%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU564^1 : 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 : n018.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 0.85s 0.40s
% Output : Refutation 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU564^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n018.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:52:41 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.23 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
% 0.23/0.37 % (104803)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.37 % (104810)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1897995088:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.37 % (104810)Instruction limit reached!
% 0.23/0.37 % (104810)------------------------------
% 0.23/0.37 % (104810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (104810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (104810)CaDiCaL version: 2.1.3
% 0.23/0.37 % (104810)Termination reason: Instruction limit
% 0.23/0.37 % (104810)Termination phase: shuffling
% 0.23/0.37 % (104810)Time elapsed: 0.001 s
% 0.23/0.37 % (104810)Peak memory usage: 10 MB
% 0.23/0.37 % (104810)Instructions burned: 4 (million)
% 0.23/0.37 % (104809)lrs+10_16_si=on:nwc=1.5:random_seed=41569705:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.37 % (104808)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3458493178:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.37 % (104814)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.37 % (104814)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
% 0.23/0.37 % (104811)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=3401419803: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)
% 0.23/0.37 % (104812)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2824774994:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.37 % (104816)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2691357145:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.37 % (104814)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=1352141581:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.37 % (104816)Instruction limit reached!
% 0.23/0.37 % (104816)------------------------------
% 0.23/0.37 % (104816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (104816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (104816)CaDiCaL version: 2.1.3
% 0.23/0.37 % (104816)Termination reason: Instruction limit
% 0.23/0.37 % (104816)Termination phase: shuffling
% 0.23/0.37 % (104816)Time elapsed: 0.001 s
% 0.23/0.37 % (104816)Peak memory usage: 10 MB
% 0.23/0.37 % (104816)Instructions burned: 4 (million)
% 0.23/0.37 % (104809)Instruction limit reached!
% 0.23/0.37 % (104809)------------------------------
% 0.23/0.37 % (104809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (104809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (104809)CaDiCaL version: 2.1.3
% 0.23/0.37 % (104809)Termination reason: Instruction limit
% 0.23/0.37 % (104809)Termination phase: Property scanning
% 0.23/0.37 % (104809)Time elapsed: 0.008 s
% 0.23/0.37 % (104809)Peak memory usage: 10 MB
% 0.23/0.37 % (104809)Instructions burned: 19 (million)
% 0.23/0.37 % (104813)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4251696451:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.37 % (104823)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3026142942:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.37 % (104812)Instruction limit reached!
% 0.23/0.37 % (104812)------------------------------
% 0.23/0.37 % (104812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (104812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (104812)CaDiCaL version: 2.1.3
% 0.23/0.37 % (104812)Termination reason: Instruction limit
% 0.23/0.37 % (104812)Termination phase: Property scanning
% 0.23/0.37 % (104812)Time elapsed: 0.017 s
% 0.23/0.37 % (104812)Peak memory usage: 11 MB
% 0.23/0.37 % (104812)Instructions burned: 24 (million)
% 0.23/0.37 % (104823)Instruction limit reached!
% 0.85/0.40 % (104823)------------------------------
% 0.85/0.40 % (104823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104823)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104823)Termination reason: Instruction limit
% 0.85/0.40 % (104823)Termination phase: shuffling
% 0.85/0.40 % (104823)Time elapsed: 0.002 s
% 0.85/0.40 % (104823)Peak memory usage: 10 MB
% 0.85/0.40 % (104823)Instructions burned: 8 (million)
% 0.85/0.40 % (104824)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.85/0.40 % (104824)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3153447375:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.85/0.40 % (104827)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2271030294:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.85/0.40 % (104827)Instruction limit reached!
% 0.85/0.40 % (104827)------------------------------
% 0.85/0.40 % (104827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104827)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104827)Termination reason: Instruction limit
% 0.85/0.40 % (104827)Termination phase: Property scanning
% 0.85/0.40 % (104827)Time elapsed: 0.003 s
% 0.85/0.40 % (104827)Peak memory usage: 10 MB
% 0.85/0.40 % (104827)Instructions burned: 13 (million)
% 0.85/0.40 % (104828)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
% 0.85/0.40 % (104828)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.85/0.40 % (104824)Instruction limit reached!
