%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU729^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:31:00 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
% 0.00/0.02 % Problem : SEU729^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:16:55 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (786391)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (786396)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3710536987:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (786402)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 % (786402)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 % (786397)lrs+10_16_si=on:nwc=1.5:random_seed=1719705138:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (786398)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1656991969:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (786402)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=727555069:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (786400)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2557370941:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (786399)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=9129485: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 % (786401)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1998579214:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (786396) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-786391-786396"...
% 0.21/0.29 % (786398)Instruction limit reached!
% 0.21/0.29 % (786398)------------------------------
% 0.21/0.29 % (786398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (786398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (786398)CaDiCaL version: 2.1.3
% 0.21/0.29 % (786398)Termination reason: Instruction limit
% 0.21/0.29 % (786398)Termination phase: Saturation
% 0.21/0.29 % (786398)Time elapsed: 0.002 s
% 0.21/0.29 % (786398)Peak memory usage: 12 MB
% 0.21/0.29 % (786398)Instructions burned: 3 (million)
% 0.21/0.29 % (786396)...printing done.
% 0.21/0.29 % (786396)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 > $i)).
% 0.21/0.29 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_3, type, setminus: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_4, type, complementT_lem: $o).
% 0.21/0.29 thf(func_def_6, type, subsetTI: $o).
% 0.21/0.29 thf(func_def_7, type, doubleComplementI1: $o).
% 0.21/0.29 thf(func_def_13, type, sK3: ($i > $i > $i > $i)).
% 0.21/0.29 thf(func_def_21, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 (complementT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 (! [X0 : $i,X1 : $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)),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI)).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 (doubleComplementI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementI1)).
% 0.21/0.29 thf(f4,conjecture,(
% 0.21/0.29 complementT_lem => (subsetTI => (doubleComplementI1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))))))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1)).
% 0.21/0.29 thf(f5,negated_conjecture,(
% 0.21/0.29 ~(complementT_lem => (subsetTI => (doubleComplementI1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1))))) <=> (complementT_lem = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ~(complementT_lem => (subsetTI => (doubleComplementI1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 0.21/0.29 inference(rectify,[],[f5])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ~((complementT_lem = $true) => ((subsetTI = $true) => ((doubleComplementI1 = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => (((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = $true)))))),
% 0.21/0.29 inference(fool_elimination,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $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)),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ X3 @ X1)) = $true) => (((in @ X3 @ X2)) = $true))) => (((subset @ X1 @ X2)) = $true)))) <=> (subsetTI = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 (doubleComplementI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (doubleComplementI1 = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = $true))))),
% 0.21/0.29 inference(fool_elimination,[],[f12])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((((subset @ X1 @ X2)) = $true) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X3 @ X0)) = $true))) | (((in @ X2 @ (powerset @ X0))) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (subsetTI = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f11])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 (subsetTI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true)) | (((in @ X2 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X2)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true))),
% 0.21/0.29 inference(flattening,[],[f14])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (complementT_lem = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f7])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ((? [X1 : $i,X0 : $i] : ((((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) != $true) & (((in @ X1 @ (powerset @ X0))) = $true)) & (doubleComplementI1 = $true)) & (subsetTI = $true)) & (complementT_lem = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f9])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 (subsetTI = $true) & (doubleComplementI1 = $true) & ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) != $true) & (((in @ X1 @ (powerset @ X0))) = $true)) & (complementT_lem = $true)),
% 0.21/0.29 inference(flattening,[],[f17])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 (doubleComplementI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X2 @ X0)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f13])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = $true) | (((in @ X2 @ X0)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (doubleComplementI1 = $true)),
