%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM752^1 : 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 : 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 08:18:46 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM752^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 12:51:09 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.09/0.26 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
% 0.24/0.30 % (3097700)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (3097710)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1872376244:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.30 % (3097710) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3097700-3097710"...
% 0.24/0.30 % (3097710)...printing done.
% 0.24/0.30 % (3097710)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% 0.24/0.30 thf(type_def_5, type, frac: $tType).
% 0.24/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.30 thf(func_def_0, type, x: frac).
% 0.24/0.30 thf(func_def_1, type, y: frac).
% 0.24/0.30 thf(func_def_2, type, z: frac).
% 0.24/0.30 thf(func_def_3, type, eq: (frac > frac > $o)).
% 0.24/0.30 thf(func_def_5, type, pf: (frac > frac > frac)).
% 0.24/0.30 thf(f1,axiom,(
% 0.24/0.30 (eq @ x @ y)),
% 0.24/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e)).
% 0.24/0.30 thf(f2,axiom,(
% 0.24/0.30 ! [X0 : frac,X2 : frac,X3 : frac,X1 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.24/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56)).
% 0.24/0.30 thf(f3,axiom,(
% 0.24/0.30 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.24/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37)).
% 0.24/0.30 thf(f4,conjecture,(
% 0.24/0.30 (eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.24/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62e)).
% 0.24/0.30 thf(f5,negated_conjecture,(
% 0.24/0.30 ~(eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.24/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.24/0.30 thf(f6,plain,(
% 0.24/0.30 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.24/0.30 inference(rectify,[],[f3])).
% 0.24/0.30 thf(f7,plain,(
% 0.24/0.30 ! [X0 : frac] : (((eq @ X0 @ X0)) = $true)),
% 0.24/0.30 inference(fool_elimination,[],[f6])).
% 0.24/0.30 thf(f8,plain,(
% 0.24/0.30 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X3) => ((eq @ X1 @ X2) => (eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2))))),
% 0.24/0.30 inference(rectify,[],[f2])).
% 0.24/0.30 thf(f9,plain,(
% 0.24/0.30 ! [X0 : frac,X3 : frac,X2 : frac,X1 : frac] : (($true = ((eq @ X0 @ X3))) => (($true = ((eq @ X1 @ X2))) => ($true = ((eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2))))))),
% 0.24/0.30 inference(fool_elimination,[],[f8])).
% 0.24/0.30 thf(f10,plain,(
% 0.24/0.30 ~(eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.24/0.30 inference(rectify,[],[f5])).
% 0.24/0.30 thf(f11,plain,(
% 0.24/0.30 ~ (((eq @ (pf @ z @ x) @ (pf @ z @ y))) = $true)),
% 0.24/0.30 inference(fool_elimination,[],[f10])).
% 0.24/0.30 thf(f12,plain,(
% 0.24/0.30 (eq @ x @ y)),
% 0.24/0.30 inference(rectify,[],[f1])).
% 0.24/0.30 thf(f13,plain,(
% 0.24/0.30 (((eq @ x @ y)) = $true)),
% 0.24/0.30 inference(fool_elimination,[],[f12])).
% 0.24/0.30 thf(f14,plain,(
% 0.24/0.30 (((eq @ (pf @ z @ x) @ (pf @ z @ y))) != $true)),
% 0.24/0.30 inference(flattening,[],[f11])).
% 0.24/0.30 thf(f15,plain,(
% 0.24/0.30 ! [X0 : frac,X3 : frac,X2 : frac,X1 : frac] : ((($true = ((eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2)))) | ($true != ((eq @ X1 @ X2)))) | ($true != ((eq @ X0 @ X3))))),
% 0.24/0.30 inference(ennf_transformation,[],[f9])).
