%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU726^2 : 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 : n010.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 08:30:59 AM UTC 2026
% Result : Theorem 0.30s 0.42s
% Output : Refutation 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU726^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n010.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 14:17:34 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running higher-order theorem proving
% 0.25/0.33 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
% 0.30/0.42 % (2922891)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.42 % (2922899)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=1124556293: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)
% 0.30/0.42 % (2922902)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.42 % (2922902)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
% 0.30/0.42 % (2922897)lrs+10_16_si=on:nwc=1.5:random_seed=4221972236:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.42 % (2922896)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2580948796:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.42 % (2922898)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1995000998:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.42 % (2922900)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1905392427:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.42 % (2922901)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=166421600:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.42 % (2922902)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=3089532990:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.42 % (2922898)Instruction limit reached!
% 0.30/0.42 % (2922898)------------------------------
% 0.30/0.42 % (2922898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.42 % (2922898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.42 % (2922898)CaDiCaL version: 2.1.3
% 0.30/0.42 % (2922898)Termination reason: Instruction limit
% 0.30/0.42 % (2922898)Termination phase: Saturation
% 0.30/0.42 % (2922898)Time elapsed: 0.003 s
% 0.30/0.42 % (2922898)Peak memory usage: 11 MB
% 0.30/0.42 % (2922898)Instructions burned: 3 (million)
% 0.30/0.42 % (2922900) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2922891-2922900"...
% 0.30/0.42 % (2922897)Instruction limit reached!
% 0.30/0.42 % (2922897)------------------------------
% 0.30/0.42 % (2922897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.42 % (2922897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.42 % (2922897)CaDiCaL version: 2.1.3
% 0.30/0.42 % (2922897)Termination reason: Instruction limit
% 0.30/0.42 % (2922897)Termination phase: Saturation
% 0.30/0.42 % (2922897)Time elapsed: 0.017 s
% 0.30/0.42 % (2922897)Peak memory usage: 12 MB
% 0.30/0.42 % (2922897)Instructions burned: 18 (million)
% 0.30/0.42 % (2922896) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2922891-2922896"...
% 0.30/0.42 % (2922900)...printing done.
% 0.30/0.42 % (2922900)Refutation found. Thanks to Tanya!
% 0.30/0.42 % SZS status Theorem for theBenchmark
% 0.30/0.42 % SZS output start Proof for theBenchmark
% 0.30/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.30/0.42 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.30/0.42 thf(func_def_1, type, powerset: ($i > $i)).
% 0.30/0.42 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.30/0.42 thf(func_def_3, type, subsetE: $o).
% 0.30/0.42 thf(func_def_5, type, setminus: ($i > $i > $i)).
% 0.30/0.42 thf(func_def_6, type, setminusI: $o).
% 0.30/0.42 thf(func_def_7, type, setminusER: $o).
% 0.30/0.42 thf(func_def_8, type, subsetTI: $o).
% 0.30/0.42 thf(func_def_14, type, sK3: ($i > $i > $i > $i)).
% 0.30/0.42 thf(f1,axiom,(
% 0.30/0.42 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.30/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.30/0.42 thf(f2,axiom,(
% 0.30/0.42 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 0.30/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI)).
% 0.30/0.42 thf(f3,axiom,(
% 0.30/0.42 (setminusER = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.30/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER)).
% 0.30/0.42 thf(f4,axiom,(
% 0.30/0.42 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))) = subsetTI)),
% 0.30/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.30/0.42 thf(f5,conjecture,(
% 0.30/0.42 subsetE => (setminusI => (setminusER => (subsetTI => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) => (subset @ X1 @ X2)))))))),
% 0.30/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT3)).
% 0.30/0.42 thf(f6,negated_conjecture,(
% 0.30/0.42 ~(subsetE => (setminusI => (setminusER => (subsetTI => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) => (subset @ X1 @ X2))))))))),
% 0.30/0.42 inference(negated_conjecture,[status(cth)],[f5])).
% 0.30/0.42 thf(f7,plain,(
% 0.30/0.42 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => ~(in @ X0 @ X1)))),
% 0.30/0.42 inference(rectify,[],[f3])).