% 0.85/0.40 % (104824)------------------------------
% 0.85/0.40 % (104824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104824)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104824)Termination reason: Instruction limit
% 0.85/0.40 % (104824)Termination phase: Property scanning
% 0.85/0.40 % (104824)Time elapsed: 0.007 s
% 0.85/0.40 % (104824)Peak memory usage: 10 MB
% 0.85/0.40 % (104824)Instructions burned: 17 (million)
% 0.85/0.40 % (104828)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1920542786:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.85/0.40 % (104808)Instruction limit reached!
% 0.85/0.40 % (104808)------------------------------
% 0.85/0.40 % (104808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104808)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104808)Termination reason: Instruction limit
% 0.85/0.40 % (104808)Termination phase: Saturation
% 0.85/0.40 % (104808)Time elapsed: 0.042 s
% 0.85/0.40 % (104808)Peak memory usage: 13 MB
% 0.85/0.40 % (104808)Instructions burned: 88 (million)
% 0.85/0.40 % (104828)Instruction limit reached!
% 0.85/0.40 % (104828)------------------------------
% 0.85/0.40 % (104828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104828)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104828)Termination reason: Instruction limit
% 0.85/0.40 % (104828)Termination phase: Function definition elimination
% 0.85/0.40 % (104828)Time elapsed: 0.011 s
% 0.85/0.40 % (104828)Peak memory usage: 10 MB
% 0.85/0.40 % (104828)Instructions burned: 28 (million)
% 0.85/0.40 % (104831)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=1298141347:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.85/0.40 % (104832)lrs+10_1_si=on:cs=on:random_seed=4177294800:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.85/0.40 % (104834)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.85/0.40 % (104832)Instruction limit reached!
% 0.85/0.40 % (104832)------------------------------
% 0.85/0.40 % (104832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104832)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104832)Termination reason: Instruction limit
% 0.85/0.40 % (104832)Termination phase: shuffling
% 0.85/0.40 % (104832)Time elapsed: 0.004 s
% 0.85/0.40 % (104832)Peak memory usage: 10 MB
% 0.85/0.40 % (104832)Instructions burned: 9 (million)
% 0.85/0.40 % (104834)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=32727729:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.85/0.40 % (104834)Instruction limit reached!
% 0.85/0.40 % (104834)------------------------------
% 0.85/0.40 % (104834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104834)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104834)Termination reason: Instruction limit
% 0.85/0.40 % (104834)Termination phase: shuffling
% 0.85/0.40 % (104834)Time elapsed: 0.003 s
% 0.85/0.40 % (104834)Peak memory usage: 10 MB
% 0.85/0.40 % (104834)Instructions burned: 7 (million)
% 0.85/0.40 % (104835)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=845394227:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.85/0.40 % (104838)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1643004393:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.85/0.40 % (104814)Instruction limit reached!
% 0.85/0.40 % (104814)------------------------------
% 0.85/0.40 % (104814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104814)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104814)Termination reason: Instruction limit
% 0.85/0.40 % (104814)Termination phase: Saturation
% 0.85/0.40 % (104814)Time elapsed: 0.066 s
% 0.85/0.40 % (104814)Peak memory usage: 14 MB
% 0.85/0.40 % (104814)Instructions burned: 159 (million)
% 0.85/0.40 % (104813)Instruction limit reached!
% 0.85/0.40 % (104813)------------------------------
% 0.85/0.40 % (104813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104813)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104813)Termination reason: Instruction limit
% 0.85/0.40 % (104813)Termination phase: Saturation
% 0.85/0.40 % (104813)Time elapsed: 0.066 s
% 0.85/0.40 % (104813)Peak memory usage: 13 MB
% 0.85/0.40 % (104813)Instructions burned: 78 (million)
% 0.85/0.40 % (104843)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1650234297:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.85/0.40 % (104840)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2284833125:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.85/0.40 % (104835)Instruction limit reached!
% 0.85/0.40 % (104835)------------------------------
% 0.85/0.40 % (104835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104835)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104835)Termination reason: Instruction limit
% 0.85/0.40 % (104835)Termination phase: Property scanning
% 0.85/0.40 % (104835)Time elapsed: 0.018 s
% 0.85/0.40 % (104835)Peak memory usage: 11 MB
% 0.85/0.40 % (104835)Instructions burned: 40 (million)
% 0.85/0.40 % (104843)Instruction limit reached!
