%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU660^2 : 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 : n013.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 08:30:34 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU660^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:03:30 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.21/0.27 % (2168683)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (2168688)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=382015555:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (2168688) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2168683-2168688"...
% 0.21/0.27 % (2168688)...printing done.
% 0.21/0.27 % (2168688)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.27 thf(func_def_1, type, kpair: ($i > $i > $i)).
% 0.21/0.27 thf(func_def_2, type, cartprod: ($i > $i > $i)).
% 0.21/0.27 thf(func_def_3, type, cartprodmempair1: $o).
% 0.21/0.27 thf(func_def_5, type, setukpairinjR: $o).
% 0.21/0.27 thf(func_def_11, type, sK3: ($i > $i > $i > $i)).
% 0.21/0.27 thf(func_def_12, type, sK4: ($i > $i > $i > $i)).
% 0.21/0.27 thf(func_def_21, type, vNOT: ($o > $o)).
% 0.21/0.27 thf(f1,axiom,(
% 0.21/0.27 (cartprodmempair1 = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((in @ X4 @ X1) & (X2 = ((kpair @ X3 @ X4)))))))),
% 0.21/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.21/0.27 thf(f2,axiom,(
% 0.21/0.27 (setukpairinjR = ! [X2 : $i,X1 : $i,X3 : $i,X0 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X1 = X3)))),
% 0.21/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR)).
% 0.21/0.27 thf(f3,conjecture,(
% 0.21/0.27 cartprodmempair1 => (setukpairinjR => ! [X2 : $i,X0 : $i,X3 : $i,X1 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X1)))),
% 0.21/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER)).
% 0.21/0.27 thf(f4,negated_conjecture,(
% 0.21/0.27 ~(cartprodmempair1 => (setukpairinjR => ! [X2 : $i,X0 : $i,X3 : $i,X1 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X1))))),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.27 thf(f5,plain,(
% 0.21/0.27 ~(cartprodmempair1 => (setukpairinjR => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((in @ (kpair @ X0 @ X2) @ (cartprod @ X1 @ X3)) => (in @ X2 @ X3))))),
% 0.21/0.27 inference(rectify,[],[f4])).
% 0.21/0.27 thf(f6,plain,(
% 0.21/0.27 ~((cartprodmempair1 = $true) => ((setukpairinjR = $true) => ! [X3 : $i,X0 : $i,X2 : $i,X1 : $i] : ((((in @ (kpair @ X0 @ X2) @ (cartprod @ X1 @ X3))) = $true) => (((in @ X2 @ X3)) = $true))))),
% 0.21/0.27 inference(fool_elimination,[],[f5])).
% 0.21/0.27 thf(f7,plain,(
% 0.21/0.27 (cartprodmempair1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X2 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X2) & ? [X4 : $i] : ((in @ X4 @ X1) & (((kpair @ X3 @ X4)) = X0)))))),
% 0.21/0.27 inference(rectify,[],[f1])).
% 0.21/0.27 thf(f8,plain,(
% 0.21/0.27 (cartprodmempair1 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X0 @ (cartprod @ X2 @ X1)))) => ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & (((in @ X4 @ X1)) = $true))))),
% 0.21/0.27 inference(fool_elimination,[],[f7])).
% 0.21/0.27 thf(f9,plain,(
% 0.21/0.27 (setukpairinjR = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X0 @ X2)) = ((kpair @ X3 @ X1))) => (X1 = X2)))),
% 0.21/0.27 inference(rectify,[],[f2])).
% 0.21/0.27 thf(f10,plain,(
% 0.21/0.27 (setukpairinjR = $true) <=> ! [X0 : $i,X3 : $i,X1 : $i,X2 : $i] : ((((kpair @ X0 @ X2)) = ((kpair @ X3 @ X1))) => (X1 = X2))),
% 0.21/0.27 inference(fool_elimination,[],[f9])).
% 0.21/0.27 thf(f11,plain,(
% 0.21/0.27 (cartprodmempair1 = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & (((in @ X4 @ X1)) = $true))) | ($true != ((in @ X0 @ (cartprod @ X2 @ X1)))))),
% 0.21/0.27 inference(ennf_transformation,[],[f8])).
% 0.21/0.27 thf(f12,plain,(
% 0.21/0.27 ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | (((kpair @ X0 @ X2)) != ((kpair @ X3 @ X1)))) <=> (setukpairinjR = $true)),
% 0.21/0.27 inference(ennf_transformation,[],[f10])).
% 0.21/0.27 thf(f13,plain,(
% 0.21/0.27 (? [X3 : $i,X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X3)) != $true) & (((in @ (kpair @ X0 @ X2) @ (cartprod @ X1 @ X3))) = $true)) & (setukpairinjR = $true)) & (cartprodmempair1 = $true)),
% 0.21/0.27 inference(ennf_transformation,[],[f6])).
