%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM751^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:19:27 AM UTC 2026
% Result : Theorem 0.26s 0.35s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM751^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 % Computer : n008.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 12:50:54 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.35 % (3097231)Will run a generic schedule for satisfiability detection.
% 0.26/0.35 % (3097237)% WARNING: option uhcvi not known.
% 0.26/0.35 % (3097237)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2205014296:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.26/0.35 % (3097237)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.35 % (3097237)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.26/0.35 % (3097242)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3834148891:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.26/0.35 % (3097237) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3097231-3097237"...
% 0.26/0.35 % (3097237)...printing done.
% 0.26/0.35 % (3097237)Refutation found. Thanks to Tanya!
% 0.26/0.35 % SZS status Theorem for theBenchmark
% 0.26/0.35 % SZS output start Proof for theBenchmark
% 0.26/0.35 thf(type_def_5, type, frac: $tType).
% 0.26/0.35 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.35 thf(func_def_0, type, x: frac).
% 0.26/0.35 thf(func_def_1, type, y: frac).
% 0.26/0.35 thf(func_def_2, type, z: frac).
% 0.26/0.35 thf(func_def_3, type, moref: (frac > frac > $o)).
% 0.26/0.35 thf(func_def_5, type, pf: (frac > frac > frac)).
% 0.26/0.35 thf(func_def_6, type, eq: (frac > frac > $o)).
% 0.26/0.35 thf(f1,axiom,(
% 0.26/0.35 (moref @ x @ y)),
% 0.26/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m)).
% 0.26/0.35 thf(f2,axiom,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.26/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44)).
% 0.26/0.35 thf(f3,axiom,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.26/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62a)).
% 0.26/0.35 thf(f4,axiom,(
% 0.26/0.35 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 0.26/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz58)).
% 0.26/0.35 thf(f5,conjecture,(
% 0.26/0.35 (moref @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.26/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62d)).
% 0.26/0.35 thf(f6,negated_conjecture,(
% 0.26/0.35 ~(moref @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.26/0.35 inference(negated_conjecture,[status(cth)],[f5])).
% 0.26/0.35 thf(f7,plain,(
% 0.26/0.35 (moref @ x @ y)),
% 0.26/0.35 inference(rectify,[],[f1])).
% 0.26/0.35 thf(f8,plain,(
% 0.26/0.35 (((moref @ x @ y)) = $true)),
% 0.26/0.35 inference(fool_elimination,[],[f7])).
% 0.26/0.35 thf(f9,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.26/0.35 inference(rectify,[],[f2])).
% 0.26/0.35 thf(f10,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X0 @ X1)) = $true) => ((((eq @ X0 @ X2)) = $true) => ((((eq @ X1 @ X3)) = $true) => (((moref @ X2 @ X3)) = $true))))),
% 0.26/0.35 inference(fool_elimination,[],[f9])).
% 0.26/0.35 thf(f11,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.26/0.35 inference(rectify,[],[f3])).
% 0.26/0.35 thf(f12,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac] : ((((moref @ X0 @ X1)) = $true) => (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true))),
% 0.26/0.35 inference(fool_elimination,[],[f11])).
% 0.26/0.35 thf(f13,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 0.26/0.35 inference(rectify,[],[f4])).
% 0.26/0.35 thf(f14,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac] : (((eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))) = $true)),
% 0.26/0.35 inference(fool_elimination,[],[f13])).
% 0.26/0.35 thf(f15,plain,(
% 0.26/0.35 ~(moref @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.26/0.35 inference(rectify,[],[f6])).
% 0.26/0.35 thf(f16,plain,(
% 0.26/0.35 ~ (((moref @ (pf @ z @ x) @ (pf @ z @ y))) = $true)),
% 0.26/0.35 inference(fool_elimination,[],[f15])).
% 0.26/0.35 thf(f17,plain,(
% 0.26/0.35 (((moref @ (pf @ z @ x) @ (pf @ z @ y))) != $true)),
% 0.26/0.35 inference(flattening,[],[f16])).
% 0.26/0.35 thf(f18,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((((moref @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true)) | (((eq @ X0 @ X2)) != $true)) | (((moref @ X0 @ X1)) != $true))),
% 0.26/0.35 inference(ennf_transformation,[],[f10])).
% 0.26/0.35 thf(f19,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true) | (((eq @ X0 @ X2)) != $true) | (((moref @ X0 @ X1)) != $true))),
% 0.26/0.35 inference(flattening,[],[f18])).
% 0.26/0.35 thf(f20,plain,(
% 0.26/0.35 ! [X0 : frac,X1 : frac,X2 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true) | (((moref @ X0 @ X1)) != $true))),
% 0.26/0.35 inference(ennf_transformation,[],[f12])).