% 0.30/0.42 thf(f8,plain,(
% 0.30/0.42 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setminus @ X2 @ X1))) = $true) => ~ ($true = ((in @ X0 @ X1))))),
% 0.30/0.42 inference(fool_elimination,[],[f7])).
% 0.30/0.42 thf(f9,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (subset @ X0 @ X2)))) = subsetTI)),
% 0.30/0.42 inference(rectify,[],[f4])).
% 0.30/0.42 thf(f10,plain,(
% 0.30/0.42 (subsetTI = $true) <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => (((subset @ X0 @ X2)) = $true))))),
% 0.30/0.42 inference(fool_elimination,[],[f9])).
% 0.30/0.42 thf(f11,plain,(
% 0.30/0.42 ~(subsetE => (setminusI => (setminusER => (subsetTI => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) => (subset @ X0 @ X2))))))))),
% 0.30/0.42 inference(rectify,[],[f6])).
% 0.30/0.42 thf(f12,plain,(
% 0.30/0.42 ~((subsetE = $true) => ((setminusI = $true) => ((setminusER = $true) => ((subsetTI = $true) => ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ((((subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) = $true) => (((subset @ X0 @ X2)) = $true))))))))),
% 0.30/0.42 inference(fool_elimination,[],[f11])).
% 0.30/0.42 thf(f13,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 0.30/0.42 inference(rectify,[],[f1])).
% 0.30/0.42 thf(f14,plain,(
% 0.30/0.42 (subsetE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true = ((subset @ X1 @ X0))) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)))),
% 0.30/0.42 inference(fool_elimination,[],[f13])).
% 0.30/0.42 thf(f15,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (setminus @ X1 @ X2)))) = setminusI)),
% 0.30/0.42 inference(rectify,[],[f2])).
% 0.30/0.42 thf(f16,plain,(
% 0.30/0.42 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) => (~ (((in @ X0 @ X2)) = $true) => (((in @ X0 @ (setminus @ X1 @ X2))) = $true))) <=> (setminusI = $true)),
% 0.30/0.42 inference(fool_elimination,[],[f15])).
% 0.30/0.42 thf(f17,plain,(
% 0.30/0.42 ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (setminus @ X2 @ X1))) = $true) => ($true != ((in @ X0 @ X1)))) <=> (setminusER = $true)),
% 0.30/0.42 inference(flattening,[],[f8])).
% 0.30/0.42 thf(f18,plain,(
% 0.30/0.42 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true = ((in @ X0 @ X1))) => ((((in @ X0 @ X2)) != $true) => (((in @ X0 @ (setminus @ X1 @ X2))) = $true)))),
% 0.30/0.42 inference(flattening,[],[f16])).
% 0.30/0.42 thf(f19,plain,(
% 0.30/0.42 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((((in @ X0 @ (setminus @ X1 @ X2))) = $true) | (((in @ X0 @ X2)) = $true)) | ($true != ((in @ X0 @ X1))))),
% 0.30/0.42 inference(ennf_transformation,[],[f18])).
% 0.30/0.42 thf(f20,plain,(
% 0.30/0.42 ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2)) = $true) | ($true != ((in @ X0 @ X1))) | (((in @ X0 @ (setminus @ X1 @ X2))) = $true)) <=> (setminusI = $true)),
% 0.30/0.42 inference(flattening,[],[f19])).
% 0.30/0.42 thf(f21,plain,(
% 0.30/0.42 (subsetE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | ($true != ((subset @ X1 @ X0))))),
% 0.30/0.42 inference(ennf_transformation,[],[f14])).
% 0.30/0.42 thf(f22,plain,(
% 0.30/0.42 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | ($true != ((subset @ X1 @ X0)))) <=> (subsetE = $true)),
% 0.30/0.42 inference(flattening,[],[f21])).
% 0.30/0.42 thf(f23,plain,(
% 0.30/0.42 (subsetTI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((((subset @ X0 @ X2)) = $true) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1)))))),
% 0.30/0.42 inference(ennf_transformation,[],[f10])).
% 0.30/0.42 thf(f24,plain,(
% 0.30/0.42 ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X2)) = $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) = $true)))) <=> (subsetTI = $true)),
% 0.30/0.42 inference(flattening,[],[f23])).
