%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU593^2 : 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 : n014.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 08:30:13 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU593^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n014.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 13:54:00 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.20/0.27 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
% 0.20/0.32 % (2700876)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (2700886)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4023730236:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (2700887)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (2700887)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
% 0.20/0.32 % (2700881)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=665863296:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (2700882)lrs+10_16_si=on:nwc=1.5:random_seed=1464350547:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (2700883)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2642452910:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (2700887)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=4207500508:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (2700884)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=138230206: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)
% 0.20/0.32 % (2700885)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=935376525:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (2700883)Instruction limit reached!
% 0.20/0.32 % (2700883)------------------------------
% 0.20/0.32 % (2700883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2700883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2700883)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2700883)Termination reason: Instruction limit
% 0.20/0.32 % (2700883)Termination phase: Saturation
% 0.20/0.32 % (2700883)Time elapsed: 0.002 s
% 0.20/0.32 % (2700883)Peak memory usage: 12 MB
% 0.20/0.32 % (2700883)Instructions burned: 3 (million)
% 0.20/0.32 % (2700881) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2700876-2700881"...
% 0.20/0.32 % (2700885) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2700876-2700885"...
% 0.20/0.32 % (2700881)...printing done.
% 0.20/0.32 % (2700881)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% 0.20/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.32 thf(func_def_1, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.20/0.32 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.20/0.32 thf(func_def_3, type, subsetI1: $o).
% 0.20/0.32 thf(func_def_5, type, subsetE: $o).
% 0.20/0.32 thf(func_def_6, type, setextsub: $o).
% 0.20/0.32 thf(func_def_7, type, binintersect: ($i > $i > $i)).
% 0.20/0.32 thf(func_def_8, type, binintersectI: $o).
% 0.20/0.32 thf(func_def_9, type, binintersectLsub: $o).
% 0.20/0.32 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.32 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.32 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.32 thf(func_def_20, type, sK5: ($i > $i > $i)).
% 0.20/0.32 thf(func_def_30, type, vNOT: ($o > $o)).
% 0.20/0.32 thf(f1,axiom,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.20/0.32 thf(f2,axiom,(
% 0.20/0.32 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.20/0.32 thf(f3,axiom,(
% 0.20/0.32 (setextsub = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub)).
% 0.20/0.32 thf(f4,axiom,(
% 0.20/0.32 (binintersect = (^[X0 : $i, X1 : $i] : ((dsetconstr @ X0 @ (^[X2 : $i] : ((in @ X2 @ X1)))))))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersect)).
% 0.20/0.32 thf(f5,axiom,(
% 0.20/0.32 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI)).
% 0.20/0.32 thf(f6,axiom,(
% 0.20/0.32 (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub)).
% 0.20/0.32 thf(f7,conjecture,(
% 0.20/0.32 subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0))))))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2)).
% 0.20/0.32 thf(f8,negated_conjecture,(
% 0.20/0.32 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)))))))),
% 0.20/0.32 inference(negated_conjecture,[status(cth)],[f7])).
% 0.20/0.32 thf(f9,plain,(
% 0.20/0.32 (binintersect = (^[X0 : $i, X1 : $i] : ((dsetconstr @ X0 @ (^[X2 : $i] : ((in @ X2 @ X1)))))))),
% 0.20/0.32 inference(rectify,[],[f4])).
% 0.20/0.32 thf(f10,plain,(
% 0.20/0.32 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 0.20/0.32 inference(fool_elimination,[],[f9])).
% 0.20/0.32 thf(f11,plain,(
% 0.20/0.32 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)))))))),
% 0.20/0.32 inference(rectify,[],[f8])).
% 0.20/0.32 thf(f12,plain,(
% 0.20/0.32 ~((subsetI1 = $true) => ((subsetE = $true) => ((setextsub = $true) => ((binintersectI = $true) => ((binintersectLsub = $true) => ! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) => (((binintersect @ X0 @ X1)) = X0)))))))),
% 0.20/0.32 inference(fool_elimination,[],[f11])).
