%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM738^1 : 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 : n005.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 08:18:42 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM738^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:46:32 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.27 % (1618167)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1618177)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2170658854:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (1618177) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1618167-1618177"...
% 0.20/0.27 % (1618177)...printing done.
% 0.20/0.27 % (1618177)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, frac: $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_0, type, x: frac).
% 0.20/0.27 thf(func_def_1, type, y: frac).
% 0.20/0.27 thf(func_def_2, type, z: frac).
% 0.20/0.27 thf(func_def_3, type, u: frac).
% 0.20/0.27 thf(func_def_4, type, lessf: (frac > frac > $o)).
% 0.20/0.27 thf(func_def_6, type, eq: (frac > frac > $o)).
% 0.20/0.27 thf(func_def_7, type, moref: (frac > frac > $o)).
% 0.20/0.27 thf(f1,axiom,(
% 0.20/0.27 (lessf @ x @ y)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l)).
% 0.20/0.27 thf(f2,axiom,(
% 0.20/0.27 (eq @ x @ z)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e)).
% 0.20/0.27 thf(f3,axiom,(
% 0.20/0.27 (eq @ y @ u)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f)).
% 0.20/0.27 thf(f4,axiom,(
% 0.20/0.27 ! [X1 : frac,X0 : frac] : ((moref @ X0 @ X1) => (lessf @ X1 @ X0))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz42)).
% 0.20/0.27 thf(f5,axiom,(
% 0.20/0.27 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44)).
% 0.20/0.27 thf(f6,axiom,(
% 0.20/0.27 ! [X1 : frac,X0 : frac] : ((lessf @ X0 @ X1) => (moref @ X1 @ X0))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz43)).
% 0.20/0.27 thf(f7,conjecture,(
% 0.20/0.27 (lessf @ z @ u)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz45)).
% 0.20/0.27 thf(f8,negated_conjecture,(
% 0.20/0.27 ~(lessf @ z @ u)),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac] : ((lessf @ X1 @ X0) => (moref @ X0 @ X1))),
% 0.20/0.27 inference(rectify,[],[f6])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac] : ((((lessf @ X1 @ X0)) = $true) => (((moref @ X0 @ X1)) = $true))),
% 0.20/0.27 inference(fool_elimination,[],[f9])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X2 @ X3) => ((eq @ X2 @ X0) => ((eq @ X3 @ X1) => (moref @ X0 @ X1))))),
% 0.20/0.27 inference(rectify,[],[f5])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 ! [X1 : frac,X3 : frac,X2 : frac,X0 : frac] : ((((moref @ X2 @ X3)) = $true) => (($true = ((eq @ X2 @ X0))) => (($true = ((eq @ X3 @ X1))) => (((moref @ X0 @ X1)) = $true))))),
% 0.20/0.27 inference(fool_elimination,[],[f11])).
% 0.20/0.27 thf(f13,plain,(
% 0.20/0.27 (lessf @ x @ y)),
% 0.20/0.27 inference(rectify,[],[f1])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 (((lessf @ x @ y)) = $true)),
% 0.20/0.27 inference(fool_elimination,[],[f13])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 (eq @ y @ u)),
% 0.20/0.27 inference(rectify,[],[f3])).
% 0.20/0.27 thf(f16,plain,(
% 0.20/0.27 (((eq @ y @ u)) = $true)),
% 0.20/0.27 inference(fool_elimination,[],[f15])).
% 0.20/0.27 thf(f17,plain,(
% 0.20/0.27 (eq @ x @ z)),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 (((eq @ x @ z)) = $true)),
% 0.20/0.27 inference(fool_elimination,[],[f17])).
% 0.20/0.27 thf(f19,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac] : ((moref @ X1 @ X0) => (lessf @ X0 @ X1))),
% 0.20/0.27 inference(rectify,[],[f4])).
% 0.20/0.27 thf(f20,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac] : ((((moref @ X1 @ X0)) = $true) => (((lessf @ X0 @ X1)) = $true))),
% 0.20/0.27 inference(fool_elimination,[],[f19])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ~(lessf @ z @ u)),
% 0.20/0.27 inference(rectify,[],[f8])).
% 0.20/0.27 thf(f22,plain,(
% 0.20/0.27 ~ (((lessf @ z @ u)) = $true)),
% 0.20/0.27 inference(fool_elimination,[],[f21])).
% 0.20/0.27 thf(f23,plain,(
% 0.20/0.27 (((lessf @ z @ u)) != $true)),
% 0.20/0.27 inference(flattening,[],[f22])).
% 0.20/0.27 thf(f24,plain,(
% 0.20/0.27 ! [X1 : frac,X3 : frac,X2 : frac,X0 : frac] : ((((((moref @ X0 @ X1)) = $true) | ($true != ((eq @ X3 @ X1)))) | ($true != ((eq @ X2 @ X0)))) | (((moref @ X2 @ X3)) != $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f12])).
% 0.20/0.27 thf(f25,plain,(
% 0.20/0.27 ! [X0 : frac,X3 : frac,X1 : frac,X2 : frac] : (($true != ((eq @ X3 @ X1))) | (((moref @ X2 @ X3)) != $true) | ($true != ((eq @ X2 @ X0))) | (((moref @ X0 @ X1)) = $true))),
% 0.20/0.27 inference(flattening,[],[f24])).
