%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU759^2 : 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 : n008.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 08:31:10 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU759^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:23:24 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.29 % (3229705)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3229715)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1271868994:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (3229713)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=1579950823: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)
% 0.22/0.29 % (3229711)lrs+10_16_si=on:nwc=1.5:random_seed=1148195891:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (3229710)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2776521564:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (3229712)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1986445975:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (3229712)Refutation not found, incomplete strategy
% 0.22/0.29 % (3229712)------------------------------
% 0.22/0.29 % (3229712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3229712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3229712)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3229712)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.29 % (3229712)Time elapsed: 0.002 s
% 0.22/0.29 % (3229712)Peak memory usage: 12 MB
% 0.22/0.29 % (3229712)Instructions burned: 3 (million)
% 0.22/0.29 % (3229712)------------------------------
% 0.22/0.29 % (3229712)------------------------------
% 0.22/0.29 % (3229715) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3229705-3229715"...
% 0.22/0.29 % (3229710) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3229705-3229710"...
% 0.22/0.29 % (3229713) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3229705-3229713"...
% 0.22/0.29 % (3229715)...printing done.
% 0.22/0.29 % (3229715)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_1, type, powerset: ($i > $i)).
% 0.22/0.30 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_3, type, subsetI1: $o).
% 0.22/0.30 thf(func_def_5, type, subsetE: $o).
% 0.22/0.30 thf(func_def_6, type, binintersect: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_7, type, binintersectEL: $o).
% 0.22/0.30 thf(func_def_10, type, sK0: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.22/0.30 thf(f2,axiom,(
% 0.22/0.30 (! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.22/0.30 thf(f3,axiom,(
% 0.22/0.30 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)) = binintersectEL)),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)).
% 0.22/0.30 thf(f4,conjecture,(
% 0.22/0.30 subsetI1 => (subsetE => (binintersectEL => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3)))))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule1)).
% 0.22/0.30 thf(f5,negated_conjecture,(
% 0.22/0.30 ~(subsetI1 => (subsetE => (binintersectEL => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2))) = subsetE)),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2)) = $true) => ((((in @ X1 @ X0)) = $true) => (((in @ X1 @ X2)) = $true)))),
% 0.22/0.30 inference(fool_elimination,[],[f6])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X1)) = binintersectEL)),
% 0.22/0.30 inference(rectify,[],[f3])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 (binintersectEL = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) = $true) => (((in @ X0 @ X1)) = $true))),
% 0.22/0.30 inference(fool_elimination,[],[f8])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.22/0.30 inference(rectify,[],[f1])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.22/0.30 inference(fool_elimination,[],[f10])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ~(subsetI1 => (subsetE => (binintersectEL => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))))))),
% 0.22/0.30 inference(rectify,[],[f5])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectEL = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ! [X3 : $i] : ((((in @ X3 @ (powerset @ X1))) = $true) => ((((subset @ X0 @ X3)) = $true) => (((subset @ (binintersect @ X0 @ X2) @ X3)) = $true))))))))),
% 0.22/0.30 inference(fool_elimination,[],[f12])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) <=> (subsetI1 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f11])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true)) <=> (binintersectEL = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f9])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((((in @ X1 @ X2)) = $true) | (((in @ X1 @ X0)) != $true)) | (((subset @ X0 @ X2)) != $true))),
% 0.22/0.30 inference(ennf_transformation,[],[f7])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true) | (((subset @ X0 @ X2)) != $true)) <=> (subsetE = $true)),
% 0.22/0.30 inference(flattening,[],[f16])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((((subset @ (binintersect @ X0 @ X2) @ X3)) != $true) & (((subset @ X0 @ X3)) = $true)) & (((in @ X3 @ (powerset @ X1))) = $true)) & (((in @ X2 @ (powerset @ X1))) = $true)) & (((in @ X0 @ (powerset @ X1))) = $true)) & (binintersectEL = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f13])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & ? [X3 : $i] : ((((in @ X3 @ (powerset @ X1))) = $true) & (((subset @ X0 @ X3)) = $true) & (((subset @ (binintersect @ X0 @ X2) @ X3)) != $true))) & (((in @ X0 @ (powerset @ X1))) = $true)) & (binintersectEL = $true) & (subsetE = $true) & (subsetI1 = $true)),
% 0.22/0.30 inference(flattening,[],[f18])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true)))),
% 0.22/0.30 inference(nnf_transformation,[],[f14])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : ((((in @ X5 @ X3)) = $true) | (((in @ X5 @ X4)) != $true)) & (((subset @ X4 @ X3)) != $true)))),
% 0.22/0.30 inference(rectify,[],[f20])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : ((($true != ((in @ (sK0 @ X1 @ X0) @ X0))) & (((in @ (sK0 @ X1 @ X0) @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | (! [X5 : $i] : (($true = ((in @ X5 @ sK1))) | (((in @ X5 @ sK2)) != $true)) & (((subset @ sK2 @ sK1)) != $true)))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f21])).
