%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU761^2 : 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 : 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 08:31:11 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 : SEU761^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % 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 14:22:39 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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 % (796999)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (797006)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1842402624:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (797006)Refutation not found, incomplete strategy
% 0.21/0.29 % (797006)------------------------------
% 0.21/0.29 % (797006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (797006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (797006)CaDiCaL version: 2.1.3
% 0.21/0.29 % (797006)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (797006)Time elapsed: 0.001 s
% 0.21/0.29 % (797006)Peak memory usage: 12 MB
% 0.21/0.29 % (797006)Instructions burned: 3 (million)
% 0.21/0.29 % (797006)------------------------------
% 0.21/0.29 % (797006)------------------------------
% 0.21/0.29 % (797004)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3846426580:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (797005)lrs+10_16_si=on:nwc=1.5:random_seed=702487656:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (797008)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2522523155:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (797007)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=2455206019: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 % (797009)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=870721665:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (797012)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3002569201:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.29 % (797012)Instruction limit reached!
% 0.21/0.29 % (797012)------------------------------
% 0.21/0.29 % (797012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (797012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (797012)CaDiCaL version: 2.1.3
% 0.21/0.29 % (797012)Termination reason: Instruction limit
% 0.21/0.29 % (797012)Termination phase: Saturation
% 0.21/0.29 % (797012)Time elapsed: 0.0000 s
% 0.21/0.29 % (797012)Peak memory usage: 10 MB
% 0.21/0.29 % (797012)Instructions burned: 2 (million)
% 0.21/0.29 % (797010)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 % (797010)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 % (797008) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-796999-797008"...
% 0.21/0.29 % (797005)Instruction limit reached!
% 0.21/0.29 % (797005)------------------------------
% 0.21/0.29 % (797005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (797005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (797005)CaDiCaL version: 2.1.3
% 0.21/0.29 % (797005)Termination reason: Instruction limit
% 0.21/0.29 % (797005)Termination phase: Saturation
% 0.21/0.29 % (797005)Time elapsed: 0.010 s
% 0.21/0.29 % (797005)Peak memory usage: 12 MB
% 0.21/0.29 % (797005)Instructions burned: 19 (million)
% 0.21/0.29 % (797008)...printing done.
% 0.21/0.29 % (797008)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, subsetI1: $o).
% 0.21/0.29 thf(func_def_5, type, subsetE: $o).
% 0.21/0.29 thf(func_def_6, type, binintersect: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_7, type, binintersectI: $o).
% 0.21/0.29 thf(func_def_22, type, sK12: ($i > $i > $i)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 (subsetE = ! [X1 : $i,X0 : $i,X2 : $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(f3,axiom,(
% 0.21/0.29 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI)).
% 0.21/0.29 thf(f4,conjecture,(
% 0.21/0.29 subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3)))))))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule3)).
% 0.21/0.29 thf(f5,negated_conjecture,(
% 0.21/0.29 ~(subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ~(subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))))))),
% 0.21/0.29 inference(rectify,[],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectI = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ (powerset @ X0))) = $true) => ((((subset @ X1 @ X2)) = $true) => ((((subset @ X1 @ X3)) = $true) => (((subset @ X1 @ (binintersect @ X2 @ X3))) = $true)))))))))),
% 0.21/0.29 inference(fool_elimination,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (binintersect @ X1 @ X2)))) = binintersectI)),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X0 @ X1))) => ((((in @ X0 @ X2)) = $true) => ($true = ((in @ X0 @ (binintersect @ X1 @ X2)))))) <=> (binintersectI = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true)) <=> (subsetI1 = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)))),
% 0.21/0.29 inference(fool_elimination,[],[f12])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f11])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((subset @ X1 @ X0)) != $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f13])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true) | (((subset @ X1 @ X0)) != $true))),
% 0.21/0.29 inference(flattening,[],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ! [X1 : $i,X2 : $i,X0 : $i] : ((($true = ((in @ X0 @ (binintersect @ X1 @ X2)))) | (((in @ X0 @ X2)) != $true)) | ($true != ((in @ X0 @ X1)))) <=> (binintersectI = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f9])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ X2)) != $true) | ($true = ((in @ X0 @ (binintersect @ X1 @ X2))))) <=> (binintersectI = $true)),
