%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU659^2 : 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 : n004.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 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU659^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:03:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.29 % (1336746)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (1336755)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=103043925:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (1336755) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1336746-1336755"...
% 0.23/0.29 % (1336755)...printing done.
% 0.23/0.29 % (1336755)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.29 thf(func_def_1, type, kpair: ($i > $i > $i)).
% 0.23/0.29 thf(func_def_2, type, cartprod: ($i > $i > $i)).
% 0.23/0.29 thf(func_def_3, type, cartprodmempair1: $o).
% 0.23/0.29 thf(func_def_5, type, setukpairinjL: $o).
% 0.23/0.29 thf(func_def_15, type, sK7: ($i > $i > $i > $i)).
% 0.23/0.29 thf(func_def_16, type, sK8: ($i > $i > $i > $i)).
% 0.23/0.29 thf(f1,axiom,(
% 0.23/0.29 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((in @ X4 @ X1) & (X2 = ((kpair @ X3 @ X4)))))) = cartprodmempair1)),
% 0.23/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.23/0.29 thf(f2,axiom,(
% 0.23/0.29 (! [X3 : $i,X2 : $i,X0 : $i,X1 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X0 = X2)) = setukpairinjL)),
% 0.23/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL)).
% 0.23/0.29 thf(f3,conjecture,(
% 0.23/0.29 cartprodmempair1 => (setukpairinjL => ! [X0 : $i,X3 : $i,X1 : $i,X2 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X2 @ X0)))),
% 0.23/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL)).
% 0.23/0.29 thf(f4,negated_conjecture,(
% 0.23/0.29 ~(cartprodmempair1 => (setukpairinjL => ! [X0 : $i,X3 : $i,X1 : $i,X2 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X2 @ X0))))),
% 0.23/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.23/0.29 thf(f5,plain,(
% 0.23/0.29 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X2 @ X3)) = ((kpair @ X1 @ X0))) => (X1 = X2)) = setukpairinjL)),
% 0.23/0.29 inference(rectify,[],[f2])).
% 0.23/0.29 thf(f6,plain,(
% 0.23/0.29 ! [X3 : $i,X2 : $i,X0 : $i,X1 : $i] : ((((kpair @ X2 @ X3)) = ((kpair @ X1 @ X0))) => (X1 = X2)) <=> (setukpairinjL = $true)),
% 0.23/0.29 inference(fool_elimination,[],[f5])).
% 0.23/0.29 thf(f7,plain,(
% 0.23/0.29 ~(cartprodmempair1 => (setukpairinjL => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((in @ (kpair @ X3 @ X1) @ (cartprod @ X0 @ X2)) => (in @ X3 @ X0))))),
% 0.23/0.29 inference(rectify,[],[f4])).
% 0.23/0.29 thf(f8,plain,(
% 0.23/0.29 ~((cartprodmempair1 = $true) => ((setukpairinjL = $true) => ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (kpair @ X3 @ X1) @ (cartprod @ X0 @ X2))) = $true) => (((in @ X3 @ X0)) = $true))))),
% 0.23/0.29 inference(fool_elimination,[],[f7])).
% 0.23/0.29 thf(f9,plain,(
% 0.23/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X0 @ X2)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((in @ X4 @ X2) & (((kpair @ X3 @ X4)) = X1)))) = cartprodmempair1)),
% 0.23/0.29 inference(rectify,[],[f1])).
% 0.23/0.29 thf(f10,plain,(
% 0.23/0.29 (cartprodmempair1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) = $true) => ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((kpair @ X3 @ X4)) = X1))))),
% 0.23/0.29 inference(fool_elimination,[],[f9])).
% 0.23/0.29 thf(f11,plain,(
% 0.23/0.29 (? [X2 : $i,X0 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X0)) != $true) & (((in @ (kpair @ X3 @ X1) @ (cartprod @ X0 @ X2))) = $true)) & (setukpairinjL = $true)) & (cartprodmempair1 = $true)),
% 0.23/0.29 inference(ennf_transformation,[],[f8])).
% 0.23/0.29 thf(f12,plain,(
% 0.23/0.29 ? [X2 : $i,X0 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X0)) != $true) & (((in @ (kpair @ X3 @ X1) @ (cartprod @ X0 @ X2))) = $true)) & (setukpairinjL = $true) & (cartprodmempair1 = $true)),
% 0.23/0.29 inference(flattening,[],[f11])).
