%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU579^2 : 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 : 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 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU579^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:56:50 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.29 % (392182)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (392197)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2564648706:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (392198)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (392198)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
% 0.21/0.29 % (392191)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2338310825:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (392193)lrs+10_16_si=on:nwc=1.5:random_seed=3892503901:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (392194)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2332102884:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (392196)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3071227065:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (392198)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=1530758006:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (392195)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=3551731787: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)
% 0.21/0.29 % (392194)Instruction limit reached!
% 0.21/0.29 % (392194)------------------------------
% 0.21/0.29 % (392194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (392194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (392194)CaDiCaL version: 2.1.3
% 0.21/0.29 % (392194)Termination reason: Instruction limit
% 0.21/0.29 % (392194)Termination phase: Saturation
% 0.21/0.29 % (392194)Time elapsed: 0.002 s
% 0.21/0.29 % (392194)Peak memory usage: 12 MB
% 0.21/0.29 % (392194)Instructions burned: 3 (million)
% 0.21/0.29 % (392196) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392182-392196"...
% 0.21/0.29 % (392191) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392182-392191"...
% 0.21/0.29 % (392193)Instruction limit reached!
% 0.21/0.29 % (392193)------------------------------
% 0.21/0.29 % (392193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (392193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (392193)CaDiCaL version: 2.1.3
% 0.21/0.29 % (392193)Termination reason: Instruction limit
% 0.21/0.29 % (392193)Termination phase: Saturation
% 0.21/0.29 % (392193)Time elapsed: 0.010 s
% 0.21/0.29 % (392193)Peak memory usage: 12 MB
% 0.21/0.29 % (392193)Instructions burned: 19 (million)
% 0.21/0.29 % (392196)...printing done.
% 0.21/0.29 % (392196)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_1, type, powerset: ($i > $i)).
% 0.21/0.29 thf(func_def_2, type, powersetI: $o).
% 0.21/0.29 thf(func_def_4, type, powersetE: $o).
% 0.21/0.29 thf(func_def_5, type, subset: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_6, type, subsetI2: $o).
% 0.21/0.29 thf(func_def_7, type, subsetE: $o).
% 0.21/0.29 thf(func_def_12, type, sK2: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_18, type, sK8: ($i > $i > $i)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 (powersetI = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 (powersetE = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.21/0.29 thf(f4,axiom,(
% 0.21/0.29 (subsetE = ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.21/0.29 thf(f5,conjecture,(
% 0.21/0.29 powersetI => (powersetE => (subsetI2 => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset)).
% 0.21/0.29 thf(f6,negated_conjecture,(
% 0.21/0.29 ~(powersetI => (powersetE => (subsetI2 => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1)))))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ~(powersetI => (powersetE => (subsetI2 => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1)))))))),
% 0.21/0.29 inference(rectify,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ~((powersetI = $true) => ((powersetE = $true) => ((subsetI2 = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) => (((subset @ (powerset @ X0) @ (powerset @ X1))) = $true))))))),
% 0.21/0.29 inference(fool_elimination,[],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => (($true = ((in @ X0 @ X2))) => ($true = ((in @ X0 @ X1))))) <=> (powersetE = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f9])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => ($true = ((in @ X0 @ (powerset @ X1))))) <=> (powersetI = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f11])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))))),
% 0.21/0.29 inference(rectify,[],[f4])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((subset @ X1 @ X2))) => (($true = ((in @ X0 @ X1))) => ($true = ((in @ X0 @ X2))))) <=> (subsetE = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f13])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.21/0.29 inference(fool_elimination,[],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)))),