% 0.21/0.27 thf(f14,plain,(
% 0.21/0.27 (cartprodmempair1 = $true) & ? [X3 : $i,X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X3)) != $true) & (((in @ (kpair @ X0 @ X2) @ (cartprod @ X1 @ X3))) = $true)) & (setukpairinjR = $true)),
% 0.21/0.27 inference(flattening,[],[f13])).
% 0.21/0.27 thf(f15,plain,(
% 0.21/0.27 ((cartprodmempair1 = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | ! [X4 : $i] : ((((kpair @ X3 @ X4)) != X0) | (((in @ X4 @ X1)) != $true))) & ($true = ((in @ X0 @ (cartprod @ X2 @ X1)))))) & (! [X2 : $i,X0 : $i,X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & (((in @ X4 @ X1)) = $true))) | ($true != ((in @ X0 @ (cartprod @ X2 @ X1))))) | (cartprodmempair1 != $true))),
% 0.21/0.27 inference(nnf_transformation,[],[f11])).
% 0.21/0.27 thf(f16,plain,(
% 0.21/0.27 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | ! [X4 : $i] : ((((kpair @ X3 @ X4)) != X1) | ($true != ((in @ X4 @ X2))))) & ($true = ((in @ X1 @ (cartprod @ X0 @ X2)))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : ((((in @ X8 @ X5)) = $true) & ? [X9 : $i] : ((((kpair @ X8 @ X9)) = X6) & ($true = ((in @ X9 @ X7))))) | (((in @ X6 @ (cartprod @ X5 @ X7))) != $true)) | (cartprodmempair1 != $true))),
% 0.21/0.27 inference(rectify,[],[f15])).
% 0.21/0.27 thf(f17,plain,(
% 0.21/0.27 ((cartprodmempair1 = $true) | (! [X3 : $i] : (($true != ((in @ X3 @ sK0))) | ! [X4 : $i] : ((((kpair @ X3 @ X4)) != sK1) | (((in @ X4 @ sK2)) != $true))) & ($true = ((in @ sK1 @ (cartprod @ sK0 @ sK2)))))) & (! [X5 : $i,X6 : $i,X7 : $i] : ((($true = ((in @ (sK3 @ X7 @ X6 @ X5) @ X5))) & ((((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5))) = X6) & (((in @ (sK4 @ X7 @ X6 @ X5) @ X7)) = $true))) | (((in @ X6 @ (cartprod @ X5 @ X7))) != $true)) | (cartprodmempair1 != $true))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X9,sK4 @ X7 @ X6 @ X5),skolemize(X9,sK4 @ X7 @ X6 @ X5)],[f16])).
% 0.21/0.27 thf(f18,plain,(
% 0.21/0.27 (cartprodmempair1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((in @ X3 @ X0)) != $true) & ($true = ((in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0))))) & (setukpairinjR = $true)),
% 0.21/0.27 inference(rectify,[],[f14])).
% 0.21/0.27 thf(f19,plain,(
% 0.21/0.27 (cartprodmempair1 = $true) & (($true != ((in @ sK8 @ sK5))) & ($true = ((in @ (kpair @ sK6 @ sK8) @ (cartprod @ sK7 @ sK5))))) & (setukpairinjR = $true)),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8)],[f18])).
% 0.21/0.27 thf(f20,plain,(
% 0.21/0.27 (! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | (((kpair @ X0 @ X2)) != ((kpair @ X3 @ X1)))) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X1 != X2) & (((kpair @ X0 @ X2)) = ((kpair @ X3 @ X1)))))),
% 0.21/0.27 inference(nnf_transformation,[],[f12])).
% 0.21/0.27 thf(f21,plain,(
% 0.21/0.27 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | (((kpair @ X2 @ X0)) != ((kpair @ X1 @ X3)))) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 != X7) & (((kpair @ X5 @ X7)) = ((kpair @ X6 @ X4)))))),
% 0.21/0.27 inference(rectify,[],[f20])).
% 0.21/0.27 thf(f22,plain,(
% 0.21/0.27 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | (((kpair @ X2 @ X0)) != ((kpair @ X1 @ X3)))) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ((sK9 != sK12) & (((kpair @ sK11 @ sK9)) = ((kpair @ sK10 @ sK12)))))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X4,sK9),skolemize(X5,sK10),skolemize(X6,sK11),skolemize(X7,sK12)],[f21])).
% 0.21/0.27 thf(f23,plain,(
% 0.21/0.27 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((in @ (sK4 @ X7 @ X6 @ X5) @ X7)) = $true) | (((in @ X6 @ (cartprod @ X5 @ X7))) != $true) | (cartprodmempair1 != $true)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f17])).
% 0.21/0.27 thf(f24,plain,(
% 0.21/0.27 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5))) = X6) | (((in @ X6 @ (cartprod @ X5 @ X7))) != $true) | (cartprodmempair1 != $true)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f17])).