% 0.22/0.30 thf(f23,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) != $true) & (((in @ X0 @ (binintersect @ X1 @ X2))) = $true)))),
% 0.22/0.30 inference(nnf_transformation,[],[f15])).
% 0.22/0.30 thf(f24,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ X4)) != $true) & (((in @ X3 @ (binintersect @ X4 @ X5))) = $true)))),
% 0.22/0.30 inference(rectify,[],[f23])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | (($true != ((in @ sK3 @ sK4))) & (((in @ sK3 @ (binintersect @ sK4 @ sK5))) = $true)))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f24])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 (! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true) | (((subset @ X0 @ X2)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) & (((in @ X1 @ X2)) != $true) & (((subset @ X0 @ X2)) = $true)))),
% 0.22/0.30 inference(nnf_transformation,[],[f17])).
% 0.22/0.30 thf(f27,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ X2)) = $true) | (((subset @ X1 @ X2)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ X4)) = $true) & (((in @ X3 @ X5)) != $true) & (((subset @ X4 @ X5)) = $true)))),
% 0.22/0.30 inference(rectify,[],[f26])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ X2)) = $true) | (((subset @ X1 @ X2)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ((((in @ sK6 @ sK7)) = $true) & (((in @ sK6 @ sK8)) != $true) & (((subset @ sK7 @ sK8)) = $true)))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8)],[f27])).
% 0.22/0.30 thf(f29,plain,(
% 0.22/0.30 (((((in @ sK11 @ (powerset @ sK10))) = $true) & ((((in @ sK12 @ (powerset @ sK10))) = $true) & (((subset @ sK9 @ sK12)) = $true) & (((subset @ (binintersect @ sK9 @ sK11) @ sK12)) != $true))) & (((in @ sK9 @ (powerset @ sK10))) = $true)) & (binintersectEL = $true) & (subsetE = $true) & (subsetI1 = $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f19])).
% 0.22/0.30 thf(f32,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) = $true) | (((subset @ X1 @ X0)) = $true) | (subsetI1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f22])).
% 0.22/0.30 thf(f33,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ X1 @ X0) @ X0))) | (((subset @ X1 @ X0)) = $true) | (subsetI1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f22])).
% 0.22/0.30 thf(f36,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | (binintersectEL != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f25])).
% 0.22/0.30 thf(f40,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ X2)) = $true) | (((subset @ X1 @ X2)) != $true) | (subsetE != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f28])).
% 0.22/0.30 thf(f41,plain,(
% 0.22/0.30 (subsetI1 = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f29])).
% 0.22/0.30 thf(f42,plain,(
% 0.22/0.30 (subsetE = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f29])).
% 0.22/0.30 thf(f43,plain,(
% 0.22/0.30 (binintersectEL = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f29])).
% 0.22/0.30 thf(f45,plain,(
% 0.22/0.30 (((subset @ (binintersect @ sK9 @ sK11) @ sK12)) != $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f29])).
