13 MB
% 1.03/0.54 % (2145859)Instructions burned: 87 (million)
% 1.03/0.54 % (2145874)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=498499410:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.03/0.54 % (2145878)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3743498320:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.03/0.54 % (2145874)Instruction limit reached!
% 1.03/0.54 % (2145874)------------------------------
% 1.03/0.54 % (2145874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145874)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145874)Termination reason: Instruction limit
% 1.03/0.54 % (2145874)Termination phase: shuffling
% 1.03/0.54 % (2145874)Time elapsed: 0.003 s
% 1.03/0.54 % (2145874)Peak memory usage: 9 MB
% 1.03/0.54 % (2145874)Instructions burned: 3 (million)
% 1.03/0.54 % (2145878)Instruction limit reached!
% 1.03/0.54 % (2145878)------------------------------
% 1.03/0.54 % (2145878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145878)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145878)Termination reason: Instruction limit
% 1.03/0.54 % (2145878)Termination phase: Property scanning
% 1.03/0.54 % (2145878)Time elapsed: 0.005 s
% 1.03/0.54 % (2145878)Peak memory usage: 10 MB
% 1.03/0.54 % (2145878)Instructions burned: 13 (million)
% 1.03/0.54 % (2145876)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1862092846:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.03/0.54 % (2145877)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.03/0.54 % (2145876)Instruction limit reached!
% 1.03/0.54 % (2145876)------------------------------
% 1.03/0.54 % (2145876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145876)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145876)Termination reason: Instruction limit
% 1.03/0.54 % (2145876)Termination phase: shuffling
% 1.03/0.54 % (2145876)Time elapsed: 0.005 s
% 1.03/0.54 % (2145876)Peak memory usage: 9 MB
% 1.03/0.54 % (2145876)Instructions burned: 5 (million)
% 1.03/0.54 % (2145877)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2299552902:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.03/0.54 % (2145877)Instruction limit reached!
% 1.03/0.54 % (2145877)------------------------------
% 1.03/0.54 % (2145877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145881)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.03/0.54 % (2145877)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145877)Termination reason: Instruction limit
% 1.03/0.54 % (2145877)Termination phase: shuffling
% 1.03/0.54 % (2145877)Time elapsed: 0.006 s
% 1.03/0.54 % (2145877)Peak memory usage: 9 MB
% 1.03/0.54 % (2145877)Instructions burned: 7 (million)
% 1.03/0.54 % (2145881)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.03/0.54 % (2145864)Instruction limit reached!
% 1.03/0.54 % (2145864)------------------------------
% 1.03/0.54 % (2145864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145864)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145864)Termination reason: Instruction limit
% 1.03/0.54 % (2145864)Termination phase: Saturation
% 1.03/0.54 % (2145864)Time elapsed: 0.064 s
% 1.03/0.54 % (2145864)Peak memory usage: 13 MB
% 1.03/0.54 % (2145864)Instructions burned: 76 (million)
% 1.03/0.54 % (2145881)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3038085572:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.03/0.54 % (2145881)Instruction limit reached!
% 1.03/0.54 % (2145881)------------------------------
% 1.03/0.54 % (2145881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145881)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145881)Termination reason: Instruction limit
% 1.03/0.54 % (2145881)Termination phase: Property scanning
% 1.03/0.54 % (2145881)Time elapsed: 0.012 s
% 1.03/0.54 % (2145881)Peak memory usage: 11 MB
% 1.03/0.54 % (2145881)Instructions burned: 31 (million)
% 1.03/0.54 % (2145883)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1972046508:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.03/0.54 % (2145885)lrs+10_1_si=on:cs=on:random_seed=1765647643:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.03/0.54 % (2145886)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.03/0.54 % (2145886)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=541220153:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.03/0.54 % (2145885)Instruction limit reached!
% 1.03/0.54 % (2145885)------------------------------
% 1.03/0.54 % (2145885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145885)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145885)Termination reason: Instruction limit
% 1.03/0.54 % (2145885)Termination phase: shuffling
% 1.03/0.54 % (2145885)Time elapsed: 0.008 s
% 1.03/0.54 % (2145885)Peak memory usage: 9 MB
% 1.03/0.54 % (2145885)Instructions burned: 8 (million)
% 1.03/0.54 % (2145889)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=734547486:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.03/0.54 % (2145886)Instruction limit reached!
% 1.03/0.54 % (2145886)------------------------------
% 1.03/0.54 % (2145886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145886)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145886)Termination reason: Instruction limit
% 1.03/0.54 % (2145886)Termination phase: shuffling
% 1.03/0.54 % (2145886)Time elapsed: 0.002 s
% 1.03/0.54 % (2145886)Peak memory usage: 9 MB
% 1.03/0.54 % (2145886)Instructions burned: 2 (million)
% 1.03/0.54 % (2145888)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2465012525:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.03/0.54 % (2145894)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2264374205:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.03/0.54 % (2145862) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2145854-2145862"...
