%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU587^2 : 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 : n018.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 08:30:12 AM UTC 2026
% Result : Theorem 0.24s 0.37s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU587^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n018.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 13:55:12 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.31 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
% 0.24/0.37 % (113577)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.37 % (113584)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=9091853:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.37 % (113584)Refutation not found, incomplete strategy
% 0.24/0.37 % (113584)------------------------------
% 0.24/0.37 % (113584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (113584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (113584)CaDiCaL version: 2.1.3
% 0.24/0.37 % (113584)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (113584)Time elapsed: 0.001 s
% 0.24/0.37 % (113584)Peak memory usage: 12 MB
% 0.24/0.37 % (113584)Instructions burned: 1 (million)
% 0.24/0.37 % (113584)------------------------------
% 0.24/0.37 % (113584)------------------------------
% 0.24/0.37 % (113588)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.37 % (113588)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
% 0.24/0.37 % (113583)lrs+10_16_si=on:nwc=1.5:random_seed=1536662624:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.37 % (113582)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1236178687:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.37 % (113585)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=2853339772: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)
% 0.24/0.37 % (113586)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1033453618:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.37 % (113587)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3432937292:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.37 % (113582) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113577-113582"...
% 0.24/0.37 % (113588)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=868027012:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.37 % (113583) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113577-113583"...
% 0.24/0.37 % (113585) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113577-113585"...
% 0.24/0.37 % (113586) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113577-113586"...
% 0.24/0.37 % (113582)...printing done.
% 0.24/0.37 % (113583)...printing done.
% 0.24/0.37 % (113587) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113577-113587"...
% 0.24/0.37 % (113582)Refutation found. Thanks to Tanya!
% 0.24/0.37 % SZS status Theorem for theBenchmark
% 0.24/0.37 % SZS output start Proof for theBenchmark
% 0.24/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.37 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.24/0.37 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.24/0.37 thf(func_def_2, type, subsetI2: $o).
% 0.24/0.37 thf(func_def_4, type, binunion: ($i > $i > $i)).
% 0.24/0.37 thf(func_def_5, type, binunionIL: $o).
% 0.24/0.37 thf(func_def_10, type, sK2: ($i > $i > $i)).
% 0.24/0.37 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.24/0.37 thf(f1,axiom,(
% 0.24/0.37 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.24/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.24/0.37 thf(f2,axiom,(
% 0.24/0.37 (binunionIL = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))))),
% 0.24/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL)).
% 0.24/0.37 thf(f3,conjecture,(
% 0.24/0.37 subsetI2 => (binunionIL => ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 0.24/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub)).
% 0.24/0.37 thf(f4,negated_conjecture,(
% 0.24/0.37 ~(subsetI2 => (binunionIL => ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1))))),
% 0.24/0.37 inference(negated_conjecture,[status(cth)],[f3])).
% 0.24/0.37 thf(f5,plain,(
% 0.24/0.37 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.24/0.37 inference(rectify,[],[f1])).
% 0.24/0.37 thf(f6,plain,(
% 0.24/0.37 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.24/0.37 inference(fool_elimination,[],[f5])).
% 0.24/0.37 thf(f7,plain,(
% 0.24/0.37 ~(subsetI2 => (binunionIL => ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1))))),
% 0.24/0.37 inference(rectify,[],[f4])).
% 0.24/0.37 thf(f8,plain,(
% 0.24/0.37 ~((subsetI2 = $true) => ((binunionIL = $true) => ! [X1 : $i,X0 : $i] : (((subset @ X0 @ (binunion @ X0 @ X1))) = $true)))),
% 0.24/0.37 inference(fool_elimination,[],[f7])).
% 0.24/0.37 thf(f9,plain,(
% 0.24/0.37 (binunionIL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X1 @ X0))))),
% 0.24/0.37 inference(rectify,[],[f2])).
% 0.24/0.37 thf(f10,plain,(
% 0.24/0.37 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) => ($true = ((in @ X2 @ (binunion @ X1 @ X0))))) <=> (binunionIL = $true)),
% 0.24/0.37 inference(fool_elimination,[],[f9])).
