%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU658^2 : 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 : 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 08:30:34 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU658^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:04:19 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.28 % (1106091)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1106096)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2046192406:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (1106096) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1106091-1106096"...
% 0.22/0.28 % (1106096)...printing done.
% 0.22/0.28 % (1106096)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.28 thf(func_def_1, type, kpair: ($i > $i > $i)).
% 0.22/0.28 thf(func_def_2, type, cartprod: ($i > $i > $i)).
% 0.22/0.28 thf(func_def_3, type, cartprodmempair1: $o).
% 0.22/0.28 thf(func_def_5, type, ksnd: ($i > $i)).
% 0.22/0.28 thf(func_def_6, type, ksndpairEq: $o).
% 0.22/0.28 thf(func_def_12, type, sK3: ($i > $i > $i > $i)).
% 0.22/0.28 thf(func_def_13, type, sK4: ($i > $i > $i > $i)).
% 0.22/0.28 thf(func_def_19, type, vNOT: ($o > $o)).
% 0.22/0.28 thf(f1,axiom,(
% 0.22/0.28 (cartprodmempair1 = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : (? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)) & (in @ X3 @ X0))))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.22/0.28 thf(f2,axiom,(
% 0.22/0.28 (! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1) = ksndpairEq)),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq)).
% 0.22/0.28 thf(f3,conjecture,(
% 0.22/0.28 cartprodmempair1 => (ksndpairEq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (ksnd @ X2) @ X1)))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin)).
% 0.22/0.28 thf(f4,negated_conjecture,(
% 0.22/0.28 ~(cartprodmempair1 => (ksndpairEq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (ksnd @ X2) @ X1))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 (cartprodmempair1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X2 @ X1)) => ? [X3 : $i] : (? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & (in @ X4 @ X1)) & (in @ X3 @ X2))))),
% 0.22/0.28 inference(rectify,[],[f1])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 (cartprodmempair1 = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (cartprod @ X2 @ X1)))) => ? [X3 : $i] : (($true = ((in @ X3 @ X2))) & ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & (((kpair @ X3 @ X4)) = X0))))),
% 0.22/0.28 inference(fool_elimination,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ~(cartprodmempair1 => (ksndpairEq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (ksnd @ X2) @ X1))))),
% 0.22/0.28 inference(rectify,[],[f4])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ~((cartprodmempair1 = $true) => ((ksndpairEq = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X2 @ (cartprod @ X0 @ X1))) = $true) => (((in @ (ksnd @ X2) @ X1)) = $true))))),
% 0.22/0.28 inference(fool_elimination,[],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1) <=> (ksndpairEq = $true)),
% 0.22/0.28 inference(fool_elimination,[],[f2])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 (? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (cartprod @ X0 @ X1))) = $true) & (((in @ (ksnd @ X2) @ X1)) != $true)) & (ksndpairEq = $true)) & (cartprodmempair1 = $true)),
% 0.22/0.28 inference(ennf_transformation,[],[f8])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 (ksndpairEq = $true) & (cartprodmempair1 = $true) & ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (cartprod @ X0 @ X1))) = $true) & (((in @ (ksnd @ X2) @ X1)) != $true))),
% 0.22/0.28 inference(flattening,[],[f10])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ! [X0 : $i,X2 : $i,X1 : $i] : (? [X3 : $i] : (($true = ((in @ X3 @ X2))) & ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & (((kpair @ X3 @ X4)) = X0))) | ($true != ((in @ X0 @ (cartprod @ X2 @ X1))))) <=> (cartprodmempair1 = $true)),
% 0.22/0.28 inference(ennf_transformation,[],[f6])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 (ksndpairEq = $true) & (cartprodmempair1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (cartprod @ X1 @ X2)))) & (((in @ (ksnd @ X0) @ X2)) != $true))),
% 0.22/0.28 inference(rectify,[],[f11])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 (ksndpairEq = $true) & (cartprodmempair1 = $true) & (($true = ((in @ sK0 @ (cartprod @ sK1 @ sK2)))) & ($true != ((in @ (ksnd @ sK0) @ sK2))))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 (! [X0 : $i,X2 : $i,X1 : $i] : (? [X3 : $i] : (($true = ((in @ X3 @ X2))) & ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & (((kpair @ X3 @ X4)) = X0))) | ($true != ((in @ X0 @ (cartprod @ X2 @ X1))))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $i] : (($true != ((in @ X3 @ X2))) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | (((kpair @ X3 @ X4)) != X0))) & ($true = ((in @ X0 @ (cartprod @ X2 @ X1))))))),
% 0.22/0.28 inference(nnf_transformation,[],[f12])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = ((in @ X3 @ X1))) & ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((kpair @ X3 @ X4)) = X0))) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2))))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : (($true != ((in @ X8 @ X6))) | ! [X9 : $i] : (($true != ((in @ X9 @ X7))) | (((kpair @ X8 @ X9)) != X5))) & ($true = ((in @ X5 @ (cartprod @ X6 @ X7))))))),
% 0.22/0.28 inference(rectify,[],[f15])).
