%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU577^1 : 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 : n016.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 08:30:09 AM UTC 2026
% Result : Theorem 0.72s 0.40s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU577^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n016.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:56:35 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.26 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
% 0.72/0.37 % (391315)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.72/0.37 % (391327)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3243781519:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.72/0.37 % (391327)Instruction limit reached!
% 0.72/0.37 % (391327)------------------------------
% 0.72/0.37 % (391327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (391327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (391327)CaDiCaL version: 2.1.3
% 0.72/0.37 % (391327)Termination reason: Instruction limit
% 0.72/0.37 % (391327)Termination phase: shuffling
% 0.72/0.37 % (391327)Time elapsed: 0.001 s
% 0.72/0.37 % (391327)Peak memory usage: 10 MB
% 0.72/0.37 % (391327)Instructions burned: 3 (million)
% 0.72/0.37 % (391331)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.72/0.37 % (391331)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
% 0.72/0.37 % (391325)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=619301852:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.72/0.37 % (391326)lrs+10_16_si=on:nwc=1.5:random_seed=3392173574:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.72/0.37 % (391328)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=3192150309: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)
% 0.72/0.37 % (391329)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=914181332:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.72/0.37 % (391330)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1042794794:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.72/0.37 % (391331)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=3172505284:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.72/0.37 % (391336)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1077085772:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.72/0.37 % (391336)Instruction limit reached!
% 0.72/0.37 % (391336)------------------------------
% 0.72/0.37 % (391336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (391336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (391336)CaDiCaL version: 2.1.3
% 0.72/0.37 % (391336)Termination reason: Instruction limit
% 0.72/0.37 % (391336)Termination phase: shuffling
% 0.72/0.37 % (391336)Time elapsed: 0.001 s
% 0.72/0.37 % (391336)Peak memory usage: 10 MB
% 0.72/0.37 % (391336)Instructions burned: 4 (million)
% 0.72/0.37 % (391326)Instruction limit reached!
% 0.72/0.37 % (391326)------------------------------
% 0.72/0.37 % (391326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (391326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (391326)CaDiCaL version: 2.1.3
% 0.72/0.37 % (391326)Termination reason: Instruction limit
% 0.72/0.37 % (391326)Termination phase: Preprocessing 3
% 0.72/0.37 % (391326)Time elapsed: 0.008 s
% 0.72/0.37 % (391326)Peak memory usage: 10 MB
% 0.72/0.37 % (391326)Instructions burned: 19 (million)
% 0.72/0.37 % (391329)Instruction limit reached!
% 0.72/0.37 % (391329)------------------------------
% 0.72/0.37 % (391329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.37 % (391329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.37 % (391329)CaDiCaL version: 2.1.3
% 0.72/0.37 % (391329)Termination reason: Instruction limit
% 0.72/0.37 % (391329)Termination phase: Preprocessing 3
% 0.72/0.37 % (391329)Time elapsed: 0.013 s
% 0.72/0.37 % (391329)Peak memory usage: 11 MB
% 0.72/0.37 % (391329)Instructions burned: 24 (million)
% 0.72/0.37 % (391345)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=627664106:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.72/0.37 % (391345)Instruction limit reached!
% 0.72/0.40 % (391345)------------------------------
% 0.72/0.40 % (391345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391345)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391345)Termination reason: Instruction limit
% 0.72/0.40 % (391345)Termination phase: shuffling
% 0.72/0.40 % (391345)Time elapsed: 0.002 s
% 0.72/0.40 % (391345)Peak memory usage: 10 MB
% 0.72/0.40 % (391345)Instructions burned: 8 (million)
% 0.72/0.40 % (391346)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.72/0.40 % (391349)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
% 0.72/0.40 % (391349)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.72/0.40 % (391346)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1378748344:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.72/0.40 % (391349)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1876278074:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.72/0.40 % (391346)Instruction limit reached!
% 0.72/0.40 % (391346)------------------------------
% 0.72/0.40 % (391346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391346)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391346)Termination reason: Instruction limit
% 0.72/0.40 % (391346)Termination phase: shuffling
% 0.72/0.40 % (391346)Time elapsed: 0.004 s
% 0.72/0.40 % (391346)Peak memory usage: 10 MB
% 0.72/0.40 % (391346)Instructions burned: 9 (million)
% 0.72/0.40 % (391347)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2497442784:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.72/0.40 % (391349)Instruction limit reached!
% 0.72/0.40 % (391349)------------------------------
% 0.72/0.40 % (391349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391349)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391349)Termination reason: Instruction limit
% 0.72/0.40 % (391349)Termination phase: Property scanning
% 0.72/0.40 % (391349)Time elapsed: 0.006 s
% 0.72/0.40 % (391349)Peak memory usage: 10 MB
% 0.72/0.40 % (391349)Instructions burned: 28 (million)
% 0.72/0.40 % (391330)Instruction limit reached!
% 0.72/0.40 % (391330)------------------------------
% 0.72/0.40 % (391330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391330)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391330)Termination reason: Instruction limit
% 0.72/0.40 % (391330)Termination phase: Saturation
% 0.72/0.40 % (391330)Time elapsed: 0.036 s
% 0.72/0.40 % (391330)Peak memory usage: 13 MB
% 0.72/0.40 % (391330)Instructions burned: 76 (million)
% 0.72/0.40 % (391347)Instruction limit reached!
% 0.72/0.40 % (391347)------------------------------
% 0.72/0.40 % (391347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391347)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391347)Termination reason: Instruction limit
% 0.72/0.40 % (391347)Termination phase: Property scanning
% 0.72/0.40 % (391347)Time elapsed: 0.005 s
% 0.72/0.40 % (391347)Peak memory usage: 10 MB
% 0.72/0.40 % (391347)Instructions burned: 12 (million)
% 0.72/0.40 % (391325)Instruction limit reached!
% 0.72/0.40 % (391325)------------------------------
% 0.72/0.40 % (391325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391325)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391325)Termination reason: Instruction limit
% 0.72/0.40 % (391325)Termination phase: Saturation
% 0.72/0.40 % (391325)Time elapsed: 0.044 s
% 0.72/0.40 % (391325)Peak memory usage: 13 MB
% 0.72/0.40 % (391325)Instructions burned: 93 (million)
% 0.72/0.40 % (391354)lrs+10_1_si=on:cs=on:random_seed=704056953:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.72/0.40 % (391354)Instruction limit reached!