% 0.24/0.37 thf(f11,plain,(
% 0.24/0.37 (? [X1 : $i,X0 : $i] : (((subset @ X0 @ (binunion @ X0 @ X1))) != $true) & (binunionIL = $true)) & (subsetI2 = $true)),
% 0.24/0.37 inference(ennf_transformation,[],[f8])).
% 0.24/0.37 thf(f12,plain,(
% 0.24/0.37 (binunionIL = $true) & (subsetI2 = $true) & ? [X1 : $i,X0 : $i] : (((subset @ X0 @ (binunion @ X0 @ X1))) != $true)),
% 0.24/0.37 inference(flattening,[],[f11])).
% 0.24/0.37 thf(f13,plain,(
% 0.24/0.37 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) <=> (subsetI2 = $true)),
% 0.24/0.37 inference(ennf_transformation,[],[f6])).
% 0.24/0.37 thf(f14,plain,(
% 0.24/0.37 (binunionIL = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) | ($true = ((in @ X2 @ (binunion @ X1 @ X0)))))),
% 0.24/0.37 inference(ennf_transformation,[],[f10])).
% 0.24/0.37 thf(f15,plain,(
% 0.24/0.37 (binunionIL = $true) & (subsetI2 = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X1 @ (binunion @ X1 @ X0))) != $true)),
% 0.24/0.37 inference(rectify,[],[f12])).
% 0.24/0.37 thf(f16,plain,(
% 0.24/0.37 (binunionIL = $true) & (subsetI2 = $true) & ($true != ((subset @ sK1 @ (binunion @ sK1 @ sK0))))),
% 0.24/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15])).
% 0.24/0.37 thf(f17,plain,(
% 0.24/0.37 (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true)))),
% 0.24/0.37 inference(nnf_transformation,[],[f13])).
% 0.24/0.37 thf(f18,plain,(
% 0.24/0.37 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true = ((in @ X5 @ X3))) | ($true != ((in @ X5 @ X4)))) & (((subset @ X4 @ X3)) != $true)))),
% 0.24/0.37 inference(rectify,[],[f17])).
% 0.24/0.37 thf(f19,plain,(
% 0.24/0.37 (! [X0 : $i,X1 : $i] : ((($true != ((in @ (sK2 @ X1 @ X0) @ X0))) & ($true = ((in @ (sK2 @ X1 @ X0) @ X1)))) | (((subset @ X1 @ X0)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | (! [X5 : $i] : (($true = ((in @ X5 @ sK3))) | ($true != ((in @ X5 @ sK4)))) & ($true != ((subset @ sK4 @ sK3)))))),
% 0.24/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK3,sK4]),skolemize(X2,sK2 @ X1 @ X0),skolemize(X3,sK3),skolemize(X4,sK4)],[f18])).
% 0.24/0.37 thf(f20,plain,(
% 0.24/0.37 ((binunionIL = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) & ($true != ((in @ X2 @ (binunion @ X1 @ X0)))))) & (! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) | ($true = ((in @ X2 @ (binunion @ X1 @ X0))))) | (binunionIL != $true))),
% 0.24/0.37 inference(nnf_transformation,[],[f14])).
% 0.24/0.37 thf(f21,plain,(
% 0.24/0.37 ((binunionIL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ X2))) & ($true != ((in @ X1 @ (binunion @ X2 @ X0)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X5))) | ($true = ((in @ X4 @ (binunion @ X5 @ X3))))) | (binunionIL != $true))),
% 0.24/0.37 inference(rectify,[],[f20])).
% 0.24/0.37 thf(f22,plain,(
% 0.24/0.37 ((binunionIL = $true) | (($true = ((in @ sK6 @ sK7))) & ($true != ((in @ sK6 @ (binunion @ sK7 @ sK5)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X5))) | ($true = ((in @ X4 @ (binunion @ X5 @ X3))))) | (binunionIL != $true))),
% 0.24/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f21])).
% 0.24/0.37 thf(f23,plain,(
% 0.24/0.37 ($true != ((subset @ sK1 @ (binunion @ sK1 @ sK0))))),
% 0.24/0.37 inference(cnf_transformation,[],[f16])).
% 0.24/0.37 thf(f24,plain,(
% 0.24/0.37 (subsetI2 = $true)),
% 0.24/0.37 inference(cnf_transformation,[],[f16])).