% 0.21/0.29 inference(flattening,[],[f17])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((((subset @ X1 @ (binintersect @ X2 @ X3))) != $true) & (((subset @ X1 @ X3)) = $true)) & (((subset @ X1 @ X2)) = $true)) & (((in @ X3 @ (powerset @ X0))) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (binintersectI = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f7])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 (binintersectI = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & ? [X3 : $i] : ((((subset @ X1 @ X3)) = $true) & (((subset @ X1 @ (binintersect @ X2 @ X3))) != $true) & (((subset @ X1 @ X2)) = $true) & (((in @ X3 @ (powerset @ X0))) = $true))) & (((in @ X1 @ (powerset @ X0))) = $true)) & (subsetI1 = $true) & (subsetE = $true)),
% 0.21/0.29 inference(flattening,[],[f19])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true) & (((subset @ X1 @ X0)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true) | (((subset @ X1 @ X0)) != $true)) | (subsetE != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f16])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true) & (((subset @ X1 @ X0)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ X5 @ X3))) | (((subset @ X4 @ X3)) != $true)) | (subsetE != $true))),
% 0.21/0.29 inference(rectify,[],[f21])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ((subsetE = $true) | ((((in @ sK2 @ sK1)) = $true) & ($true != ((in @ sK2 @ sK0))) & (((subset @ sK1 @ sK0)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ X5 @ X3))) | (((subset @ X4 @ X3)) != $true)) | (subsetE != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f22])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 (binintersectI = $true) & (((((in @ sK5 @ (powerset @ sK3))) = $true) & ((((subset @ sK4 @ sK6)) = $true) & (((subset @ sK4 @ (binintersect @ sK5 @ sK6))) != $true) & (((subset @ sK4 @ sK5)) = $true) & (((in @ sK6 @ (powerset @ sK3))) = $true))) & (((in @ sK4 @ (powerset @ sK3))) = $true)) & (subsetI1 = $true) & (subsetE = $true)),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f20])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ X2)) != $true) | ($true = ((in @ X0 @ (binintersect @ X1 @ X2))))) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) & (((in @ X0 @ X2)) = $true) & ($true != ((in @ X0 @ (binintersect @ X1 @ X2))))))),
% 0.21/0.29 inference(nnf_transformation,[],[f18])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ X2)) != $true) | ($true = ((in @ X0 @ (binintersect @ X1 @ X2))))) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X3 @ X4))) & ($true = ((in @ X3 @ X5))) & (((in @ X3 @ (binintersect @ X4 @ X5))) != $true)))),
% 0.21/0.29 inference(rectify,[],[f25])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ X2)) != $true) | ($true = ((in @ X0 @ (binintersect @ X1 @ X2))))) | (binintersectI != $true)) & ((binintersectI = $true) | (($true = ((in @ sK7 @ sK8))) & (((in @ sK7 @ sK9)) = $true) & ($true != ((in @ sK7 @ (binintersect @ sK8 @ sK9))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f26])).
% 0.21/0.29 thf(f28,plain,(
% 0.21/0.29 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((subset @ X1 @ X0)) != $true))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI1 != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f14])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((subset @ X1 @ X0)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true != ((in @ X5 @ X3))) & (((in @ X5 @ X4)) = $true)) | (((subset @ X4 @ X3)) = $true)) | (subsetI1 != $true))),
% 0.21/0.29 inference(rectify,[],[f28])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 ((subsetI1 = $true) | (! [X2 : $i] : ((((in @ X2 @ sK10)) = $true) | ($true != ((in @ X2 @ sK11)))) & ($true != ((subset @ sK11 @ sK10))))) & (! [X3 : $i,X4 : $i] : (((((in @ (sK12 @ X4 @ X3) @ X3)) != $true) & ($true = ((in @ (sK12 @ X4 @ X3) @ X4)))) | (((subset @ X4 @ X3)) = $true)) | (subsetI1 != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,vAPP]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X5,sK12 @ X4 @ X3)],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((subset @ X4 @ X3)) != $true) | ($true = ((in @ X5 @ X3))) | (((in @ X5 @ X4)) != $true) | (subsetE != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 (subsetE = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f36,plain,(
% 0.21/0.29 (subsetI1 = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 (((subset @ sK4 @ sK5)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f40,plain,(
% 0.21/0.29 (((subset @ sK4 @ (binintersect @ sK5 @ sK6))) != $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f41,plain,(
% 0.21/0.29 (((subset @ sK4 @ sK6)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f43,plain,(
% 0.21/0.29 (binintersectI = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f47,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X1))) | (((in @ X0 @ X2)) != $true) | (binintersectI != $true) | ($true = ((in @ X0 @ (binintersect @ X1 @ X2))))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f27])).
% 0.21/0.29 thf(f48,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | ($true = ((in @ (sK12 @ X4 @ X3) @ X4))) | (subsetI1 != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f30])).
% 0.21/0.29 thf(f49,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : ((subsetI1 != $true) | (((subset @ X4 @ X3)) = $true) | (((in @ (sK12 @ X4 @ X3) @ X3)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f30])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK12 @ X4 @ X3) @ X4))) | (((subset @ X4 @ X3)) = $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f48,f36])).