% 0.21/0.29 inference(flattening,[],[f19])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X2)) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true) & (((subset @ X1 @ X2)) != $true)) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true)) | (((in @ X2 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X2)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) | (subsetTI != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f15])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X2)) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true) & (((subset @ X1 @ X2)) != $true)) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (? [X7 : $i] : (($true = ((in @ X7 @ X4))) & ($true = ((in @ X7 @ X5))) & ($true != ((in @ X7 @ X6)))) | ($true != ((in @ X6 @ (powerset @ X4)))) | (((subset @ X5 @ X6)) = $true)) | ($true != ((in @ X5 @ (powerset @ X4))))) | (subsetTI != $true))),
% 0.21/0.29 inference(rectify,[],[f21])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ((subsetTI = $true) | ((! [X3 : $i] : (($true != ((in @ X3 @ sK0))) | (((in @ X3 @ sK1)) != $true) | (((in @ X3 @ sK2)) = $true)) & ($true = ((in @ sK2 @ (powerset @ sK0)))) & ($true != ((subset @ sK1 @ sK2)))) & ($true = ((in @ sK1 @ (powerset @ sK0)))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : ((($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X4))) & ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))) & ($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6)))) | ($true != ((in @ X6 @ (powerset @ X4)))) | (((subset @ X5 @ X6)) = $true)) | ($true != ((in @ X5 @ (powerset @ X4))))) | (subsetTI != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X7,sK3 @ X6 @ X5 @ X4)],[f22])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 (subsetTI = $true) & (doubleComplementI1 = $true) & ? [X0 : $i,X1 : $i] : (($true != ((subset @ X0 @ (setminus @ X1 @ (setminus @ X1 @ X0))))) & ($true = ((in @ X0 @ (powerset @ X1))))) & (complementT_lem = $true)),
% 0.21/0.29 inference(rectify,[],[f18])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 (subsetTI = $true) & (doubleComplementI1 = $true) & ((((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) != $true) & (((in @ sK4 @ (powerset @ sK5))) = $true)) & (complementT_lem = $true)),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f24])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = $true) | (((in @ X2 @ X0)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) | (doubleComplementI1 != $true)) & ((doubleComplementI1 = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) != $true) & (((in @ X2 @ X0)) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)))),
% 0.21/0.29 inference(nnf_transformation,[],[f20])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) = $true) | (((in @ X2 @ X1)) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) | (doubleComplementI1 != $true)) & ((doubleComplementI1 = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ X3))) & ($true != ((in @ X5 @ (setminus @ X4 @ (setminus @ X4 @ X3))))) & ($true = ((in @ X5 @ X4)))) & ($true = ((in @ X3 @ (powerset @ X4))))))),
% 0.21/0.29 inference(rectify,[],[f26])).
% 0.21/0.29 thf(f28,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) = $true) | (((in @ X2 @ X1)) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) | (doubleComplementI1 != $true)) & ((doubleComplementI1 = $true) | (((((in @ sK8 @ sK6)) = $true) & (((in @ sK8 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)))) != $true) & ($true = ((in @ sK8 @ sK7)))) & ($true = ((in @ sK6 @ (powerset @ sK7))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8)],[f27])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : (($true != ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) & ($true = ((in @ X0 @ (powerset @ X1))))))),
% 0.21/0.29 inference(nnf_transformation,[],[f16])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (($true != ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)))) & ($true = ((in @ X2 @ (powerset @ X3))))))),
% 0.21/0.29 inference(rectify,[],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (complementT_lem != $true)) & ((complementT_lem = $true) | (($true != ((in @ (setminus @ sK10 @ sK9) @ (powerset @ sK10)))) & ($true = ((in @ sK9 @ (powerset @ sK10))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X2,sK9),skolemize(X3,sK10)],[f30])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6))) | ($true != ((in @ X6 @ (powerset @ X4)))) | (((subset @ X5 @ X6)) = $true) | ($true != ((in @ X5 @ (powerset @ X4)))) | (subsetTI != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))) | ($true != ((in @ X6 @ (powerset @ X4)))) | (((subset @ X5 @ X6)) = $true) | ($true != ((in @ X5 @ (powerset @ X4)))) | (subsetTI != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f34,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X4))) | ($true != ((in @ X6 @ (powerset @ X4)))) | (((subset @ X5 @ X6)) = $true) | ($true != ((in @ X5 @ (powerset @ X4)))) | (subsetTI != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 (complementT_lem = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f40,plain,(
% 0.21/0.29 (((in @ sK4 @ (powerset @ sK5))) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f41,plain,(
% 0.21/0.29 (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) != $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f42,plain,(
% 0.21/0.29 (doubleComplementI1 = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f43,plain,(
% 0.21/0.29 (subsetTI = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f48,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) = $true) | (((in @ X2 @ X1)) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (doubleComplementI1 != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 thf(f51,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (complementT_lem != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f31])).