% 0.72/0.40 % (391354)------------------------------
% 0.72/0.40 % (391354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391354)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391354)Termination reason: Instruction limit
% 0.72/0.40 % (391354)Termination phase: shuffling
% 0.72/0.40 % (391354)Time elapsed: 0.002 s
% 0.72/0.40 % (391354)Peak memory usage: 10 MB
% 0.72/0.40 % (391354)Instructions burned: 10 (million)
% 0.72/0.40 % (391355)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.72/0.40 % (391353)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=1366113003:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.72/0.40 % (391355)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=936297406:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.72/0.40 % (391355)Instruction limit reached!
% 0.72/0.40 % (391355)------------------------------
% 0.72/0.40 % (391355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391355)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391355)Termination reason: Instruction limit
% 0.72/0.40 % (391355)Termination phase: shuffling
% 0.72/0.40 % (391355)Time elapsed: 0.002 s
% 0.72/0.40 % (391355)Peak memory usage: 10 MB
% 0.72/0.40 % (391355)Instructions burned: 3 (million)
% 0.72/0.40 % (391356)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=607217399:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.72/0.40 % (391359)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3419153050:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.72/0.40 % (391357)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=745241767:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.72/0.40 % (391359)Instruction limit reached!
% 0.72/0.40 % (391359)------------------------------
% 0.72/0.40 % (391359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391359)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391359)Termination reason: Instruction limit
% 0.72/0.40 % (391359)Termination phase: Preprocessing 3
% 0.72/0.40 % (391359)Time elapsed: 0.006 s
% 0.72/0.40 % (391359)Peak memory usage: 11 MB
% 0.72/0.40 % (391359)Instructions burned: 25 (million)
% 0.72/0.40 % (391331)Instruction limit reached!
% 0.72/0.40 % (391331)------------------------------
% 0.72/0.40 % (391331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391331)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391331)Termination reason: Instruction limit
% 0.72/0.40 % (391331)Termination phase: Saturation
% 0.72/0.40 % (391331)Time elapsed: 0.068 s
% 0.72/0.40 % (391331)Peak memory usage: 14 MB
% 0.72/0.40 % (391331)Instructions burned: 158 (million)
% 0.72/0.40 % (391366)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1503734883:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.72/0.40 % (391363)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2902239743:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.72/0.40 % (391356)Instruction limit reached!
% 0.72/0.40 % (391356)------------------------------
% 0.72/0.40 % (391356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391356)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391356)Termination reason: Instruction limit
% 0.72/0.40 % (391356)Termination phase: Property scanning
% 0.72/0.40 % (391356)Time elapsed: 0.019 s
% 0.72/0.40 % (391356)Peak memory usage: 11 MB
% 0.72/0.40 % (391356)Instructions burned: 39 (million)
% 0.72/0.40 % (391363)Instruction limit reached!
% 0.72/0.40 % (391363)------------------------------
% 0.72/0.40 % (391363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391363)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391363)Termination reason: Instruction limit
% 0.72/0.40 % (391363)Termination phase: Property scanning
% 0.72/0.40 % (391363)Time elapsed: 0.006 s
% 0.72/0.40 % (391363)Peak memory usage: 10 MB
% 0.72/0.40 % (391363)Instructions burned: 14 (million)
% 0.72/0.40 % (391367)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2359938060:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.72/0.40 % (391353)Instruction limit reached!
% 0.72/0.40 % (391353)------------------------------
% 0.72/0.40 % (391353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391353)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391353)Termination reason: Instruction limit
% 0.72/0.40 % (391353)Termination phase: Saturation
% 0.72/0.40 % (391353)Time elapsed: 0.037 s
% 0.72/0.40 % (391353)Peak memory usage: 12 MB
% 0.72/0.40 % (391353)Instructions burned: 86 (million)
% 0.72/0.40 % (391367)Instruction limit reached!
% 0.72/0.40 % (391367)------------------------------
% 0.72/0.40 % (391367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391367)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391367)Termination reason: Instruction limit
% 0.72/0.40 % (391367)Termination phase: Property scanning
% 0.72/0.40 % (391367)Time elapsed: 0.006 s
% 0.72/0.40 % (391367)Peak memory usage: 10 MB
% 0.72/0.40 % (391367)Instructions burned: 14 (million)
% 0.72/0.40 % (391370)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3518210544:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.72/0.40 % (391328) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-391315-391328"...
% 0.72/0.40 % (391370)Instruction limit reached!
% 0.72/0.40 % (391370)------------------------------
% 0.72/0.40 % (391370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391370)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391370)Termination reason: Instruction limit
% 0.72/0.40 % (391370)Termination phase: shuffling
% 0.72/0.40 % (391370)Time elapsed: 0.002 s
% 0.72/0.40 % (391370)Peak memory usage: 10 MB
% 0.72/0.40 % (391370)Instructions burned: 4 (million)
% 0.72/0.40 % (391371)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1614549413:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.72/0.40 % (391328)...printing done.
% 0.72/0.40 % (391328)Refutation found. Thanks to Tanya!
% 0.72/0.40 % SZS status Theorem for theBenchmark
% 0.72/0.40 % SZS output start Proof for theBenchmark
% 0.72/0.40 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.72/0.40 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.72/0.40 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.72/0.40 thf(func_def_3, type, setextAx: $o).
% 0.72/0.40 thf(func_def_5, type, emptysetAx: $o).
% 0.72/0.40 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_7, type, setadjoinAx: $o).
% 0.72/0.40 thf(func_def_8, type, powerset: ($i > $i)).
% 0.72/0.40 thf(func_def_9, type, powersetAx: $o).
% 0.72/0.40 thf(func_def_10, type, setunion: ($i > $i)).
% 0.72/0.40 thf(func_def_11, type, setunionAx: $o).
% 0.72/0.40 thf(func_def_13, type, omega0Ax: $o).
% 0.72/0.40 thf(func_def_14, type, omegaSAx: $o).
% 0.72/0.40 thf(func_def_15, type, omegaIndAx: $o).
% 0.72/0.40 thf(func_def_16, type, replAx: $o).
% 0.72/0.40 thf(func_def_17, type, foundationAx: $o).
% 0.72/0.40 thf(func_def_18, type, wellorderingAx: $o).
% 0.72/0.40 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.72/0.40 thf(func_def_20, type, descrp: $o).
% 0.72/0.40 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_22, type, dsetconstrI: $o).