% 0.30/0.42 thf(f25,plain,(
% 0.30/0.42 (((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (((((subset @ X0 @ X2)) != $true) & (((subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) = $true)) & (((in @ X2 @ (powerset @ X1))) = $true)) & ($true = ((in @ X0 @ (powerset @ X1))))) & (subsetTI = $true)) & (setminusER = $true)) & (setminusI = $true)) & (subsetE = $true)),
% 0.30/0.42 inference(ennf_transformation,[],[f12])).
% 0.30/0.42 thf(f26,plain,(
% 0.30/0.42 ? [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & (((subset @ X0 @ X2)) != $true) & (((subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) = $true))) & (subsetE = $true) & (setminusI = $true) & (subsetTI = $true) & (setminusER = $true)),
% 0.30/0.42 inference(flattening,[],[f25])).
% 0.30/0.42 thf(f27,plain,(
% 0.30/0.42 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ (setminus @ X2 @ X1))) != $true)) <=> (setminusER = $true)),
% 0.30/0.42 inference(ennf_transformation,[],[f17])).
% 0.30/0.42 thf(f28,plain,(
% 0.30/0.42 (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2)) = $true) | ($true != ((in @ X0 @ X1))) | (((in @ X0 @ (setminus @ X1 @ X2))) = $true)) | (setminusI != $true)) & ((setminusI = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2)) != $true) & ($true = ((in @ X0 @ X1))) & (((in @ X0 @ (setminus @ X1 @ X2))) != $true)))),
% 0.30/0.42 inference(nnf_transformation,[],[f20])).
% 0.30/0.42 thf(f29,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | ($true = ((in @ X2 @ (setminus @ X1 @ X0))))) | (setminusI != $true)) & ((setminusI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ X3))) & (((in @ X5 @ X4)) = $true) & (((in @ X5 @ (setminus @ X4 @ X3))) != $true)))),
% 0.30/0.42 inference(rectify,[],[f28])).
% 0.30/0.42 thf(f30,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | ($true = ((in @ X2 @ (setminus @ X1 @ X0))))) | (setminusI != $true)) & ((setminusI = $true) | (($true != ((in @ sK2 @ sK0))) & (((in @ sK2 @ sK1)) = $true) & (((in @ sK2 @ (setminus @ sK1 @ sK0))) != $true)))),
% 0.30/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f29])).
% 0.30/0.42 thf(f31,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X2)) = $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) = $true)))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & (((subset @ X0 @ X2)) != $true) & ! [X3 : $i] : ((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) != $true)))))),
% 0.30/0.42 inference(nnf_transformation,[],[f24])).
% 0.30/0.42 thf(f32,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X2)) = $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) = $true)))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X4 : $i,X5 : $i] : ((((in @ X4 @ (powerset @ X5))) = $true) & ? [X6 : $i] : ((((in @ X6 @ (powerset @ X5))) = $true) & (((subset @ X4 @ X6)) != $true) & ! [X7 : $i] : (($true = ((in @ X7 @ X6))) | ($true != ((in @ X7 @ X5))) | (((in @ X7 @ X4)) != $true)))))),
% 0.30/0.42 inference(rectify,[],[f31])).
% 0.30/0.42 thf(f33,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X2)) = $true) | ((((in @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true) & (((in @ (sK3 @ X2 @ X1 @ X0) @ X1)) = $true) & (((in @ (sK3 @ X2 @ X1 @ X0) @ X0)) = $true)))) | (subsetTI != $true)) & ((subsetTI = $true) | (($true = ((in @ sK4 @ (powerset @ sK5)))) & (($true = ((in @ sK6 @ (powerset @ sK5)))) & ($true != ((subset @ sK4 @ sK6))) & ! [X7 : $i] : ((((in @ X7 @ sK6)) = $true) | ($true != ((in @ X7 @ sK5))) | (((in @ X7 @ sK4)) != $true)))))),
% 0.30/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK4,sK5,sK6]),skolemize(X3,sK3 @ X2 @ X1 @ X0),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f32])).
% 0.30/0.42 thf(f34,plain,(
% 0.30/0.42 ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & (((subset @ X1 @ X2)) != $true) & (((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) = $true))) & (subsetE = $true) & (setminusI = $true) & (subsetTI = $true) & (setminusER = $true)),
% 0.30/0.42 inference(rectify,[],[f26])).
