%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU730^2 : 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 : n012.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 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU730^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:17:04 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.16 % (169520)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.16 % (169531)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.16 % (169531)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
% 0.08/0.16 % (169525)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3534636489:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.16 % (169526)lrs+10_16_si=on:nwc=1.5:random_seed=841146086:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.16 % (169527)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1399672865:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.16 % (169528)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=824975696: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)
% 0.08/0.16 % (169529)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3752611770:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.16 % (169530)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3622055484:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.16 % (169531)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=1267750473:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.16 % (169527)Refutation not found, incomplete strategy
% 0.08/0.16 % (169527)------------------------------
% 0.08/0.16 % (169527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (169527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (169527)CaDiCaL version: 2.1.3
% 0.08/0.16 % (169527)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.16 % (169527)Time elapsed: 0.001 s
% 0.08/0.16 % (169527)Peak memory usage: 12 MB
% 0.08/0.16 % (169527)Instructions burned: 3 (million)
% 0.08/0.16 % (169527)------------------------------
% 0.08/0.16 % (169527)------------------------------
% 0.08/0.16 % (169525) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169520-169525"...
% 0.08/0.16 % (169529) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169520-169529"...
% 0.08/0.16 % (169526)Instruction limit reached!
% 0.08/0.16 % (169526)------------------------------
% 0.08/0.16 % (169526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (169526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (169526)CaDiCaL version: 2.1.3
% 0.08/0.16 % (169526)Termination reason: Instruction limit
% 0.08/0.16 % (169526)Termination phase: Saturation
% 0.08/0.16 % (169526)Time elapsed: 0.006 s
% 0.08/0.16 % (169526)Peak memory usage: 12 MB
% 0.08/0.16 % (169526)Instructions burned: 21 (million)
% 0.08/0.16 % (169525)...printing done.
% 0.08/0.16 % (169529)...printing done.
% 0.08/0.16 % (169525)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% 0.08/0.16 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.16 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.16 thf(func_def_1, type, powerset: ($i > $i)).
% 0.08/0.16 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.08/0.16 thf(func_def_3, type, setminus: ($i > $i > $i)).
% 0.08/0.16 thf(func_def_4, type, complementT_lem: $o).
% 0.08/0.16 thf(func_def_6, type, subsetTI: $o).
% 0.08/0.16 thf(func_def_7, type, doubleComplementE1: $o).
% 0.08/0.16 thf(func_def_15, type, sK5: ($i > $i > $i > $i)).
% 0.08/0.16 thf(func_def_21, type, vNOT: ($o > $o)).
% 0.08/0.16 thf(f1,axiom,(
% 0.08/0.16 (complementT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.08/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 0.08/0.16 thf(f2,axiom,(
% 0.08/0.16 (subsetTI = ! [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)))))),
% 0.08/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.08/0.16 thf(f3,axiom,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X2 @ X1)))) = doubleComplementE1)),
% 0.08/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1)).
% 0.08/0.16 thf(f4,conjecture,(
% 0.08/0.16 complementT_lem => (subsetTI => (doubleComplementE1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1))))),
% 0.08/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub2)).
% 0.08/0.16 thf(f5,negated_conjecture,(
% 0.08/0.16 ~(complementT_lem => (subsetTI => (doubleComplementE1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1)))))),
% 0.08/0.16 inference(negated_conjecture,[status(cth)],[f4])).
% 0.08/0.16 thf(f6,plain,(
% 0.08/0.16 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 0.08/0.16 inference(rectify,[],[f1])).
% 0.08/0.16 thf(f7,plain,(
% 0.08/0.16 (complementT_lem = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => (((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true))),
% 0.08/0.16 inference(fool_elimination,[],[f6])).
% 0.08/0.16 thf(f8,plain,(
% 0.08/0.16 (subsetTI = ! [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)))))),
% 0.08/0.16 inference(rectify,[],[f2])).
% 0.08/0.16 thf(f9,plain,(
% 0.08/0.16 ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => (((subset @ X0 @ X2)) = $true)))) <=> (subsetTI = $true)),
% 0.08/0.16 inference(fool_elimination,[],[f8])).
% 0.08/0.16 thf(f10,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X2 @ X1)))) = doubleComplementE1)),
% 0.08/0.16 inference(rectify,[],[f3])).
% 0.08/0.16 thf(f11,plain,(
% 0.08/0.16 ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => ((((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = $true) => (((in @ X2 @ X1)) = $true)))) <=> (doubleComplementE1 = $true)),
% 0.08/0.16 inference(fool_elimination,[],[f10])).