% 0.72/0.40 thf(func_def_23, type, dsetconstrEL: $o).
% 0.72/0.40 thf(func_def_24, type, dsetconstrER: $o).
% 0.72/0.40 thf(func_def_25, type, exuE1: $o).
% 0.72/0.40 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.72/0.40 thf(func_def_27, type, prop2setE: $o).
% 0.72/0.40 thf(func_def_28, type, emptysetE: $o).
% 0.72/0.40 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.72/0.40 thf(func_def_30, type, notinemptyset: $o).
% 0.72/0.40 thf(func_def_31, type, exuE3e: $o).
% 0.72/0.40 thf(func_def_32, type, setext: $o).
% 0.72/0.40 thf(func_def_33, type, emptyI: $o).
% 0.72/0.40 thf(func_def_34, type, noeltsimpempty: $o).
% 0.72/0.40 thf(func_def_35, type, setbeta: $o).
% 0.72/0.40 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.72/0.40 thf(func_def_37, type, nonemptyE1: $o).
% 0.72/0.40 thf(func_def_38, type, nonemptyI: $o).
% 0.72/0.40 thf(func_def_39, type, nonemptyI1: $o).
% 0.72/0.40 thf(func_def_40, type, setadjoinIL: $o).
% 0.72/0.40 thf(func_def_41, type, emptyinunitempty: $o).
% 0.72/0.40 thf(func_def_42, type, setadjoinIR: $o).
% 0.72/0.40 thf(func_def_43, type, setadjoinE: $o).
% 0.72/0.40 thf(func_def_44, type, setadjoinOr: $o).
% 0.72/0.40 thf(func_def_45, type, setoftrueEq: $o).
% 0.72/0.40 thf(func_def_46, type, powersetI: $o).
% 0.72/0.40 thf(func_def_47, type, emptyinPowerset: $o).
% 0.72/0.40 thf(func_def_48, type, emptyInPowerset: $o).
% 0.72/0.40 thf(func_def_49, type, powersetE: $o).
% 0.72/0.40 thf(func_def_50, type, setunionI: $o).
% 0.72/0.40 thf(func_def_51, type, setunionE: $o).
% 0.72/0.40 thf(func_def_52, type, subPowSU: $o).
% 0.72/0.40 thf(func_def_53, type, exuE2: $o).
% 0.72/0.40 thf(func_def_54, type, nonemptyImpWitness: $o).
% 0.72/0.40 thf(func_def_55, type, uniqinunit: $o).
% 0.72/0.40 thf(func_def_56, type, notinsingleton: $o).
% 0.72/0.40 thf(func_def_57, type, eqinunit: $o).
% 0.72/0.40 thf(func_def_58, type, singletonsswitch: $o).
% 0.72/0.40 thf(func_def_59, type, upairsetE: $o).
% 0.72/0.40 thf(func_def_60, type, upairsetIL: $o).
% 0.72/0.40 thf(func_def_61, type, upairsetIR: $o).
% 0.72/0.40 thf(func_def_62, type, emptyE1: $o).
% 0.72/0.40 thf(func_def_63, type, vacuousDall: $o).
% 0.72/0.40 thf(func_def_64, type, quantDeMorgan1: $o).
% 0.72/0.40 thf(func_def_65, type, quantDeMorgan2: $o).
% 0.72/0.40 thf(func_def_66, type, quantDeMorgan3: $o).
% 0.72/0.40 thf(func_def_67, type, quantDeMorgan4: $o).
% 0.72/0.40 thf(func_def_68, type, prop2setI: $o).
% 0.72/0.40 thf(func_def_69, type, set2prop: ($i > $o)).
% 0.72/0.40 thf(func_def_70, type, prop2set2propI: $o).
% 0.72/0.40 thf(func_def_71, type, notdexE: $o).
% 0.72/0.40 thf(func_def_72, type, notdallE: $o).
% 0.72/0.40 thf(func_def_73, type, exuI1: $o).
% 0.72/0.40 thf(func_def_74, type, exuI3: $o).
% 0.72/0.40 thf(func_def_75, type, exuI2: $o).
% 0.72/0.40 thf(func_def_76, type, inCongP: $o).
% 0.72/0.40 thf(func_def_77, type, in__Cong: $o).
% 0.72/0.40 thf(func_def_78, type, exuE3u: $o).
% 0.72/0.40 thf(func_def_79, type, exu__Cong: $o).
% 0.72/0.40 thf(func_def_80, type, emptyset__Cong: $o).
% 0.72/0.40 thf(func_def_81, type, setadjoin__Cong: $o).
% 0.72/0.40 thf(func_def_82, type, powerset__Cong: $o).
% 0.72/0.40 thf(func_def_83, type, setunion__Cong: $o).
% 0.72/0.40 thf(func_def_84, type, omega__Cong: $o).
% 0.72/0.40 thf(func_def_85, type, exuEu: $o).
% 0.72/0.40 thf(func_def_86, type, descr__Cong: $o).
% 0.72/0.40 thf(func_def_87, type, dsetconstr__Cong: $o).
% 0.72/0.40 thf(func_def_88, type, subset: ($i > $i > $o)).
% 0.72/0.40 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 0.72/0.40 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 0.72/0.40 thf(func_def_91, type, subsetI1: $o).
% 0.72/0.40 thf(func_def_92, type, eqimpsubset2: $o).
% 0.72/0.40 thf(func_def_93, type, eqimpsubset1: $o).
% 0.72/0.40 thf(func_def_94, type, subsetI2: $o).
% 0.72/0.40 thf(func_def_95, type, emptysetsubset: $o).
% 0.72/0.40 thf(func_def_96, type, subsetE: $o).
% 0.72/0.40 thf(func_def_97, type, subsetE2: $o).
% 0.72/0.40 thf(func_def_98, type, notsubsetI: $o).
% 0.72/0.40 thf(func_def_99, type, notequalI1: $o).
% 0.72/0.40 thf(func_def_100, type, notequalI2: $o).
% 0.72/0.40 thf(func_def_101, type, subsetRefl: $o).
% 0.72/0.40 thf(func_def_102, type, subsetTrans: $o).
% 0.72/0.40 thf(func_def_103, type, setadjoinSub: $o).
% 0.72/0.40 thf(func_def_104, type, setadjoinSub2: $o).
% 0.72/0.40 thf(func_def_105, type, subset2powerset: $o).