% 0.85/0.40 % (104843)------------------------------
% 0.85/0.40 % (104843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104843)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104843)Termination reason: Instruction limit
% 0.85/0.40 % (104843)Termination phase: Property scanning
% 0.85/0.40 % (104843)Time elapsed: 0.004 s
% 0.85/0.40 % (104843)Peak memory usage: 10 MB
% 0.85/0.40 % (104843)Instructions burned: 17 (million)
% 0.85/0.40 % (104831)Instruction limit reached!
% 0.85/0.40 % (104831)------------------------------
% 0.85/0.40 % (104831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104831)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104831)Termination reason: Instruction limit
% 0.85/0.40 % (104831)Termination phase: Saturation
% 0.85/0.40 % (104831)Time elapsed: 0.037 s
% 0.85/0.40 % (104831)Peak memory usage: 13 MB
% 0.85/0.40 % (104831)Instructions burned: 87 (million)
% 0.85/0.40 % (104840)Instruction limit reached!
% 0.85/0.40 % (104840)------------------------------
% 0.85/0.40 % (104840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104840)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104840)Termination reason: Instruction limit
% 0.85/0.40 % (104840)Termination phase: Preprocessing 3
% 0.85/0.40 % (104840)Time elapsed: 0.012 s
% 0.85/0.40 % (104840)Peak memory usage: 11 MB
% 0.85/0.40 % (104840)Instructions burned: 25 (million)
% 0.85/0.40 % (104848)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3569218144: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)
% 0.85/0.40 % (104848)Instruction limit reached!
% 0.85/0.40 % (104848)------------------------------
% 0.85/0.40 % (104848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104848)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104848)Termination reason: Instruction limit
% 0.85/0.40 % (104848)Termination phase: shuffling
% 0.85/0.40 % (104848)Time elapsed: 0.001 s
% 0.85/0.40 % (104848)Peak memory usage: 10 MB
% 0.85/0.40 % (104848)Instructions burned: 4 (million)
% 0.85/0.40 % (104847)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2397886271:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.85/0.40 % (104838) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-104803-104838"...
% 0.85/0.40 % (104852)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1723619866:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.85/0.40 % (104847)Instruction limit reached!
% 0.85/0.40 % (104847)------------------------------
% 0.85/0.40 % (104847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104847)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104847)Termination reason: Instruction limit
% 0.85/0.40 % (104847)Termination phase: Property scanning
% 0.85/0.40 % (104847)Time elapsed: 0.006 s
% 0.85/0.40 % (104847)Peak memory usage: 10 MB
% 0.85/0.40 % (104847)Instructions burned: 14 (million)
% 0.85/0.40 % (104849)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3013630573:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.85/0.40 % (104838)...printing done.
% 0.85/0.40 % (104838)Refutation found. Thanks to Tanya!
% 0.85/0.40 % SZS status Theorem for theBenchmark
% 0.85/0.40 % SZS output start Proof for theBenchmark
% 0.85/0.40 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.85/0.40 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.85/0.40 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.85/0.40 thf(func_def_3, type, setextAx: $o).
% 0.85/0.40 thf(func_def_5, type, emptysetAx: $o).
% 0.85/0.40 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_7, type, setadjoinAx: $o).
% 0.85/0.40 thf(func_def_8, type, powerset: ($i > $i)).
% 0.85/0.40 thf(func_def_9, type, powersetAx: $o).
% 0.85/0.40 thf(func_def_10, type, setunion: ($i > $i)).
% 0.85/0.40 thf(func_def_11, type, setunionAx: $o).
% 0.85/0.40 thf(func_def_13, type, omega0Ax: $o).
% 0.85/0.40 thf(func_def_14, type, omegaSAx: $o).
% 0.85/0.40 thf(func_def_15, type, omegaIndAx: $o).
% 0.85/0.40 thf(func_def_16, type, replAx: $o).
% 0.85/0.40 thf(func_def_17, type, foundationAx: $o).
% 0.85/0.40 thf(func_def_18, type, wellorderingAx: $o).
% 0.85/0.40 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.85/0.40 thf(func_def_20, type, descrp: $o).
% 0.85/0.40 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_22, type, dsetconstrI: $o).