% 0.08/0.16 thf(f12,plain,(
% 0.08/0.16 ~(complementT_lem => (subsetTI => (doubleComplementE1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)))))),
% 0.08/0.16 inference(rectify,[],[f5])).
% 0.08/0.16 thf(f13,plain,(
% 0.08/0.16 ~((complementT_lem = $true) => ((subsetTI = $true) => ((doubleComplementE1 = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => (((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)) = $true)))))),
% 0.08/0.16 inference(fool_elimination,[],[f12])).
% 0.08/0.16 thf(f14,plain,(
% 0.08/0.16 ! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) <=> (complementT_lem = $true)),
% 0.08/0.16 inference(ennf_transformation,[],[f7])).
% 0.08/0.16 thf(f15,plain,(
% 0.08/0.16 ! [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)) <=> (doubleComplementE1 = $true)),
% 0.08/0.16 inference(ennf_transformation,[],[f11])).
% 0.08/0.16 thf(f16,plain,(
% 0.08/0.16 ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) != $true) | (((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true))) <=> (doubleComplementE1 = $true)),
% 0.08/0.16 inference(flattening,[],[f15])).
% 0.08/0.16 thf(f17,plain,(
% 0.08/0.16 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((((subset @ X0 @ X2)) = $true) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) | ($true != ((in @ X2 @ (powerset @ X1))))) | (((in @ X0 @ (powerset @ X1))) != $true)) <=> (subsetTI = $true)),
% 0.08/0.16 inference(ennf_transformation,[],[f9])).
% 0.08/0.16 thf(f18,plain,(
% 0.08/0.16 (subsetTI = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | ! [X2 : $i] : ((((subset @ X0 @ X2)) = $true) | ($true != ((in @ X2 @ (powerset @ X1)))) | ? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) = $true))))),
% 0.08/0.16 inference(flattening,[],[f17])).
% 0.08/0.16 thf(f19,plain,(
% 0.08/0.16 ((? [X0 : $i,X1 : $i] : ((((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)) != $true) & (((in @ X0 @ (powerset @ X1))) = $true)) & (doubleComplementE1 = $true)) & (subsetTI = $true)) & (complementT_lem = $true)),
% 0.08/0.16 inference(ennf_transformation,[],[f13])).
% 0.08/0.16 thf(f20,plain,(
% 0.08/0.16 (complementT_lem = $true) & ? [X0 : $i,X1 : $i] : ((((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)) != $true) & (((in @ X0 @ (powerset @ X1))) = $true)) & (subsetTI = $true) & (doubleComplementE1 = $true)),
% 0.08/0.16 inference(flattening,[],[f19])).
% 0.08/0.16 thf(f21,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) != $true) & (((in @ X0 @ (powerset @ X1))) = $true)))),
% 0.08/0.16 inference(nnf_transformation,[],[f14])).
% 0.08/0.16 thf(f22,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : ((((in @ (setminus @ X3 @ X2) @ (powerset @ X3))) != $true) & (((in @ X2 @ (powerset @ X3))) = $true)))),
% 0.08/0.16 inference(rectify,[],[f21])).
% 0.08/0.16 thf(f23,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ((((in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) != $true) & (((in @ sK0 @ (powerset @ sK1))) = $true)))),
% 0.08/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f22])).
% 0.08/0.16 thf(f24,plain,(
% 0.08/0.16 ((subsetTI = $true) | ? [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : ((((subset @ X0 @ X2)) != $true) & ($true = ((in @ X2 @ (powerset @ X1)))) & ! [X3 : $i] : ((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) != $true))))) & (! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | ! [X2 : $i] : ((((subset @ X0 @ X2)) = $true) | ($true != ((in @ X2 @ (powerset @ X1)))) | ? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) = $true)))) | (subsetTI != $true))),
% 0.08/0.16 inference(nnf_transformation,[],[f18])).
% 0.08/0.16 thf(f25,plain,(
% 0.08/0.16 ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : ((((subset @ X1 @ X2)) != $true) & (((in @ X2 @ (powerset @ X0))) = $true) & ! [X3 : $i] : ((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) != $true))))) & (! [X4 : $i,X5 : $i] : ((((in @ X5 @ (powerset @ X4))) != $true) | ! [X6 : $i] : ((((subset @ X5 @ X6)) = $true) | (((in @ X6 @ (powerset @ X4))) != $true) | ? [X7 : $i] : ((((in @ X7 @ X6)) != $true) & (((in @ X7 @ X5)) = $true) & ($true = ((in @ X7 @ X4)))))) | (subsetTI != $true))),
% 0.08/0.16 inference(rectify,[],[f24])).