% 0.30/0.42 thf(f35,plain,(
% 0.30/0.42 ((((in @ sK8 @ (powerset @ sK7))) = $true) & ((((in @ sK9 @ (powerset @ sK7))) = $true) & ($true != ((subset @ sK8 @ sK9))) & (((subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) = $true))) & (subsetE = $true) & (setminusI = $true) & (subsetTI = $true) & (setminusER = $true)),
% 0.30/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f34])).
% 0.30/0.42 thf(f36,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | ($true != ((subset @ X1 @ X0)))) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true) & ($true = ((subset @ X1 @ X0)))))),
% 0.30/0.42 inference(nnf_transformation,[],[f22])).
% 0.30/0.42 thf(f37,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | ($true != ((subset @ X1 @ X0)))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ X3))) & (((in @ X5 @ X4)) = $true) & ($true = ((subset @ X4 @ X3)))))),
% 0.30/0.42 inference(rectify,[],[f36])).
% 0.30/0.42 thf(f38,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | ($true != ((subset @ X1 @ X0)))) | (subsetE != $true)) & ((subsetE = $true) | (($true != ((in @ sK12 @ sK10))) & ($true = ((in @ sK12 @ sK11))) & (((subset @ sK11 @ sK10)) = $true)))),
% 0.30/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f37])).
% 0.30/0.42 thf(f39,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ (setminus @ X2 @ X1))) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) & (((in @ X0 @ (setminus @ X2 @ X1))) = $true)))),
% 0.30/0.42 inference(nnf_transformation,[],[f27])).
% 0.30/0.42 thf(f40,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ (setminus @ X2 @ X1))) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X3 @ X4))) & (((in @ X3 @ (setminus @ X5 @ X4))) = $true)))),
% 0.30/0.42 inference(rectify,[],[f39])).
% 0.30/0.42 thf(f41,plain,(
% 0.30/0.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ (setminus @ X2 @ X1))) != $true)) | (setminusER != $true)) & ((setminusER = $true) | (($true = ((in @ sK13 @ sK14))) & ($true = ((in @ sK13 @ (setminus @ sK15 @ sK14))))))),
% 0.30/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X3,sK13),skolemize(X4,sK14),skolemize(X5,sK15)],[f40])).
% 0.30/0.42 thf(f45,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X2 @ (setminus @ X1 @ X0)))) | (setminusI != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) )),
% 0.30/0.42 inference(cnf_transformation,[],[f30])).
% 0.30/0.42 thf(f50,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((subsetTI != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((subset @ X0 @ X2)) = $true) | (((in @ (sK3 @ X2 @ X1 @ X0) @ X0)) = $true)) )),
% 0.30/0.42 inference(cnf_transformation,[],[f33])).
% 0.30/0.42 thf(f51,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK3 @ X2 @ X1 @ X0) @ X1)) = $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true) | (subsetTI != $true) | (((subset @ X0 @ X2)) = $true)) )),
% 0.30/0.42 inference(cnf_transformation,[],[f33])).
% 0.30/0.42 thf(f52,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X2)) = $true) | (subsetTI != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true)) )),
% 0.30/0.42 inference(cnf_transformation,[],[f33])).
% 0.30/0.42 thf(f53,plain,(
% 0.30/0.42 (setminusER = $true)),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f54,plain,(
% 0.30/0.42 (subsetTI = $true)),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f55,plain,(
% 0.30/0.42 (setminusI = $true)),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f56,plain,(
% 0.30/0.42 (subsetE = $true)),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f57,plain,(
% 0.30/0.42 (((subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) = $true)),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f58,plain,(
% 0.30/0.42 ($true != ((subset @ sK8 @ sK9)))),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f59,plain,(
% 0.30/0.42 (((in @ sK9 @ (powerset @ sK7))) = $true)),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f60,plain,(
% 0.30/0.42 (((in @ sK8 @ (powerset @ sK7))) = $true)),
% 0.30/0.42 inference(cnf_transformation,[],[f35])).
% 0.30/0.42 thf(f64,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | ($true != ((subset @ X1 @ X0))) | (subsetE != $true)) )),
% 0.30/0.42 inference(cnf_transformation,[],[f38])).
