%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU594^2 : 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 08:30:14 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU594^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n018.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 13:56:27 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.20/0.26 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
% 0.20/0.31 % (115626)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (115637)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.31 % (115637)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
% 0.20/0.31 % (115632)lrs+10_16_si=on:nwc=1.5:random_seed=3110783413:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (115631)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2288889611:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (115633)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3605168878:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (115635)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=949205792:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.31 % (115634)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=669569216: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)
% 0.20/0.31 % (115636)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2191674878:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.31 % (115637)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=887520024:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.31 % (115633)Refutation not found, incomplete strategy
% 0.20/0.31 % (115633)------------------------------
% 0.20/0.31 % (115633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (115633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (115633)CaDiCaL version: 2.1.3
% 0.20/0.31 % (115633)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (115633)Time elapsed: 0.002 s
% 0.20/0.31 % (115633)Peak memory usage: 12 MB
% 0.20/0.31 % (115633)Instructions burned: 3 (million)
% 0.20/0.31 % (115633)------------------------------
% 0.20/0.31 % (115633)------------------------------
% 0.20/0.31 % (115635) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-115626-115635"...
% 0.20/0.31 % (115634) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-115626-115634"...
% 0.20/0.31 % (115635)...printing done.
% 0.20/0.31 % (115634)...printing done.
% 0.20/0.31 % (115635)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.31 thf(func_def_1, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.20/0.31 thf(func_def_2, type, in__Cong: $o).
% 0.20/0.31 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.20/0.31 thf(func_def_5, type, subsetI1: $o).
% 0.20/0.31 thf(func_def_6, type, binintersect: ($i > $i > $i)).
% 0.20/0.31 thf(func_def_7, type, binintersectEL: $o).
% 0.20/0.31 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(func_def_21, type, sK8: ($i > $i > $i)).
% 0.20/0.31 thf(f2,axiom,(
% 0.20/0.31 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.20/0.31 thf(f4,axiom,(
% 0.20/0.31 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)) = binintersectEL)),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)).
% 0.20/0.31 thf(f5,conjecture,(
% 0.20/0.31 in__Cong => (subsetI1 => (binintersectEL => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0))))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3)).
% 0.20/0.31 thf(f6,negated_conjecture,(
% 0.20/0.31 ~(in__Cong => (subsetI1 => (binintersectEL => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)))))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f5])).
% 0.20/0.31 thf(f11,plain,(
% 0.20/0.31 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f12,plain,(
% 0.20/0.31 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true)) <=> (subsetI1 = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f11])).
% 0.20/0.31 thf(f13,plain,(
% 0.20/0.31 ~(in__Cong => (subsetI1 => (binintersectEL => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)))))),
% 0.20/0.31 inference(rectify,[],[f6])).
% 0.20/0.31 thf(f14,plain,(
% 0.20/0.31 ~((in__Cong = $true) => ((subsetI1 = $true) => ((binintersectEL = $true) => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (((subset @ X1 @ X0)) = $true)))))),
% 0.20/0.31 inference(fool_elimination,[],[f13])).
% 0.20/0.31 thf(f15,plain,(
% 0.20/0.31 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X2 @ X1)) => (in @ X0 @ X2)) = binintersectEL)),
% 0.20/0.31 inference(rectify,[],[f4])).
% 0.20/0.31 thf(f16,plain,(
% 0.20/0.31 (binintersectEL = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) = $true) => ($true = ((in @ X0 @ X2))))),
% 0.20/0.31 inference(fool_elimination,[],[f15])).
% 0.20/0.31 thf(f17,plain,(
% 0.20/0.31 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))),
% 0.20/0.31 inference(ennf_transformation,[],[f12])).
% 0.20/0.31 thf(f19,plain,(
% 0.20/0.31 ((? [X1 : $i,X0 : $i] : ((((binintersect @ X0 @ X1)) = X1) & (((subset @ X1 @ X0)) != $true)) & (binintersectEL = $true)) & (subsetI1 = $true)) & (in__Cong = $true)),
% 0.20/0.31 inference(ennf_transformation,[],[f14])).
% 0.20/0.31 thf(f20,plain,(
% 0.20/0.31 (subsetI1 = $true) & (binintersectEL = $true) & (in__Cong = $true) & ? [X1 : $i,X0 : $i] : ((((binintersect @ X0 @ X1)) = X1) & (((subset @ X1 @ X0)) != $true))),
% 0.20/0.31 inference(flattening,[],[f19])).
% 0.20/0.31 thf(f21,plain,(
% 0.20/0.31 (binintersectEL = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) != $true) | ($true = ((in @ X0 @ X2))))),
% 0.20/0.31 inference(ennf_transformation,[],[f16])).
% 0.20/0.31 thf(f22,plain,(
% 0.20/0.31 (subsetI1 = $true) & (binintersectEL = $true) & (in__Cong = $true) & ? [X0 : $i,X1 : $i] : ((((binintersect @ X1 @ X0)) = X0) & (((subset @ X0 @ X1)) != $true))),
% 0.20/0.31 inference(rectify,[],[f20])).
% 0.20/0.31 thf(f23,plain,(
% 0.20/0.31 (subsetI1 = $true) & (binintersectEL = $true) & (in__Cong = $true) & ((sK0 = ((binintersect @ sK1 @ sK0))) & ($true != ((subset @ sK0 @ sK1))))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f22])).
% 0.20/0.31 thf(f27,plain,(
% 0.20/0.31 ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))) & (! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true))),
% 0.20/0.31 inference(nnf_transformation,[],[f17])).