% 0.08/0.16 thf(f26,plain,(
% 0.08/0.16 ((subsetTI = $true) | (($true = ((in @ sK3 @ (powerset @ sK2)))) & ((((subset @ sK3 @ sK4)) != $true) & (((in @ sK4 @ (powerset @ sK2))) = $true) & ! [X3 : $i] : ((((in @ X3 @ sK4)) = $true) | (((in @ X3 @ sK3)) != $true) | (((in @ X3 @ sK2)) != $true))))) & (! [X4 : $i,X5 : $i] : ((((in @ X5 @ (powerset @ X4))) != $true) | ! [X6 : $i] : ((((subset @ X5 @ X6)) = $true) | (((in @ X6 @ (powerset @ X4))) != $true) | ((((in @ (sK5 @ X6 @ X5 @ X4) @ X6)) != $true) & (((in @ (sK5 @ X6 @ X5 @ X4) @ X5)) = $true) & ($true = ((in @ (sK5 @ X6 @ X5 @ X4) @ X4)))))) | (subsetTI != $true))),
% 0.08/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,vAPP]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X7,sK5 @ X6 @ X5 @ X4)],[f25])).
% 0.08/0.16 thf(f27,plain,(
% 0.08/0.16 (complementT_lem = $true) & ((((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) != $true) & ($true = ((in @ sK6 @ (powerset @ sK7))))) & (subsetTI = $true) & (doubleComplementE1 = $true)),
% 0.08/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f20])).
% 0.08/0.16 thf(f28,plain,(
% 0.08/0.16 (! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) != $true) | (((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true))) | (doubleComplementE1 != $true)) & ((doubleComplementE1 = $true) | ? [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = $true) & (((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))))),
% 0.08/0.16 inference(nnf_transformation,[],[f16])).
% 0.08/0.16 thf(f29,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true))) | (doubleComplementE1 != $true)) & ((doubleComplementE1 = $true) | ? [X3 : $i,X4 : $i] : ((((in @ X3 @ (powerset @ X4))) = $true) & ? [X5 : $i] : ((((in @ X5 @ (setminus @ X4 @ (setminus @ X4 @ X3)))) = $true) & ($true != ((in @ X5 @ X3))) & (((in @ X5 @ X4)) = $true))))),
% 0.08/0.16 inference(rectify,[],[f28])).
% 0.08/0.16 thf(f30,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true))) | (doubleComplementE1 != $true)) & ((doubleComplementE1 = $true) | ((((in @ sK8 @ (powerset @ sK9))) = $true) & (($true = ((in @ sK10 @ (setminus @ sK9 @ (setminus @ sK9 @ sK8))))) & (((in @ sK10 @ sK8)) != $true) & (((in @ sK10 @ sK9)) = $true))))),
% 0.08/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X3,sK8),skolemize(X4,sK9),skolemize(X5,sK10)],[f29])).
% 0.08/0.16 thf(f33,plain,(
% 0.08/0.16 ( ! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | (((in @ X0 @ (powerset @ X1))) != $true) | (complementT_lem != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f23])).
% 0.08/0.16 thf(f34,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (powerset @ X4))) != $true) | (((subset @ X5 @ X6)) = $true) | (((in @ X6 @ (powerset @ X4))) != $true) | ($true = ((in @ (sK5 @ X6 @ X5 @ X4) @ X4))) | (subsetTI != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f26])).
% 0.08/0.16 thf(f35,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (powerset @ X4))) != $true) | (((subset @ X5 @ X6)) = $true) | (((in @ X6 @ (powerset @ X4))) != $true) | (((in @ (sK5 @ X6 @ X5 @ X4) @ X5)) = $true) | (subsetTI != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f26])).
% 0.08/0.16 thf(f36,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (powerset @ X4))) != $true) | (((subset @ X5 @ X6)) = $true) | (((in @ X6 @ (powerset @ X4))) != $true) | (((in @ (sK5 @ X6 @ X5 @ X4) @ X6)) != $true) | (subsetTI != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f26])).
% 0.08/0.16 thf(f41,plain,(
% 0.08/0.16 (doubleComplementE1 = $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f27])).
% 0.08/0.16 thf(f42,plain,(
% 0.08/0.16 (subsetTI = $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f27])).
