%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU570^2 : 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 : n020.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 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU570^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 13:51:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.28 % (1088572)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1088577)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1910508344:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (1088577) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1088572-1088577"...
% 0.21/0.28 % (1088577)...printing done.
% 0.21/0.28 % (1088577)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_2, type, subsetI2: $o).
% 0.21/0.28 thf(func_def_4, type, subsetE: $o).
% 0.21/0.28 thf(func_def_13, type, sK6: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 (! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.21/0.28 thf(f3,conjecture,(
% 0.21/0.28 subsetI2 => (subsetE => ! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans)).
% 0.21/0.28 thf(f4,negated_conjecture,(
% 0.21/0.28 ~(subsetI2 => (subsetE => ! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2)))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~(subsetI2 => (subsetE => ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((subset @ X2 @ X1) => (subset @ X0 @ X1)))))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ~((subsetI2 = $true) => ((subsetE = $true) => ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) = $true) => ((((subset @ X2 @ X1)) = $true) => (((subset @ X0 @ X1)) = $true)))))),
% 0.21/0.28 inference(fool_elimination,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))) = subsetE)),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ! [X1 : $i,X0 : $i,X2 : $i] : ((((subset @ X2 @ X1)) = $true) => (($true = ((in @ X0 @ X2))) => ($true = ((in @ X0 @ X1))))) <=> (subsetE = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f9])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) <=> (subsetI2 = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f8])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = ((in @ X0 @ X1))) | ($true != ((in @ X0 @ X2)))) | (((subset @ X2 @ X1)) != $true)) <=> (subsetE = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f10])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X2 @ X1)) != $true) | ($true != ((in @ X0 @ X2))) | ($true = ((in @ X0 @ X1)))) <=> (subsetE = $true)),
% 0.21/0.28 inference(flattening,[],[f12])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 (? [X2 : $i,X0 : $i,X1 : $i] : (((((subset @ X0 @ X1)) != $true) & (((subset @ X2 @ X1)) = $true)) & (((subset @ X0 @ X2)) = $true)) & (subsetE = $true)) & (subsetI2 = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f6])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ? [X2 : $i,X1 : $i,X0 : $i] : ((((subset @ X2 @ X1)) = $true) & (((subset @ X0 @ X2)) = $true) & (((subset @ X0 @ X1)) != $true)) & (subsetE = $true) & (subsetI2 = $true)),
% 0.21/0.28 inference(flattening,[],[f14])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ? [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X1)) = $true) & ($true = ((subset @ X2 @ X0))) & (((subset @ X2 @ X1)) != $true)) & (subsetE = $true) & (subsetI2 = $true)),
% 0.21/0.28 inference(rectify,[],[f15])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 (($true = ((subset @ sK0 @ sK1))) & ($true = ((subset @ sK2 @ sK0))) & (((subset @ sK2 @ sK1)) != $true)) & (subsetE = $true) & (subsetI2 = $true)),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 (! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X2 @ X1)) != $true) | ($true != ((in @ X0 @ X2))) | ($true = ((in @ X0 @ X1)))) | (subsetE != $true)) & ((subsetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X2 @ X1)) = $true) & ($true = ((in @ X0 @ X2))) & ($true != ((in @ X0 @ X1)))))),
% 0.21/0.28 inference(nnf_transformation,[],[f13])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2)) != $true) | ($true != ((in @ X1 @ X0))) | ($true = ((in @ X1 @ X2)))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = ((subset @ X3 @ X5))) & ($true = ((in @ X4 @ X3))) & ($true != ((in @ X4 @ X5)))))),
% 0.21/0.28 inference(rectify,[],[f18])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2)) != $true) | ($true != ((in @ X1 @ X0))) | ($true = ((in @ X1 @ X2)))) | (subsetE != $true)) & ((subsetE = $true) | (($true = ((subset @ sK3 @ sK5))) & ($true = ((in @ sK4 @ sK3))) & ($true != ((in @ sK4 @ sK5)))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f19])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 (! [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)))),
% 0.21/0.28 inference(nnf_transformation,[],[f11])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | ($true = ((subset @ X1 @ X0)))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true = ((in @ X5 @ X3))) | ($true != ((in @ X5 @ X4)))) & (((subset @ X4 @ X3)) != $true)))),
% 0.21/0.28 inference(rectify,[],[f21])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : ((($true != ((in @ (sK6 @ X1 @ X0) @ X0))) & ($true = ((in @ (sK6 @ X1 @ X0) @ X1)))) | ($true = ((subset @ X1 @ X0)))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (! [X5 : $i] : (($true = ((in @ X5 @ sK7))) | ($true != ((in @ X5 @ sK8)))) & ($true != ((subset @ sK8 @ sK7)))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK7,sK8]),skolemize(X2,sK6 @ X1 @ X0),skolemize(X3,sK7),skolemize(X4,sK8)],[f22])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 (subsetI2 = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f17])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 (subsetE = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f17])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 (((subset @ sK2 @ sK1)) != $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f17])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ($true = ((subset @ sK2 @ sK0)))),
% 0.21/0.28 inference(cnf_transformation,[],[f17])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ($true = ((subset @ sK0 @ sK1)))),
% 0.21/0.28 inference(cnf_transformation,[],[f17])).