% 0.20/0.31 thf(f28,plain,(
% 0.20/0.31 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | ? [X5 : $i] : ((((in @ X5 @ X3)) = $true) & ($true != ((in @ X5 @ X4))))) | (subsetI1 != $true))),
% 0.20/0.31 inference(rectify,[],[f27])).
% 0.20/0.31 thf(f29,plain,(
% 0.20/0.31 ((subsetI1 = $true) | ((((subset @ sK6 @ sK7)) != $true) & ! [X2 : $i] : (($true != ((in @ X2 @ sK6))) | ($true = ((in @ X2 @ sK7)))))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | (($true = ((in @ (sK8 @ X4 @ X3) @ X3))) & ($true != ((in @ (sK8 @ X4 @ X3) @ X4))))) | (subsetI1 != $true))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,vAPP]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X5,sK8 @ X4 @ X3)],[f28])).
% 0.20/0.31 thf(f30,plain,(
% 0.20/0.31 ((binintersectEL = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) = $true) & ($true != ((in @ X0 @ X2))))) & (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) != $true) | ($true = ((in @ X0 @ X2)))) | (binintersectEL != $true))),
% 0.20/0.31 inference(nnf_transformation,[],[f21])).
% 0.20/0.31 thf(f31,plain,(
% 0.20/0.31 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (binintersect @ X0 @ X1))) = $true) & (((in @ X2 @ X0)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (binintersect @ X3 @ X4)))) | (((in @ X5 @ X3)) = $true)) | (binintersectEL != $true))),
% 0.20/0.31 inference(rectify,[],[f30])).
% 0.20/0.31 thf(f32,plain,(
% 0.20/0.31 ((binintersectEL = $true) | (($true = ((in @ sK11 @ (binintersect @ sK9 @ sK10)))) & ($true != ((in @ sK11 @ sK9))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (binintersect @ X3 @ X4)))) | (((in @ X5 @ X3)) = $true)) | (binintersectEL != $true))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f31])).
% 0.20/0.31 thf(f33,plain,(
% 0.20/0.31 ($true != ((subset @ sK0 @ sK1)))),
% 0.20/0.31 inference(cnf_transformation,[],[f23])).
% 0.20/0.31 thf(f34,plain,(
% 0.20/0.31 (sK0 = ((binintersect @ sK1 @ sK0)))),
% 0.20/0.31 inference(cnf_transformation,[],[f23])).
% 0.20/0.31 thf(f36,plain,(
% 0.20/0.31 (binintersectEL = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f23])).
% 0.20/0.31 thf(f37,plain,(
% 0.20/0.31 (subsetI1 = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f23])).
% 0.20/0.31 thf(f42,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK8 @ X4 @ X3) @ X4))) | (subsetI1 != $true) | ($true = ((subset @ X3 @ X4)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f29])).
% 0.20/0.31 thf(f43,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i] : ((subsetI1 != $true) | ($true = ((subset @ X3 @ X4))) | ($true = ((in @ (sK8 @ X4 @ X3) @ X3)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f29])).
% 0.20/0.31 thf(f47,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (binintersect @ X3 @ X4)))) | (binintersectEL != $true) | (((in @ X5 @ X3)) = $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f32])).
% 0.20/0.31 thf(f62,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK8 @ X4 @ X3) @ X4))) | ($true = ((subset @ X3 @ X4)))) )),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f42,f37])).
% 0.20/0.31 thf(f69,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK8 @ X4 @ X3) @ X3))) | ($true = ((subset @ X3 @ X4)))) )),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f43,f37])).
% 0.20/0.31 thf(f79,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (binintersect @ X3 @ X4)))) | (((in @ X5 @ X3)) = $true)) )),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f47,f36])).
% 0.20/0.31 thf(f80,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((((in @ X0 @ sK1)) = $true) | (((in @ X0 @ sK0)) != $true)) )),
% 0.20/0.31 inference(superposition,[],[f79,f34])).
% 0.20/0.31 thf(f88,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((((in @ (sK8 @ sK1 @ X0) @ sK0)) != $true) | (((subset @ X0 @ sK1)) = $true) | ($true != $true)) )),
% 0.20/0.31 inference(superposition,[],[f62,f80])).
% 0.20/0.31 thf(f90,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((((in @ (sK8 @ sK1 @ X0) @ sK0)) != $true) | (((subset @ X0 @ sK1)) = $true)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f88])).
% 0.20/0.31 thf(f108,plain,(
% 0.20/0.31 ($true = ((subset @ sK0 @ sK1))) | ($true != $true) | ($true = ((subset @ sK0 @ sK1)))),
% 0.20/0.31 inference(superposition,[],[f90,f69])).
% 0.20/0.31 thf(f110,plain,(
% 0.20/0.31 ($true = ((subset @ sK0 @ sK1))) | ($true != $true)),
% 0.20/0.31 inference(duplicate_literal_removal,[],[f108])).
% 0.20/0.31 thf(f111,plain,(
% 0.20/0.31 ($true = ((subset @ sK0 @ sK1)))),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f110])).
% 0.20/0.31 thf(f113,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f111,f33])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (115635)------------------------------
% 0.20/0.31 % (115635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (115635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (115635)CaDiCaL version: 2.1.3
% 0.20/0.31 % (115635)Termination reason: Refutation
% 0.20/0.31 % (115635)Time elapsed: 0.006 s
% 0.20/0.31 % (115635)Peak memory usage: 12 MB
% 0.20/0.31 % (115635)Instructions burned: 8 (million)
% 0.20/0.31 % (115626)Success in time 0.038 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------