% 0.08/0.16 thf(f43,plain,(
% 0.08/0.16 ($true = ((in @ sK6 @ (powerset @ sK7))))),
% 0.08/0.16 inference(cnf_transformation,[],[f27])).
% 0.08/0.16 thf(f44,plain,(
% 0.08/0.16 (((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) != $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f27])).
% 0.08/0.16 thf(f45,plain,(
% 0.08/0.16 (complementT_lem = $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f27])).
% 0.08/0.16 thf(f50,plain,(
% 0.08/0.16 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | (((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | (doubleComplementE1 != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f30])).
% 0.08/0.16 thf(f53,plain,(
% 0.08/0.16 ( ! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | (((in @ X0 @ (powerset @ X1))) != $true) | ($true != $true)) )),
% 0.08/0.16 inference(definition_unfolding,[],[f33,f45])).
% 0.08/0.16 thf(f60,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X6 @ (powerset @ X4))) != $true) | (((in @ X5 @ (powerset @ X4))) != $true) | (((subset @ X5 @ X6)) = $true) | (((in @ (sK5 @ X6 @ X5 @ X4) @ X6)) != $true) | ($true != $true)) )),
% 0.08/0.16 inference(definition_unfolding,[],[f36,f42])).
% 0.08/0.16 thf(f61,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X6 @ (powerset @ X4))) != $true) | (((subset @ X5 @ X6)) = $true) | (((in @ (sK5 @ X6 @ X5 @ X4) @ X5)) = $true) | ($true != $true) | (((in @ X5 @ (powerset @ X4))) != $true)) )),
% 0.08/0.16 inference(definition_unfolding,[],[f35,f42])).
% 0.08/0.16 thf(f62,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true = ((in @ (sK5 @ X6 @ X5 @ X4) @ X4))) | (((subset @ X5 @ X6)) = $true) | (((in @ X5 @ (powerset @ X4))) != $true) | (((in @ X6 @ (powerset @ X4))) != $true)) )),
% 0.08/0.16 inference(definition_unfolding,[],[f34,f42])).
% 0.08/0.16 thf(f63,plain,(
% 0.08/0.16 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ X0 @ (powerset @ X1))) != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) != $true)) )),
% 0.08/0.16 inference(definition_unfolding,[],[f50,f41])).
% 0.08/0.16 thf(f68,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X6 @ (powerset @ X4))) != $true) | ($true = ((in @ (sK5 @ X6 @ X5 @ X4) @ X4))) | (((subset @ X5 @ X6)) = $true) | (((in @ X5 @ (powerset @ X4))) != $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f62])).
% 0.08/0.16 thf(f69,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ (sK5 @ X6 @ X5 @ X4) @ X6)) != $true) | (((in @ X5 @ (powerset @ X4))) != $true) | (((subset @ X5 @ X6)) = $true) | (((in @ X6 @ (powerset @ X4))) != $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f60])).
% 0.08/0.16 thf(f70,plain,(
% 0.08/0.16 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | (((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f53])).
% 0.08/0.16 thf(f71,plain,(
% 0.08/0.16 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X6 @ (powerset @ X4))) != $true) | (((in @ (sK5 @ X6 @ X5 @ X4) @ X5)) = $true) | (((in @ X5 @ (powerset @ X4))) != $true) | (((subset @ X5 @ X6)) = $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f61])).
% 0.08/0.16 thf(f72,plain,(
% 0.08/0.16 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f63])).
% 0.08/0.16 thf(f73,plain,(
% 0.08/0.16 ($true = ((in @ (setminus @ sK7 @ sK6) @ (powerset @ sK7)))) | ($true != $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f70,f43])).
% 0.08/0.16 thf(f74,plain,(
% 0.08/0.16 ($true = ((in @ (setminus @ sK7 @ sK6) @ (powerset @ sK7))))),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f73])).
% 0.08/0.16 thf(f75,plain,(
% 0.08/0.16 (((in @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ (powerset @ sK7))) = $true) | ($true != $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f70,f74])).
% 0.08/0.16 thf(f76,plain,(
% 0.08/0.16 (((in @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ (powerset @ sK7))) = $true)),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f75])).
% 0.08/0.16 thf(f87,plain,(
% 0.08/0.16 ( ! [X0 : $i] : (($true != $true) | (((in @ (sK5 @ sK6 @ X0 @ sK7) @ sK7)) = $true) | (((in @ X0 @ (powerset @ sK7))) != $true) | (((subset @ X0 @ sK6)) = $true)) )),
% 0.08/0.16 inference(constrained_superposition,[],[f68,f43])).