% 0.22/0.30 thf(f46,plain,(
% 0.22/0.30 (((subset @ sK9 @ sK12)) = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f29])).
% 0.22/0.30 thf(f51,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ($true != ((in @ (sK0 @ X1 @ X0) @ X0))) | ($true != $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f33,f41])).
% 0.22/0.30 thf(f52,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) = $true) | ($true != $true) | (((subset @ X1 @ X0)) = $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f32,f41])).
% 0.22/0.30 thf(f55,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | ($true != $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f36,f43])).
% 0.22/0.30 thf(f58,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((subset @ X1 @ X2)) != $true) | (((in @ X0 @ X2)) = $true) | ($true != $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f40,f42])).
% 0.22/0.30 thf(f62,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ X1 @ X0) @ X0))) | (((subset @ X1 @ X0)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f51])).
% 0.22/0.30 thf(f63,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X1 @ X2)) != $true) | (((in @ X0 @ X2)) = $true) | (((in @ X0 @ X1)) != $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f58])).
% 0.22/0.30 thf(f64,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | (((in @ X0 @ X1)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f55])).
% 0.22/0.30 thf(f65,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) = $true) | (((subset @ X1 @ X0)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f52])).
% 0.22/0.30 thf(f66,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((subset @ (binintersect @ X0 @ X1) @ X2)) = $true) | (((in @ (sK0 @ (binintersect @ X0 @ X1) @ X2) @ X0)) = $true)) )),
% 0.22/0.30 inference(constrained_superposition,[],[f64,f65])).
% 0.22/0.30 thf(f68,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK0 @ (binintersect @ X0 @ X1) @ X2) @ X0)) = $true) | (((subset @ (binintersect @ X0 @ X1) @ X2)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f66])).
% 0.22/0.30 thf(f71,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK9))) | ($true != $true) | (((in @ X0 @ sK12)) = $true)) )),
% 0.22/0.30 inference(constrained_superposition,[],[f63,f46])).
% 0.22/0.30 thf(f72,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK9))) | (((in @ X0 @ sK12)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f71])).
% 0.22/0.30 thf(f80,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK0 @ (binintersect @ sK9 @ X0) @ X1) @ sK12))) | ($true != $true) | (((subset @ (binintersect @ sK9 @ X0) @ X1)) = $true)) )),
% 0.22/0.30 inference(constrained_superposition,[],[f72,f68])).
% 0.22/0.30 thf(f83,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK0 @ (binintersect @ sK9 @ X0) @ X1) @ sK12))) | (((subset @ (binintersect @ sK9 @ X0) @ X1)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f80])).
% 0.22/0.30 thf(f88,plain,(
% 0.22/0.30 ( ! [X0 : $i] : ((((subset @ (binintersect @ sK9 @ X0) @ sK12)) = $true) | ($true != $true) | (((subset @ (binintersect @ sK9 @ X0) @ sK12)) = $true)) )),
% 0.22/0.30 inference(constrained_superposition,[],[f62,f83])).
% 0.22/0.30 thf(f89,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != $true) | (((subset @ (binintersect @ sK9 @ X0) @ sK12)) = $true)) )),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f88])).
% 0.22/0.30 thf(f90,plain,(
% 0.22/0.30 ( ! [X0 : $i] : ((((subset @ (binintersect @ sK9 @ X0) @ sK12)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f89])).
% 0.22/0.30 thf(f91,plain,(
% 0.22/0.30 ($true != $true)),
% 0.22/0.30 inference(backward_demodulation,[],[f45,f90])).
% 0.22/0.30 thf(f92,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f91])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (3229715)------------------------------
% 0.22/0.30 % (3229715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3229715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3229715)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3229715)Termination reason: Refutation
% 0.22/0.30 % (3229715)Time elapsed: 0.006 s
% 0.22/0.30 % (3229715)Peak memory usage: 12 MB
% 0.22/0.30 % (3229715)Instructions burned: 10 (million)
% 0.22/0.30 % (3229705)Success in time 0.038 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------