% 1.03/0.54 % (2145895)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1737398784:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.03/0.54 % (2145865)Instruction limit reached!
% 1.03/0.54 % (2145865)------------------------------
% 1.03/0.54 % (2145865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145865)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145865)Termination reason: Instruction limit
% 1.03/0.54 % (2145865)Termination phase: Saturation
% 1.03/0.54 % (2145865)Time elapsed: 0.129 s
% 1.03/0.54 % (2145865)Peak memory usage: 14 MB
% 1.03/0.54 % (2145865)Instructions burned: 158 (million)
% 1.03/0.54 % (2145888)Instruction limit reached!
% 1.03/0.54 % (2145888)------------------------------
% 1.03/0.54 % (2145888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145888)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145888)Termination reason: Instruction limit
% 1.03/0.54 % (2145888)Termination phase: Property scanning
% 1.03/0.54 % (2145888)Time elapsed: 0.033 s
% 1.03/0.54 % (2145888)Peak memory usage: 12 MB
% 1.03/0.54 % (2145888)Instructions burned: 38 (million)
% 1.03/0.54 % (2145889) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2145854-2145889"...
% 1.03/0.54 % (2145862)...printing done.
% 1.03/0.54 % (2145894)Instruction limit reached!
% 1.03/0.54 % (2145894)------------------------------
% 1.03/0.54 % (2145894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145894)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145894)Termination reason: Instruction limit
% 1.03/0.54 % (2145894)Termination phase: Property scanning
% 1.03/0.54 % (2145894)Time elapsed: 0.016 s
% 1.03/0.54 % (2145894)Peak memory usage: 11 MB
% 1.03/0.54 % (2145894)Instructions burned: 26 (million)
% 1.03/0.54 % (2145862)Refutation found. Thanks to Tanya!
% 1.03/0.54 % SZS status Theorem for theBenchmark
% 1.03/0.54 % SZS output start Proof for theBenchmark
% 1.03/0.54 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.03/0.54 thf(func_def_0, type, in: ($i > $i > $o)).
% 1.03/0.54 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 1.03/0.54 thf(func_def_3, type, setextAx: $o).
% 1.03/0.54 thf(func_def_5, type, emptysetAx: $o).
% 1.03/0.54 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_7, type, setadjoinAx: $o).
% 1.03/0.54 thf(func_def_8, type, powerset: ($i > $i)).
% 1.03/0.54 thf(func_def_9, type, powersetAx: $o).
% 1.03/0.54 thf(func_def_10, type, setunion: ($i > $i)).
% 1.03/0.54 thf(func_def_11, type, setunionAx: $o).
% 1.03/0.54 thf(func_def_13, type, omega0Ax: $o).
% 1.03/0.54 thf(func_def_14, type, omegaSAx: $o).
% 1.03/0.54 thf(func_def_15, type, omegaIndAx: $o).
% 1.03/0.54 thf(func_def_16, type, replAx: $o).
% 1.03/0.54 thf(func_def_17, type, foundationAx: $o).
% 1.03/0.54 thf(func_def_18, type, wellorderingAx: $o).
% 1.03/0.54 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 1.03/0.54 thf(func_def_20, type, descrp: $o).
% 1.03/0.54 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_22, type, dsetconstrI: $o).
% 1.03/0.54 thf(func_def_23, type, dsetconstrEL: $o).
% 1.03/0.54 thf(func_def_24, type, dsetconstrER: $o).
% 1.03/0.54 thf(func_def_25, type, exuE1: $o).
% 1.03/0.54 thf(func_def_26, type, prop2set: ($o > $i)).
% 1.03/0.54 thf(func_def_27, type, prop2setE: $o).
% 1.03/0.54 thf(func_def_28, type, emptysetE: $o).
% 1.03/0.54 thf(func_def_29, type, emptysetimpfalse: $o).
% 1.03/0.54 thf(func_def_30, type, notinemptyset: $o).
% 1.03/0.54 thf(func_def_31, type, exuE3e: $o).
% 1.03/0.54 thf(func_def_32, type, setext: $o).
% 1.03/0.54 thf(func_def_33, type, emptyI: $o).
% 1.03/0.54 thf(func_def_34, type, noeltsimpempty: $o).
% 1.03/0.54 thf(func_def_35, type, setbeta: $o).
% 1.03/0.54 thf(func_def_36, type, nonempty: ($i > $o)).
% 1.03/0.54 thf(func_def_37, type, nonemptyE1: $o).
% 1.03/0.54 thf(func_def_38, type, nonemptyI: $o).
% 1.03/0.54 thf(func_def_39, type, nonemptyI1: $o).
% 1.03/0.54 thf(func_def_40, type, setadjoinIL: $o).
% 1.03/0.54 thf(func_def_41, type, emptyinunitempty: $o).
% 1.03/0.54 thf(func_def_42, type, setadjoinIR: $o).
% 1.03/0.54 thf(func_def_43, type, setadjoinE: $o).