% 0.72/0.40 thf(func_def_106, type, setextsub: $o).
% 0.72/0.40 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 0.72/0.40 thf(func_def_108, type, powersetI1: $o).
% 0.72/0.40 thf(func_def_111, type, db0: !>[X0: $tType]:(X0)).
% 0.72/0.40 thf(func_def_112, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.72/0.40 thf(func_def_113, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.72/0.40 thf(func_def_114, type, vNOT: ($o > $o)).
% 0.72/0.40 thf(func_def_115, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.72/0.40 thf(func_def_116, type, vAND: ($o > $o > $o)).
% 0.72/0.40 thf(func_def_117, type, db1: !>[X0: $tType]:(X0)).
% 0.72/0.40 thf(func_def_118, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.72/0.40 thf(func_def_119, type, vIMP: ($o > $o > $o)).
% 0.72/0.40 thf(func_def_120, type, db2: !>[X0: $tType]:(X0)).
% 0.72/0.40 thf(func_def_121, type, sP0: ($i > $i > $o)).
% 0.72/0.40 thf(func_def_122, type, sP1: ($i > $o)).
% 0.72/0.40 thf(func_def_123, type, sP2: $o).
% 0.72/0.40 thf(func_def_126, type, sK5: (($i > $i > $o) > $i > $i)).
% 0.72/0.40 thf(func_def_127, type, sK6: (($i > $i > $o) > $i > $i)).
% 0.72/0.40 thf(func_def_128, type, sK7: ($i > ($i > $i > $o) > $i > $i)).
% 0.72/0.40 thf(func_def_130, type, sK9: ($i > $i > $o)).
% 0.72/0.40 thf(func_def_131, type, sK10: ($i > $i)).
% 0.72/0.40 thf(func_def_132, type, sK11: ($i > $i)).
% 0.72/0.40 thf(func_def_134, type, sK13: ($i > $o)).
% 0.72/0.40 thf(func_def_141, type, sK20: ($i > $o)).
% 0.72/0.40 thf(func_def_142, type, sK21: ($i > $o)).
% 0.72/0.40 thf(func_def_143, type, sK22: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 0.72/0.40 thf(func_def_144, type, sK23: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 0.72/0.40 thf(func_def_145, type, sK24: ($i > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_146, type, sK25: ($i > $o)).
% 0.72/0.40 thf(func_def_151, type, sK30: ($i > $o)).
% 0.72/0.40 thf(func_def_152, type, sK31: $o).
% 0.72/0.40 thf(func_def_160, type, sK39: $o).
% 0.72/0.40 thf(func_def_166, type, sK45: ($i > $o)).
% 0.72/0.40 thf(func_def_168, type, sK47: ($i > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_169, type, sK48: ($i > $o)).
% 0.72/0.40 thf(func_def_170, type, sK49: ($i > $o)).
% 0.72/0.40 thf(func_def_171, type, sK50: (($i > $o) > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_172, type, sK51: (($i > $o) > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_178, type, sK57: ($i > $o)).
% 0.72/0.40 thf(func_def_181, type, sK60: ($i > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_182, type, sK61: (($i > $o) > $i)).
% 0.72/0.40 thf(func_def_183, type, sK62: ($i > $o)).
% 0.72/0.40 thf(func_def_184, type, sK63: ($i > $i)).
% 0.72/0.40 thf(func_def_185, type, sK64: (($i > $o) > $i > $i)).
% 0.72/0.40 thf(func_def_187, type, sK66: ($i > $o)).
% 0.72/0.40 thf(func_def_189, type, sK68: ($i > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_190, type, sK69: ($i > $o)).
% 0.72/0.40 thf(func_def_198, type, sK77: ($o > $i > $i > $i)).
% 0.72/0.40 thf(func_def_201, type, sK80: $o).
% 0.72/0.40 thf(func_def_213, type, sK92: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_214, type, sK93: (($i > $o) > $i)).
% 0.72/0.40 thf(func_def_215, type, sK94: (($i > $o) > $i)).
% 0.72/0.40 thf(func_def_216, type, sK95: ($i > $o)).
% 0.72/0.40 thf(func_def_219, type, sK98: ($i > $i)).
% 0.72/0.40 thf(func_def_220, type, sK99: ($i > $i)).
% 0.72/0.40 thf(func_def_221, type, sK100: ($i > $i)).
% 0.72/0.40 thf(func_def_222, type, sK101: ($i > $i)).
% 0.72/0.40 thf(func_def_223, type, sK102: ($i > $i)).
% 0.72/0.40 thf(func_def_224, type, sK103: ($i > $i > $i > $i)).
% 0.72/0.40 thf(func_def_225, type, sK104: ($i > $i)).
% 0.72/0.40 thf(func_def_226, type, sK105: ($i > $i)).
% 0.72/0.40 thf(func_def_227, type, sK106: ($i > $i)).
% 0.72/0.40 thf(func_def_228, type, sK107: ($i > $i)).
% 0.72/0.40 thf(func_def_229, type, sK108: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_230, type, sK109: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_231, type, sK110: ($i > $i > $i > $i)).
% 0.72/0.40 thf(func_def_232, type, sK111: ($i > $i > $i > $i)).
% 0.72/0.40 thf(func_def_233, type, sK112: ($i > $i > $i > $i)).
% 0.72/0.40 thf(func_def_234, type, sK113: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_235, type, sK114: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_236, type, sK115: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_237, type, sK116: ($i > $o)).
% 0.72/0.40 thf(func_def_246, type, sK125: ($i > $o)).
% 0.72/0.40 thf(func_def_249, type, sK128: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_251, type, sK130: $o).
% 0.72/0.40 thf(func_def_258, type, sK137: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_261, type, sK140: ($i > $o)).
% 0.72/0.40 thf(func_def_264, type, sK143: (($i > $o) > $i)).
% 0.72/0.40 thf(func_def_265, type, sK144: ($i > $o)).
% 0.72/0.40 thf(func_def_266, type, sK145: ($i > $i)).
% 0.72/0.40 thf(func_def_275, type, sK154: ($i > $o)).
% 0.72/0.40 thf(func_def_287, type, sK166: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_294, type, sK173: ($i > $i)).
% 0.72/0.40 thf(func_def_302, type, sK181: $o).
% 0.72/0.40 thf(func_def_305, type, sK184: ($i > $i)).
% 0.72/0.40 thf(func_def_307, type, sK186: ($i > $i)).