% 0.85/0.40 thf(func_def_23, type, dsetconstrEL: $o).
% 0.85/0.40 thf(func_def_24, type, dsetconstrER: $o).
% 0.85/0.40 thf(func_def_25, type, exuE1: $o).
% 0.85/0.40 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.85/0.40 thf(func_def_27, type, prop2setE: $o).
% 0.85/0.40 thf(func_def_28, type, emptysetE: $o).
% 0.85/0.40 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.85/0.40 thf(func_def_30, type, notinemptyset: $o).
% 0.85/0.40 thf(func_def_31, type, exuE3e: $o).
% 0.85/0.40 thf(func_def_32, type, setext: $o).
% 0.85/0.40 thf(func_def_33, type, emptyI: $o).
% 0.85/0.40 thf(func_def_34, type, noeltsimpempty: $o).
% 0.85/0.40 thf(func_def_35, type, setbeta: $o).
% 0.85/0.40 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.85/0.40 thf(func_def_37, type, nonemptyE1: $o).
% 0.85/0.40 thf(func_def_38, type, nonemptyI: $o).
% 0.85/0.40 thf(func_def_39, type, nonemptyI1: $o).
% 0.85/0.40 thf(func_def_40, type, setadjoinIL: $o).
% 0.85/0.40 thf(func_def_41, type, emptyinunitempty: $o).
% 0.85/0.40 thf(func_def_42, type, setadjoinIR: $o).
% 0.85/0.40 thf(func_def_43, type, setadjoinE: $o).
% 0.85/0.40 thf(func_def_44, type, setadjoinOr: $o).
% 0.85/0.40 thf(func_def_45, type, setoftrueEq: $o).
% 0.85/0.40 thf(func_def_46, type, powersetI: $o).
% 0.85/0.40 thf(func_def_47, type, emptyinPowerset: $o).
% 0.85/0.40 thf(func_def_48, type, emptyInPowerset: $o).
% 0.85/0.40 thf(func_def_49, type, powersetE: $o).
% 0.85/0.40 thf(func_def_50, type, setunionI: $o).
% 0.85/0.40 thf(func_def_51, type, setunionE: $o).
% 0.85/0.40 thf(func_def_52, type, subPowSU: $o).
% 0.85/0.40 thf(func_def_53, type, exuE2: $o).
% 0.85/0.40 thf(func_def_54, type, nonemptyImpWitness: $o).
% 0.85/0.40 thf(func_def_55, type, uniqinunit: $o).
% 0.85/0.40 thf(func_def_56, type, notinsingleton: $o).
% 0.85/0.40 thf(func_def_57, type, eqinunit: $o).
% 0.85/0.40 thf(func_def_58, type, singletonsswitch: $o).
% 0.85/0.40 thf(func_def_59, type, upairsetE: $o).
% 0.85/0.40 thf(func_def_60, type, upairsetIL: $o).
% 0.85/0.40 thf(func_def_61, type, upairsetIR: $o).
% 0.85/0.40 thf(func_def_62, type, emptyE1: $o).
% 0.85/0.40 thf(func_def_63, type, vacuousDall: $o).
% 0.85/0.40 thf(func_def_64, type, quantDeMorgan1: $o).
% 0.85/0.40 thf(func_def_65, type, quantDeMorgan2: $o).
% 0.85/0.40 thf(func_def_66, type, quantDeMorgan3: $o).
% 0.85/0.40 thf(func_def_67, type, quantDeMorgan4: $o).
% 0.85/0.40 thf(func_def_68, type, prop2setI: $o).
% 0.85/0.40 thf(func_def_69, type, set2prop: ($i > $o)).
% 0.85/0.40 thf(func_def_70, type, prop2set2propI: $o).
% 0.85/0.40 thf(func_def_71, type, notdexE: $o).
% 0.85/0.40 thf(func_def_72, type, notdallE: $o).
% 0.85/0.40 thf(func_def_73, type, exuI1: $o).
% 0.85/0.40 thf(func_def_74, type, exuI3: $o).
% 0.85/0.40 thf(func_def_75, type, exuI2: $o).
% 0.85/0.40 thf(func_def_76, type, inCongP: $o).
% 0.85/0.40 thf(func_def_77, type, in__Cong: $o).