% 1.03/0.54 thf(func_def_44, type, setadjoinOr: $o).
% 1.03/0.54 thf(func_def_45, type, setoftrueEq: $o).
% 1.03/0.54 thf(func_def_46, type, powersetI: $o).
% 1.03/0.54 thf(func_def_47, type, emptyinPowerset: $o).
% 1.03/0.54 thf(func_def_48, type, emptyInPowerset: $o).
% 1.03/0.54 thf(func_def_49, type, powersetE: $o).
% 1.03/0.54 thf(func_def_50, type, setunionI: $o).
% 1.03/0.54 thf(func_def_51, type, setunionE: $o).
% 1.03/0.54 thf(func_def_52, type, subPowSU: $o).
% 1.03/0.54 thf(func_def_53, type, exuE2: $o).
% 1.03/0.54 thf(func_def_54, type, nonemptyImpWitness: $o).
% 1.03/0.54 thf(func_def_55, type, uniqinunit: $o).
% 1.03/0.54 thf(func_def_56, type, notinsingleton: $o).
% 1.03/0.54 thf(func_def_57, type, eqinunit: $o).
% 1.03/0.54 thf(func_def_58, type, singletonsswitch: $o).
% 1.03/0.54 thf(func_def_59, type, upairsetE: $o).
% 1.03/0.54 thf(func_def_60, type, upairsetIL: $o).
% 1.03/0.54 thf(func_def_61, type, upairsetIR: $o).
% 1.03/0.54 thf(func_def_62, type, emptyE1: $o).
% 1.03/0.54 thf(func_def_63, type, vacuousDall: $o).
% 1.03/0.54 thf(func_def_64, type, quantDeMorgan1: $o).
% 1.03/0.54 thf(func_def_65, type, quantDeMorgan2: $o).
% 1.03/0.54 thf(func_def_66, type, quantDeMorgan3: $o).
% 1.03/0.54 thf(func_def_67, type, quantDeMorgan4: $o).
% 1.03/0.54 thf(func_def_68, type, prop2setI: $o).
% 1.03/0.54 thf(func_def_69, type, set2prop: ($i > $o)).
% 1.03/0.54 thf(func_def_70, type, prop2set2propI: $o).
% 1.03/0.54 thf(func_def_71, type, notdexE: $o).
% 1.03/0.54 thf(func_def_72, type, notdallE: $o).
% 1.03/0.54 thf(func_def_73, type, exuI1: $o).
% 1.03/0.54 thf(func_def_74, type, exuI3: $o).
% 1.03/0.54 thf(func_def_75, type, exuI2: $o).
% 1.03/0.54 thf(func_def_76, type, inCongP: $o).
% 1.03/0.54 thf(func_def_77, type, in__Cong: $o).
% 1.03/0.54 thf(func_def_78, type, exuE3u: $o).
% 1.03/0.54 thf(func_def_79, type, exu__Cong: $o).
% 1.03/0.54 thf(func_def_80, type, emptyset__Cong: $o).
% 1.03/0.54 thf(func_def_81, type, setadjoin__Cong: $o).
% 1.03/0.54 thf(func_def_82, type, powerset__Cong: $o).
% 1.03/0.54 thf(func_def_83, type, setunion__Cong: $o).
% 1.03/0.54 thf(func_def_84, type, omega__Cong: $o).
% 1.03/0.54 thf(func_def_85, type, exuEu: $o).
% 1.03/0.54 thf(func_def_86, type, descr__Cong: $o).
% 1.03/0.54 thf(func_def_87, type, dsetconstr__Cong: $o).
% 1.03/0.54 thf(func_def_88, type, subset: ($i > $i > $o)).
% 1.03/0.54 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 1.03/0.54 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 1.03/0.54 thf(func_def_91, type, subsetI1: $o).
% 1.03/0.54 thf(func_def_92, type, eqimpsubset2: $o).
% 1.03/0.54 thf(func_def_93, type, eqimpsubset1: $o).
% 1.03/0.54 thf(func_def_94, type, db0: !>[X0: $tType]:(X0)).
% 1.03/0.54 thf(func_def_95, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.03/0.54 thf(func_def_98, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.03/0.54 thf(func_def_99, type, vIMP: ($o > $o > $o)).
% 1.03/0.54 thf(func_def_100, type, db2: !>[X0: $tType]:(X0)).
% 1.03/0.54 thf(func_def_101, type, db1: !>[X0: $tType]:(X0)).
% 1.03/0.54 thf(func_def_102, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.03/0.54 thf(func_def_103, type, vAND: ($o > $o > $o)).
% 1.03/0.54 thf(func_def_104, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.03/0.54 thf(func_def_105, type, vNOT: ($o > $o)).
% 1.03/0.54 thf(func_def_106, type, sP0: ($i > $i > $o)).
% 1.03/0.54 thf(func_def_107, type, sP1: ($i > $o)).
% 1.03/0.54 thf(func_def_108, type, sP2: $o).