% 0.08/0.16 thf(f96,plain,(
% 0.08/0.16 ( ! [X0 : $i] : ((((in @ X0 @ (powerset @ sK7))) != $true) | (((subset @ X0 @ sK6)) = $true) | (((in @ (sK5 @ sK6 @ X0 @ sK7) @ sK7)) = $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f87])).
% 0.08/0.16 thf(f103,plain,(
% 0.08/0.16 ($true != $true) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK7)) = $true) | (((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) = $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f96,f76])).
% 0.08/0.16 thf(f113,plain,(
% 0.08/0.16 (((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) = $true) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK7)) = $true)),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f103])).
% 0.08/0.16 thf(f160,plain,(
% 0.08/0.16 (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK7)) = $true)),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f113,f44])).
% 0.08/0.16 thf(f170,plain,(
% 0.08/0.16 ( ! [X0 : $i] : (($true != $true) | (((subset @ X0 @ sK6)) = $true) | (((in @ X0 @ (powerset @ sK7))) != $true) | (((in @ (sK5 @ sK6 @ X0 @ sK7) @ X0)) = $true)) )),
% 0.08/0.16 inference(constrained_superposition,[],[f71,f43])).
% 0.08/0.16 thf(f179,plain,(
% 0.08/0.16 ( ! [X0 : $i] : ((((in @ X0 @ (powerset @ sK7))) != $true) | (((in @ (sK5 @ sK6 @ X0 @ sK7) @ X0)) = $true) | (((subset @ X0 @ sK6)) = $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f170])).
% 0.08/0.16 thf(f186,plain,(
% 0.08/0.16 (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)))) = $true) | ($true != $true) | (((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) = $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f179,f76])).
% 0.08/0.16 thf(f197,plain,(
% 0.08/0.16 (((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) = $true) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)))) = $true)),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f186])).
% 0.08/0.16 thf(f218,plain,(
% 0.08/0.16 (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)))) = $true)),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f197,f44])).
% 0.08/0.16 thf(f219,plain,(
% 0.08/0.16 ($true != ((in @ sK6 @ (powerset @ sK7)))) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK6)) = $true) | ($true != $true) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK7)) != $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f72,f218])).
% 0.08/0.16 thf(f220,plain,(
% 0.08/0.16 ($true != ((in @ sK6 @ (powerset @ sK7)))) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK6)) = $true) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK7)) != $true)),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f219])).
% 0.08/0.16 thf(f221,plain,(
% 0.08/0.16 (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK7)) != $true) | (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK6)) = $true)),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f220,f43])).
% 0.08/0.16 thf(f222,plain,(
% 0.08/0.16 (((in @ (sK5 @ sK6 @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK7) @ sK6)) = $true)),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f221,f160])).
% 0.08/0.16 thf(f223,plain,(
% 0.08/0.16 ($true != ((in @ sK6 @ (powerset @ sK7)))) | (((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) = $true) | (((in @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ (powerset @ sK7))) != $true) | ($true != $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f69,f222])).
% 0.08/0.16 thf(f224,plain,(
% 0.08/0.16 (((subset @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ sK6)) = $true) | ($true != ((in @ sK6 @ (powerset @ sK7)))) | (((in @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ (powerset @ sK7))) != $true)),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f223])).
% 0.08/0.16 thf(f225,plain,(
% 0.08/0.16 (((in @ (setminus @ sK7 @ (setminus @ sK7 @ sK6)) @ (powerset @ sK7))) != $true) | ($true != ((in @ sK6 @ (powerset @ sK7))))),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f224,f44])).
% 0.08/0.16 thf(f226,plain,(
% 0.08/0.16 ($true != ((in @ sK6 @ (powerset @ sK7))))),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f225,f76])).
% 0.08/0.16 thf(f227,plain,(
% 0.08/0.16 $false),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f226,f43])).
% 0.08/0.16 % SZS output end Proof for theBenchmark
% 0.08/0.16 % (169525)------------------------------
% 0.08/0.16 % (169525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (169525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (169525)CaDiCaL version: 2.1.3
% 0.08/0.16 % (169525)Termination reason: Refutation
% 0.08/0.16 % (169525)Time elapsed: 0.006 s
% 0.08/0.16 % (169525)Peak memory usage: 12 MB
% 0.08/0.16 % (169525)Instructions burned: 22 (million)
% 0.08/0.16 % (169520)Success in time 0.031 s
% 0.08/0.16 % Vampire exiting
%------------------------------------------------------------------------------