%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU805^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:34 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU805^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % 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 14:32:10 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.29 % (807477)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.29 % (807483)lrs+10_16_si=on:nwc=1.5:random_seed=1842318609:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.29 % (807488)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.29 % (807488)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
% 0.19/0.29 % (807483)Instruction limit reached!
% 0.19/0.29 % (807483)------------------------------
% 0.19/0.29 % (807483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (807483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (807483)CaDiCaL version: 2.1.3
% 0.19/0.29 % (807483)Termination reason: Instruction limit
% 0.19/0.29 % (807483)Termination phase: Saturation
% 0.19/0.29 % (807483)Time elapsed: 0.006 s
% 0.19/0.29 % (807483)Peak memory usage: 12 MB
% 0.19/0.29 % (807483)Instructions burned: 21 (million)
% 0.19/0.29 % (807482)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=408155154:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.29 % (807484)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4081654584:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.29 % (807487)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2953620361:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.29 % (807486)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3115427729:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.29 % (807485)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=2417470030: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)
% 0.19/0.29 % (807488)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=3693191750:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.29 % (807484)Refutation not found, incomplete strategy
% 0.19/0.29 % (807484)------------------------------
% 0.19/0.29 % (807484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (807484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (807484)CaDiCaL version: 2.1.3
% 0.19/0.29 % (807484)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (807484)Time elapsed: 0.002 s
% 0.19/0.29 % (807484)Peak memory usage: 12 MB
% 0.19/0.29 % (807484)Instructions burned: 2 (million)
% 0.19/0.29 % (807484)------------------------------
% 0.19/0.29 % (807484)------------------------------
% 0.19/0.29 % (807482) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-807477-807482"...
% 0.19/0.29 % (807485) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-807477-807485"...
% 0.19/0.29 % (807486) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-807477-807486"...
% 0.19/0.29 % (807487) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-807477-807487"...
% 0.19/0.29 % (807482)...printing done.
% 0.19/0.29 % (807482)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% 0.19/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.19/0.29 thf(func_def_2, type, foundationAx: $o).
% 0.19/0.29 thf(func_def_4, type, nonempty: ($i > $o)).
% 0.19/0.29 thf(func_def_5, type, nonemptyE1: $o).
% 0.19/0.29 thf(func_def_6, type, binintersect: ($i > $i > $i)).
% 0.19/0.29 thf(func_def_7, type, disjointsetsI1: $o).
% 0.19/0.29 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.29 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.29 thf(func_def_12, type, vNOT: ($o > $o)).
% 0.19/0.29 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.29 thf(func_def_16, type, sK2: ($i > $i)).
% 0.19/0.29 thf(func_def_17, type, sK3: ($i > $i)).
% 0.19/0.29 thf(func_def_19, type, sK5: ($i > $i > $i)).
% 0.19/0.29 thf(func_def_23, type, sK9: ($i > $i)).
% 0.19/0.29 thf(f1,axiom,(
% 0.19/0.29 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : ((in @ X2 @ X0) & ~ ? [X1 : $i] : ((in @ X1 @ X2) & (in @ X1 @ X0)))) = foundationAx)),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx)).
% 0.19/0.29 thf(f2,axiom,(
% 0.19/0.29 ((^[X0 : $i] : ((X0 != emptyset))) = nonempty)),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)).
% 0.19/0.29 thf(f3,axiom,(
% 0.19/0.29 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1)).
% 0.19/0.29 thf(f4,axiom,(
% 0.19/0.29 (! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (((binintersect @ X0 @ X1)) = emptyset)) = disjointsetsI1)),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1)).
% 0.19/0.29 thf(f5,conjecture,(
% 0.19/0.29 foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & (((binintersect @ X1 @ X0)) = emptyset)))))),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundation2)).
% 0.19/0.29 thf(f6,negated_conjecture,(
% 0.19/0.29 ~(foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & (((binintersect @ X1 @ X0)) = emptyset))))))),
% 0.19/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.19/0.29 thf(f7,plain,(
% 0.19/0.29 (! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = ((binintersect @ X1 @ X0)))) = disjointsetsI1)),
% 0.19/0.29 inference(rectify,[],[f4])).
% 0.19/0.29 thf(f8,plain,(
% 0.19/0.29 (disjointsetsI1 = $true) <=> ! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)) => (emptyset = ((binintersect @ X1 @ X0))))),
% 0.19/0.29 inference(fool_elimination,[],[f7])).