% 0.20/0.32 thf(f13,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ (binintersect @ X2 @ X0)))) = binintersectI)),
% 0.20/0.32 inference(rectify,[],[f5])).
% 0.20/0.32 thf(f14,plain,(
% 0.20/0.32 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ X2)) = $true) => ((((in @ X1 @ X0)) = $true) => (((in @ X1 @ (binintersect @ X2 @ X0))) = $true))) <=> (binintersectI = $true)),
% 0.20/0.32 inference(fool_elimination,[],[f13])).
% 0.20/0.32 thf(f15,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.20/0.32 inference(rectify,[],[f1])).
% 0.20/0.32 thf(f16,plain,(
% 0.20/0.32 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.20/0.32 inference(fool_elimination,[],[f15])).
% 0.20/0.32 thf(f17,plain,(
% 0.20/0.32 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))))),
% 0.20/0.32 inference(rectify,[],[f3])).
% 0.20/0.32 thf(f18,plain,(
% 0.20/0.32 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) => ((((subset @ X0 @ X1)) = $true) => (X0 = X1)))),
% 0.20/0.32 inference(fool_elimination,[],[f17])).
% 0.20/0.32 thf(f19,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 0.20/0.32 inference(rectify,[],[f2])).
% 0.20/0.32 thf(f20,plain,(
% 0.20/0.32 ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X1 @ X0)) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true))) <=> (subsetE = $true)),
% 0.20/0.32 inference(fool_elimination,[],[f19])).
% 0.20/0.32 thf(f21,plain,(
% 0.20/0.32 (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 0.20/0.32 inference(rectify,[],[f6])).
% 0.20/0.32 thf(f22,plain,(
% 0.20/0.32 (binintersectLsub = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) = $true)),
% 0.20/0.32 inference(fool_elimination,[],[f21])).
% 0.20/0.32 thf(f23,plain,(
% 0.20/0.32 ! [X0 : $i,X1 : $i,X2 : $i] : (((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((subset @ X1 @ X0)) != $true)) <=> (subsetE = $true)),
% 0.20/0.32 inference(ennf_transformation,[],[f20])).
% 0.20/0.32 thf(f24,plain,(
% 0.20/0.32 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) | (((subset @ X1 @ X0)) != $true) | (((in @ X2 @ X0)) = $true)) <=> (subsetE = $true)),
% 0.20/0.32 inference(flattening,[],[f23])).
% 0.20/0.32 thf(f25,plain,(
% 0.20/0.32 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | (((subset @ X0 @ X1)) != $true)) | (((subset @ X1 @ X0)) != $true))),
% 0.20/0.32 inference(ennf_transformation,[],[f18])).
% 0.20/0.32 thf(f26,plain,(
% 0.20/0.32 ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (X0 = X1) | (((subset @ X1 @ X0)) != $true)) <=> (setextsub = $true)),
% 0.20/0.32 inference(flattening,[],[f25])).
% 0.20/0.32 thf(f27,plain,(
% 0.20/0.32 ((((? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) & (((binintersect @ X0 @ X1)) != X0)) & (binintersectLsub = $true)) & (binintersectI = $true)) & (setextsub = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 0.20/0.32 inference(ennf_transformation,[],[f12])).
% 0.20/0.32 thf(f28,plain,(
% 0.20/0.32 ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) & (((binintersect @ X0 @ X1)) != X0)) & (subsetI1 = $true) & (subsetE = $true) & (binintersectI = $true) & (setextsub = $true) & (binintersectLsub = $true)),
% 0.20/0.32 inference(flattening,[],[f27])).