% 0.24/0.30 thf(f16,plain,(
% 0.24/0.30 ! [X3 : frac,X0 : frac,X1 : frac,X2 : frac] : (($true != ((eq @ X1 @ X2))) | ($true = ((eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2)))) | ($true != ((eq @ X0 @ X3))))),
% 0.24/0.30 inference(flattening,[],[f15])).
% 0.24/0.30 thf(f17,plain,(
% 0.24/0.30 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ X2 @ X3)) != $true) | ($true = ((eq @ (pf @ X1 @ X2) @ (pf @ X0 @ X3)))) | ($true != ((eq @ X1 @ X0))))),
% 0.24/0.30 inference(rectify,[],[f16])).
% 0.24/0.30 thf(f18,plain,(
% 0.24/0.30 (((eq @ (pf @ z @ x) @ (pf @ z @ y))) != $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f14])).
% 0.24/0.30 thf(f19,plain,(
% 0.24/0.30 ( ! [X0 : frac] : ((((eq @ X0 @ X0)) = $true)) )),
% 0.24/0.30 inference(cnf_transformation,[],[f7])).
% 0.24/0.30 thf(f20,plain,(
% 0.24/0.30 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X1 @ X0))) | ($true = ((eq @ (pf @ X1 @ X2) @ (pf @ X0 @ X3)))) | (((eq @ X2 @ X3)) != $true)) )),
% 0.24/0.30 inference(cnf_transformation,[],[f17])).
% 0.24/0.30 thf(f21,plain,(
% 0.24/0.30 (((eq @ x @ y)) = $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f13])).
% 0.24/0.30 thf(f23,definition,(
% 0.24/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.24/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.24/0.30 thf(f26,plain,(
% 0.24/0.30 (((eq @ (pf @ z @ x) @ (pf @ z @ y))) = $false) | ($true != $true)),
% 0.24/0.30 inference(constrained_superposition,[],[f18,f23])).
% 0.24/0.30 thf(f32,plain,(
% 0.24/0.30 (((eq @ (pf @ z @ x) @ (pf @ z @ y))) = $false)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f26])).
% 0.24/0.30 thf(f37,plain,(
% 0.24/0.30 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = ((eq @ (pf @ X0 @ X1) @ (pf @ X0 @ X2)))) | ($true != ((eq @ X1 @ X2))) | ($true != $true)) )),
% 0.24/0.30 inference(constrained_superposition,[],[f20,f19])).
% 0.24/0.30 thf(f40,plain,(
% 0.24/0.30 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X1 @ X2))) | ($true = ((eq @ (pf @ X0 @ X1) @ (pf @ X0 @ X2))))) )),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f37])).
% 0.24/0.30 thf(f46,plain,(
% 0.24/0.30 ( ! [X0 : frac] : (($true != $true) | (((eq @ (pf @ X0 @ x) @ (pf @ X0 @ y))) = $true)) )),
% 0.24/0.30 inference(constrained_superposition,[],[f40,f21])).
% 0.24/0.30 thf(f48,plain,(
% 0.24/0.30 ( ! [X0 : frac] : ((((eq @ (pf @ X0 @ x) @ (pf @ X0 @ y))) = $true)) )),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f46])).
% 0.24/0.30 thf(f50,plain,(
% 0.24/0.30 ($true = $false)),
% 0.24/0.30 inference(backward_demodulation,[],[f32,f48])).
% 0.24/0.30 thf(f51,plain,(
% 0.24/0.30 $false),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f50])).
% 0.24/0.30 % SZS output end Proof for theBenchmark
% 0.24/0.30 % (3097710)------------------------------
% 0.24/0.30 % (3097710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (3097710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (3097710)CaDiCaL version: 2.1.3
% 0.24/0.30 % (3097710)Termination reason: Refutation
% 0.24/0.30 % (3097710)Time elapsed: 0.003 s
% 0.24/0.30 % (3097710)Peak memory usage: 12 MB
% 0.24/0.30 % (3097710)Instructions burned: 4 (million)
% 0.24/0.30 % (3097700)Success in time 0.027 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------