% 0.21/0.29 thf(f58,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X6 @ (powerset @ X4)))) | ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X4))) | ($true != ((in @ X5 @ (powerset @ X4)))) | ($true != $true) | (((subset @ X5 @ X6)) = $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f34,f43])).
% 0.21/0.29 thf(f59,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X6 @ (powerset @ X4)))) | ($true != $true) | (((subset @ X5 @ X6)) = $true) | ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))) | ($true != ((in @ X5 @ (powerset @ X4))))) )),
% 0.21/0.29 inference(definition_unfolding,[],[f33,f43])).
% 0.21/0.29 thf(f60,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (powerset @ X4)))) | ($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6))) | ($true != $true) | (((subset @ X5 @ X6)) = $true) | ($true != ((in @ X6 @ (powerset @ X4))))) )),
% 0.21/0.29 inference(definition_unfolding,[],[f32,f43])).
% 0.21/0.29 thf(f61,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) = $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true != $true) | (((in @ X2 @ X0)) != $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f48,f42])).
% 0.21/0.29 thf(f66,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != $true) | ($true != ((in @ X0 @ (powerset @ X1))))) )),
% 0.21/0.29 inference(definition_unfolding,[],[f51,f39])).
% 0.21/0.29 thf(f69,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X6 @ (powerset @ X4)))) | ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))) | ($true != ((in @ X5 @ (powerset @ X4)))) | (((subset @ X5 @ X6)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f59])).
% 0.21/0.29 thf(f70,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X6 @ (powerset @ X4)))) | ($true != ((in @ X5 @ (powerset @ X4)))) | (((subset @ X5 @ X6)) = $true) | ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X4)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f58])).
% 0.21/0.29 thf(f71,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f66])).
% 0.21/0.29 thf(f72,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) = $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) != $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f61])).
% 0.21/0.29 thf(f73,plain,(
% 0.21/0.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6))) | (((subset @ X5 @ X6)) = $true) | ($true != ((in @ X5 @ (powerset @ X4)))) | ($true != ((in @ X6 @ (powerset @ X4))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f60])).
% 0.21/0.29 thf(f74,plain,(
% 0.21/0.29 (((in @ (setminus @ sK5 @ sK4) @ (powerset @ sK5))) = $true) | ($true != $true)),
% 0.21/0.29 inference(constrained_superposition,[],[f71,f40])).
% 0.21/0.29 thf(f75,plain,(
% 0.21/0.29 (((in @ (setminus @ sK5 @ sK4) @ (powerset @ sK5))) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f74])).
% 0.21/0.29 thf(f76,plain,(
% 0.21/0.29 ($true != $true) | ($true = ((in @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ (powerset @ sK5))))),
% 0.21/0.29 inference(constrained_superposition,[],[f71,f75])).
% 0.21/0.29 thf(f77,plain,(
% 0.21/0.29 ($true = ((in @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ (powerset @ sK5))))),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f76])).
% 0.21/0.29 thf(f86,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ X0 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4))))) | (((in @ X0 @ sK5)) != $true) | (((in @ X0 @ sK4)) != $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f72,f40])).
% 0.21/0.29 thf(f94,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK5)) != $true) | (((in @ X0 @ sK4)) != $true) | ($true = ((in @ X0 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f86])).