% 0.20/0.32 thf(f29,plain,(
% 0.20/0.32 ! [X1 : $i,X0 : $i,X2 : $i] : (((((in @ X1 @ (binintersect @ X2 @ X0))) = $true) | (((in @ X1 @ X0)) != $true)) | (((in @ X1 @ X2)) != $true)) <=> (binintersectI = $true)),
% 0.20/0.32 inference(ennf_transformation,[],[f14])).
% 0.20/0.32 thf(f30,plain,(
% 0.20/0.32 ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X1 @ (binintersect @ X2 @ X0))) = $true) | (((in @ X1 @ X0)) != $true)) <=> (binintersectI = $true)),
% 0.20/0.32 inference(flattening,[],[f29])).
% 0.20/0.32 thf(f31,plain,(
% 0.20/0.32 ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) <=> (subsetI1 = $true)),
% 0.20/0.32 inference(ennf_transformation,[],[f16])).
% 0.20/0.32 thf(f32,plain,(
% 0.20/0.32 (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X1 @ (binintersect @ X2 @ X0))) = $true) | (((in @ X1 @ X0)) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X1 @ (binintersect @ X2 @ X0))) != $true) & (((in @ X1 @ X0)) = $true)))),
% 0.20/0.32 inference(nnf_transformation,[],[f30])).
% 0.20/0.32 thf(f33,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ (binintersect @ X0 @ X2))) = $true) | (((in @ X1 @ X2)) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) & ($true != ((in @ X4 @ (binintersect @ X3 @ X5)))) & ($true = ((in @ X4 @ X5)))))),
% 0.20/0.32 inference(rectify,[],[f32])).
% 0.20/0.32 thf(f34,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ (binintersect @ X0 @ X2))) = $true) | (((in @ X1 @ X2)) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | (($true = ((in @ sK1 @ sK0))) & ($true != ((in @ sK1 @ (binintersect @ sK0 @ sK2)))) & ($true = ((in @ sK1 @ sK2)))))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f33])).
% 0.20/0.32 thf(f35,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (X0 = X1) | (((subset @ X1 @ X0)) != $true)) | (setextsub != $true)) & ((setextsub = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) & (X0 != X1) & (((subset @ X1 @ X0)) = $true)))),
% 0.20/0.32 inference(nnf_transformation,[],[f26])).
% 0.20/0.32 thf(f36,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (X0 = X1) | (((subset @ X1 @ X0)) != $true)) | (setextsub != $true)) & ((setextsub = $true) | ? [X2 : $i,X3 : $i] : (($true = ((subset @ X2 @ X3))) & (X2 != X3) & ($true = ((subset @ X3 @ X2)))))),
% 0.20/0.32 inference(rectify,[],[f35])).
% 0.20/0.32 thf(f37,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (X0 = X1) | (((subset @ X1 @ X0)) != $true)) | (setextsub != $true)) & ((setextsub = $true) | (($true = ((subset @ sK3 @ sK4))) & (sK3 != sK4) & ($true = ((subset @ sK4 @ sK3)))))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3),skolemize(X3,sK4)],[f36])).
% 0.20/0.32 thf(f38,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true))))),
% 0.20/0.32 inference(nnf_transformation,[],[f31])).
% 0.20/0.32 thf(f39,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) != $true) & ! [X5 : $i] : (($true = ((in @ X5 @ X4))) | ($true != ((in @ X5 @ X3))))))),
% 0.20/0.32 inference(rectify,[],[f38])).
% 0.20/0.32 thf(f40,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (($true != ((in @ (sK5 @ X1 @ X0) @ X1))) & ($true = ((in @ (sK5 @ X1 @ X0) @ X0))))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != ((subset @ sK6 @ sK7))) & ! [X5 : $i] : (($true = ((in @ X5 @ sK7))) | ($true != ((in @ X5 @ sK6))))))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK6,sK7]),skolemize(X2,sK5 @ X1 @ X0),skolemize(X3,sK6),skolemize(X4,sK7)],[f39])).