% 0.21/0.27 thf(f28,plain,(
% 0.21/0.27 (setukpairinjR = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f19])).
% 0.21/0.27 thf(f29,plain,(
% 0.21/0.27 ($true = ((in @ (kpair @ sK6 @ sK8) @ (cartprod @ sK7 @ sK5))))),
% 0.21/0.27 inference(cnf_transformation,[],[f19])).
% 0.21/0.27 thf(f30,plain,(
% 0.21/0.27 ($true != ((in @ sK8 @ sK5)))),
% 0.21/0.27 inference(cnf_transformation,[],[f19])).
% 0.21/0.27 thf(f31,plain,(
% 0.21/0.27 (cartprodmempair1 = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f19])).
% 0.21/0.27 thf(f34,plain,(
% 0.21/0.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 = X3) | (((kpair @ X2 @ X0)) != ((kpair @ X1 @ X3))) | (setukpairinjR != $true)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f22])).
% 0.21/0.27 thf(f40,plain,(
% 0.21/0.27 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != $true) | (((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5))) = X6) | (((in @ X6 @ (cartprod @ X5 @ X7))) != $true)) )),
% 0.21/0.27 inference(definition_unfolding,[],[f24,f31])).
% 0.21/0.27 thf(f41,plain,(
% 0.21/0.27 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != $true) | (((in @ X6 @ (cartprod @ X5 @ X7))) != $true) | (((in @ (sK4 @ X7 @ X6 @ X5) @ X7)) = $true)) )),
% 0.21/0.27 inference(definition_unfolding,[],[f23,f31])).
% 0.21/0.27 thf(f42,plain,(
% 0.21/0.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((kpair @ X2 @ X0)) != ((kpair @ X1 @ X3))) | ($true != $true) | (X0 = X3)) )),
% 0.21/0.27 inference(definition_unfolding,[],[f34,f28])).
% 0.21/0.27 thf(f45,plain,(
% 0.21/0.27 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((in @ X6 @ (cartprod @ X5 @ X7))) != $true) | (((in @ (sK4 @ X7 @ X6 @ X5) @ X7)) = $true)) )),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f41])).
% 0.21/0.27 thf(f46,plain,(
% 0.21/0.27 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((in @ X6 @ (cartprod @ X5 @ X7))) != $true) | (((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5))) = X6)) )),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f40])).
% 0.21/0.27 thf(f48,plain,(
% 0.21/0.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((kpair @ X2 @ X0)) != ((kpair @ X1 @ X3))) | (X0 = X3)) )),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f42])).
% 0.21/0.27 thf(f50,plain,(
% 0.21/0.27 ($true = ((in @ (sK4 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7) @ sK5))) | ($true != $true)),
% 0.21/0.27 inference(constrained_superposition,[],[f45,f29])).
% 0.21/0.27 thf(f51,plain,(
% 0.21/0.27 ($true = ((in @ (sK4 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7) @ sK5)))),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f50])).
% 0.21/0.27 thf(f54,plain,(
% 0.21/0.27 ($true != $true) | (((kpair @ sK6 @ sK8)) = ((kpair @ (sK3 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7) @ (sK4 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7))))),
% 0.21/0.27 inference(constrained_superposition,[],[f46,f29])).
% 0.21/0.27 thf(f55,plain,(
% 0.21/0.27 (((kpair @ sK6 @ sK8)) = ((kpair @ (sK3 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7) @ (sK4 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7))))),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f54])).
% 0.21/0.27 thf(f56,plain,(
% 0.21/0.27 ( ! [X0 : $i,X1 : $i] : ((((kpair @ X0 @ X1)) != ((kpair @ sK6 @ sK8))) | (((sK4 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7)) = X1)) )),
% 0.21/0.27 inference(constrained_superposition,[],[f48,f55])).
% 0.21/0.27 thf(f58,plain,(
% 0.21/0.27 (((sK4 @ sK5 @ (kpair @ sK6 @ sK8) @ sK7)) = sK8)),
% 0.21/0.27 inference(equality_resolution,[],[f56])).
% 0.21/0.27 thf(f60,plain,(
% 0.21/0.27 ($true = ((in @ sK8 @ sK5)))),
% 0.21/0.27 inference(constrained_superposition,[],[f51,f58])).
% 0.21/0.27 thf(f61,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(forward_subsumption_resolution,[],[f60,f30])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (2168688)------------------------------
% 0.21/0.27 % (2168688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2168688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2168688)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2168688)Termination reason: Refutation
% 0.21/0.27 % (2168688)Time elapsed: 0.003 s
% 0.21/0.27 % (2168688)Peak memory usage: 12 MB
% 0.21/0.27 % (2168688)Instructions burned: 7 (million)
% 0.21/0.27 % (2168683)Success in time 0.028 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------