% 1.03/0.54 thf(func_def_109, type, sK3: ($i > $o)).
% 1.03/0.54 thf(func_def_113, type, sK7: ($i > $o)).
% 1.03/0.54 thf(func_def_117, type, sK11: (($i > $o) > $i > $i)).
% 1.03/0.54 thf(func_def_119, type, sK13: ($i > $o)).
% 1.03/0.54 thf(func_def_128, type, sK22: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_129, type, sK23: ($i > $o)).
% 1.03/0.54 thf(func_def_132, type, sK26: ($i > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_133, type, sK27: $o).
% 1.03/0.54 thf(func_def_134, type, sK28: ($i > $i)).
% 1.03/0.54 thf(func_def_138, type, sK32: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_139, type, sK33: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_140, type, sK34: (($i > $o) > $i)).
% 1.03/0.54 thf(func_def_141, type, sK35: ($i > $o)).
% 1.03/0.54 thf(func_def_142, type, sK36: ($i > $i)).
% 1.03/0.54 thf(func_def_143, type, sK37: ($i > $o)).
% 1.03/0.54 thf(func_def_144, type, sK38: ($i > $o)).
% 1.03/0.54 thf(func_def_145, type, sK39: (($i > $o) > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_146, type, sK40: (($i > $o) > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_147, type, sK41: ($i > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_148, type, sK42: ($i > $o)).
% 1.03/0.54 thf(func_def_156, type, sK50: ($i > $o)).
% 1.03/0.54 thf(func_def_157, type, sK51: (($i > $o) > $i)).
% 1.03/0.54 thf(func_def_158, type, sK52: (($i > $o) > $i > $i)).
% 1.03/0.54 thf(func_def_160, type, sK54: ($i > $o)).
% 1.03/0.54 thf(func_def_164, type, sK58: ($i > $o)).
% 1.03/0.54 thf(func_def_169, type, sK63: ($i > $o)).
% 1.03/0.54 thf(func_def_171, type, sK65: ($i > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_173, type, sK67: ($i > $o)).
% 1.03/0.54 thf(func_def_176, type, sK70: ($i > $o)).
% 1.03/0.54 thf(func_def_177, type, sK71: ($i > $o)).
% 1.03/0.54 thf(func_def_178, type, sK72: (($i > $o) > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_179, type, sK73: (($i > $o) > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_188, type, sK82: ($i > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_189, type, sK83: ($i > $o)).
% 1.03/0.54 thf(func_def_192, type, sK86: ($i > $o)).
% 1.03/0.54 thf(func_def_195, type, sK89: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_198, type, sK92: (($i > $o) > $i)).
% 1.03/0.54 thf(func_def_199, type, sK93: (($i > $o) > $i)).
% 1.03/0.54 thf(func_def_200, type, sK94: ($i > $o)).
% 1.03/0.54 thf(func_def_204, type, sK98: ($i > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_205, type, sK99: ($i > $o)).
% 1.03/0.54 thf(func_def_209, type, sK103: ($i > $i)).
% 1.03/0.54 thf(func_def_210, type, sK104: ($i > $o)).
% 1.03/0.54 thf(func_def_212, type, sK106: $o).
% 1.03/0.54 thf(func_def_216, type, sK110: ($i > $i)).
% 1.03/0.54 thf(func_def_217, type, sK111: ($i > $i)).
% 1.03/0.54 thf(func_def_218, type, sK112: ($i > $i)).
% 1.03/0.54 thf(func_def_219, type, sK113: ($i > $i)).
% 1.03/0.54 thf(func_def_220, type, sK114: ($i > $i)).
% 1.03/0.54 thf(func_def_221, type, sK115: ($i > $i > $i > $i)).
% 1.03/0.54 thf(func_def_222, type, sK116: ($i > $i)).
% 1.03/0.54 thf(func_def_223, type, sK117: ($i > $i)).
% 1.03/0.54 thf(func_def_224, type, sK118: ($i > $i)).
% 1.03/0.54 thf(func_def_225, type, sK119: ($i > $i)).
% 1.03/0.54 thf(func_def_226, type, sK120: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_227, type, sK121: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_228, type, sK122: ($i > $i > $i > $i)).
% 1.03/0.54 thf(func_def_229, type, sK123: ($i > $i > $i > $i)).
% 1.03/0.54 thf(func_def_230, type, sK124: ($i > $i > $i > $i)).
% 1.03/0.54 thf(func_def_231, type, sK125: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_232, type, sK126: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_233, type, sK127: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_236, type, sK130: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_240, type, sK134: ($i > $i)).
% 1.03/0.54 thf(func_def_242, type, sK136: ($i > $i)).
% 1.03/0.54 thf(func_def_246, type, sK140: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_247, type, sK141: ($i > $o)).
% 1.03/0.54 thf(func_def_249, type, sK143: ($i > ($i > $o) > $i)).
% 1.03/0.54 thf(func_def_250, type, sK144: ($i > $i)).
% 1.03/0.54 thf(func_def_252, type, sK146: ($i > $o)).