% 0.23/0.29 thf(f13,plain,(
% 0.23/0.29 (setukpairinjL = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i,X3 : $i] : ((X1 = X2) | (((kpair @ X2 @ X3)) != ((kpair @ X1 @ X0))))),
% 0.23/0.29 inference(ennf_transformation,[],[f6])).
% 0.23/0.29 thf(f14,plain,(
% 0.23/0.29 (cartprodmempair1 = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((kpair @ X3 @ X4)) = X1))) | (((in @ X1 @ (cartprod @ X0 @ X2))) != $true))),
% 0.23/0.29 inference(ennf_transformation,[],[f10])).
% 0.23/0.29 thf(f15,plain,(
% 0.23/0.29 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ (kpair @ X2 @ X3) @ (cartprod @ X1 @ X0))) = $true)) & (setukpairinjL = $true) & (cartprodmempair1 = $true)),
% 0.23/0.29 inference(rectify,[],[f12])).
% 0.23/0.29 thf(f16,plain,(
% 0.23/0.29 ((((in @ sK2 @ sK1)) != $true) & (((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK1 @ sK0))) = $true)) & (setukpairinjL = $true) & (cartprodmempair1 = $true)),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15])).
% 0.23/0.29 thf(f17,plain,(
% 0.23/0.29 ((cartprodmempair1 = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | ! [X4 : $i] : ((((in @ X4 @ X2)) != $true) | (((kpair @ X3 @ X4)) != X1))) & (((in @ X1 @ (cartprod @ X0 @ X2))) = $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((kpair @ X3 @ X4)) = X1))) | (((in @ X1 @ (cartprod @ X0 @ X2))) != $true)) | (cartprodmempair1 != $true))),
% 0.23/0.29 inference(nnf_transformation,[],[f14])).
% 0.23/0.29 thf(f18,plain,(
% 0.23/0.29 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | ! [X4 : $i] : ((((in @ X4 @ X2)) != $true) | (((kpair @ X3 @ X4)) != X0))) & (((in @ X0 @ (cartprod @ X1 @ X2))) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : ((((in @ X8 @ X6)) = $true) & ? [X9 : $i] : ((((in @ X9 @ X7)) = $true) & (((kpair @ X8 @ X9)) = X5))) | (((in @ X5 @ (cartprod @ X6 @ X7))) != $true)) | (cartprodmempair1 != $true))),
% 0.23/0.29 inference(rectify,[],[f17])).
% 0.23/0.29 thf(f19,plain,(
% 0.23/0.29 ((cartprodmempair1 = $true) | (! [X3 : $i] : ((((in @ X3 @ sK5)) != $true) | ! [X4 : $i] : ((((in @ X4 @ sK6)) != $true) | (((kpair @ X3 @ X4)) != sK4))) & (((in @ sK4 @ (cartprod @ sK5 @ sK6))) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (((((in @ (sK7 @ X7 @ X6 @ X5) @ X6)) = $true) & ((((in @ (sK8 @ X7 @ X6 @ X5) @ X7)) = $true) & (((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5))) = X5))) | (((in @ X5 @ (cartprod @ X6 @ X7))) != $true)) | (cartprodmempair1 != $true))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,vAPP,vAPP]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X9,sK8 @ X7 @ X6 @ X5),skolemize(X9,sK8 @ X7 @ X6 @ X5)],[f18])).
% 0.23/0.29 thf(f20,plain,(
% 0.23/0.29 ((setukpairinjL = $true) | ? [X2 : $i,X0 : $i,X1 : $i,X3 : $i] : ((X1 != X2) & (((kpair @ X2 @ X3)) = ((kpair @ X1 @ X0))))) & (! [X2 : $i,X0 : $i,X1 : $i,X3 : $i] : ((X1 = X2) | (((kpair @ X2 @ X3)) != ((kpair @ X1 @ X0)))) | (setukpairinjL != $true))),
% 0.23/0.29 inference(nnf_transformation,[],[f13])).
% 0.23/0.29 thf(f21,plain,(
% 0.23/0.29 ((setukpairinjL = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X2) & (((kpair @ X0 @ X3)) = ((kpair @ X2 @ X1))))) & (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 = X6) | (((kpair @ X4 @ X7)) != ((kpair @ X6 @ X5)))) | (setukpairinjL != $true))),
% 0.23/0.29 inference(rectify,[],[f20])).
