%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU522^2 : 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 : n008.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 08:29:54 AM UTC 2026
% Result : Theorem 0.29s 0.42s
% Output : Refutation 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU522^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n008.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 13:48:39 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.34 Running higher-order theorem proving
% 0.29/0.35 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
% 0.29/0.42 % (3179411)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.29/0.42 % (3179416)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2326349108:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.29/0.42 % (3179416) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3179411-3179416"...
% 0.29/0.42 % (3179416)...printing done.
% 0.29/0.42 % (3179416)Refutation found. Thanks to Tanya!
% 0.29/0.42 % SZS status Theorem for theBenchmark
% 0.29/0.42 % SZS output start Proof for theBenchmark
% 0.29/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.29/0.42 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.29/0.42 thf(func_def_1, type, setunion: ($i > $i)).
% 0.29/0.42 thf(func_def_2, type, setunionAx: $o).
% 0.29/0.42 thf(func_def_12, type, sK6: ($i > $i > $i)).
% 0.29/0.42 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.29/0.42 thf(f1,axiom,(
% 0.29/0.42 (setunionAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0))))),
% 0.29/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx)).
% 0.29/0.42 thf(f2,conjecture,(
% 0.29/0.42 setunionAx => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0))))),
% 0.29/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)).
% 0.29/0.42 thf(f3,negated_conjecture,(
% 0.29/0.42 ~(setunionAx => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 0.29/0.42 inference(negated_conjecture,[status(cth)],[f2])).
% 0.29/0.42 thf(f4,plain,(
% 0.29/0.42 (setunionAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0))))),
% 0.29/0.42 inference(rectify,[],[f1])).
% 0.29/0.42 thf(f5,plain,(
% 0.29/0.42 (setunionAx = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) <=> ? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)))),
% 0.29/0.42 inference(fool_elimination,[],[f4])).
% 0.29/0.42 thf(f6,plain,(
% 0.29/0.42 ~(setunionAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X2 @ X1) => (in @ X0 @ (setunion @ X1)))))),
% 0.29/0.42 inference(rectify,[],[f3])).
% 0.29/0.42 thf(f7,plain,(
% 0.29/0.42 ~((setunionAx = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2)) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X0 @ (setunion @ X1))) = $true))))),
% 0.29/0.42 inference(fool_elimination,[],[f6])).
% 0.29/0.42 thf(f8,plain,(
% 0.29/0.42 ? [X2 : $i,X1 : $i,X0 : $i] : (((((in @ X0 @ (setunion @ X1))) != $true) & (((in @ X2 @ X1)) = $true)) & (((in @ X0 @ X2)) = $true)) & (setunionAx = $true)),
% 0.29/0.42 inference(ennf_transformation,[],[f7])).
% 0.29/0.42 thf(f9,plain,(
% 0.29/0.42 ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ (setunion @ X1))) != $true) & (((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true)) & (setunionAx = $true)),
% 0.29/0.42 inference(flattening,[],[f8])).
% 0.29/0.42 thf(f10,plain,(
% 0.29/0.42 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setunion @ X2))) != $true) & (((in @ X0 @ X1)) = $true) & (((in @ X1 @ X2)) = $true)) & (setunionAx = $true)),
% 0.29/0.42 inference(rectify,[],[f9])).
% 0.29/0.42 thf(f11,plain,(
% 0.29/0.42 ((((in @ sK0 @ (setunion @ sK2))) != $true) & (((in @ sK0 @ sK1)) = $true) & (((in @ sK1 @ sK2)) = $true)) & (setunionAx = $true)),
% 0.29/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10])).
% 0.29/0.42 thf(f12,plain,(
% 0.29/0.42 ((setunionAx = $true) | ? [X1 : $i,X0 : $i] : ((! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true)) | (((in @ X1 @ (setunion @ X0))) != $true)) & (? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (setunion @ X0))) = $true)))) & (! [X1 : $i,X0 : $i] : (((((in @ X1 @ (setunion @ X0))) = $true) | ! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true))) & (? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (setunion @ X0))) != $true))) | (setunionAx != $true))),
% 0.29/0.42 inference(nnf_transformation,[],[f5])).
% 0.29/0.42 thf(f13,plain,(
% 0.29/0.42 ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : ((! [X2 : $i] : ((((in @ X0 @ X2)) != $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X0 @ (setunion @ X1))) != $true)) & (? [X3 : $i] : ((((in @ X0 @ X3)) = $true) & (((in @ X3 @ X1)) = $true)) | (((in @ X0 @ (setunion @ X1))) = $true)))) & (! [X4 : $i,X5 : $i] : (((((in @ X4 @ (setunion @ X5))) = $true) | ! [X6 : $i] : ((((in @ X4 @ X6)) != $true) | (((in @ X6 @ X5)) != $true))) & (? [X7 : $i] : ((((in @ X4 @ X7)) = $true) & (((in @ X7 @ X5)) = $true)) | (((in @ X4 @ (setunion @ X5))) != $true))) | (setunionAx != $true))),
% 0.29/0.42 inference(rectify,[],[f12])).