% 0.72/0.40 thf(func_def_315, type, sK194: ($i > $o)).
% 0.72/0.40 thf(func_def_317, type, sK196: (($i > $o) > $i > $i)).
% 0.72/0.40 thf(func_def_318, type, sK197: (($i > $o) > $i)).
% 0.72/0.40 thf(func_def_319, type, sK198: ($i > $o)).
% 0.72/0.40 thf(func_def_321, type, sK200: ($i > $i)).
% 0.72/0.40 thf(func_def_323, type, sK202: ($i > $o)).
% 0.72/0.40 thf(func_def_328, type, sK207: ($i > $o)).
% 0.72/0.40 thf(func_def_336, type, sK215: (($i > $o) > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_337, type, sK216: (($i > $o) > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_338, type, sK217: ($i > $o)).
% 0.72/0.40 thf(func_def_339, type, sK218: ($i > $o)).
% 0.72/0.40 thf(func_def_341, type, sK220: ($i > $i)).
% 0.72/0.40 thf(func_def_342, type, sK221: $o).
% 0.72/0.40 thf(func_def_343, type, sK222: ($i > $o)).
% 0.72/0.40 thf(func_def_346, type, sK225: ($i > $o)).
% 0.72/0.40 thf(func_def_348, type, sK227: ($i > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_350, type, sK229: ($i > $o)).
% 0.72/0.40 thf(func_def_353, type, sK232: ($i > ($i > $o) > $i)).
% 0.72/0.40 thf(func_def_359, type, sK238: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_360, type, sK239: ($i > $i)).
% 0.72/0.40 thf(func_def_365, type, sK244: ($i > $o)).
% 0.72/0.40 thf(func_def_368, type, sK247: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_369, type, sK248: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_375, type, sK254: ($i > $i > $i)).
% 0.72/0.40 thf(func_def_377, type, sK256: ($i > $i)).
% 0.72/0.40 thf(f5,axiom,(
% 0.72/0.40 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetAx)),
% 0.72/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 0.72/0.40 thf(f78,axiom,(
% 0.72/0.40 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.72/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.72/0.40 thf(f96,conjecture,(
% 0.72/0.40 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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.72/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1)).
% 0.72/0.40 thf(f97,negated_conjecture,(
% 0.72/0.40 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.72/0.40 inference(negated_conjecture,[status(cth)],[f96])).
% 0.72/0.40 thf(f157,plain,(
% 0.72/0.40 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.72/0.40 inference(rectify,[],[f78])).
% 0.72/0.40 thf(f158,plain,(
% 0.72/0.40 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true)) <=> (subsetI1 = $true)),
% 0.72/0.40 inference(fool_elimination,[],[f157])).
% 0.72/0.40 thf(f189,plain,(
% 0.72/0.40 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetAx)),
% 0.72/0.40 inference(rectify,[],[f5])).
% 0.72/0.40 thf(f190,plain,(
% 0.72/0.40 (powersetAx = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) <=> ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)))),
% 0.72/0.40 inference(fool_elimination,[],[f189])).
% 0.72/0.40 thf(f242,plain,(
% 0.72/0.40 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.72/0.40 inference(rectify,[],[f97])).
% 0.72/0.40 thf(f243,plain,(
% 0.72/0.40 ~((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) => ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => (((subset @ X1 @ X0)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.72/0.40 inference(fool_elimination,[],[f242])).
% 0.72/0.40 thf(f316,plain,(
% 0.72/0.40 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) & (((in @ X1 @ (powerset @ X0))) = $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)),
% 0.72/0.40 inference(ennf_transformation,[],[f243])).
% 0.72/0.40 thf(f317,plain,(
% 0.72/0.40 (eqimpsubset2 = $true) & (emptyinPowerset = $true) & (upairsetIR = $true) & (subsetRefl = $true) & (quantDeMorgan1 = $true) & (nonemptyImpWitness = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (powersetAx = $true) & (setextsub = $true) & (nonemptyI = $true) & (eqimpsubset1 = $true) & (subsetemptysetimpeq = $true) & (notdexE = $true) & (emptysetimpfalse = $true) & (emptyE1 = $true) & (dsetconstr__Cong = $true) & (subsetE = $true) & (setunion__Cong = $true) & (vacuousDall = $true) & (exuE1 = $true) & (subsetI2 = $true) & (uniqinunit = $true) & (setbeta = $true) & (exuEu = $true) & (subPowSU = $true) & ? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) & (((in @ X1 @ (powerset @ X0))) = $true)) & (singletonsswitch = $true) & (notequalI1 = $true) & (wellorderingAx = $true) & (in__Cong = $true) & (emptyI = $true) & (inCongP = $true) & (prop2set2propI = $true) & (powersetE = $true) & (emptysetE = $true) & (quantDeMorgan4 = $true) & (omega__Cong = $true) & (exuE2 = $true) & (powerset__Cong = $true) & (nonemptyE1 = $true) & (dsetconstrI = $true) & (notinsingleton = $true) & (setadjoinAx = $true) & (replAx = $true) & (emptysetsubset = $true) & (exuI1 = $true) & (omegaIndAx = $true) & (upairsetE = $true) & (prop2setE = $true) & (setadjoinSub2 = $true) & (notequalI2 = $true) & (notsubsetI = $true) & (noeltsimpempty = $true) & (exuI3 = $true) & (eqinunit = $true) & (dsetconstrER = $true) & (setadjoinE = $true) & (powersetI1 = $true) & (subset2powerset = $true) & (notdallE = $true) & (exuE3u = $true) & (notinemptyset = $true) & (foundationAx = $true) & (powersetI = $true) & (upairsetIL = $true) & (exuE3e = $true) & (omegaSAx = $true) & (quantDeMorgan3 = $true) & (setextAx = $true) & (emptysetAx = $true) & (subsetTrans = $true) & (setoftrueEq = $true) & (setunionAx = $true) & (exu__Cong = $true) & (omega0Ax = $true) & (subsetE2 = $true) & (emptyset__Cong = $true) & (descr__Cong = $true) & (setadjoinOr = $true) & (emptyinunitempty = $true) & (emptyInPowerset = $true) & (prop2setI = $true) & (setadjoinSub = $true) & (dsetconstrEL = $true) & (descrp = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (setunionI = $true) & (setadjoinIR = $true) & (setunionE = $true) & (setadjoin__Cong = $true) & (exuI2 = $true) & (setext = $true)),
% 0.72/0.40 inference(flattening,[],[f316])).