% 0.85/0.40 thf(func_def_78, type, exuE3u: $o).
% 0.85/0.40 thf(func_def_79, type, exu__Cong: $o).
% 0.85/0.40 thf(func_def_80, type, emptyset__Cong: $o).
% 0.85/0.40 thf(func_def_81, type, setadjoin__Cong: $o).
% 0.85/0.40 thf(func_def_82, type, powerset__Cong: $o).
% 0.85/0.40 thf(func_def_83, type, setunion__Cong: $o).
% 0.85/0.40 thf(func_def_84, type, omega__Cong: $o).
% 0.85/0.40 thf(func_def_85, type, exuEu: $o).
% 0.85/0.40 thf(func_def_86, type, descr__Cong: $o).
% 0.85/0.40 thf(func_def_87, type, dsetconstr__Cong: $o).
% 0.85/0.40 thf(func_def_88, type, subset: ($i > $i > $o)).
% 0.85/0.40 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 0.85/0.40 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 0.85/0.40 thf(func_def_91, type, subsetI1: $o).
% 0.85/0.40 thf(func_def_92, type, eqimpsubset2: $o).
% 0.85/0.40 thf(func_def_93, type, eqimpsubset1: $o).
% 0.85/0.40 thf(func_def_94, type, subsetI2: $o).
% 0.85/0.40 thf(func_def_95, type, emptysetsubset: $o).
% 0.85/0.40 thf(func_def_96, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.85/0.40 thf(func_def_97, type, vIMP: ($o > $o > $o)).
% 0.85/0.40 thf(func_def_98, type, db1: !>[X0: $tType]:(X0)).
% 0.85/0.40 thf(func_def_99, type, db0: !>[X0: $tType]:(X0)).
% 0.85/0.40 thf(func_def_100, type, db2: !>[X0: $tType]:(X0)).
% 0.85/0.40 thf(func_def_101, type, vOR: ($o > $o > $o)).
% 0.85/0.40 thf(func_def_102, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.85/0.40 thf(func_def_103, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.85/0.40 thf(func_def_104, type, vNOT: ($o > $o)).
% 0.85/0.40 thf(func_def_105, type, vIFF: ($o > $o > $o)).
% 0.85/0.40 thf(func_def_106, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.85/0.40 thf(func_def_107, type, vAND: ($o > $o > $o)).
% 0.85/0.40 thf(func_def_108, type, db3: !>[X0: $tType]:(X0)).
% 0.85/0.40 thf(func_def_109, type, db4: !>[X0: $tType]:(X0)).
% 0.85/0.40 thf(func_def_112, type, db5: !>[X0: $tType]:(X0)).
% 0.85/0.40 thf(func_def_116, type, sK3: (($i > $o) > $i)).
% 0.85/0.40 thf(func_def_117, type, sK4: (($i > $o) > $i)).
% 0.85/0.40 thf(func_def_118, type, sK5: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_119, type, sK6: ($i > $i)).
% 0.85/0.40 thf(func_def_120, type, sK7: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_121, type, sK8: ($i > $i)).
% 0.85/0.40 thf(func_def_122, type, sK9: (($i > $o) > $i > ($i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_123, type, sK10: ($i > $i > ($i > $o) > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_124, type, sK11: ($i > $i)).
% 0.85/0.40 thf(func_def_125, type, sK12: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_126, type, sK13: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_127, type, sK14: ($i > $i)).
% 0.85/0.40 thf(func_def_128, type, sK15: (($i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_129, type, sK16: ($i > $o > $i > $i)).
% 0.85/0.40 thf(func_def_130, type, sK17: (($i > $i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_131, type, sK18: (($i > $i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_132, type, sK19: (($i > $i > $o) > $i > $i > $i)).
% 0.85/0.40 thf(func_def_133, type, sK20: (($i > $i > $o) > $i > $i > $i)).
% 0.85/0.40 thf(func_def_134, type, sK21: (($i > $o) > $i)).
% 0.85/0.40 thf(func_def_135, type, sK22: (($i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_136, type, sK23: (($i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_137, type, sK24: ($i > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_138, type, sK25: (($i > $o) > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_139, type, sK26: (($i > $o) > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_140, type, sK27: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_141, type, sK28: (($i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_142, type, sK29: (($i > $o) > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_143, type, sK30: (($i > $o) > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_144, type, sK31: (($i > $o) > $i)).