% 0.21/0.29 inference(ennf_transformation,[],[f16])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 (((? [X1 : $i,X0 : $i] : ((((subset @ (powerset @ X0) @ (powerset @ X1))) != $true) & (((subset @ X0 @ X1)) = $true)) & (subsetE = $true)) & (subsetI2 = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f8])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 (powersetE = $true) & (powersetI = $true) & (subsetE = $true) & (subsetI2 = $true) & ? [X1 : $i,X0 : $i] : ((((subset @ (powerset @ X0) @ (powerset @ X1))) != $true) & (((subset @ X0 @ X1)) = $true))),
% 0.21/0.29 inference(flattening,[],[f18])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = ((in @ X0 @ X1))) | ($true != ((in @ X0 @ X2)))) | ($true != ((in @ X2 @ (powerset @ X1))))) <=> (powersetE = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f10])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X2))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((in @ X0 @ X1)))) <=> (powersetE = $true)),
% 0.21/0.29 inference(flattening,[],[f20])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 (powersetI = $true) <=> ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)))),
% 0.21/0.29 inference(ennf_transformation,[],[f12])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ X1)))) | ($true != ((subset @ X1 @ X2)))) <=> (subsetE = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f14])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ X1))) | ($true != ((subset @ X1 @ X2))))),
% 0.21/0.29 inference(flattening,[],[f23])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 ((powersetI = $true) | ? [X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (powersetI != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f22])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((in @ X4 @ (powerset @ X3)))) | ? [X5 : $i] : (($true != ((in @ X5 @ X3))) & (((in @ X5 @ X4)) = $true))) | (powersetI != $true))),
% 0.21/0.29 inference(rectify,[],[f25])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 ((powersetI = $true) | (($true != ((in @ sK1 @ (powerset @ sK0)))) & ! [X2 : $i] : (($true = ((in @ X2 @ sK0))) | (((in @ X2 @ sK1)) != $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((in @ X4 @ (powerset @ X3)))) | ((((in @ (sK2 @ X4 @ X3) @ X3)) != $true) & ($true = ((in @ (sK2 @ X4 @ X3) @ X4))))) | (powersetI != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X3)],[f26])).
% 0.21/0.29 thf(f28,plain,(
% 0.21/0.29 ((subsetE = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true != ((in @ X0 @ X2))) & ($true = ((in @ X0 @ X1))) & ($true = ((subset @ X1 @ X2))))) & (! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ X1))) | ($true != ((subset @ X1 @ X2)))) | (subsetE != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f24])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) & ($true = ((in @ X0 @ X2))) & ($true = ((subset @ X2 @ X1))))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ X4)) = $true) | ($true != ((in @ X3 @ X5))) | ($true != ((subset @ X5 @ X4)))) | (subsetE != $true))),
% 0.21/0.29 inference(rectify,[],[f28])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 ((subsetE = $true) | (($true != ((in @ sK3 @ sK4))) & ($true = ((in @ sK3 @ sK5))) & ($true = ((subset @ sK5 @ sK4))))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ X4)) = $true) | ($true != ((in @ X3 @ X5))) | ($true != ((subset @ X5 @ X4)))) | (subsetE != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (subsetI2 != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f17])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ? [X5 : $i] : ((((in @ X5 @ X4)) != $true) & ($true = ((in @ X5 @ X3))))) | (subsetI2 != $true))),
% 0.21/0.29 inference(rectify,[],[f31])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 ((subsetI2 = $true) | (($true != ((subset @ sK6 @ sK7))) & ! [X2 : $i] : (($true = ((in @ X2 @ sK7))) | ($true != ((in @ X2 @ sK6)))))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | (($true != ((in @ (sK8 @ X4 @ X3) @ X4))) & ($true = ((in @ (sK8 @ X4 @ X3) @ X3))))) | (subsetI2 != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,vAPP]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X5,sK2 @ X4 @ X3)],[f32])).
% 0.21/0.29 thf(f34,plain,(
% 0.21/0.29 (powersetE = $true) & (powersetI = $true) & (subsetE = $true) & (subsetI2 = $true) & ? [X0 : $i,X1 : $i] : (($true != ((subset @ (powerset @ X1) @ (powerset @ X0)))) & ($true = ((subset @ X1 @ X0))))),
% 0.21/0.29 inference(rectify,[],[f19])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 (powersetE = $true) & (powersetI = $true) & (subsetE = $true) & (subsetI2 = $true) & (($true != ((subset @ (powerset @ sK10) @ (powerset @ sK9)))) & (((subset @ sK10 @ sK9)) = $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f34])).