% 0.72/0.40 thf(f323,plain,(
% 0.72/0.40 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true))),
% 0.72/0.40 inference(ennf_transformation,[],[f158])).
% 0.72/0.40 thf(f367,plain,(
% 0.72/0.40 (powersetAx = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) <=> (((in @ X1 @ (powerset @ X0))) = $true))),
% 0.72/0.40 inference(ennf_transformation,[],[f190])).
% 0.72/0.40 thf(f532,plain,(
% 0.72/0.40 ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true))),
% 0.72/0.40 inference(nnf_transformation,[],[f323])).
% 0.72/0.40 thf(f533,plain,(
% 0.72/0.40 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((subset @ X1 @ X0)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : ((((in @ X5 @ X3)) != $true) & (((in @ X5 @ X4)) = $true)) | (((subset @ X4 @ X3)) = $true)) | (subsetI1 != $true))),
% 0.72/0.40 inference(rectify,[],[f532])).
% 0.72/0.40 thf(f534,plain,(
% 0.72/0.40 ((subsetI1 = $true) | (! [X2 : $i] : ((((in @ X2 @ sK126)) = $true) | (((in @ X2 @ sK127)) != $true)) & (((subset @ sK127 @ sK126)) != $true))) & (! [X3 : $i,X4 : $i] : ((($true != ((in @ (sK128 @ X4 @ X3) @ X3))) & (((in @ (sK128 @ X4 @ X3) @ X4)) = $true)) | (((subset @ X4 @ X3)) = $true)) | (subsetI1 != $true))),
% 0.72/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK126,sK127,vAPP]),skolemize(X0,sK126),skolemize(X1,sK127),skolemize(X13,sK11 @ X10)],[f533])).
% 0.72/0.40 thf(f608,plain,(
% 0.72/0.40 (eqimpsubset2 = $true) & (emptyinPowerset = $true) & (upairsetIR = $true) & (subsetRefl = $true) & (quantDeMorgan1 = $true) & (nonemptyImpWitness = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (powersetAx = $true) & (setextsub = $true) & (nonemptyI = $true) & (eqimpsubset1 = $true) & (subsetemptysetimpeq = $true) & (notdexE = $true) & (emptysetimpfalse = $true) & (emptyE1 = $true) & (dsetconstr__Cong = $true) & (subsetE = $true) & (setunion__Cong = $true) & (vacuousDall = $true) & (exuE1 = $true) & (subsetI2 = $true) & (uniqinunit = $true) & (setbeta = $true) & (exuEu = $true) & (subPowSU = $true) & ((((subset @ sK189 @ sK188)) != $true) & (((in @ sK189 @ (powerset @ sK188))) = $true)) & (singletonsswitch = $true) & (notequalI1 = $true) & (wellorderingAx = $true) & (in__Cong = $true) & (emptyI = $true) & (inCongP = $true) & (prop2set2propI = $true) & (powersetE = $true) & (emptysetE = $true) & (quantDeMorgan4 = $true) & (omega__Cong = $true) & (exuE2 = $true) & (powerset__Cong = $true) & (nonemptyE1 = $true) & (dsetconstrI = $true) & (notinsingleton = $true) & (setadjoinAx = $true) & (replAx = $true) & (emptysetsubset = $true) & (exuI1 = $true) & (omegaIndAx = $true) & (upairsetE = $true) & (prop2setE = $true) & (setadjoinSub2 = $true) & (notequalI2 = $true) & (notsubsetI = $true) & (noeltsimpempty = $true) & (exuI3 = $true) & (eqinunit = $true) & (dsetconstrER = $true) & (setadjoinE = $true) & (powersetI1 = $true) & (subset2powerset = $true) & (notdallE = $true) & (exuE3u = $true) & (notinemptyset = $true) & (foundationAx = $true) & (powersetI = $true) & (upairsetIL = $true) & (exuE3e = $true) & (omegaSAx = $true) & (quantDeMorgan3 = $true) & (setextAx = $true) & (emptysetAx = $true) & (subsetTrans = $true) & (setoftrueEq = $true) & (setunionAx = $true) & (exu__Cong = $true) & (omega0Ax = $true) & (subsetE2 = $true) & (emptyset__Cong = $true) & (descr__Cong = $true) & (setadjoinOr = $true) & (emptyinunitempty = $true) & (emptyInPowerset = $true) & (prop2setI = $true) & (setadjoinSub = $true) & (dsetconstrEL = $true) & (descrp = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (setunionI = $true) & (setadjoinIR = $true) & (setunionE = $true) & (setadjoin__Cong = $true) & (exuI2 = $true) & (setext = $true)),
% 0.72/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK188,sK189]),skolemize(X0,sK188),skolemize(X1,sK189)],[f317])).
% 0.72/0.40 thf(f678,plain,(
% 0.72/0.40 ((powersetAx = $true) | ? [X1 : $i,X0 : $i] : (((((in @ X1 @ (powerset @ X0))) != $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) & ((((in @ X1 @ (powerset @ X0))) = $true) | ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true))))) & (! [X1 : $i,X0 : $i] : ((! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) & ((((in @ X1 @ (powerset @ X0))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)))) | (powersetAx != $true))),
% 0.72/0.40 inference(nnf_transformation,[],[f367])).
% 0.72/0.40 thf(f679,plain,(
% 0.72/0.40 ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : (((((in @ X0 @ (powerset @ X1))) != $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) & ((((in @ X0 @ (powerset @ X1))) = $true) | ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | (((in @ X3 @ X0)) != $true))))) & (! [X4 : $i,X5 : $i] : ((! [X6 : $i] : ((((in @ X6 @ X5)) = $true) | (((in @ X6 @ X4)) != $true)) | ($true != ((in @ X4 @ (powerset @ X5))))) & (($true = ((in @ X4 @ (powerset @ X5)))) | ? [X7 : $i] : (($true != ((in @ X7 @ X5))) & (((in @ X7 @ X4)) = $true)))) | (powersetAx != $true))),
% 0.72/0.40 inference(rectify,[],[f678])).