% 0.19/0.29 thf(f9,plain,(
% 0.19/0.29 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : ((in @ X2 @ X0) & ~ ? [X3 : $i] : ((in @ X3 @ X2) & (in @ X3 @ X0)))) = foundationAx)),
% 0.19/0.29 inference(rectify,[],[f1])).
% 0.19/0.29 thf(f10,plain,(
% 0.19/0.29 (foundationAx = $true) <=> ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) => ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & ~ ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X2)) = $true))))),
% 0.19/0.29 inference(fool_elimination,[],[f9])).
% 0.19/0.29 thf(f11,plain,(
% 0.19/0.29 ~(foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & (((binintersect @ X1 @ X0)) = emptyset))))))),
% 0.19/0.29 inference(rectify,[],[f6])).
% 0.19/0.29 thf(f12,plain,(
% 0.19/0.29 ~((foundationAx = $true) => ((nonemptyE1 = $true) => ((disjointsetsI1 = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : ((((in @ X1 @ X0)) = $true) & (emptyset = ((binintersect @ X1 @ X0))))))))),
% 0.19/0.29 inference(fool_elimination,[],[f11])).
% 0.19/0.29 thf(f13,plain,(
% 0.19/0.29 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.19/0.29 inference(fool_elimination,[],[f2])).
% 0.19/0.29 thf(f14,plain,(
% 0.19/0.29 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 0.19/0.29 inference(rectify,[],[f3])).
% 0.19/0.29 thf(f15,plain,(
% 0.19/0.29 ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : (((in @ X1 @ X0)) = $true)) <=> (nonemptyE1 = $true)),
% 0.19/0.29 inference(fool_elimination,[],[f14])).
% 0.19/0.29 thf(f16,plain,(
% 0.19/0.29 (foundationAx = $true) <=> ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) | ? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((in @ X3 @ X0)) != $true)) & (((in @ X2 @ X0)) = $true)))),
% 0.19/0.29 inference(ennf_transformation,[],[f10])).
% 0.19/0.29 thf(f17,plain,(
% 0.19/0.29 ((? [X0 : $i] : (! [X1 : $i] : ((((in @ X1 @ X0)) != $true) | (emptyset != ((binintersect @ X1 @ X0)))) & (((nonempty @ X0)) = $true)) & (disjointsetsI1 = $true)) & (nonemptyE1 = $true)) & (foundationAx = $true)),
% 0.19/0.29 inference(ennf_transformation,[],[f12])).
% 0.19/0.29 thf(f18,plain,(
% 0.19/0.29 (nonemptyE1 = $true) & (foundationAx = $true) & ? [X0 : $i] : (! [X1 : $i] : ((((in @ X1 @ X0)) != $true) | (emptyset != ((binintersect @ X1 @ X0)))) & (((nonempty @ X0)) = $true)) & (disjointsetsI1 = $true)),
% 0.19/0.29 inference(flattening,[],[f17])).
% 0.19/0.29 thf(f19,plain,(
% 0.19/0.29 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)) | (emptyset = ((binintersect @ X1 @ X0)))) <=> (disjointsetsI1 = $true)),
% 0.19/0.29 inference(ennf_transformation,[],[f8])).
% 0.19/0.29 thf(f20,plain,(
% 0.19/0.29 (nonemptyE1 = $true) <=> ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (((nonempty @ X0)) != $true))),
% 0.19/0.29 inference(ennf_transformation,[],[f15])).
% 0.19/0.29 thf(f21,plain,(
% 0.19/0.29 ((foundationAx = $true) | ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) & ! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((in @ X3 @ X0)) = $true)) | (((in @ X2 @ X0)) != $true)))) & (! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) | ? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((in @ X3 @ X0)) != $true)) & (((in @ X2 @ X0)) = $true))) | (foundationAx != $true))),
% 0.19/0.29 inference(nnf_transformation,[],[f16])).
% 0.19/0.29 thf(f22,plain,(
% 0.19/0.29 ((foundationAx = $true) | ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) & ! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((in @ X3 @ X0)) = $true)) | (((in @ X2 @ X0)) != $true)))) & (! [X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4)) != $true) | ? [X6 : $i] : (! [X7 : $i] : ((((in @ X7 @ X6)) != $true) | (((in @ X7 @ X4)) != $true)) & (((in @ X6 @ X4)) = $true))) | (foundationAx != $true))),
% 0.19/0.29 inference(rectify,[],[f21])).