% 0.21/0.29 thf(f36,plain,(
% 0.21/0.29 (! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X2))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((in @ X0 @ X1)))) | (powersetE != $true)) & ((powersetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) & ($true = ((in @ X2 @ (powerset @ X1)))) & ($true != ((in @ X0 @ X1)))))),
% 0.21/0.29 inference(nnf_transformation,[],[f21])).
% 0.21/0.29 thf(f37,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | ($true != ((in @ X0 @ (powerset @ X2)))) | ($true = ((in @ X1 @ X2)))) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) & ($true = ((in @ X3 @ (powerset @ X5)))) & ($true != ((in @ X4 @ X5)))))),
% 0.21/0.29 inference(rectify,[],[f36])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | ($true != ((in @ X0 @ (powerset @ X2)))) | ($true = ((in @ X1 @ X2)))) | (powersetE != $true)) & ((powersetE = $true) | (($true = ((in @ sK12 @ sK11))) & ($true = ((in @ sK11 @ (powerset @ sK13)))) & ($true != ((in @ sK12 @ sK13)))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X3,sK11),skolemize(X4,sK12),skolemize(X5,sK13)],[f37])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK2 @ X4 @ X3) @ X4))) | ($true = ((in @ X4 @ (powerset @ X3)))) | (powersetI != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f27])).
% 0.21/0.29 thf(f40,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : ((powersetI != $true) | (((in @ (sK2 @ X4 @ X3) @ X3)) != $true) | ($true = ((in @ X4 @ (powerset @ X3))))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f27])).
% 0.21/0.29 thf(f43,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ X4)) = $true) | (subsetE != $true) | ($true != ((in @ X3 @ X5))) | ($true != ((subset @ X5 @ X4)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f30])).
% 0.21/0.29 thf(f47,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK8 @ X4 @ X3) @ X3))) | (((subset @ X3 @ X4)) = $true) | (subsetI2 != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f48,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK8 @ X4 @ X3) @ X4))) | (((subset @ X3 @ X4)) = $true) | (subsetI2 != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f51,plain,(
% 0.21/0.29 (((subset @ sK10 @ sK9)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f52,plain,(
% 0.21/0.29 ($true != ((subset @ (powerset @ sK10) @ (powerset @ sK9))))),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f53,plain,(
% 0.21/0.29 (subsetI2 = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f54,plain,(
% 0.21/0.29 (subsetE = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f55,plain,(
% 0.21/0.29 (powersetI = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 (powersetE = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f60,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X2)))) | ($true = ((in @ X1 @ X2))) | (powersetE != $true) | (((in @ X1 @ X0)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f38])).
% 0.21/0.29 thf(f66,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK8 @ X4 @ X3) @ X3))) | (((subset @ X3 @ X4)) = $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f47,f53])).
% 0.21/0.29 thf(f67,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK8 @ X4 @ X3) @ X4))) | (((subset @ X3 @ X4)) = $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f48,f53])).
% 0.21/0.29 thf(f71,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((subset @ X5 @ X4))) | ($true != ((in @ X3 @ X5))) | (((in @ X3 @ X4)) = $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f43,f54])).
% 0.21/0.29 thf(f72,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK9))) | ($true != ((in @ X0 @ sK10))) | ($true != $true)) )),
% 0.21/0.29 inference(superposition,[],[f71,f51])).
% 0.21/0.29 thf(f74,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK9))) | ($true != ((in @ X0 @ sK10)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f72])).
% 0.21/0.29 thf(f80,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK2 @ X4 @ X3) @ X4))) | ($true = ((in @ X4 @ (powerset @ X3))))) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f39,f55])).
% 0.21/0.29 thf(f81,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) != $true) | ($true = ((in @ X4 @ (powerset @ X3))))) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f40,f55])).