% 0.29/0.42 thf(f14,plain,(
% 0.29/0.42 ((setunionAx = $true) | ((! [X2 : $i] : ((((in @ sK3 @ X2)) != $true) | (((in @ X2 @ sK4)) != $true)) | ($true != ((in @ sK3 @ (setunion @ sK4))))) & (((((in @ sK3 @ sK5)) = $true) & (((in @ sK5 @ sK4)) = $true)) | ($true = ((in @ sK3 @ (setunion @ sK4))))))) & (! [X4 : $i,X5 : $i] : (((((in @ X4 @ (setunion @ X5))) = $true) | ! [X6 : $i] : ((((in @ X4 @ X6)) != $true) | (((in @ X6 @ X5)) != $true))) & ((($true = ((in @ X4 @ (sK6 @ X5 @ X4)))) & ($true = ((in @ (sK6 @ X5 @ X4) @ X5)))) | (((in @ X4 @ (setunion @ X5))) != $true))) | (setunionAx != $true))),
% 0.29/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,vAPP]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X3,sK5),skolemize(X7,sK6 @ X5 @ X4)],[f13])).
% 0.29/0.42 thf(f15,plain,(
% 0.29/0.42 (setunionAx = $true)),
% 0.29/0.42 inference(cnf_transformation,[],[f11])).
% 0.29/0.42 thf(f16,plain,(
% 0.29/0.42 (((in @ sK1 @ sK2)) = $true)),
% 0.29/0.42 inference(cnf_transformation,[],[f11])).
% 0.29/0.42 thf(f17,plain,(
% 0.29/0.42 (((in @ sK0 @ sK1)) = $true)),
% 0.29/0.42 inference(cnf_transformation,[],[f11])).
% 0.29/0.42 thf(f18,plain,(
% 0.29/0.42 (((in @ sK0 @ (setunion @ sK2))) != $true)),
% 0.29/0.42 inference(cnf_transformation,[],[f11])).
% 0.29/0.42 thf(f21,plain,(
% 0.29/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ (setunion @ X5))) = $true) | (((in @ X4 @ X6)) != $true) | (((in @ X6 @ X5)) != $true) | (setunionAx != $true)) )),
% 0.29/0.42 inference(cnf_transformation,[],[f14])).
% 0.29/0.42 thf(f30,plain,(
% 0.29/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X6 @ X5)) != $true) | ($true != $true) | (((in @ X4 @ X6)) != $true) | (((in @ X4 @ (setunion @ X5))) = $true)) )),
% 0.29/0.42 inference(definition_unfolding,[],[f21,f15])).
% 0.29/0.42 thf(f33,plain,(
% 0.29/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ X6 @ X5)) != $true) | (((in @ X4 @ X6)) != $true) | (((in @ X4 @ (setunion @ X5))) = $true)) )),
% 0.29/0.42 inference(trivial_inequality_removal,[],[f30])).
% 0.29/0.42 thf(f36,plain,(
% 0.29/0.42 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK1))) | (((in @ X0 @ (setunion @ sK2))) = $true) | ($true != $true)) )),
% 0.29/0.42 inference(constrained_superposition,[],[f33,f16])).
% 0.29/0.42 thf(f39,plain,(
% 0.29/0.42 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK1))) | (((in @ X0 @ (setunion @ sK2))) = $true)) )),
% 0.29/0.42 inference(trivial_inequality_removal,[],[f36])).
% 0.29/0.42 thf(f40,plain,(
% 0.29/0.42 (((in @ sK0 @ (setunion @ sK2))) = $true) | ($true != $true)),
% 0.29/0.42 inference(constrained_superposition,[],[f39,f17])).
% 0.29/0.42 thf(f41,plain,(
% 0.29/0.42 (((in @ sK0 @ (setunion @ sK2))) = $true)),
% 0.29/0.42 inference(trivial_inequality_removal,[],[f40])).
% 0.29/0.42 thf(f42,plain,(
% 0.29/0.42 $false),
% 0.29/0.42 inference(forward_subsumption_resolution,[],[f41,f18])).
% 0.29/0.42 % SZS output end Proof for theBenchmark
% 0.29/0.42 % (3179416)------------------------------
% 0.29/0.42 % (3179416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.42 % (3179416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.42 % (3179416)CaDiCaL version: 2.1.3
% 0.29/0.42 % (3179416)Termination reason: Refutation
% 0.29/0.42 % (3179416)Time elapsed: 0.006 s
% 0.29/0.42 % (3179416)Peak memory usage: 12 MB
% 0.29/0.42 % (3179416)Instructions burned: 4 (million)
% 0.29/0.42 % (3179411)Success in time 0.052 s
% 0.29/0.42 % Vampire exiting
%------------------------------------------------------------------------------