% 0.72/0.40 thf(f680,plain,(
% 0.72/0.40 ((powersetAx = $true) | (((((in @ sK251 @ (powerset @ sK252))) != $true) | ((((in @ sK253 @ sK252)) != $true) & (((in @ sK253 @ sK251)) = $true))) & ((((in @ sK251 @ (powerset @ sK252))) = $true) | ! [X3 : $i] : ((((in @ X3 @ sK252)) = $true) | (((in @ X3 @ sK251)) != $true))))) & (! [X4 : $i,X5 : $i] : ((! [X6 : $i] : ((((in @ X6 @ X5)) = $true) | (((in @ X6 @ X4)) != $true)) | ($true != ((in @ X4 @ (powerset @ X5))))) & (($true = ((in @ X4 @ (powerset @ X5)))) | ((((in @ (sK254 @ X5 @ X4) @ X5)) != $true) & (((in @ (sK254 @ X5 @ X4) @ X4)) = $true)))) | (powersetAx != $true))),
% 0.72/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK251,sK252,sK253,vAPP]),skolemize(X0,sK251),skolemize(X1,sK252),skolemize(X2,sK253),skolemize(X13,sK11 @ X10)],[f679])).
% 0.72/0.40 thf(f887,plain,(
% 0.72/0.40 ( ! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | (subsetI1 != $true) | (((in @ (sK128 @ X4 @ X3) @ X4)) = $true)) )),
% 0.72/0.40 inference(cnf_transformation,[],[f534])).
% 0.72/0.40 thf(f888,plain,(
% 0.72/0.40 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK128 @ X4 @ X3) @ X3))) | (((subset @ X4 @ X3)) = $true) | (subsetI1 != $true)) )),
% 0.72/0.40 inference(cnf_transformation,[],[f534])).
% 0.72/0.40 thf(f988,plain,(
% 0.72/0.40 (subsetI1 = $true)),
% 0.72/0.40 inference(cnf_transformation,[],[f608])).
% 0.72/0.40 thf(f1048,plain,(
% 0.72/0.40 (((in @ sK189 @ (powerset @ sK188))) = $true)),
% 0.72/0.40 inference(cnf_transformation,[],[f608])).
% 0.72/0.40 thf(f1049,plain,(
% 0.72/0.40 (((subset @ sK189 @ sK188)) != $true)),
% 0.72/0.40 inference(cnf_transformation,[],[f608])).
% 0.72/0.40 thf(f1067,plain,(
% 0.72/0.40 (powersetAx = $true)),
% 0.72/0.40 inference(cnf_transformation,[],[f608])).
% 0.72/0.40 thf(f1165,plain,(
% 0.72/0.40 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ (powerset @ X5)))) | (powersetAx != $true) | (((in @ X6 @ X5)) = $true) | (((in @ X6 @ X4)) != $true)) )),
% 0.72/0.40 inference(cnf_transformation,[],[f680])).
% 0.72/0.40 thf(f1415,definition,(
% 0.72/0.40 spl261_24 <=> (subsetI1 = $true)),
% 0.72/0.40 introduced(definition,[new_symbols(definition,[spl261_24])],[avatar_definition])).
% 0.72/0.40 thf(f1609,definition,(
% 0.72/0.40 spl261_67 <=> (powersetAx = $true)),
% 0.72/0.40 introduced(definition,[new_symbols(definition,[spl261_67])],[avatar_definition])).
% 0.72/0.40 thf(f1773,definition,(
% 0.72/0.40 spl261_104 <=> ! [X4 : $i,X3 : $i] : ((((subset @ X4 @ X3)) = $true) | (((in @ (sK128 @ X4 @ X3) @ X4)) = $true))),
% 0.72/0.40 introduced(definition,[new_symbols(definition,[spl261_104])],[avatar_definition])).
% 0.72/0.40 thf(f1774,plain,(
% 0.72/0.40 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK128 @ X4 @ X3) @ X4)) = $true) | (((subset @ X4 @ X3)) = $true)) ) | ~spl261_104),
% 0.72/0.40 inference(avatar_component_clause,[],[f1773])).
% 0.72/0.40 thf(f1775,plain,(
% 0.72/0.40 ~spl261_24 | spl261_104),
% 0.72/0.40 inference(avatar_split_clause,[],[f887,f1773,f1415])).
% 0.72/0.40 thf(f2002,definition,(
% 0.72/0.40 spl261_154 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (((in @ X0 @ X1)) = $true))),
% 0.72/0.40 introduced(definition,[new_symbols(definition,[spl261_154])],[avatar_definition])).
% 0.72/0.40 thf(f2003,plain,(
% 0.72/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true)) ) | ~spl261_154),
% 0.72/0.40 inference(avatar_component_clause,[],[f2002])).
% 0.72/0.40 thf(f2065,definition,(
% 0.72/0.40 spl261_168 <=> (((in @ sK189 @ (powerset @ sK188))) = $true)),
% 0.72/0.40 introduced(definition,[new_symbols(definition,[spl261_168])],[avatar_definition])).
% 0.72/0.40 thf(f2067,plain,(
% 0.72/0.40 (((in @ sK189 @ (powerset @ sK188))) = $true) | ~spl261_168),
% 0.72/0.40 inference(avatar_component_clause,[],[f2065])).
% 0.72/0.40 thf(f2068,plain,(
% 0.72/0.40 spl261_168),
% 0.72/0.40 inference(avatar_split_clause,[],[f1048,f2065])).
% 0.72/0.40 thf(f2302,plain,(
% 0.72/0.40 spl261_154 | ~spl261_67),
% 0.72/0.40 inference(avatar_split_clause,[],[f1165,f1609,f2002])).
% 0.72/0.40 thf(f2417,definition,(
% 0.72/0.40 spl261_245 <=> ! [X4 : $i,X3 : $i] : (($true != ((in @ (sK128 @ X4 @ X3) @ X3))) | (((subset @ X4 @ X3)) = $true))),
% 0.72/0.40 introduced(definition,[new_symbols(definition,[spl261_245])],[avatar_definition])).
% 0.72/0.40 thf(f2418,plain,(
% 0.72/0.40 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK128 @ X4 @ X3) @ X3))) | (((subset @ X4 @ X3)) = $true)) ) | ~spl261_245),
% 0.72/0.40 inference(avatar_component_clause,[],[f2417])).
% 0.72/0.40 thf(f2419,plain,(
% 0.72/0.40 spl261_245 | ~spl261_24),
% 0.72/0.40 inference(avatar_split_clause,[],[f888,f1415,f2417])).
% 0.72/0.40 thf(f2610,plain,(
% 0.72/0.40 spl261_67),
% 0.72/0.40 inference(avatar_split_clause,[],[f1067,f1609])).