% 0.19/0.29 thf(f23,plain,(
% 0.19/0.29 ((foundationAx = $true) | ((((in @ sK1 @ sK0)) = $true) & ! [X2 : $i] : (((((in @ (sK2 @ X2) @ X2)) = $true) & (((in @ (sK2 @ X2) @ sK0)) = $true)) | (((in @ X2 @ sK0)) != $true)))) & (! [X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4)) != $true) | (! [X7 : $i] : ((((in @ X7 @ (sK3 @ X4))) != $true) | (((in @ X7 @ X4)) != $true)) & ($true = ((in @ (sK3 @ X4) @ X4))))) | (foundationAx != $true))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X6,sK3 @ X4),skolemize(X6,sK3 @ X4)],[f22])).
% 0.19/0.29 thf(f24,plain,(
% 0.19/0.29 (nonemptyE1 = $true) & (foundationAx = $true) & (! [X1 : $i] : (($true != ((in @ X1 @ sK4))) | (emptyset != ((binintersect @ X1 @ sK4)))) & (((nonempty @ sK4)) = $true)) & (disjointsetsI1 = $true)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f18])).
% 0.19/0.29 thf(f25,plain,(
% 0.19/0.29 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)) | (emptyset = ((binintersect @ X1 @ X0)))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) != $true)) & (emptyset != ((binintersect @ X1 @ X0)))))),
% 0.19/0.29 inference(nnf_transformation,[],[f19])).
% 0.19/0.29 thf(f26,plain,(
% 0.19/0.29 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)) | (emptyset = ((binintersect @ X1 @ X0)))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : ((((in @ X5 @ X4)) != $true) | (((in @ X5 @ X3)) != $true)) & (emptyset != ((binintersect @ X4 @ X3)))))),
% 0.19/0.29 inference(rectify,[],[f25])).
% 0.19/0.29 thf(f27,plain,(
% 0.19/0.29 (! [X0 : $i,X1 : $i] : (((((in @ (sK5 @ X1 @ X0) @ X1)) = $true) & (((in @ (sK5 @ X1 @ X0) @ X0)) = $true)) | (emptyset = ((binintersect @ X1 @ X0)))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | (! [X5 : $i] : ((((in @ X5 @ sK7)) != $true) | (((in @ X5 @ sK6)) != $true)) & (emptyset != ((binintersect @ sK7 @ sK6)))))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK6,sK7]),skolemize(X6,sK3 @ X4),skolemize(X3,sK6),skolemize(X4,sK7)],[f26])).
% 0.19/0.29 thf(f28,plain,(
% 0.19/0.29 ((nonemptyE1 = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (((nonempty @ X0)) = $true))) & (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (((nonempty @ X0)) != $true)) | (nonemptyE1 != $true))),
% 0.19/0.29 inference(nnf_transformation,[],[f20])).
% 0.19/0.29 thf(f29,plain,(
% 0.19/0.29 ((nonemptyE1 = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (((nonempty @ X0)) = $true))) & (! [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X2)) = $true) | (((nonempty @ X2)) != $true)) | (nonemptyE1 != $true))),
% 0.19/0.29 inference(rectify,[],[f28])).
% 0.19/0.29 thf(f30,plain,(
% 0.19/0.29 ((nonemptyE1 = $true) | (! [X1 : $i] : (((in @ X1 @ sK8)) != $true) & (((nonempty @ sK8)) = $true))) & (! [X2 : $i] : ((((in @ (sK9 @ X2) @ X2)) = $true) | (((nonempty @ X2)) != $true)) | (nonemptyE1 != $true))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,vAPP]),skolemize(X0,sK8),skolemize(X6,sK3 @ X4)],[f29])).
% 0.19/0.29 thf(f31,plain,(
% 0.19/0.29 ( ! [X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ (sK3 @ X4) @ X4))) | (foundationAx != $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f23])).
% 0.19/0.29 thf(f32,plain,(
% 0.19/0.29 ( ! [X7 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | (((in @ X7 @ (sK3 @ X4))) != $true) | (((in @ X7 @ X4)) != $true) | (foundationAx != $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f23])).
% 0.19/0.29 thf(f36,plain,(
% 0.19/0.29 (disjointsetsI1 = $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f37,plain,(
% 0.19/0.29 (((nonempty @ sK4)) = $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f38,plain,(
% 0.19/0.29 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK4))) | (emptyset != ((binintersect @ X1 @ sK4)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f39,plain,(
% 0.19/0.29 (foundationAx = $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f40,plain,(
% 0.19/0.29 (nonemptyE1 = $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f43,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X0)) = $true) | (emptyset = ((binintersect @ X1 @ X0))) | (disjointsetsI1 != $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f44,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X1)) = $true) | (emptyset = ((binintersect @ X1 @ X0))) | (disjointsetsI1 != $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f45,plain,(
% 0.19/0.29 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.19/0.29 inference(cnf_transformation,[],[f13])).