% 0.21/0.29 thf(f104,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((subset @ X0 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4))))) | ($true != $true) | ($true != ((in @ X0 @ (powerset @ sK5)))) | ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ X0 @ sK5) @ X0)))) )),
% 0.21/0.29 inference(constrained_superposition,[],[f69,f77])).
% 0.21/0.29 thf(f112,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((in @ X0 @ (powerset @ sK5)))) | ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ X0 @ sK5) @ X0))) | ($true = ((subset @ X0 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f104])).
% 0.21/0.29 thf(f195,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((in @ X0 @ (powerset @ sK5)))) | ($true = ((subset @ X0 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4))))) | ($true != $true) | (((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ X0 @ sK5) @ sK5)) = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f70,f77])).
% 0.21/0.29 thf(f203,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((in @ X0 @ (powerset @ sK5)))) | ($true = ((subset @ X0 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4))))) | (((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ X0 @ sK5) @ sK5)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f195])).
% 0.21/0.29 thf(f432,plain,(
% 0.21/0.29 ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK4))) | ($true != $true) | (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true)),
% 0.21/0.29 inference(constrained_superposition,[],[f112,f40])).
% 0.21/0.29 thf(f449,plain,(
% 0.21/0.29 ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK4))) | (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f432])).
% 0.21/0.29 thf(f522,plain,(
% 0.21/0.29 ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK4)))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f449,f41])).
% 0.21/0.29 thf(f523,plain,(
% 0.21/0.29 ($true != $true) | ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK5))) | (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true)),
% 0.21/0.29 inference(constrained_superposition,[],[f203,f40])).
% 0.21/0.29 thf(f533,plain,(
% 0.21/0.29 ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK5))) | (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f523])).
% 0.21/0.29 thf(f546,plain,(
% 0.21/0.29 ($true = ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK5)))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f533,f41])).
% 0.21/0.29 thf(f557,plain,(
% 0.21/0.29 (((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true) | ($true != ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK4))) | ($true != $true)),
% 0.21/0.29 inference(constrained_superposition,[],[f94,f546])).
% 0.21/0.29 thf(f558,plain,(
% 0.21/0.29 ($true != ((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ sK4))) | (((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f557])).
% 0.21/0.29 thf(f559,plain,(
% 0.21/0.29 (((in @ (sK3 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ sK4 @ sK5) @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f558,f522])).
% 0.21/0.29 thf(f567,plain,(
% 0.21/0.29 ($true != $true) | (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true) | (((in @ sK4 @ (powerset @ sK5))) != $true) | ($true != ((in @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ (powerset @ sK5))))),
% 0.21/0.29 inference(constrained_superposition,[],[f73,f559])).
% 0.21/0.29 thf(f569,plain,(
% 0.21/0.29 (((in @ sK4 @ (powerset @ sK5))) != $true) | ($true != ((in @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ (powerset @ sK5)))) | (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f567])).
% 0.21/0.29 thf(f571,plain,(
% 0.21/0.29 (((subset @ sK4 @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)))) = $true) | ($true != ((in @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ (powerset @ sK5))))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f569,f40])).
% 0.21/0.29 thf(f573,plain,(
% 0.21/0.29 ($true != ((in @ (setminus @ sK5 @ (setminus @ sK5 @ sK4)) @ (powerset @ sK5))))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f571,f41])).
% 0.21/0.29 thf(f574,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f573,f77])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (786396)------------------------------
% 0.21/0.29 % (786396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (786396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (786396)CaDiCaL version: 2.1.3
% 0.21/0.29 % (786396)Termination reason: Refutation
% 0.21/0.29 % (786396)Time elapsed: 0.012 s
% 0.21/0.29 % (786396)Peak memory usage: 12 MB
% 0.21/0.29 % (786396)Instructions burned: 44 (million)
% 0.21/0.29 % (786391)Success in time 0.043 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------