% 0.23/0.29 thf(f22,plain,(
% 0.23/0.29 ((setukpairinjL = $true) | ((sK11 != sK9) & (((kpair @ sK9 @ sK12)) = ((kpair @ sK11 @ sK10))))) & (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 = X6) | (((kpair @ X4 @ X7)) != ((kpair @ X6 @ X5)))) | (setukpairinjL != $true))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f21])).
% 0.23/0.29 thf(f23,plain,(
% 0.23/0.29 (cartprodmempair1 = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f16])).
% 0.23/0.29 thf(f24,plain,(
% 0.23/0.29 (setukpairinjL = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f16])).
% 0.23/0.29 thf(f25,plain,(
% 0.23/0.29 (((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK1 @ sK0))) = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f16])).
% 0.23/0.29 thf(f26,plain,(
% 0.23/0.29 (((in @ sK2 @ sK1)) != $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f16])).
% 0.23/0.29 thf(f27,plain,(
% 0.23/0.29 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5))) = X5) | (cartprodmempair1 != $true) | (((in @ X5 @ (cartprod @ X6 @ X7))) != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f29,plain,(
% 0.23/0.29 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((in @ (sK7 @ X7 @ X6 @ X5) @ X6)) = $true) | (cartprodmempair1 != $true) | (((in @ X5 @ (cartprod @ X6 @ X7))) != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f32,plain,(
% 0.23/0.29 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((setukpairinjL != $true) | (((kpair @ X4 @ X7)) != ((kpair @ X6 @ X5))) | (X4 = X6)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f22])).
% 0.23/0.29 thf(f38,plain,(
% 0.23/0.29 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((kpair @ X4 @ X7)) != ((kpair @ X6 @ X5))) | (X4 = X6)) )),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f32,f24])).
% 0.23/0.29 thf(f41,plain,(
% 0.23/0.29 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((in @ (sK7 @ X7 @ X6 @ X5) @ X6)) = $true) | (((in @ X5 @ (cartprod @ X6 @ X7))) != $true)) )),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f29,f23])).
% 0.23/0.29 thf(f42,plain,(
% 0.23/0.29 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5))) = X5) | (((in @ X5 @ (cartprod @ X6 @ X7))) != $true)) )),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f27,f23])).
% 0.23/0.29 thf(f43,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X0 @ (cartprod @ X4 @ X3))) != $true) | (((kpair @ X1 @ X2)) != X0) | (((sK7 @ X3 @ X4 @ X0)) = X1)) )),
% 0.23/0.30 inference(superposition,[],[f38,f42])).
% 0.23/0.30 thf(f45,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((sK7 @ sK0 @ sK1 @ (kpair @ sK2 @ sK3))) = X0) | (((kpair @ X0 @ X1)) != ((kpair @ sK2 @ sK3)))) )),
% 0.23/0.30 inference(superposition,[],[f43,f25])).
% 0.23/0.30 thf(f50,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : ((((kpair @ X0 @ X1)) != ((kpair @ sK2 @ sK3))) | (((sK7 @ sK0 @ sK1 @ (kpair @ sK2 @ sK3))) = X0)) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f45])).
% 0.23/0.30 thf(f52,plain,(
% 0.23/0.30 (((sK7 @ sK0 @ sK1 @ (kpair @ sK2 @ sK3))) = sK2)),
% 0.23/0.30 inference(equality_resolution,[],[f50])).
% 0.23/0.30 thf(f54,plain,(
% 0.23/0.30 (((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK1 @ sK0))) != $true) | (((in @ sK2 @ sK1)) = $true)),
% 0.23/0.30 inference(superposition,[],[f41,f52])).
% 0.23/0.30 thf(f55,plain,(
% 0.23/0.30 (((in @ sK2 @ sK1)) = $true)),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f54,f25])).
% 0.23/0.30 thf(f57,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f55,f26])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (1336755)------------------------------
% 0.23/0.30 % (1336755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1336755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1336755)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1336755)Termination reason: Refutation
% 0.23/0.30 % (1336755)Time elapsed: 0.003 s
% 0.23/0.30 % (1336755)Peak memory usage: 12 MB
% 0.23/0.30 % (1336755)Instructions burned: 7 (million)
% 0.23/0.30 % (1336746)Success in time 0.038 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------