% 0.21/0.28 thf(f32,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | ($true != ((in @ X1 @ X0))) | ($true = ((in @ X1 @ X2))) | (subsetE != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f20])).
% 0.21/0.28 thf(f35,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK6 @ X1 @ X0) @ X1))) | ($true = ((subset @ X1 @ X0))) | (subsetI2 != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f23])).
% 0.21/0.28 thf(f36,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK6 @ X1 @ X0) @ X0))) | ($true = ((subset @ X1 @ X0))) | (subsetI2 != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f23])).
% 0.21/0.28 thf(f39,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ X2))) | ($true != $true) | (((subset @ X0 @ X2)) != $true) | ($true != ((in @ X1 @ X0)))) )),
% 0.21/0.28 inference(definition_unfolding,[],[f32,f25])).
% 0.21/0.28 thf(f43,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ X1 @ X0))) | ($true != ((in @ (sK6 @ X1 @ X0) @ X0)))) )),
% 0.21/0.28 inference(definition_unfolding,[],[f36,f24])).
% 0.21/0.28 thf(f44,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ X1 @ X0))) | ($true = ((in @ (sK6 @ X1 @ X0) @ X1)))) )),
% 0.21/0.28 inference(definition_unfolding,[],[f35,f24])).
% 0.21/0.28 thf(f47,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK6 @ X1 @ X0) @ X0))) | ($true = ((subset @ X1 @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f43])).
% 0.21/0.28 thf(f48,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK6 @ X1 @ X0) @ X1))) | ($true = ((subset @ X1 @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f44])).
% 0.21/0.28 thf(f49,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ X0))) | (((subset @ X0 @ X2)) != $true) | ($true = ((in @ X1 @ X2)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f39])).
% 0.21/0.28 thf(f53,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((subset @ X0 @ X2)) != $true) | ($true = ((in @ (sK6 @ X0 @ X1) @ X2))) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f49,f48])).
% 0.21/0.28 thf(f54,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | ($true = ((in @ (sK6 @ X0 @ X1) @ X2))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f53])).
% 0.21/0.28 thf(f55,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true = ((in @ (sK6 @ sK2 @ X0) @ sK0))) | ($true = ((subset @ sK2 @ X0))) | ($true != $true)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f54,f27])).
% 0.21/0.28 thf(f59,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true = ((in @ (sK6 @ sK2 @ X0) @ sK0))) | ($true = ((subset @ sK2 @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f55])).
% 0.21/0.28 thf(f62,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != ((subset @ sK0 @ X1))) | ($true = ((subset @ sK2 @ X0))) | ($true = ((in @ (sK6 @ sK2 @ X0) @ X1)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f49,f59])).
% 0.21/0.28 thf(f63,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((subset @ sK0 @ X1))) | ($true = ((in @ (sK6 @ sK2 @ X0) @ X1))) | ($true = ((subset @ sK2 @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f62])).
% 0.21/0.28 thf(f71,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true = ((subset @ sK2 @ X0))) | ($true != $true) | ($true = ((in @ (sK6 @ sK2 @ X0) @ sK1)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f63,f28])).
% 0.21/0.28 thf(f73,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true = ((in @ (sK6 @ sK2 @ X0) @ sK1))) | ($true = ((subset @ sK2 @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f71])).
% 0.21/0.28 thf(f75,plain,(
% 0.21/0.28 (((subset @ sK2 @ sK1)) = $true) | ($true != $true) | (((subset @ sK2 @ sK1)) = $true)),
% 0.21/0.28 inference(constrained_superposition,[],[f47,f73])).
% 0.21/0.28 thf(f78,plain,(
% 0.21/0.28 (((subset @ sK2 @ sK1)) = $true) | ($true != $true)),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f75])).
% 0.21/0.28 thf(f79,plain,(
% 0.21/0.28 (((subset @ sK2 @ sK1)) = $true)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f78])).
% 0.21/0.28 thf(f80,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f79,f26])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (1088577)------------------------------
% 0.21/0.28 % (1088577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1088577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1088577)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1088577)Termination reason: Refutation
% 0.21/0.28 % (1088577)Time elapsed: 0.002 s
% 0.21/0.28 % (1088577)Peak memory usage: 12 MB
% 0.21/0.28 % (1088577)Instructions burned: 7 (million)
% 0.21/0.28 % (1088572)Success in time 0.033 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------