% 0.85/0.40 thf(func_def_145, type, sK32: ($i > $i)).
% 0.85/0.40 thf(func_def_146, type, sK33: ($i > $i)).
% 0.85/0.40 thf(func_def_147, type, sK34: ($i > ($i > $o) > $i)).
% 0.85/0.40 thf(func_def_148, type, sK35: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_149, type, sK36: (($i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_150, type, sK37: (($i > $o) > $i)).
% 0.85/0.40 thf(func_def_151, type, sK38: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_152, type, sK39: (($i > $o) > $i > $i)).
% 0.85/0.40 thf(func_def_153, type, sK40: ($i > $i)).
% 0.85/0.40 thf(func_def_154, type, sK41: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_155, type, sK42: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_156, type, sK43: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_157, type, sK44: ($i > $i > $i)).
% 0.85/0.40 thf(func_def_158, type, sK45: ($i > $i > $i > $i)).
% 0.85/0.40 thf(func_def_159, type, sK46: ($i > $i > $i)).
% 0.85/0.40 thf(f78,axiom,(
% 0.85/0.40 (subset = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))))),
% 0.85/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset)).
% 0.85/0.40 thf(f84,conjecture,(
% 0.85/0.40 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 => ! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.85/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.85/0.40 thf(f85,negated_conjecture,(
% 0.85/0.40 ~(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 => ! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.85/0.40 inference(negated_conjecture,[status(cth)],[f84])).
% 0.85/0.40 thf(f176,plain,(
% 0.85/0.40 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.85/0.40 inference(rectify,[],[f85])).
% 0.85/0.40 thf(f177,plain,(
% 0.85/0.40 ~((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) => ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((subset @ X2 @ X1))) => (($true = ((in @ X0 @ X2))) => ($true = ((in @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.85/0.40 inference(fool_elimination,[],[f176])).
% 0.85/0.40 thf(f202,plain,(
% 0.85/0.40 (subset = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))))),
% 0.85/0.40 inference(rectify,[],[f78])).
% 0.85/0.40 thf(f203,plain,(
% 0.85/0.40 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 0.85/0.40 inference(fool_elimination,[],[f202])).
% 0.85/0.40 thf(f246,plain,(
% 0.85/0.40 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X1 : $i,X2 : $i,X0 : $i] : ((($true != ((in @ X0 @ X1))) & ($true = ((in @ X0 @ X2)))) & ($true = ((subset @ X2 @ X1)))) & (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)),
% 0.85/0.40 inference(ennf_transformation,[],[f177])).
% 0.85/0.40 thf(f247,plain,(
% 0.85/0.40 (setadjoinE = $true) & (notdallE = $true) & (eqimpsubset1 = $true) & (quantDeMorgan2 = $true) & (subPowSU = $true) & (prop2set2propI = $true) & (eqimpsubset2 = $true) & (powersetE = $true) & (vacuousDall = $true) & (dsetconstrEL = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (inCongP = $true) & (notdexE = $true) & (exuEu = $true) & (upairsetIR = $true) & (omega__Cong = $true) & (in__Cong = $true) & (exuE2 = $true) & (eqinunit = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (powersetI = $true) & (quantDeMorgan1 = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (emptyI = $true) & (wellorderingAx = $true) & (replAx = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) & ($true != ((in @ X0 @ X1))) & ($true = ((subset @ X2 @ X1)))) & (setunionI = $true) & (omegaSAx = $true) & (exuE3e = $true) & (setadjoinIL = $true) & (powerset__Cong = $true) & (emptyset__Cong = $true) & (quantDeMorgan3 = $true) & (noeltsimpempty = $true) & (nonemptyE1 = $true) & (singletonsswitch = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (setoftrueEq = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (emptyE1 = $true) & (exuE3u = $true) & (dsetconstrI = $true) & (setunionE = $true) & (setext = $true) & (foundationAx = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (setunion__Cong = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (emptyinunitempty = $true) & (descr__Cong = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (upairsetIL = $true) & (setadjoin__Cong = $true) & (setadjoinOr = $true) & (powersetAx = $true) & (descrp = $true) & (exuI2 = $true) & (exuI1 = $true) & (setbeta = $true) & (subsetI1 = $true) & (nonemptyImpWitness = $true) & (exu__Cong = $true) & (emptyInPowerset = $true) & (dsetconstr__Cong = $true) & (upairsetE = $true) & (uniqinunit = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (setextAx = $true) & (emptysetE = $true) & (emptysetAx = $true) & (subsetI2 = $true)),
% 0.85/0.40 inference(flattening,[],[f246])).