% 0.19/0.29 thf(f46,plain,(
% 0.19/0.29 ( ! [X2 : $i] : ((((in @ (sK9 @ X2) @ X2)) = $true) | (((nonempty @ X2)) != $true) | (nonemptyE1 != $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f30])).
% 0.19/0.29 thf(f54,plain,(
% 0.19/0.29 ( ! [X7 : $i,X4 : $i,X5 : $i] : ((((in @ X7 @ X4)) != $true) | (((in @ X7 @ (sK3 @ X4))) != $true) | (((in @ X5 @ X4)) != $true) | ($true != $true)) )),
% 0.19/0.29 inference(definition_unfolding,[],[f32,f39])).
% 0.19/0.29 thf(f55,plain,(
% 0.19/0.29 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK3 @ X4) @ X4))) | ($true != $true) | (((in @ X5 @ X4)) != $true)) )),
% 0.19/0.29 inference(definition_unfolding,[],[f31,f39])).
% 0.19/0.29 thf(f56,plain,(
% 0.19/0.29 ((((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK4)) = $true)),
% 0.19/0.29 inference(definition_unfolding,[],[f37,f45])).
% 0.19/0.29 thf(f57,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((emptyset = ((binintersect @ X1 @ X0))) | ($true != $true) | (((in @ (sK5 @ X1 @ X0) @ X1)) = $true)) )),
% 0.19/0.29 inference(definition_unfolding,[],[f44,f36])).
% 0.19/0.29 thf(f58,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((emptyset = ((binintersect @ X1 @ X0))) | ($true != $true) | (((in @ (sK5 @ X1 @ X0) @ X0)) = $true)) )),
% 0.19/0.29 inference(definition_unfolding,[],[f43,f36])).
% 0.19/0.29 thf(f63,plain,(
% 0.19/0.29 ( ! [X2 : $i] : ((((in @ (sK9 @ X2) @ X2)) = $true) | ((((^[Y0 : $i]: (~ (emptyset = Y0))) @ X2)) != $true) | ($true != $true)) )),
% 0.19/0.29 inference(definition_unfolding,[],[f46,f45,f40])).
% 0.19/0.29 thf(f64,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X1)) = $true) | (emptyset = ((binintersect @ X1 @ X0)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f57])).
% 0.19/0.29 thf(f65,plain,(
% 0.19/0.29 ( ! [X7 : $i,X4 : $i,X5 : $i] : ((((in @ X7 @ (sK3 @ X4))) != $true) | (((in @ X7 @ X4)) != $true) | (((in @ X5 @ X4)) != $true)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f54])).
% 0.19/0.29 thf(f66,plain,(
% 0.19/0.29 (((~ (emptyset = sK4))) = $true)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f56])).
% 0.19/0.29 thf(f67,plain,(
% 0.19/0.29 (((emptyset = sK4)) = $false)),
% 0.19/0.29 inference(not_proxy_clausification,[],[f66])).
% 0.19/0.29 thf(f68,plain,(
% 0.19/0.29 (emptyset != sK4)),
% 0.19/0.29 inference(equality_proxy_clausification,[],[f67])).
% 0.19/0.29 thf(f69,plain,(
% 0.19/0.29 ( ! [X2 : $i] : ((((in @ (sK9 @ X2) @ X2)) = $true) | ((((^[Y0 : $i]: (~ (emptyset = Y0))) @ X2)) != $true)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f63])).
% 0.19/0.29 thf(f70,plain,(
% 0.19/0.29 ( ! [X2 : $i] : ((((in @ (sK9 @ X2) @ X2)) = $true) | (((~ (emptyset = X2))) != $true)) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f69])).
% 0.19/0.29 thf(f71,plain,(
% 0.19/0.29 ( ! [X2 : $i] : ((((emptyset = X2)) = $true) | (((in @ (sK9 @ X2) @ X2)) = $true)) )),
% 0.19/0.29 inference(not_proxy_clausification,[],[f70])).
% 0.19/0.29 thf(f72,plain,(
% 0.19/0.29 ( ! [X2 : $i] : ((((in @ (sK9 @ X2) @ X2)) = $true) | (emptyset = X2)) )),
% 0.19/0.29 inference(equality_proxy_clausification,[],[f71])).
% 0.19/0.29 thf(f73,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X0)) = $true) | (emptyset = ((binintersect @ X1 @ X0)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f58])).
% 0.19/0.29 thf(f74,plain,(
% 0.19/0.29 ( ! [X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ (sK3 @ X4) @ X4)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f55])).