% 0.22/0.28 thf(f17,plain,(
% 0.22/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((($true = ((in @ (sK3 @ X2 @ X1 @ X0) @ X1))) & (($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X2))) & (((kpair @ (sK3 @ X2 @ X1 @ X0) @ (sK4 @ X2 @ X1 @ X0))) = X0))) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2))))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | (! [X8 : $i] : (($true != ((in @ X8 @ sK6))) | ! [X9 : $i] : (($true != ((in @ X9 @ sK7))) | (sK5 != ((kpair @ X8 @ X9))))) & ($true = ((in @ sK5 @ (cartprod @ sK6 @ sK7))))))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK5,sK6,sK7]),skolemize(X4,sK4 @ X2 @ X1 @ X0),skolemize(X4,sK4 @ X2 @ X1 @ X0),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f16])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 (! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1))) != X1))),
% 0.22/0.28 inference(nnf_transformation,[],[f9])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 (! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X2 : $i,X3 : $i] : (((ksnd @ (kpair @ X2 @ X3))) != X3))),
% 0.22/0.28 inference(rectify,[],[f18])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 (! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | (sK9 != ((ksnd @ (kpair @ sK8 @ sK9)))))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,sK8),skolemize(X3,sK9)],[f19])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ($true != ((in @ (ksnd @ sK0) @ sK2)))),
% 0.22/0.28 inference(cnf_transformation,[],[f14])).
% 0.22/0.28 thf(f22,plain,(
% 0.22/0.28 ($true = ((in @ sK0 @ (cartprod @ sK1 @ sK2))))),
% 0.22/0.28 inference(cnf_transformation,[],[f14])).
% 0.22/0.28 thf(f23,plain,(
% 0.22/0.28 (cartprodmempair1 = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f14])).
% 0.22/0.28 thf(f24,plain,(
% 0.22/0.28 (ksndpairEq = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f14])).
% 0.22/0.28 thf(f27,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((kpair @ (sK3 @ X2 @ X1 @ X0) @ (sK4 @ X2 @ X1 @ X0))) = X0) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2)))) | (cartprodmempair1 != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f17])).
% 0.22/0.28 thf(f28,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X2))) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2)))) | (cartprodmempair1 != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f17])).
% 0.22/0.28 thf(f31,plain,(
% 0.22/0.28 ( ! [X0 : $i,X1 : $i] : ((((ksnd @ (kpair @ X0 @ X1))) = X1) | (ksndpairEq != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f20])).
% 0.22/0.28 thf(f35,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X2))) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2)))) | ($true != $true)) )),
% 0.22/0.28 inference(definition_unfolding,[],[f28,f23])).
% 0.22/0.28 thf(f36,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((kpair @ (sK3 @ X2 @ X1 @ X0) @ (sK4 @ X2 @ X1 @ X0))) = X0) | ($true != $true) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2))))) )),
% 0.22/0.28 inference(definition_unfolding,[],[f27,f23])).
% 0.22/0.28 thf(f39,plain,(
% 0.22/0.28 ( ! [X0 : $i,X1 : $i] : ((((ksnd @ (kpair @ X0 @ X1))) = X1) | ($true != $true)) )),
% 0.22/0.28 inference(definition_unfolding,[],[f31,f24])).
% 0.22/0.28 thf(f42,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (cartprod @ X1 @ X2)))) | (((kpair @ (sK3 @ X2 @ X1 @ X0) @ (sK4 @ X2 @ X1 @ X0))) = X0)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f36])).
% 0.22/0.28 thf(f43,plain,(
% 0.22/0.28 ( ! [X0 : $i,X1 : $i] : ((((ksnd @ (kpair @ X0 @ X1))) = X1)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f39])).
% 0.22/0.28 thf(f44,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (cartprod @ X1 @ X2)))) | ($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X2)))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f35])).
% 0.22/0.28 thf(f47,plain,(
% 0.22/0.28 ($true != $true) | ($true = ((in @ (sK4 @ sK2 @ sK1 @ sK0) @ sK2)))),
% 0.22/0.28 inference(constrained_superposition,[],[f44,f22])).
% 0.22/0.28 thf(f48,plain,(
% 0.22/0.28 ($true = ((in @ (sK4 @ sK2 @ sK1 @ sK0) @ sK2)))),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f47])).
% 0.22/0.28 thf(f49,plain,(
% 0.22/0.28 ($true != $true) | (((kpair @ (sK3 @ sK2 @ sK1 @ sK0) @ (sK4 @ sK2 @ sK1 @ sK0))) = sK0)),
% 0.22/0.28 inference(constrained_superposition,[],[f42,f22])).
% 0.22/0.28 thf(f50,plain,(
% 0.22/0.28 (((kpair @ (sK3 @ sK2 @ sK1 @ sK0) @ (sK4 @ sK2 @ sK1 @ sK0))) = sK0)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f49])).
% 0.22/0.28 thf(f51,plain,(
% 0.22/0.28 (((ksnd @ sK0)) = ((sK4 @ sK2 @ sK1 @ sK0)))),
% 0.22/0.28 inference(constrained_superposition,[],[f43,f50])).
% 0.22/0.28 thf(f53,plain,(
% 0.22/0.28 ($true = ((in @ (ksnd @ sK0) @ sK2)))),
% 0.22/0.28 inference(constrained_superposition,[],[f48,f51])).
% 0.22/0.28 thf(f54,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f53,f21])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (1106096)------------------------------
% 0.22/0.28 % (1106096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1106096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1106096)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1106096)Termination reason: Refutation
% 0.22/0.28 % (1106096)Time elapsed: 0.002 s
% 0.22/0.28 % (1106096)Peak memory usage: 12 MB
% 0.22/0.28 % (1106096)Instructions burned: 6 (million)
% 0.22/0.28 % (1106091)Success in time 0.029 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------