% 0.20/0.32 thf(f41,plain,(
% 0.20/0.32 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) != $true)) & (! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) = $true) | (binintersectLsub != $true))),
% 0.20/0.32 inference(nnf_transformation,[],[f22])).
% 0.20/0.32 thf(f42,plain,(
% 0.20/0.32 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) != $true)) & (! [X2 : $i,X3 : $i] : ($true = ((subset @ (binintersect @ X2 @ X3) @ X2))) | (binintersectLsub != $true))),
% 0.20/0.32 inference(rectify,[],[f41])).
% 0.20/0.32 thf(f43,plain,(
% 0.20/0.32 ((binintersectLsub = $true) | (((subset @ (binintersect @ sK8 @ sK9) @ sK8)) != $true)) & (! [X2 : $i,X3 : $i] : ($true = ((subset @ (binintersect @ X2 @ X3) @ X2))) | (binintersectLsub != $true))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f42])).
% 0.20/0.32 thf(f44,plain,(
% 0.20/0.32 ((((subset @ sK10 @ sK11)) = $true) & (((binintersect @ sK10 @ sK11)) != sK10)) & (subsetI1 = $true) & (subsetE = $true) & (binintersectI = $true) & (setextsub = $true) & (binintersectLsub = $true)),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f28])).
% 0.20/0.32 thf(f45,plain,(
% 0.20/0.32 (! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) | (((subset @ X1 @ X0)) != $true) | (((in @ X2 @ X0)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) & (((subset @ X1 @ X0)) = $true) & (((in @ X2 @ X0)) != $true)))),
% 0.20/0.32 inference(nnf_transformation,[],[f24])).
% 0.20/0.32 thf(f46,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X2))) | ($true != ((subset @ X2 @ X1))) | (((in @ X0 @ X1)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X3 @ X5))) & ($true = ((subset @ X5 @ X4))) & (((in @ X3 @ X4)) != $true)))),
% 0.20/0.32 inference(rectify,[],[f45])).
% 0.20/0.32 thf(f47,plain,(
% 0.20/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X2))) | ($true != ((subset @ X2 @ X1))) | (((in @ X0 @ X1)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | (($true = ((in @ sK12 @ sK14))) & (((subset @ sK14 @ sK13)) = $true) & ($true != ((in @ sK12 @ sK13)))))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X3,sK12),skolemize(X4,sK13),skolemize(X5,sK14)],[f46])).
% 0.20/0.32 thf(f51,plain,(
% 0.20/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ (binintersect @ X0 @ X2))) = $true) | (((in @ X1 @ X2)) != $true) | (binintersectI != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f34])).
% 0.20/0.32 thf(f55,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (X0 = X1) | (((subset @ X1 @ X0)) != $true) | (setextsub != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f37])).
% 0.20/0.32 thf(f58,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ($true = ((in @ (sK5 @ X1 @ X0) @ X0))) | (subsetI1 != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f40])).
% 0.20/0.32 thf(f59,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ($true != ((in @ (sK5 @ X1 @ X0) @ X1))) | (subsetI1 != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f40])).
% 0.20/0.32 thf(f60,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i] : (($true = ((subset @ (binintersect @ X2 @ X3) @ X2))) | (binintersectLsub != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f43])).
% 0.20/0.32 thf(f62,plain,(
% 0.20/0.32 (binintersectLsub = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f44])).
% 0.20/0.32 thf(f63,plain,(
% 0.20/0.32 (setextsub = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f44])).
% 0.20/0.32 thf(f64,plain,(
% 0.20/0.32 (binintersectI = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f44])).
% 0.20/0.32 thf(f65,plain,(
% 0.20/0.32 (subsetE = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f44])).
% 0.20/0.32 thf(f66,plain,(
% 0.20/0.32 (subsetI1 = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f44])).
% 0.20/0.32 thf(f67,plain,(
% 0.20/0.32 (((binintersect @ sK10 @ sK11)) != sK10)),
% 0.20/0.32 inference(cnf_transformation,[],[f44])).