% 0.21/0.29 thf(f57,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK12 @ X4 @ X3) @ X3)) != $true) | (((subset @ X4 @ X3)) = $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f49,f36])).
% 0.21/0.29 thf(f61,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((subset @ X4 @ X3)) != $true) | ($true = ((in @ X5 @ X3))) | (((in @ X5 @ X4)) != $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f31,f35])).
% 0.21/0.29 thf(f63,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK5))) | (((in @ X0 @ sK4)) != $true) | ($true != $true)) )),
% 0.21/0.29 inference(superposition,[],[f61,f39])).
% 0.21/0.29 thf(f64,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK6)) = $true) | (((in @ X0 @ sK4)) != $true) | ($true != $true)) )),
% 0.21/0.29 inference(superposition,[],[f61,f41])).
% 0.21/0.29 thf(f65,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK5))) | (((in @ X0 @ sK4)) != $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f63])).
% 0.21/0.29 thf(f66,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK6)) = $true) | (((in @ X0 @ sK4)) != $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f64])).
% 0.21/0.29 thf(f69,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (binintersect @ X1 @ X2)))) | ($true != ((in @ X0 @ X1))) | (((in @ X0 @ X2)) != $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f47,f43])).
% 0.21/0.29 thf(f78,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X1))) | ($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X2))) | (((subset @ X0 @ (binintersect @ X1 @ X2))) = $true) | ($true != $true)) )),
% 0.21/0.29 inference(superposition,[],[f57,f69])).
% 0.21/0.29 thf(f79,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X2))) | (((subset @ X0 @ (binintersect @ X1 @ X2))) = $true) | ($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X1)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f78])).
% 0.21/0.29 thf(f83,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ sK6)) @ X1))) | (((subset @ X0 @ (binintersect @ X1 @ sK6))) = $true) | ($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ sK6)) @ sK4))) | ($true != $true)) )),
% 0.21/0.29 inference(superposition,[],[f79,f66])).
% 0.21/0.29 thf(f85,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ sK6)) @ sK4))) | ($true != ((in @ (sK12 @ X0 @ (binintersect @ X1 @ sK6)) @ X1))) | (((subset @ X0 @ (binintersect @ X1 @ sK6))) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f83])).
% 0.21/0.29 thf(f109,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((subset @ sK4 @ (binintersect @ X0 @ sK6))) = $true) | ($true != $true) | ($true != ((in @ (sK12 @ sK4 @ (binintersect @ X0 @ sK6)) @ X0))) | (((subset @ sK4 @ (binintersect @ X0 @ sK6))) = $true)) )),
% 0.21/0.29 inference(superposition,[],[f85,f56])).
% 0.21/0.29 thf(f110,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((subset @ sK4 @ (binintersect @ X0 @ sK6))) = $true) | ($true != ((in @ (sK12 @ sK4 @ (binintersect @ X0 @ sK6)) @ X0)))) )),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f109])).
% 0.21/0.29 thf(f111,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != ((in @ (sK12 @ sK4 @ (binintersect @ X0 @ sK6)) @ X0))) | (((subset @ sK4 @ (binintersect @ X0 @ sK6))) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f110])).
% 0.21/0.29 thf(f155,plain,(
% 0.21/0.29 (((subset @ sK4 @ (binintersect @ sK5 @ sK6))) = $true) | ($true != ((in @ (sK12 @ sK4 @ (binintersect @ sK5 @ sK6)) @ sK4))) | ($true != $true)),
% 0.21/0.29 inference(superposition,[],[f111,f65])).
% 0.21/0.29 thf(f158,plain,(
% 0.21/0.29 (((subset @ sK4 @ (binintersect @ sK5 @ sK6))) = $true) | ($true != ((in @ (sK12 @ sK4 @ (binintersect @ sK5 @ sK6)) @ sK4)))),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f155])).
% 0.21/0.29 thf(f166,plain,(
% 0.21/0.29 (((subset @ sK4 @ (binintersect @ sK5 @ sK6))) = $true)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f158,f56])).
% 0.21/0.29 thf(f169,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f166,f40])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (797008)------------------------------
% 0.21/0.29 % (797008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (797008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (797008)CaDiCaL version: 2.1.3
% 0.21/0.29 % (797008)Termination reason: Refutation
% 0.21/0.29 % (797008)Time elapsed: 0.010 s
% 0.21/0.29 % (797008)Peak memory usage: 12 MB
% 0.21/0.29 % (797008)Instructions burned: 18 (million)
% 0.21/0.29 % (796999)Success in time 0.048 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------