% 0.85/0.40 thf(f248,plain,(
% 0.85/0.40 (setadjoinE = $true) & (notdallE = $true) & (eqimpsubset1 = $true) & (quantDeMorgan2 = $true) & (subPowSU = $true) & (prop2set2propI = $true) & (eqimpsubset2 = $true) & (powersetE = $true) & (vacuousDall = $true) & (dsetconstrEL = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (inCongP = $true) & (notdexE = $true) & (exuEu = $true) & (upairsetIR = $true) & (omega__Cong = $true) & (in__Cong = $true) & (exuE2 = $true) & (eqinunit = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (powersetI = $true) & (quantDeMorgan1 = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (emptyI = $true) & (wellorderingAx = $true) & (replAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) & ($true != ((in @ X0 @ X2))) & ($true = ((subset @ X1 @ X2)))) & (setunionI = $true) & (omegaSAx = $true) & (exuE3e = $true) & (setadjoinIL = $true) & (powerset__Cong = $true) & (emptyset__Cong = $true) & (quantDeMorgan3 = $true) & (noeltsimpempty = $true) & (nonemptyE1 = $true) & (singletonsswitch = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (setoftrueEq = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (emptyE1 = $true) & (exuE3u = $true) & (dsetconstrI = $true) & (setunionE = $true) & (setext = $true) & (foundationAx = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (setunion__Cong = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (emptyinunitempty = $true) & (descr__Cong = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (upairsetIL = $true) & (setadjoin__Cong = $true) & (setadjoinOr = $true) & (powersetAx = $true) & (descrp = $true) & (exuI2 = $true) & (exuI1 = $true) & (setbeta = $true) & (subsetI1 = $true) & (nonemptyImpWitness = $true) & (exu__Cong = $true) & (emptyInPowerset = $true) & (dsetconstr__Cong = $true) & (upairsetE = $true) & (uniqinunit = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (setextAx = $true) & (emptysetE = $true) & (emptysetAx = $true) & (subsetI2 = $true)),
% 0.85/0.40 inference(rectify,[],[f247])).
% 0.85/0.40 thf(f249,plain,(
% 0.85/0.40 (setadjoinE = $true) & (notdallE = $true) & (eqimpsubset1 = $true) & (quantDeMorgan2 = $true) & (subPowSU = $true) & (prop2set2propI = $true) & (eqimpsubset2 = $true) & (powersetE = $true) & (vacuousDall = $true) & (dsetconstrEL = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (inCongP = $true) & (notdexE = $true) & (exuEu = $true) & (upairsetIR = $true) & (omega__Cong = $true) & (in__Cong = $true) & (exuE2 = $true) & (eqinunit = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (powersetI = $true) & (quantDeMorgan1 = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (emptyI = $true) & (wellorderingAx = $true) & (replAx = $true) & (($true = ((in @ sK0 @ sK1))) & ($true != ((in @ sK0 @ sK2))) & ($true = ((subset @ sK1 @ sK2)))) & (setunionI = $true) & (omegaSAx = $true) & (exuE3e = $true) & (setadjoinIL = $true) & (powerset__Cong = $true) & (emptyset__Cong = $true) & (quantDeMorgan3 = $true) & (noeltsimpempty = $true) & (nonemptyE1 = $true) & (singletonsswitch = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (setoftrueEq = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (emptyE1 = $true) & (exuE3u = $true) & (dsetconstrI = $true) & (setunionE = $true) & (setext = $true) & (foundationAx = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (setunion__Cong = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (emptyinunitempty = $true) & (descr__Cong = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (upairsetIL = $true) & (setadjoin__Cong = $true) & (setadjoinOr = $true) & (powersetAx = $true) & (descrp = $true) & (exuI2 = $true) & (exuI1 = $true) & (setbeta = $true) & (subsetI1 = $true) & (nonemptyImpWitness = $true) & (exu__Cong = $true) & (emptyInPowerset = $true) & (dsetconstr__Cong = $true) & (upairsetE = $true) & (uniqinunit = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (setextAx = $true) & (emptysetE = $true) & (emptysetAx = $true) & (subsetI2 = $true)),
% 0.85/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f248])).