% 1.03/0.54 thf(func_def_255, type, sK149: ($i > $o)).
% 1.03/0.54 thf(func_def_256, type, sK150: ($i > $i)).
% 1.03/0.54 thf(func_def_257, type, sK151: (($i > $o) > $i)).
% 1.03/0.54 thf(func_def_258, type, sK152: ($i > $i)).
% 1.03/0.54 thf(func_def_261, type, sK155: ($i > $o)).
% 1.03/0.54 thf(func_def_269, type, sK163: ($i > ($i > $i > $o) > $i)).
% 1.03/0.54 thf(func_def_270, type, sK164: ($i > $i > ($i > $i > $o) > $i)).
% 1.03/0.54 thf(func_def_271, type, sK165: ($i > ($i > $i > $o) > $i)).
% 1.03/0.54 thf(func_def_272, type, sK166: ($i > $i > $o)).
% 1.03/0.54 thf(func_def_274, type, sK168: ($i > $i)).
% 1.03/0.54 thf(func_def_275, type, sK169: ($i > $i)).
% 1.03/0.54 thf(func_def_281, type, sK175: ($i > $i)).
% 1.03/0.54 thf(func_def_286, type, sK180: $o).
% 1.03/0.54 thf(func_def_289, type, sK183: ($i > $o)).
% 1.03/0.54 thf(func_def_290, type, sK184: ($i > $o)).
% 1.03/0.54 thf(func_def_291, type, sK185: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 1.03/0.54 thf(func_def_292, type, sK186: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 1.03/0.54 thf(func_def_296, type, sK190: $o).
% 1.03/0.54 thf(func_def_301, type, sK195: ($i > $i > $i)).
% 1.03/0.54 thf(func_def_304, type, sK198: ($i > $o)).
% 1.03/0.54 thf(func_def_311, type, sK205: $o).
% 1.03/0.54 thf(func_def_312, type, sK206: ($o > $i > $i > $i)).
% 1.03/0.54 thf(func_def_322, type, sK216: $o).
% 1.03/0.54 thf(func_def_326, type, sK220: ($i > $o)).
% 1.03/0.54 thf(f79,axiom,(
% 1.03/0.54 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.03/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 1.03/0.54 thf(f82,conjecture,(
% 1.03/0.54 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 => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.03/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 1.03/0.54 thf(f83,negated_conjecture,(
% 1.03/0.54 ~(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 => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.03/0.54 inference(negated_conjecture,[status(cth)],[f82])).
% 1.03/0.54 thf(f205,plain,(
% 1.03/0.54 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.03/0.54 inference(rectify,[],[f79])).
% 1.03/0.54 thf(f206,plain,(
% 1.03/0.54 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 1.03/0.54 inference(fool_elimination,[],[f205])).
% 1.03/0.54 thf(f216,plain,(
% 1.03/0.54 ~(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 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.03/0.54 inference(rectify,[],[f83])).
% 1.03/0.54 thf(f217,plain,(
% 1.03/0.54 ~((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) => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.03/0.54 inference(fool_elimination,[],[f216])).
% 1.03/0.54 thf(f304,plain,(
% 1.03/0.54 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $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)),
% 1.03/0.54 inference(ennf_transformation,[],[f217])).
% 1.03/0.54 thf(f305,plain,(
% 1.03/0.54 (omega__Cong = $true) & (dsetconstrI = $true) & (exuE3u = $true) & (subsetI1 = $true) & (upairsetIR = $true) & (setadjoinIL = $true) & (exuI1 = $true) & (setunionE = $true) & (nonemptyI1 = $true) & (foundationAx = $true) & (emptyinunitempty = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (quantDeMorgan2 = $true) & (emptyset__Cong = $true) & (powersetE = $true) & (emptysetE = $true) & (eqimpsubset2 = $true) & (wellorderingAx = $true) & (exuEu = $true) & (upairsetE = $true) & ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true))) & (prop2setE = $true) & (exuE3e = $true) & (uniqinunit = $true) & (exuE1 = $true) & (powersetAx = $true) & (setunionAx = $true) & (setadjoinIR = $true) & (in__Cong = $true) & (setadjoin__Cong = $true) & (prop2set2propI = $true) & (notdexE = $true) & (setoftrueEq = $true) & (upairsetIL = $true) & (emptyInPowerset = $true) & (eqinunit = $true) & (exu__Cong = $true) & (notinsingleton = $true) & (singletonsswitch = $true) & (dsetconstr__Cong = $true) & (nonemptyE1 = $true) & (setext = $true) & (inCongP = $true) & (powerset__Cong = $true) & (quantDeMorgan4 = $true) & (emptysetAx = $true) & (notdallE = $true) & (setbeta = $true) & (setunion__Cong = $true) & (quantDeMorgan3 = $true) & (descrp = $true) & (setadjoinAx = $true) & (emptyI = $true) & (powersetI = $true) & (dsetconstrER = $true) & (omegaIndAx = $true) & (exuE2 = $true) & (descr__Cong = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (emptysetimpfalse = $true) & (subPowSU = $true) & (noeltsimpempty = $true) & (emptyE1 = $true) & (exuI2 = $true) & (omegaSAx = $true) & (eqimpsubset1 = $true) & (quantDeMorgan1 = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (prop2setI = $true) & (vacuousDall = $true) & (setunionI = $true) & (exuI3 = $true) & (setadjoinE = $true) & (notinemptyset = $true) & (dsetconstrEL = $true) & (replAx = $true)),
% 1.03/0.54 inference(flattening,[],[f304])).
