%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU599^2 : 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 : n005.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 08:30:15 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU599^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n005.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
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:56:16 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 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
% 0.20/0.28 % (1704337)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1704346)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4040827309:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (1704346) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1704337-1704346"...
% 0.20/0.28 % (1704346)...printing done.
% 0.20/0.28 % (1704346)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.28 thf(func_def_1, type, in__Cong: $o).
% 0.20/0.28 thf(func_def_3, type, subset: ($i > $i > $o)).
% 0.20/0.28 thf(func_def_4, type, subsetI1: $o).
% 0.20/0.28 thf(func_def_5, type, binintersect: ($i > $i > $i)).
% 0.20/0.28 thf(func_def_6, type, binintersectER: $o).
% 0.20/0.28 thf(func_def_9, type, sK0: ($i > $i > $i)).
% 0.20/0.28 thf(f2,axiom,(
% 0.20/0.28 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.20/0.28 thf(f3,axiom,(
% 0.20/0.28 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
% 0.20/0.28 thf(f4,conjecture,(
% 0.20/0.28 in__Cong => (subsetI1 => (binintersectER => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1))))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1)).
% 0.20/0.28 thf(f5,negated_conjecture,(
% 0.20/0.28 ~(in__Cong => (subsetI1 => (binintersectER => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)))))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ~(in__Cong => (subsetI1 => (binintersectER => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)))))),
% 0.20/0.28 inference(rectify,[],[f5])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ~((in__Cong = $true) => ((subsetI1 = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (((subset @ X0 @ X1)) = $true)))))),
% 0.20/0.28 inference(fool_elimination,[],[f8])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X2)) = binintersectER)),
% 0.20/0.28 inference(rectify,[],[f3])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 (binintersectER = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X1 @ (binintersect @ X0 @ X2)))) => ($true = ((in @ X1 @ X2))))),
% 0.20/0.28 inference(fool_elimination,[],[f12])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 ((? [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) != $true) & (((binintersect @ X0 @ X1)) = X0)) & (binintersectER = $true)) & (subsetI1 = $true)) & (in__Cong = $true)),
% 0.20/0.28 inference(ennf_transformation,[],[f9])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 (in__Cong = $true) & (subsetI1 = $true) & ? [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) != $true) & (((binintersect @ X0 @ X1)) = X0)) & (binintersectER = $true)),
% 0.20/0.28 inference(flattening,[],[f14])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 (binintersectER = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ X2))) | ($true != ((in @ X1 @ (binintersect @ X0 @ X2)))))),
% 0.20/0.28 inference(ennf_transformation,[],[f13])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) <=> (subsetI1 = $true)),
% 0.20/0.28 inference(ennf_transformation,[],[f7])).
% 0.20/0.28 thf(f19,plain,(
% 0.20/0.28 (! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true))))),
% 0.20/0.28 inference(nnf_transformation,[],[f18])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) != $true) & ! [X5 : $i] : ((((in @ X5 @ X3)) != $true) | (((in @ X5 @ X4)) = $true))))),
% 0.20/0.28 inference(rectify,[],[f19])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) & ($true != ((in @ (sK0 @ X1 @ X0) @ X1))))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ((((subset @ sK1 @ sK2)) != $true) & ! [X5 : $i] : ((((in @ X5 @ sK1)) != $true) | (((in @ X5 @ sK2)) = $true))))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f20])).
% 0.20/0.28 thf(f25,plain,(
% 0.20/0.28 ((binintersectER = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ X2))) & ($true = ((in @ X1 @ (binintersect @ X0 @ X2)))))) & (! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ X2))) | ($true != ((in @ X1 @ (binintersect @ X0 @ X2))))) | (binintersectER != $true))),
% 0.20/0.28 inference(nnf_transformation,[],[f16])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ (binintersect @ X1 @ X0))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) = $true) | (((in @ X5 @ (binintersect @ X4 @ X3))) != $true)) | (binintersectER != $true))),
% 0.20/0.28 inference(rectify,[],[f25])).