% 0.20/0.27 thf(f26,plain,(
% 0.20/0.27 ! [X1 : frac,X0 : frac] : ((((moref @ X1 @ X0)) != $true) | (((lessf @ X0 @ X1)) = $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f20])).
% 0.20/0.27 thf(f27,plain,(
% 0.20/0.27 ! [X1 : frac,X0 : frac] : ((((moref @ X0 @ X1)) = $true) | (((lessf @ X1 @ X0)) != $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f10])).
% 0.20/0.27 thf(f28,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((lessf @ X1 @ X0)) = $true))),
% 0.20/0.27 inference(rectify,[],[f26])).
% 0.20/0.27 thf(f29,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac] : ((((moref @ X1 @ X0)) = $true) | (((lessf @ X0 @ X1)) != $true))),
% 0.20/0.27 inference(rectify,[],[f27])).
% 0.20/0.27 thf(f30,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != ((eq @ X1 @ X2))) | ($true != ((moref @ X3 @ X1))) | ($true != ((eq @ X3 @ X0))) | (((moref @ X0 @ X2)) = $true))),
% 0.20/0.27 inference(rectify,[],[f25])).
% 0.20/0.27 thf(f31,plain,(
% 0.20/0.27 (((lessf @ z @ u)) != $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f23])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 ( ! [X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((lessf @ X1 @ X0)) = $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f28])).
% 0.20/0.27 thf(f33,plain,(
% 0.20/0.27 ( ! [X0 : frac,X1 : frac] : ((((lessf @ X0 @ X1)) != $true) | (((moref @ X1 @ X0)) = $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f29])).
% 0.20/0.27 thf(f34,plain,(
% 0.20/0.27 (((eq @ x @ z)) = $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f18])).
% 0.20/0.27 thf(f35,plain,(
% 0.20/0.27 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((moref @ X3 @ X1))) | ($true != ((eq @ X3 @ X0))) | ($true != ((eq @ X1 @ X2))) | (((moref @ X0 @ X2)) = $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f30])).
% 0.20/0.27 thf(f36,plain,(
% 0.20/0.27 (((eq @ y @ u)) = $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f16])).
% 0.20/0.27 thf(f37,plain,(
% 0.20/0.27 (((lessf @ x @ y)) = $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f14])).
% 0.20/0.27 thf(f39,definition,(
% 0.20/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.27 thf(f42,plain,(
% 0.20/0.27 ($true != $true) | (((lessf @ z @ u)) = $false)),
% 0.20/0.27 inference(constrained_superposition,[],[f31,f39])).
% 0.20/0.27 thf(f44,plain,(
% 0.20/0.27 (((lessf @ z @ u)) = $false)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f42])).
% 0.20/0.27 thf(f54,plain,(
% 0.20/0.27 ($true = ((moref @ y @ x))) | ($true != $true)),
% 0.20/0.27 inference(constrained_superposition,[],[f33,f37])).
% 0.20/0.27 thf(f57,plain,(
% 0.20/0.27 ($true = ((moref @ y @ x)))),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f54])).
% 0.20/0.27 thf(f61,plain,(
% 0.20/0.27 ( ! [X0 : frac,X1 : frac] : (($true != ((eq @ y @ X0))) | (((eq @ x @ X1)) != $true) | (((moref @ X0 @ X1)) = $true) | ($true != $true)) )),
% 0.20/0.27 inference(constrained_superposition,[],[f35,f57])).
% 0.20/0.27 thf(f64,plain,(
% 0.20/0.27 ( ! [X0 : frac,X1 : frac] : (($true != ((eq @ y @ X0))) | (((eq @ x @ X1)) != $true) | (((moref @ X0 @ X1)) = $true)) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.27 thf(f65,plain,(
% 0.20/0.27 ( ! [X0 : frac] : (($true != $true) | ($true != ((eq @ x @ X0))) | ($true = ((moref @ u @ X0)))) )),
% 0.20/0.27 inference(constrained_superposition,[],[f64,f36])).
% 0.20/0.27 thf(f68,plain,(
% 0.20/0.27 ( ! [X0 : frac] : (($true != ((eq @ x @ X0))) | ($true = ((moref @ u @ X0)))) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f65])).
% 0.20/0.27 thf(f69,plain,(
% 0.20/0.27 ($true = ((moref @ u @ z))) | ($true != $true)),
% 0.20/0.27 inference(constrained_superposition,[],[f68,f34])).
% 0.20/0.27 thf(f71,plain,(
% 0.20/0.27 ($true = ((moref @ u @ z)))),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f69])).
% 0.20/0.27 thf(f74,plain,(
% 0.20/0.27 (((lessf @ z @ u)) = $true) | ($true != $true)),
% 0.20/0.27 inference(constrained_superposition,[],[f32,f71])).
% 0.20/0.27 thf(f75,plain,(
% 0.20/0.27 (((lessf @ z @ u)) = $true)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f74])).
% 0.20/0.27 thf(f77,plain,(
% 0.20/0.27 ($true = $false)),
% 0.20/0.27 inference(forward_demodulation,[],[f75,f44])).
% 0.20/0.27 thf(f78,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f77])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (1618177)------------------------------
% 0.20/0.27 % (1618177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1618177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1618177)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1618177)Termination reason: Refutation
% 0.20/0.27 % (1618177)Time elapsed: 0.002 s
% 0.20/0.27 % (1618177)Peak memory usage: 12 MB
% 0.20/0.27 % (1618177)Instructions burned: 5 (million)
% 0.20/0.27 % (1618167)Success in time 0.03 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------