% 1.03/0.54 thf(f312,plain,(
% 1.03/0.54 ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) <=> (subsetI1 = $true)),
% 1.03/0.54 inference(ennf_transformation,[],[f206])).
% 1.03/0.54 thf(f425,plain,(
% 1.03/0.54 (omega__Cong = $true) & (dsetconstrI = $true) & (exuE3u = $true) & (subsetI1 = $true) & (upairsetIR = $true) & (setadjoinIL = $true) & (exuI1 = $true) & (setunionE = $true) & (nonemptyI1 = $true) & (foundationAx = $true) & (emptyinunitempty = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (quantDeMorgan2 = $true) & (emptyset__Cong = $true) & (powersetE = $true) & (emptysetE = $true) & (eqimpsubset2 = $true) & (wellorderingAx = $true) & (exuEu = $true) & (upairsetE = $true) & ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true))) & (prop2setE = $true) & (exuE3e = $true) & (uniqinunit = $true) & (exuE1 = $true) & (powersetAx = $true) & (setunionAx = $true) & (setadjoinIR = $true) & (in__Cong = $true) & (setadjoin__Cong = $true) & (prop2set2propI = $true) & (notdexE = $true) & (setoftrueEq = $true) & (upairsetIL = $true) & (emptyInPowerset = $true) & (eqinunit = $true) & (exu__Cong = $true) & (notinsingleton = $true) & (singletonsswitch = $true) & (dsetconstr__Cong = $true) & (nonemptyE1 = $true) & (setext = $true) & (inCongP = $true) & (powerset__Cong = $true) & (quantDeMorgan4 = $true) & (emptysetAx = $true) & (notdallE = $true) & (setbeta = $true) & (setunion__Cong = $true) & (quantDeMorgan3 = $true) & (descrp = $true) & (setadjoinAx = $true) & (emptyI = $true) & (powersetI = $true) & (dsetconstrER = $true) & (omegaIndAx = $true) & (exuE2 = $true) & (descr__Cong = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (emptysetimpfalse = $true) & (subPowSU = $true) & (noeltsimpempty = $true) & (emptyE1 = $true) & (exuI2 = $true) & (omegaSAx = $true) & (eqimpsubset1 = $true) & (quantDeMorgan1 = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (prop2setI = $true) & (vacuousDall = $true) & (setunionI = $true) & (exuI3 = $true) & (setadjoinE = $true) & (notinemptyset = $true) & (dsetconstrEL = $true) & (replAx = $true)),
% 1.03/0.54 inference(rectify,[],[f305])).
% 1.03/0.54 thf(f426,plain,(
% 1.03/0.54 (omega__Cong = $true) & (dsetconstrI = $true) & (exuE3u = $true) & (subsetI1 = $true) & (upairsetIR = $true) & (setadjoinIL = $true) & (exuI1 = $true) & (setunionE = $true) & (nonemptyI1 = $true) & (foundationAx = $true) & (emptyinunitempty = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (quantDeMorgan2 = $true) & (emptyset__Cong = $true) & (powersetE = $true) & (emptysetE = $true) & (eqimpsubset2 = $true) & (wellorderingAx = $true) & (exuEu = $true) & (upairsetE = $true) & ((((subset @ sK74 @ sK75)) != $true) & ! [X2 : $i] : (($true != ((in @ X2 @ sK74))) | (((in @ X2 @ sK75)) = $true))) & (prop2setE = $true) & (exuE3e = $true) & (uniqinunit = $true) & (exuE1 = $true) & (powersetAx = $true) & (setunionAx = $true) & (setadjoinIR = $true) & (in__Cong = $true) & (setadjoin__Cong = $true) & (prop2set2propI = $true) & (notdexE = $true) & (setoftrueEq = $true) & (upairsetIL = $true) & (emptyInPowerset = $true) & (eqinunit = $true) & (exu__Cong = $true) & (notinsingleton = $true) & (singletonsswitch = $true) & (dsetconstr__Cong = $true) & (nonemptyE1 = $true) & (setext = $true) & (inCongP = $true) & (powerset__Cong = $true) & (quantDeMorgan4 = $true) & (emptysetAx = $true) & (notdallE = $true) & (setbeta = $true) & (setunion__Cong = $true) & (quantDeMorgan3 = $true) & (descrp = $true) & (setadjoinAx = $true) & (emptyI = $true) & (powersetI = $true) & (dsetconstrER = $true) & (omegaIndAx = $true) & (exuE2 = $true) & (descr__Cong = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (emptysetimpfalse = $true) & (subPowSU = $true) & (noeltsimpempty = $true) & (emptyE1 = $true) & (exuI2 = $true) & (omegaSAx = $true) & (eqimpsubset1 = $true) & (quantDeMorgan1 = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (prop2setI = $true) & (vacuousDall = $true) & (setunionI = $true) & (exuI3 = $true) & (setadjoinE = $true) & (notinemptyset = $true) & (dsetconstrEL = $true) & (replAx = $true)),
% 1.03/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK74,sK75]),skolemize(X0,sK74),skolemize(X1,sK75)],[f425])).