% 0.20/0.32 thf(f68,plain,(
% 0.20/0.32 (((subset @ sK10 @ sK11)) = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f44])).
% 0.20/0.32 thf(f69,plain,(
% 0.20/0.32 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 0.20/0.32 inference(cnf_transformation,[],[f10])).
% 0.20/0.32 thf(f73,plain,(
% 0.20/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X2))) | ($true != ((subset @ X2 @ X1))) | (((in @ X0 @ X1)) = $true) | (subsetE != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f47])).
% 0.20/0.32 thf(f76,plain,(
% 0.20/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | ($true != $true) | ($true = ((in @ X1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X0 @ X2)))) | (((in @ X1 @ X0)) != $true)) )),
% 0.20/0.32 inference(definition_unfolding,[],[f51,f69,f64])).
% 0.20/0.32 thf(f80,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ X1 @ X0)) != $true) | (X0 = X1) | (((subset @ X0 @ X1)) != $true)) )),
% 0.20/0.32 inference(definition_unfolding,[],[f55,f63])).
% 0.20/0.32 thf(f84,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ X0 @ X1)) = $true) | ($true != ((in @ (sK5 @ X1 @ X0) @ X1)))) )),
% 0.20/0.32 inference(definition_unfolding,[],[f59,f66])).
% 0.20/0.32 thf(f85,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ (sK5 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.20/0.32 inference(definition_unfolding,[],[f58,f66])).
% 0.20/0.32 thf(f89,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i] : (($true != $true) | (((subset @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X2 @ X3) @ X2)) = $true)) )),
% 0.20/0.32 inference(definition_unfolding,[],[f60,f69,f62])).
% 0.20/0.32 thf(f90,plain,(
% 0.20/0.32 ((((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK10 @ sK11)) != sK10)),
% 0.20/0.32 inference(definition_unfolding,[],[f67,f69])).
% 0.20/0.32 thf(f91,plain,(
% 0.20/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ X0 @ X2))) | ($true != ((subset @ X2 @ X1))) | (((in @ X0 @ X1)) = $true)) )),
% 0.20/0.32 inference(definition_unfolding,[],[f73,f65])).
% 0.20/0.32 thf(f95,plain,(
% 0.20/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((subset @ X2 @ X1))) | ($true != ((in @ X0 @ X2))) | (((in @ X0 @ X1)) = $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f91])).
% 0.20/0.32 thf(f96,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) | (X0 = X1) | (((subset @ X0 @ X1)) != $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f80])).
% 0.20/0.32 thf(f97,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i] : ((((subset @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X2 @ X3) @ X2)) = $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f89])).
% 0.20/0.32 thf(f98,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i] : (($true = ((subset @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ Y0 @ X3))) @ X2)))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f97])).
% 0.20/0.32 thf(f99,plain,(
% 0.20/0.32 (((dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11)))) != sK10)),
% 0.20/0.32 inference(beta-eta_normalization,[],[f90])).
% 0.20/0.32 thf(f100,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK5 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f85])).
% 0.20/0.32 thf(f101,plain,(
% 0.20/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X0 @ X2)))) | (((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) != $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f76])).
% 0.20/0.32 thf(f102,plain,(
% 0.20/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X1 @ X0)) != $true) | (((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ Y0 @ X2))))) = $true)) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f101])).
% 0.20/0.32 thf(f103,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK5 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f84])).
% 0.20/0.32 thf(f118,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true != $true) | (((in @ X0 @ sK11)) = $true) | ($true != ((in @ X0 @ sK10)))) )),
% 0.20/0.32 inference(constrained_superposition,[],[f95,f68])).
% 0.20/0.32 thf(f120,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK10))) | (((in @ X0 @ sK11)) = $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f118])).