% 0.21/0.29 thf(f83,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((in @ (sK2 @ X0 @ sK9) @ sK10))) | ($true != $true) | ($true = ((in @ X0 @ (powerset @ sK9))))) )),
% 0.21/0.29 inference(superposition,[],[f81,f74])).
% 0.21/0.29 thf(f86,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((in @ (sK2 @ X0 @ sK9) @ sK10))) | ($true = ((in @ X0 @ (powerset @ sK9))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f83])).
% 0.21/0.29 thf(f87,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X2)))) | (((in @ X1 @ X0)) != $true) | ($true = ((in @ X1 @ X2)))) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f60,f56])).
% 0.21/0.29 thf(f91,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (sK8 @ X0 @ (powerset @ X1))))) | ($true = ((subset @ (powerset @ X1) @ X0))) | ($true != $true) | (((in @ X2 @ X1)) = $true)) )),
% 0.21/0.29 inference(superposition,[],[f87,f66])).
% 0.21/0.29 thf(f96,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (sK8 @ X0 @ (powerset @ X1))))) | (((in @ X2 @ X1)) = $true) | ($true = ((subset @ (powerset @ X1) @ X0)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f91])).
% 0.21/0.29 thf(f99,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ (sK8 @ X0 @ (powerset @ X1)) @ X2) @ X1))) | ($true = ((in @ (sK8 @ X0 @ (powerset @ X1)) @ (powerset @ X2)))) | ($true != $true) | ($true = ((subset @ (powerset @ X1) @ X0)))) )),
% 0.21/0.29 inference(superposition,[],[f96,f80])).
% 0.21/0.29 thf(f100,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ (sK8 @ X0 @ (powerset @ X1)) @ X2) @ X1))) | ($true = ((subset @ (powerset @ X1) @ X0))) | ($true = ((in @ (sK8 @ X0 @ (powerset @ X1)) @ (powerset @ X2))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f99])).
% 0.21/0.29 thf(f129,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((subset @ (powerset @ sK10) @ X0)) = $true) | ($true = ((in @ (sK8 @ X0 @ (powerset @ sK10)) @ (powerset @ sK9)))) | ($true = ((in @ (sK8 @ X0 @ (powerset @ sK10)) @ (powerset @ sK9))))) )),
% 0.21/0.29 inference(superposition,[],[f86,f100])).
% 0.21/0.29 thf(f136,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((in @ (sK8 @ X0 @ (powerset @ sK10)) @ (powerset @ sK9)))) | ($true != $true) | (((subset @ (powerset @ sK10) @ X0)) = $true)) )),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f129])).
% 0.21/0.29 thf(f137,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((in @ (sK8 @ X0 @ (powerset @ sK10)) @ (powerset @ sK9)))) | (((subset @ (powerset @ sK10) @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f136])).
% 0.21/0.29 thf(f142,plain,(
% 0.21/0.29 ($true != $true) | ($true = ((subset @ (powerset @ sK10) @ (powerset @ sK9)))) | ($true = ((subset @ (powerset @ sK10) @ (powerset @ sK9))))),
% 0.21/0.29 inference(superposition,[],[f67,f137])).
% 0.21/0.29 thf(f144,plain,(
% 0.21/0.29 ($true = ((subset @ (powerset @ sK10) @ (powerset @ sK9)))) | ($true != $true)),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f142])).
% 0.21/0.29 thf(f145,plain,(
% 0.21/0.29 ($true = ((subset @ (powerset @ sK10) @ (powerset @ sK9))))),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f144])).
% 0.21/0.29 thf(f147,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f145,f52])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (392196)------------------------------
% 0.21/0.29 % (392196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (392196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (392196)CaDiCaL version: 2.1.3
% 0.21/0.29 % (392196)Termination reason: Refutation
% 0.21/0.29 % (392196)Time elapsed: 0.010 s
% 0.21/0.29 % (392196)Peak memory usage: 12 MB
% 0.21/0.29 % (392196)Instructions burned: 17 (million)
% 0.21/0.29 % (392182)Success in time 0.035 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------