%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU569^2 : 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 : n026.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 08:30:07 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 : SEU569^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n026.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 13:53:42 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.25 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 % (629080)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (629094)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=68171679:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (629094) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-629080-629094"...
% 0.22/0.29 % (629094)...printing done.
% 0.22/0.29 % (629094)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.29 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.22/0.29 thf(func_def_2, type, subsetI2: $o).
% 0.22/0.29 thf(func_def_7, type, sK1: ($i > $i > $i)).
% 0.22/0.29 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.22/0.29 thf(f1,axiom,(
% 0.22/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.22/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.22/0.29 thf(f2,conjecture,(
% 0.22/0.29 subsetI2 => ! [X0 : $i] : (subset @ X0 @ X0)),
% 0.22/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl)).
% 0.22/0.29 thf(f3,negated_conjecture,(
% 0.22/0.29 ~(subsetI2 => ! [X0 : $i] : (subset @ X0 @ X0))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f2])).
% 0.22/0.29 thf(f4,plain,(
% 0.22/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.22/0.29 inference(rectify,[],[f1])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true)) <=> (subsetI2 = $true)),
% 0.22/0.29 inference(fool_elimination,[],[f4])).
% 0.22/0.29 thf(f6,plain,(
% 0.22/0.29 ~(subsetI2 => ! [X0 : $i] : (subset @ X0 @ X0))),
% 0.22/0.29 inference(rectify,[],[f3])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 ~((subsetI2 = $true) => ! [X0 : $i] : (((subset @ X0 @ X0)) = $true))),
% 0.22/0.29 inference(fool_elimination,[],[f6])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) <=> (subsetI2 = $true)),
% 0.22/0.29 inference(ennf_transformation,[],[f5])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 ? [X0 : $i] : (((subset @ X0 @ X0)) != $true) & (subsetI2 = $true)),
% 0.22/0.29 inference(ennf_transformation,[],[f7])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 ($true != ((subset @ sK0 @ sK0))) & (subsetI2 = $true)),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f9])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 (! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true))))),
% 0.22/0.29 inference(nnf_transformation,[],[f8])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 (! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (($true != ((subset @ X4 @ X3))) & ! [X5 : $i] : (($true = ((in @ X5 @ X3))) | ($true != ((in @ X5 @ X4))))))),
% 0.22/0.29 inference(rectify,[],[f11])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 (! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | (($true != ((in @ (sK1 @ X1 @ X0) @ X0))) & ($true = ((in @ (sK1 @ X1 @ X0) @ X1))))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (($true != ((subset @ sK3 @ sK2))) & ! [X5 : $i] : (($true = ((in @ X5 @ sK2))) | ($true != ((in @ X5 @ sK3))))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK2,sK3]),skolemize(X2,sK1 @ X1 @ X0),skolemize(X3,sK2),skolemize(X4,sK3)],[f12])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 (subsetI2 = $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f10])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 ($true != ((subset @ sK0 @ sK0)))),
% 0.22/0.29 inference(cnf_transformation,[],[f10])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ($true = ((in @ (sK1 @ X1 @ X0) @ X1))) | (subsetI2 != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f13])).
% 0.22/0.29 thf(f19,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ($true != ((in @ (sK1 @ X1 @ X0) @ X0))) | (subsetI2 != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f13])).
% 0.22/0.29 thf(f22,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ X1 @ X0))) | ($true != ((in @ (sK1 @ X1 @ X0) @ X0)))) )),
% 0.22/0.29 inference(definition_unfolding,[],[f19,f14])).
% 0.22/0.29 thf(f23,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ X1 @ X0))) | ($true = ((in @ (sK1 @ X1 @ X0) @ X1)))) )),
% 0.22/0.29 inference(definition_unfolding,[],[f18,f14])).
% 0.22/0.29 thf(f26,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK1 @ X1 @ X0) @ X0))) | ($true = ((subset @ X1 @ X0)))) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f22])).
% 0.22/0.29 thf(f27,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK1 @ X1 @ X0) @ X1))) | ($true = ((subset @ X1 @ X0)))) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f23])).
% 0.22/0.29 thf(f28,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((subset @ X0 @ X0)) = $true) | ($true != $true) | (((subset @ X0 @ X0)) = $true)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f26,f27])).
% 0.22/0.29 thf(f29,plain,(
% 0.22/0.29 ( ! [X0 : $i] : (($true != $true) | (((subset @ X0 @ X0)) = $true)) )),
% 0.22/0.29 inference(duplicate_literal_removal,[],[f28])).
% 0.22/0.29 thf(f30,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((subset @ X0 @ X0)) = $true)) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f29])).
% 0.22/0.29 thf(f31,plain,(
% 0.22/0.29 ($true != $true)),
% 0.22/0.29 inference(backward_demodulation,[],[f15,f30])).
% 0.22/0.29 thf(f32,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f31])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (629094)------------------------------
% 0.22/0.29 % (629094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (629094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (629094)CaDiCaL version: 2.1.3
% 0.22/0.29 % (629094)Termination reason: Refutation
% 0.22/0.29 % (629094)Time elapsed: 0.001 s
% 0.22/0.29 % (629094)Peak memory usage: 12 MB
% 0.22/0.29 % (629094)Instructions burned: 2 (million)
% 0.22/0.29 % (629080)Success in time 0.028 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------