% 1.03/0.54 thf(f442,plain,(
% 1.03/0.54 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true))))),
% 1.03/0.54 inference(nnf_transformation,[],[f312])).
% 1.03/0.54 thf(f443,plain,(
% 1.03/0.54 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) != $true) & ! [X5 : $i] : ((((in @ X5 @ X3)) != $true) | ($true = ((in @ X5 @ X4))))))),
% 1.03/0.54 inference(rectify,[],[f442])).
% 1.03/0.54 thf(f444,plain,(
% 1.03/0.54 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ((((in @ (sK89 @ X1 @ X0) @ X0)) = $true) & (((in @ (sK89 @ X1 @ X0) @ X1)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != ((subset @ sK90 @ sK91))) & ! [X5 : $i] : (($true != ((in @ X5 @ sK90))) | (((in @ X5 @ sK91)) = $true))))),
% 1.03/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK90,sK91]),skolemize(X2,sK11 @ X1 @ X0),skolemize(X3,sK90),skolemize(X4,sK91)],[f443])).
% 1.03/0.54 thf(f744,plain,(
% 1.03/0.54 ( ! [X2 : $i] : ((((in @ X2 @ sK75)) = $true) | ($true != ((in @ X2 @ sK74)))) )),
% 1.03/0.54 inference(cnf_transformation,[],[f426])).
% 1.03/0.54 thf(f745,plain,(
% 1.03/0.54 (((subset @ sK74 @ sK75)) != $true)),
% 1.03/0.54 inference(cnf_transformation,[],[f426])).
% 1.03/0.54 thf(f763,plain,(
% 1.03/0.54 (subsetI1 = $true)),
% 1.03/0.54 inference(cnf_transformation,[],[f426])).
% 1.03/0.54 thf(f787,plain,(
% 1.03/0.54 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ (sK89 @ X1 @ X0) @ X1)) != $true) | (subsetI1 != $true)) )),
% 1.03/0.54 inference(cnf_transformation,[],[f444])).
% 1.03/0.54 thf(f788,plain,(
% 1.03/0.54 ( ! [X0 : $i,X1 : $i] : ((subsetI1 != $true) | (((subset @ X0 @ X1)) = $true) | (((in @ (sK89 @ X1 @ X0) @ X0)) = $true)) )),
% 1.03/0.54 inference(cnf_transformation,[],[f444])).
% 1.03/0.54 thf(f1374,definition,(
% 1.03/0.54 spl227_53 <=> (((subset @ sK74 @ sK75)) = $true)),
% 1.03/0.54 introduced(definition,[new_symbols(definition,[spl227_53])],[avatar_definition])).
% 1.03/0.54 thf(f1376,plain,(
% 1.03/0.54 (((subset @ sK74 @ sK75)) != $true) | spl227_53),
% 1.03/0.54 inference(avatar_component_clause,[],[f1374])).
% 1.03/0.54 thf(f1377,plain,(
% 1.03/0.54 ~spl227_53),
% 1.03/0.54 inference(avatar_split_clause,[],[f745,f1374])).
% 1.03/0.54 thf(f1956,definition,(
% 1.03/0.54 spl227_184 <=> ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ (sK89 @ X1 @ X0) @ X1)) != $true))),
% 1.03/0.54 introduced(definition,[new_symbols(definition,[spl227_184])],[avatar_definition])).
% 1.03/0.54 thf(f1957,plain,(
% 1.03/0.54 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK89 @ X1 @ X0) @ X1)) != $true) | (((subset @ X0 @ X1)) = $true)) ) | ~spl227_184),
% 1.03/0.54 inference(avatar_component_clause,[],[f1956])).
% 1.03/0.54 thf(f1959,definition,(
% 1.03/0.54 spl227_185 <=> (subsetI1 = $true)),
% 1.03/0.54 introduced(definition,[new_symbols(definition,[spl227_185])],[avatar_definition])).
% 1.03/0.54 thf(f1962,plain,(
% 1.03/0.54 spl227_184 | ~spl227_185),
% 1.03/0.54 inference(avatar_split_clause,[],[f787,f1959,f1956])).