% 0.24/0.37 thf(f25,plain,(
% 0.24/0.37 (binunionIL = $true)),
% 0.24/0.37 inference(cnf_transformation,[],[f16])).
% 0.24/0.37 thf(f28,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X1 @ X0) @ X1))) | (((subset @ X1 @ X0)) = $true) | (subsetI2 != $true)) )),
% 0.24/0.37 inference(cnf_transformation,[],[f19])).
% 0.24/0.37 thf(f29,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK2 @ X1 @ X0) @ X0))) | (((subset @ X1 @ X0)) = $true) | (subsetI2 != $true)) )),
% 0.24/0.37 inference(cnf_transformation,[],[f19])).
% 0.24/0.37 thf(f30,plain,(
% 0.24/0.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X5))) | ($true = ((in @ X4 @ (binunion @ X5 @ X3)))) | (binunionIL != $true)) )),
% 0.24/0.37 inference(cnf_transformation,[],[f22])).
% 0.24/0.37 thf(f35,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ X1 @ X0)) = $true) | ($true != ((in @ (sK2 @ X1 @ X0) @ X0)))) )),
% 0.24/0.37 inference(definition_unfolding,[],[f29,f24])).
% 0.24/0.37 thf(f36,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X1 @ X0) @ X1))) | (((subset @ X1 @ X0)) = $true) | ($true != $true)) )),
% 0.24/0.37 inference(definition_unfolding,[],[f28,f24])).
% 0.24/0.37 thf(f41,plain,(
% 0.24/0.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X5))) | ($true = ((in @ X4 @ (binunion @ X5 @ X3)))) | ($true != $true)) )),
% 0.24/0.37 inference(definition_unfolding,[],[f30,f25])).
% 0.24/0.37 thf(f42,plain,(
% 0.24/0.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X5))) | ($true = ((in @ X4 @ (binunion @ X5 @ X3))))) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f41])).
% 0.24/0.37 thf(f43,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X1 @ X0) @ X1))) | (((subset @ X1 @ X0)) = $true)) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f36])).
% 0.24/0.37 thf(f44,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK2 @ X1 @ X0) @ X0))) | (((subset @ X1 @ X0)) = $true)) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f35])).
% 0.24/0.37 thf(f45,plain,(
% 0.24/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK2 @ X0 @ X1) @ (binunion @ X0 @ X2))) = $true) | (((subset @ X0 @ X1)) = $true) | ($true != $true)) )),
% 0.24/0.37 inference(constrained_superposition,[],[f42,f43])).
% 0.24/0.37 thf(f46,plain,(
% 0.24/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK2 @ X0 @ X1) @ (binunion @ X0 @ X2))) = $true) | (((subset @ X0 @ X1)) = $true)) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f45])).
% 0.24/0.37 thf(f51,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ (binunion @ X0 @ X1))) = $true) | ($true != $true) | (((subset @ X0 @ (binunion @ X0 @ X1))) = $true)) )),
% 0.24/0.37 inference(constrained_superposition,[],[f44,f46])).
% 0.24/0.37 thf(f53,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ X0 @ (binunion @ X0 @ X1))) = $true)) )),
% 0.24/0.37 inference(duplicate_literal_removal,[],[f51])).
% 0.24/0.37 thf(f54,plain,(
% 0.24/0.37 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ (binunion @ X0 @ X1))) = $true)) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f53])).
% 0.24/0.37 thf(f55,plain,(
% 0.24/0.37 ($true != $true)),
% 0.24/0.37 inference(constrained_superposition,[],[f23,f54])).
% 0.24/0.37 thf(f56,plain,(
% 0.24/0.37 $false),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f55])).
% 0.24/0.37 % SZS output end Proof for theBenchmark
% 0.24/0.37 % (113582)------------------------------
% 0.24/0.37 % (113582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (113582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (113582)CaDiCaL version: 2.1.3
% 0.24/0.37 % (113582)Termination reason: Refutation
% 0.24/0.37 % (113582)Time elapsed: 0.006 s
% 0.24/0.37 % (113582)Peak memory usage: 12 MB
% 0.24/0.37 % (113582)Instructions burned: 4 (million)
% 0.24/0.37 % (113577)Success in time 0.044 s
% 0.24/0.37 % Vampire exiting
%------------------------------------------------------------------------------