% 0.30/0.42 thf(f67,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setminus @ X2 @ X1))) != $true) | ($true != ((in @ X0 @ X1))) | (setminusER != $true)) )),
% 0.30/0.42 inference(cnf_transformation,[],[f41])).
% 0.30/0.42 thf(f73,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setminus @ X2 @ X1))) != $true) | ($true != ((in @ X0 @ X1)))) )),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f67,f53])).
% 0.30/0.42 thf(f74,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) )),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f64,f56])).
% 0.30/0.42 thf(f75,plain,(
% 0.30/0.42 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ X0 @ (setminus @ sK7 @ sK8)))) | (((in @ X0 @ (setminus @ sK7 @ sK9))) != $true)) )),
% 0.30/0.42 inference(superposition,[],[f74,f57])).
% 0.30/0.42 thf(f76,plain,(
% 0.30/0.42 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setminus @ sK7 @ sK8)))) | (((in @ X0 @ (setminus @ sK7 @ sK9))) != $true)) )),
% 0.30/0.42 inference(trivial_inequality_removal,[],[f75])).
% 0.30/0.42 thf(f77,plain,(
% 0.30/0.42 ( ! [X0 : $i] : ((((in @ X0 @ (setminus @ sK7 @ sK9))) != $true) | ($true != ((in @ X0 @ sK8))) | ($true != $true)) )),
% 0.30/0.42 inference(superposition,[],[f73,f76])).
% 0.30/0.42 thf(f78,plain,(
% 0.30/0.42 ( ! [X0 : $i] : ((((in @ X0 @ (setminus @ sK7 @ sK9))) != $true) | ($true != ((in @ X0 @ sK8)))) )),
% 0.30/0.42 inference(trivial_inequality_removal,[],[f77])).
% 0.30/0.42 thf(f79,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X2 @ (setminus @ X1 @ X0)))) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) )),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f45,f55])).
% 0.30/0.42 thf(f81,plain,(
% 0.30/0.42 ( ! [X0 : $i] : ((((in @ X0 @ sK9)) = $true) | ($true != ((in @ X0 @ sK7))) | ($true != $true) | ($true != ((in @ X0 @ sK8)))) )),
% 0.30/0.42 inference(superposition,[],[f78,f79])).
% 0.30/0.42 thf(f82,plain,(
% 0.30/0.42 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK8))) | (((in @ X0 @ sK9)) = $true) | ($true != ((in @ X0 @ sK7)))) )),
% 0.30/0.42 inference(trivial_inequality_removal,[],[f81])).
% 0.30/0.42 thf(f83,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK3 @ X2 @ X1 @ X0) @ X0)) = $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((subset @ X0 @ X2)) = $true)) )),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f50,f54])).
% 0.30/0.42 thf(f86,plain,(
% 0.30/0.42 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK3 @ X0 @ X1 @ sK8) @ sK9)) = $true) | ($true != $true) | ($true != ((in @ sK8 @ (powerset @ X1)))) | ($true != ((in @ (sK3 @ X0 @ X1 @ sK8) @ sK7))) | (((subset @ sK8 @ X0)) = $true) | ($true != ((in @ X0 @ (powerset @ X1))))) )),
% 0.30/0.42 inference(superposition,[],[f82,f83])).
% 0.30/0.42 thf(f88,plain,(
% 0.30/0.42 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK3 @ X0 @ X1 @ sK8) @ sK9)) = $true) | ($true != ((in @ (sK3 @ X0 @ X1 @ sK8) @ sK7))) | (((subset @ sK8 @ X0)) = $true) | ($true != ((in @ sK8 @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) )),
% 0.30/0.42 inference(trivial_inequality_removal,[],[f86])).
% 0.30/0.42 thf(f96,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK3 @ X2 @ X1 @ X0) @ X1)) = $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X2)) = $true) | ($true != ((in @ X0 @ (powerset @ X1))))) )),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f51,f54])).
% 0.30/0.42 thf(f112,plain,(
% 0.30/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X2)) = $true)) )),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f52,f54])).