% 0.72/0.40 thf(f2823,plain,(
% 0.72/0.40 spl261_24),
% 0.72/0.40 inference(avatar_split_clause,[],[f988,f1415])).
% 0.72/0.40 thf(f3194,definition,(
% 0.72/0.40 spl261_406 <=> (((subset @ sK189 @ sK188)) = $true)),
% 0.72/0.40 introduced(definition,[new_symbols(definition,[spl261_406])],[avatar_definition])).
% 0.72/0.40 thf(f3196,plain,(
% 0.72/0.40 (((subset @ sK189 @ sK188)) != $true) | spl261_406),
% 0.72/0.40 inference(avatar_component_clause,[],[f3194])).
% 0.72/0.40 thf(f3197,plain,(
% 0.72/0.40 ~spl261_406),
% 0.72/0.40 inference(avatar_split_clause,[],[f1049,f3194])).
% 0.72/0.40 thf(f4015,plain,(
% 0.72/0.40 ( ! [X0 : $i] : (($true != $true) | (((in @ X0 @ sK189)) != $true) | (((in @ X0 @ sK188)) = $true)) ) | (~spl261_154 | ~spl261_168)),
% 0.72/0.40 inference(superposition,[],[f2003,f2067])).
% 0.72/0.40 thf(f4040,plain,(
% 0.72/0.40 ( ! [X0 : $i] : ((((in @ X0 @ sK188)) = $true) | (((in @ X0 @ sK189)) != $true)) ) | (~spl261_154 | ~spl261_168)),
% 0.72/0.40 inference(trivial_inequality_removal,[],[f4015])).
% 0.72/0.40 thf(f4354,plain,(
% 0.72/0.40 ( ! [X0 : $i] : (($true != $true) | (((in @ (sK128 @ X0 @ sK188) @ sK189)) != $true) | (((subset @ X0 @ sK188)) = $true)) ) | (~spl261_154 | ~spl261_168 | ~spl261_245)),
% 0.72/0.40 inference(superposition,[],[f2418,f4040])).
% 0.72/0.40 thf(f4362,plain,(
% 0.72/0.40 ( ! [X0 : $i] : ((((in @ (sK128 @ X0 @ sK188) @ sK189)) != $true) | (((subset @ X0 @ sK188)) = $true)) ) | (~spl261_154 | ~spl261_168 | ~spl261_245)),
% 0.72/0.40 inference(trivial_inequality_removal,[],[f4354])).
% 0.72/0.40 thf(f4452,plain,(
% 0.72/0.40 (((subset @ sK189 @ sK188)) = $true) | (((subset @ sK189 @ sK188)) = $true) | ($true != $true) | (~spl261_104 | ~spl261_154 | ~spl261_168 | ~spl261_245)),
% 0.72/0.40 inference(superposition,[],[f4362,f1774])).
% 0.72/0.40 thf(f4455,plain,(
% 0.72/0.40 ($true != $true) | (((subset @ sK189 @ sK188)) = $true) | (~spl261_104 | ~spl261_154 | ~spl261_168 | ~spl261_245)),
% 0.72/0.40 inference(duplicate_literal_removal,[],[f4452])).
% 0.72/0.40 thf(f4456,plain,(
% 0.72/0.40 (((subset @ sK189 @ sK188)) = $true) | (~spl261_104 | ~spl261_154 | ~spl261_168 | ~spl261_245)),
% 0.72/0.40 inference(trivial_inequality_removal,[],[f4455])).
% 0.72/0.40 thf(f4457,plain,(
% 0.72/0.40 $false | (~spl261_104 | ~spl261_154 | ~spl261_168 | ~spl261_245 | spl261_406)),
% 0.72/0.40 inference(forward_subsumption_resolution,[],[f4456,f3196])).
% 0.72/0.40 thf(f4458,plain,(
% 0.72/0.40 ~spl261_104 | ~spl261_154 | ~spl261_168 | ~spl261_245 | spl261_406),
% 0.72/0.40 inference(avatar_contradiction_clause,[],[f4457])).
% 0.72/0.40 cnf(s67, plain, ~spl261_24 | spl261_104, inference(sat_conversion,[],[f1775])).
% 0.72/0.40 cnf(s124, plain, spl261_168, inference(sat_conversion,[],[f2068])).
% 0.72/0.40 cnf(s175, plain, ~spl261_67 | spl261_154, inference(sat_conversion,[],[f2302])).
% 0.72/0.40 cnf(s199, plain, ~spl261_24 | spl261_245, inference(sat_conversion,[],[f2419])).
% 0.72/0.40 cnf(s246, plain, spl261_67, inference(sat_conversion,[],[f2610])).
% 0.72/0.40 cnf(s304, plain, spl261_24, inference(sat_conversion,[],[f2823])).
% 0.72/0.40 cnf(s407, plain, ~spl261_406, inference(sat_conversion,[],[f3197])).
% 0.72/0.40 cnf(s501, plain, ~spl261_104 | ~spl261_154 | ~spl261_168 | ~spl261_245 | spl261_406, inference(sat_conversion,[],[f4458])).
% 0.72/0.40 cnf(s556, plain, spl261_245, inference(rat,[],[s199,s304])).
% 0.72/0.40 cnf(s569, plain, spl261_154, inference(rat,[],[s175,s246])).
% 0.72/0.40 cnf(s581, plain, ~spl261_104, inference(rat,[],[s501,s407,s556,s569,s124])).
% 0.72/0.40 cnf(s602, plain, $false, inference(rat,[],[s67,s581,s304])).
% 0.72/0.40 thf(f4459,plain,(
% 0.72/0.40 $false),
% 0.72/0.40 inference(avatar_sat_refutation,[],[s602])).
% 0.72/0.40 % SZS output end Proof for theBenchmark
% 0.72/0.40 % (391328)------------------------------
% 0.72/0.40 % (391328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.40 % (391328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.40 % (391328)CaDiCaL version: 2.1.3
% 0.72/0.40 % (391328)Termination reason: Refutation
% 0.72/0.40 % (391328)Time elapsed: 0.102 s
% 0.72/0.40 % (391328)Peak memory usage: 16 MB
% 0.72/0.40 % (391328)Instructions burned: 188 (million)
% 0.72/0.40 % (391315)Success in time 0.133 s
% 0.72/0.40 % Vampire exiting
%------------------------------------------------------------------------------