% 0.20/0.32 thf(f121,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ (sK5 @ X0 @ sK10) @ sK11))) | ($true = ((subset @ sK10 @ X0)))) )),
% 0.20/0.32 inference(constrained_superposition,[],[f120,f100])).
% 0.20/0.32 thf(f122,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true = ((in @ (sK5 @ X0 @ sK10) @ sK11))) | ($true = ((subset @ sK10 @ X0)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f121])).
% 0.20/0.32 thf(f133,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ sK10 @ X0))) | ($true = ((in @ (sK5 @ X0 @ sK10) @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ Y0 @ sK11)))))) | ($true != ((in @ (sK5 @ X0 @ sK10) @ X1))) | ($true != $true)) )),
% 0.20/0.32 inference(constrained_superposition,[],[f102,f122])).
% 0.20/0.32 thf(f135,plain,(
% 0.20/0.32 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK5 @ X0 @ sK10) @ X1))) | ($true = ((in @ (sK5 @ X0 @ sK10) @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ Y0 @ sK11)))))) | ($true = ((subset @ sK10 @ X0)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f133])).
% 0.20/0.32 thf(f189,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true = ((subset @ sK10 @ X0))) | ($true != $true) | ($true = ((subset @ sK10 @ X0))) | (((in @ (sK5 @ X0 @ sK10) @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))))) = $true)) )),
% 0.20/0.32 inference(constrained_superposition,[],[f135,f100])).
% 0.20/0.32 thf(f197,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true = ((subset @ sK10 @ X0))) | (((in @ (sK5 @ X0 @ sK10) @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))))) = $true) | ($true != $true)) )),
% 0.20/0.32 inference(duplicate_literal_removal,[],[f189])).
% 0.20/0.32 thf(f198,plain,(
% 0.20/0.32 ( ! [X0 : $i] : ((((in @ (sK5 @ X0 @ sK10) @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))))) = $true) | ($true = ((subset @ sK10 @ X0)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f197])).
% 0.20/0.32 thf(f203,plain,(
% 0.20/0.32 (((subset @ sK10 @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))))) = $true) | ($true != $true) | (((subset @ sK10 @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))))) = $true)),
% 0.20/0.32 inference(constrained_superposition,[],[f103,f198])).
% 0.20/0.32 thf(f208,plain,(
% 0.20/0.32 (((subset @ sK10 @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))))) = $true) | ($true != $true)),
% 0.20/0.32 inference(duplicate_literal_removal,[],[f203])).
% 0.20/0.32 thf(f209,plain,(
% 0.20/0.32 (((subset @ sK10 @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))))) = $true)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f208])).
% 0.20/0.32 thf(f218,plain,(
% 0.20/0.32 (((subset @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))) @ sK10)) != $true) | ($true != $true) | (((dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11)))) = sK10)),
% 0.20/0.32 inference(constrained_superposition,[],[f96,f209])).
% 0.20/0.32 thf(f219,plain,(
% 0.20/0.32 (((subset @ (dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11))) @ sK10)) != $true) | (((dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11)))) = sK10)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f218])).
% 0.20/0.32 thf(f221,plain,(
% 0.20/0.32 (((dsetconstr @ sK10 @ (^[Y0 : $i]: (in @ Y0 @ sK11)))) = sK10)),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f219,f98])).
% 0.20/0.32 thf(f222,plain,(
% 0.20/0.32 $false),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f221,f99])).
% 0.20/0.32 % SZS output end Proof for theBenchmark
% 0.20/0.32 % (2700881)------------------------------
% 0.20/0.32 % (2700881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2700881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2700881)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2700881)Termination reason: Refutation
% 0.20/0.32 % (2700881)Time elapsed: 0.011 s
% 0.20/0.32 % (2700881)Peak memory usage: 12 MB
% 0.20/0.32 % (2700881)Instructions burned: 18 (million)
% 0.20/0.32 % (2700876)Success in time 0.043 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------