% 0.85/0.40 thf(f305,plain,(
% 0.85/0.40 ($true = ((subset @ sK1 @ sK2)))),
% 0.85/0.40 inference(cnf_transformation,[],[f249])).
% 0.85/0.40 thf(f306,plain,(
% 0.85/0.40 ($true != ((in @ sK0 @ sK2)))),
% 0.85/0.40 inference(cnf_transformation,[],[f249])).
% 0.85/0.40 thf(f307,plain,(
% 0.85/0.40 ($true = ((in @ sK0 @ sK1)))),
% 0.85/0.40 inference(cnf_transformation,[],[f249])).
% 0.85/0.40 thf(f409,plain,(
% 0.85/0.40 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 0.85/0.40 inference(cnf_transformation,[],[f203])).
% 0.85/0.40 thf(f415,definition,(
% 0.85/0.40 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.85/0.40 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.85/0.40 thf(f420,plain,(
% 0.85/0.40 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))) @ sK1 @ sK2)))),
% 0.85/0.40 inference(definition_unfolding,[],[f305,f409])).
% 0.85/0.40 thf(f570,plain,(
% 0.85/0.40 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ sK2))))) = $true)),
% 0.85/0.40 inference(beta-eta_normalization,[],[f420])).
% 0.85/0.40 thf(f571,plain,(
% 0.85/0.40 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ sK2))) @ X1)))) )),
% 0.85/0.40 inference(pi_proxy_clausification,[],[f570])).
% 0.85/0.40 thf(f572,plain,(
% 0.85/0.40 ( ! [X1 : $i] : (($true = (((in @ X1 @ sK1) => (in @ X1 @ sK2))))) )),
% 0.85/0.40 inference(beta-eta_normalization,[],[f571])).
% 0.85/0.40 thf(f573,plain,(
% 0.85/0.40 ( ! [X1 : $i] : ((((in @ X1 @ sK2)) = $true) | (((in @ X1 @ sK1)) = $false)) )),
% 0.85/0.40 inference(imp_proxy_clausification,[],[f572])).
% 0.85/0.40 thf(f1310,plain,(
% 0.85/0.40 (((in @ sK0 @ sK2)) = $false) | ($true != $true)),
% 0.85/0.40 inference(superposition,[],[f306,f415])).
% 0.85/0.40 thf(f1311,plain,(
% 0.85/0.40 (((in @ sK0 @ sK2)) = $false)),
% 0.85/0.40 inference(trivial_inequality_removal,[],[f1310])).
% 0.85/0.40 thf(f1445,plain,(
% 0.85/0.40 ($true = $false) | (((in @ sK0 @ sK1)) = $false)),
% 0.85/0.40 inference(superposition,[],[f573,f1311])).
% 0.85/0.40 thf(f1451,plain,(
% 0.85/0.40 (((in @ sK0 @ sK1)) = $false)),
% 0.85/0.40 inference(trivial_inequality_removal,[],[f1445])).
% 0.85/0.40 thf(f1487,plain,(
% 0.85/0.40 ($true = $false)),
% 0.85/0.40 inference(superposition,[],[f307,f1451])).
% 0.85/0.40 thf(f1488,plain,(
% 0.85/0.40 $false),
% 0.85/0.40 inference(trivial_inequality_removal,[],[f1487])).
% 0.85/0.40 % SZS output end Proof for theBenchmark
% 0.85/0.40 % (104838)------------------------------
% 0.85/0.40 % (104838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.40 % (104838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.40 % (104838)CaDiCaL version: 2.1.3
% 0.85/0.40 % (104838)Termination reason: Refutation
% 0.85/0.40 % (104838)Time elapsed: 0.041 s
% 0.85/0.40 % (104838)Peak memory usage: 13 MB
% 0.85/0.40 % (104838)Instructions burned: 86 (million)
% 0.85/0.40 % (104803)Success in time 0.161 s
% 0.85/0.40 % Vampire exiting
%------------------------------------------------------------------------------