% 0.20/0.28 thf(f27,plain,(
% 0.20/0.28 ((binintersectER = $true) | ((((in @ sK9 @ sK7)) != $true) & (((in @ sK9 @ (binintersect @ sK8 @ sK7))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) = $true) | (((in @ X5 @ (binintersect @ X4 @ X3))) != $true)) | (binintersectER != $true))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f26])).
% 0.20/0.28 thf(f28,plain,(
% 0.20/0.28 (in__Cong = $true) & (subsetI1 = $true) & ? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) & (((binintersect @ X1 @ X0)) = X1)) & (binintersectER = $true)),
% 0.20/0.28 inference(rectify,[],[f15])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 (in__Cong = $true) & (subsetI1 = $true) & ((((subset @ sK11 @ sK10)) != $true) & (((binintersect @ sK11 @ sK10)) = sK11)) & (binintersectER = $true)),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f28])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (subsetI1 != $true) | ($true != ((in @ (sK0 @ X1 @ X0) @ X1)))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f21])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | (((subset @ X0 @ X1)) = $true) | (subsetI1 != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f21])).
% 0.20/0.28 thf(f38,plain,(
% 0.20/0.28 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) = $true) | (binintersectER != $true) | (((in @ X5 @ (binintersect @ X4 @ X3))) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f27])).
% 0.20/0.28 thf(f41,plain,(
% 0.20/0.28 (binintersectER = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f29])).
% 0.20/0.28 thf(f42,plain,(
% 0.20/0.28 (((binintersect @ sK11 @ sK10)) = sK11)),
% 0.20/0.28 inference(cnf_transformation,[],[f29])).
% 0.20/0.28 thf(f43,plain,(
% 0.20/0.28 (((subset @ sK11 @ sK10)) != $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f29])).
% 0.20/0.28 thf(f44,plain,(
% 0.20/0.28 (subsetI1 = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f29])).
% 0.20/0.28 thf(f58,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f32,f44])).
% 0.20/0.28 thf(f65,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | (((subset @ X0 @ X1)) = $true)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f33,f44])).
% 0.20/0.28 thf(f75,plain,(
% 0.20/0.28 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (binintersect @ X4 @ X3))) != $true) | (((in @ X5 @ X3)) = $true)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f38,f41])).
% 0.20/0.28 thf(f76,plain,(
% 0.20/0.28 ( ! [X0 : $i] : ((((in @ X0 @ sK10)) = $true) | ($true != ((in @ X0 @ sK11)))) )),
% 0.20/0.28 inference(superposition,[],[f75,f42])).
% 0.20/0.28 thf(f84,plain,(
% 0.20/0.28 ( ! [X0 : $i] : ((((subset @ X0 @ sK10)) = $true) | ($true != $true) | ($true != ((in @ (sK0 @ sK10 @ X0) @ sK11)))) )),
% 0.20/0.28 inference(superposition,[],[f58,f76])).
% 0.20/0.28 thf(f86,plain,(
% 0.20/0.28 ( ! [X0 : $i] : (($true != ((in @ (sK0 @ sK10 @ X0) @ sK11))) | (((subset @ X0 @ sK10)) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f84])).
% 0.20/0.28 thf(f104,plain,(
% 0.20/0.28 ($true != $true) | (((subset @ sK11 @ sK10)) = $true) | (((subset @ sK11 @ sK10)) = $true)),
% 0.20/0.28 inference(superposition,[],[f86,f65])).
% 0.20/0.28 thf(f107,plain,(
% 0.20/0.28 (((subset @ sK11 @ sK10)) = $true) | ($true != $true)),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f104])).
% 0.20/0.28 thf(f108,plain,(
% 0.20/0.28 (((subset @ sK11 @ sK10)) = $true)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f107])).
% 0.20/0.28 thf(f109,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f108,f43])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (1704346)------------------------------
% 0.20/0.28 % (1704346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1704346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1704346)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1704346)Termination reason: Refutation
% 0.20/0.28 % (1704346)Time elapsed: 0.003 s
% 0.20/0.28 % (1704346)Peak memory usage: 12 MB
% 0.20/0.28 % (1704346)Instructions burned: 8 (million)
% 0.20/0.28 % (1704337)Success in time 0.041 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------