% 0.30/0.42 thf(f117,plain,(
% 0.30/0.42 ( ! [X0 : $i] : (($true != ((in @ sK9 @ (powerset @ X0)))) | ($true != ((in @ sK9 @ (powerset @ X0)))) | ($true = ((subset @ sK8 @ sK9))) | ($true != ((in @ (sK3 @ sK9 @ X0 @ sK8) @ sK7))) | ($true != $true) | (((in @ sK8 @ (powerset @ X0))) != $true) | ($true = ((subset @ sK8 @ sK9))) | (((in @ sK8 @ (powerset @ X0))) != $true)) )),
% 0.30/0.42 inference(superposition,[],[f112,f88])).
% 0.30/0.42 thf(f118,plain,(
% 0.30/0.42 ( ! [X0 : $i] : (($true != ((in @ (sK3 @ sK9 @ X0 @ sK8) @ sK7))) | ($true = ((subset @ sK8 @ sK9))) | ($true != ((in @ sK9 @ (powerset @ X0)))) | ($true != $true) | (((in @ sK8 @ (powerset @ X0))) != $true)) )),
% 0.30/0.42 inference(duplicate_literal_removal,[],[f117])).
% 0.30/0.42 thf(f119,plain,(
% 0.30/0.42 ( ! [X0 : $i] : (($true != ((in @ (sK3 @ sK9 @ X0 @ sK8) @ sK7))) | ($true != ((in @ sK9 @ (powerset @ X0)))) | ($true = ((subset @ sK8 @ sK9))) | (((in @ sK8 @ (powerset @ X0))) != $true)) )),
% 0.30/0.42 inference(trivial_inequality_removal,[],[f118])).
% 0.30/0.42 thf(f126,plain,(
% 0.30/0.42 ( ! [X0 : $i] : (($true != ((in @ (sK3 @ sK9 @ X0 @ sK8) @ sK7))) | ($true != ((in @ sK9 @ (powerset @ X0)))) | (((in @ sK8 @ (powerset @ X0))) != $true)) )),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f119,f58])).
% 0.30/0.42 thf(f137,plain,(
% 0.30/0.42 ($true = ((subset @ sK8 @ sK9))) | (((in @ sK8 @ (powerset @ sK7))) != $true) | ($true != $true) | (((in @ sK9 @ (powerset @ sK7))) != $true) | (((in @ sK8 @ (powerset @ sK7))) != $true) | (((in @ sK9 @ (powerset @ sK7))) != $true)),
% 0.30/0.42 inference(superposition,[],[f126,f96])).
% 0.30/0.42 thf(f138,plain,(
% 0.30/0.42 (((in @ sK9 @ (powerset @ sK7))) != $true) | ($true = ((subset @ sK8 @ sK9))) | (((in @ sK8 @ (powerset @ sK7))) != $true) | ($true != $true)),
% 0.30/0.42 inference(duplicate_literal_removal,[],[f137])).
% 0.30/0.42 thf(f139,plain,(
% 0.30/0.42 ($true = ((subset @ sK8 @ sK9))) | (((in @ sK9 @ (powerset @ sK7))) != $true) | (((in @ sK8 @ (powerset @ sK7))) != $true)),
% 0.30/0.42 inference(trivial_inequality_removal,[],[f138])).
% 0.30/0.42 thf(f140,plain,(
% 0.30/0.42 (((in @ sK8 @ (powerset @ sK7))) != $true) | (((in @ sK9 @ (powerset @ sK7))) != $true)),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f139,f58])).
% 0.30/0.42 thf(f141,plain,(
% 0.30/0.42 (((in @ sK9 @ (powerset @ sK7))) != $true)),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f140,f60])).
% 0.30/0.42 thf(f142,plain,(
% 0.30/0.42 $false),
% 0.30/0.42 inference(forward_subsumption_resolution,[],[f141,f59])).
% 0.30/0.42 % SZS output end Proof for theBenchmark
% 0.30/0.42 % (2922900)------------------------------
% 0.30/0.42 % (2922900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.42 % (2922900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.42 % (2922900)CaDiCaL version: 2.1.3
% 0.30/0.42 % (2922900)Termination reason: Refutation
% 0.30/0.42 % (2922900)Time elapsed: 0.020 s
% 0.30/0.42 % (2922900)Peak memory usage: 12 MB
% 0.30/0.42 % (2922900)Instructions burned: 21 (million)
% 0.30/0.42 % (2922891)Success in time 0.081 s
% 0.30/0.42 % Vampire exiting
%------------------------------------------------------------------------------