% 1.03/0.54 thf(f2172,definition,(
% 1.03/0.54 spl227_230 <=> ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ (sK89 @ X1 @ X0) @ X0)) = $true))),
% 1.03/0.54 introduced(definition,[new_symbols(definition,[spl227_230])],[avatar_definition])).
% 1.03/0.54 thf(f2173,plain,(
% 1.03/0.54 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK89 @ X1 @ X0) @ X0)) = $true) | (((subset @ X0 @ X1)) = $true)) ) | ~spl227_230),
% 1.03/0.54 inference(avatar_component_clause,[],[f2172])).
% 1.03/0.54 thf(f2174,plain,(
% 1.03/0.54 spl227_230 | ~spl227_185),
% 1.03/0.54 inference(avatar_split_clause,[],[f788,f1959,f2172])).
% 1.03/0.54 thf(f2442,plain,(
% 1.03/0.54 spl227_185),
% 1.03/0.54 inference(avatar_split_clause,[],[f763,f1959])).
% 1.03/0.54 thf(f3240,plain,(
% 1.03/0.54 ( ! [X0 : $i] : (($true != $true) | (((subset @ X0 @ sK75)) = $true) | (((in @ (sK89 @ sK75 @ X0) @ sK74)) != $true)) ) | ~spl227_184),
% 1.03/0.54 inference(superposition,[],[f1957,f744])).
% 1.03/0.54 thf(f3244,plain,(
% 1.03/0.54 ( ! [X0 : $i] : ((((in @ (sK89 @ sK75 @ X0) @ sK74)) != $true) | (((subset @ X0 @ sK75)) = $true)) ) | ~spl227_184),
% 1.03/0.54 inference(trivial_inequality_removal,[],[f3240])).
% 1.03/0.54 thf(f3614,plain,(
% 1.03/0.54 (((subset @ sK74 @ sK75)) = $true) | ($true != $true) | (((subset @ sK74 @ sK75)) = $true) | (~spl227_184 | ~spl227_230)),
% 1.03/0.54 inference(superposition,[],[f3244,f2173])).
% 1.03/0.54 thf(f3615,plain,(
% 1.03/0.54 ($true != $true) | (((subset @ sK74 @ sK75)) = $true) | (~spl227_184 | ~spl227_230)),
% 1.03/0.54 inference(duplicate_literal_removal,[],[f3614])).
% 1.03/0.54 thf(f3616,plain,(
% 1.03/0.54 (((subset @ sK74 @ sK75)) = $true) | (~spl227_184 | ~spl227_230)),
% 1.03/0.54 inference(trivial_inequality_removal,[],[f3615])).
% 1.03/0.54 thf(f3617,plain,(
% 1.03/0.54 $false | (spl227_53 | ~spl227_184 | ~spl227_230)),
% 1.03/0.54 inference(forward_subsumption_resolution,[],[f3616,f1376])).
% 1.03/0.54 thf(f3618,plain,(
% 1.03/0.54 spl227_53 | ~spl227_184 | ~spl227_230),
% 1.03/0.54 inference(avatar_contradiction_clause,[],[f3617])).
% 1.03/0.54 cnf(s32, plain, ~spl227_53, inference(sat_conversion,[],[f1377])).
% 1.03/0.54 cnf(s139, plain, spl227_184 | ~spl227_185, inference(sat_conversion,[],[f1962])).
% 1.03/0.54 cnf(s185, plain, ~spl227_185 | spl227_230, inference(sat_conversion,[],[f2174])).
% 1.03/0.54 cnf(s253, plain, spl227_185, inference(sat_conversion,[],[f2442])).
% 1.03/0.54 cnf(s429, plain, spl227_53 | ~spl227_184 | ~spl227_230, inference(sat_conversion,[],[f3618])).
% 1.03/0.54 cnf(s469, plain, spl227_230, inference(rat,[],[s185,s253])).
% 1.03/0.54 cnf(s484, plain, spl227_184, inference(rat,[],[s139,s253])).
% 1.03/0.54 cnf(s485, plain, spl227_53, inference(rat,[],[s429,s469,s484])).
% 1.03/0.54 cnf(s528, plain, $false, inference(rat,[],[s32,s485])).
% 1.03/0.54 thf(f3619,plain,(
% 1.03/0.54 $false),
% 1.03/0.54 inference(avatar_sat_refutation,[],[s528])).
% 1.03/0.54 % SZS output end Proof for theBenchmark
% 1.03/0.54 % (2145862)------------------------------
% 1.03/0.54 % (2145862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.54 % (2145862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.54 % (2145862)CaDiCaL version: 2.1.3
% 1.03/0.54 % (2145862)Termination reason: Refutation
% 1.03/0.54 % (2145862)Time elapsed: 0.131 s
% 1.03/0.54 % (2145862)Peak memory usage: 15 MB
% 1.03/0.54 % (2145862)Instructions burned: 140 (million)
% 1.03/0.54 % (2145854)Success in time 0.18 s
% 1.03/0.54 % Vampire exiting
%------------------------------------------------------------------------------