% 0.19/0.29 thf(f78,plain,(
% 0.19/0.29 ( ! [X0 : $i] : ((emptyset = X0) | (((in @ (sK3 @ X0) @ X0)) = $true) | ($true != $true)) )),
% 0.19/0.29 inference(constrained_superposition,[],[f74,f72])).
% 0.19/0.29 thf(f79,plain,(
% 0.19/0.29 ( ! [X0 : $i] : ((((in @ (sK3 @ X0) @ X0)) = $true) | (emptyset = X0)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f78])).
% 0.19/0.29 thf(f80,plain,(
% 0.19/0.29 ($true != $true) | (emptyset != ((binintersect @ (sK3 @ sK4) @ sK4))) | (emptyset = sK4)),
% 0.19/0.29 inference(constrained_superposition,[],[f38,f79])).
% 0.19/0.29 thf(f81,plain,(
% 0.19/0.29 (emptyset = sK4) | (emptyset != ((binintersect @ (sK3 @ sK4) @ sK4)))),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f80])).
% 0.19/0.29 thf(f82,plain,(
% 0.19/0.29 (emptyset != ((binintersect @ (sK3 @ sK4) @ sK4)))),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f81,f68])).
% 0.19/0.29 thf(f90,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((emptyset = ((binintersect @ X0 @ X1))) | (((in @ (sK3 @ X1) @ X1)) = $true) | ($true != $true)) )),
% 0.19/0.29 inference(constrained_superposition,[],[f74,f73])).
% 0.19/0.29 thf(f91,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK3 @ X1) @ X1)) = $true) | (emptyset = ((binintersect @ X0 @ X1)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f90])).
% 0.19/0.29 thf(f95,plain,(
% 0.19/0.29 (((in @ (sK3 @ sK4) @ sK4)) = $true) | (emptyset != emptyset)),
% 0.19/0.29 inference(constrained_superposition,[],[f82,f91])).
% 0.19/0.29 thf(f96,plain,(
% 0.19/0.29 (((in @ (sK3 @ sK4) @ sK4)) = $true)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f95])).
% 0.19/0.29 thf(f109,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ X2 @ X0)) != $true) | (emptyset = ((binintersect @ (sK3 @ X0) @ X1))) | (((in @ (sK5 @ (sK3 @ X0) @ X1) @ X0)) != $true)) )),
% 0.19/0.29 inference(constrained_superposition,[],[f65,f64])).
% 0.19/0.29 thf(f112,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK5 @ (sK3 @ X0) @ X1) @ X0)) != $true) | (emptyset = ((binintersect @ (sK3 @ X0) @ X1))) | (((in @ X2 @ X0)) != $true)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f109])).
% 0.19/0.29 thf(f117,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((emptyset = ((binintersect @ (sK3 @ X0) @ X0))) | (emptyset = ((binintersect @ (sK3 @ X0) @ X0))) | (((in @ X1 @ X0)) != $true) | ($true != $true)) )),
% 0.19/0.29 inference(constrained_superposition,[],[f112,f73])).
% 0.19/0.29 thf(f118,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((emptyset = ((binintersect @ (sK3 @ X0) @ X0))) | ($true != $true) | (((in @ X1 @ X0)) != $true)) )),
% 0.19/0.29 inference(duplicate_literal_removal,[],[f117])).
% 0.19/0.29 thf(f119,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | (emptyset = ((binintersect @ (sK3 @ X0) @ X0)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f118])).
% 0.19/0.29 thf(f126,plain,(
% 0.19/0.29 ($true != $true) | (emptyset = ((binintersect @ (sK3 @ sK4) @ sK4)))),
% 0.19/0.29 inference(constrained_superposition,[],[f119,f96])).
% 0.19/0.29 thf(f127,plain,(
% 0.19/0.29 (emptyset = ((binintersect @ (sK3 @ sK4) @ sK4)))),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f126])).
% 0.19/0.29 thf(f134,plain,(
% 0.19/0.29 $false),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f127,f82])).
% 0.19/0.29 % SZS output end Proof for theBenchmark
% 0.19/0.29 % (807482)------------------------------
% 0.19/0.29 % (807482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (807482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (807482)CaDiCaL version: 2.1.3
% 0.19/0.29 % (807482)Termination reason: Refutation
% 0.19/0.29 % (807482)Time elapsed: 0.007 s
% 0.19/0.29 % (807482)Peak memory usage: 12 MB
% 0.19/0.29 % (807482)Instructions burned: 11 (million)
% 0.19/0.29 % (807477)Success in time 0.057 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------