% 0.26/0.35 thf(f21,plain,(
% 0.26/0.35 (((moref @ x @ y)) = $true)),
% 0.26/0.35 inference(cnf_transformation,[],[f8])).
% 0.26/0.35 thf(f22,plain,(
% 0.26/0.35 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X1 @ X3)) != $true) | (((moref @ X2 @ X3)) = $true) | (((eq @ X0 @ X2)) != $true) | (((moref @ X0 @ X1)) != $true)) )),
% 0.26/0.35 inference(cnf_transformation,[],[f19])).
% 0.26/0.35 thf(f23,plain,(
% 0.26/0.35 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true)) )),
% 0.26/0.35 inference(cnf_transformation,[],[f20])).
% 0.26/0.35 thf(f24,plain,(
% 0.26/0.35 ( ! [X0 : frac,X1 : frac] : ((((eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))) = $true)) )),
% 0.26/0.35 inference(cnf_transformation,[],[f14])).
% 0.26/0.35 thf(f25,plain,(
% 0.26/0.35 (((moref @ (pf @ z @ x) @ (pf @ z @ y))) != $true)),
% 0.26/0.35 inference(cnf_transformation,[],[f17])).
% 0.26/0.35 thf(f27,definition,(
% 0.26/0.35 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.26/0.35 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.26/0.35 thf(f30,plain,(
% 0.26/0.35 ($true != $true) | (((moref @ (pf @ z @ x) @ (pf @ z @ y))) = $false)),
% 0.26/0.35 inference(constrained_superposition,[],[f25,f27])).
% 0.26/0.35 thf(f32,plain,(
% 0.26/0.35 (((moref @ (pf @ z @ x) @ (pf @ z @ y))) = $false)),
% 0.26/0.35 inference(trivial_inequality_removal,[],[f30])).
% 0.26/0.35 thf(f42,plain,(
% 0.26/0.35 ( ! [X0 : frac] : (($true != $true) | ($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.26/0.35 inference(constrained_superposition,[],[f23,f21])).
% 0.26/0.35 thf(f43,plain,(
% 0.26/0.35 ( ! [X0 : frac] : (($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.26/0.35 inference(trivial_inequality_removal,[],[f42])).
% 0.26/0.35 thf(f48,plain,(
% 0.26/0.35 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((moref @ X2 @ (pf @ X1 @ X0)))) | ($true != ((eq @ X3 @ X2))) | ($true != ((moref @ X3 @ (pf @ X0 @ X1))))) )),
% 0.26/0.35 inference(constrained_superposition,[],[f22,f24])).
% 0.26/0.35 thf(f49,plain,(
% 0.26/0.35 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((moref @ X3 @ (pf @ X0 @ X1)))) | ($true != ((eq @ X3 @ X2))) | ($true = ((moref @ X2 @ (pf @ X1 @ X0))))) )),
% 0.26/0.35 inference(trivial_inequality_removal,[],[f48])).
% 0.26/0.35 thf(f97,plain,(
% 0.26/0.35 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ($true != ((eq @ (pf @ x @ X0) @ X1))) | ($true = ((moref @ X1 @ (pf @ X0 @ y))))) )),
% 0.26/0.35 inference(constrained_superposition,[],[f49,f43])).
% 0.26/0.35 thf(f102,plain,(
% 0.26/0.35 ( ! [X0 : frac,X1 : frac] : (($true != ((eq @ (pf @ x @ X0) @ X1))) | ($true = ((moref @ X1 @ (pf @ X0 @ y))))) )),
% 0.26/0.35 inference(trivial_inequality_removal,[],[f97])).
% 0.26/0.35 thf(f105,plain,(
% 0.26/0.35 ( ! [X0 : frac] : (($true != $true) | ($true = ((moref @ (pf @ X0 @ x) @ (pf @ X0 @ y))))) )),
% 0.26/0.35 inference(constrained_superposition,[],[f102,f24])).
% 0.26/0.35 thf(f106,plain,(
% 0.26/0.35 ( ! [X0 : frac] : (($true = ((moref @ (pf @ X0 @ x) @ (pf @ X0 @ y))))) )),
% 0.26/0.35 inference(trivial_inequality_removal,[],[f105])).
% 0.26/0.35 thf(f145,plain,(
% 0.26/0.35 ($true = $false)),
% 0.26/0.35 inference(constrained_superposition,[],[f32,f106])).
% 0.26/0.35 thf(f148,plain,(
% 0.26/0.35 $false),
% 0.26/0.35 inference(trivial_inequality_removal,[],[f145])).
% 0.26/0.35 % SZS output end Proof for theBenchmark
% 0.26/0.35 % (3097237)------------------------------
% 0.26/0.35 % (3097237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.35 % (3097237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.35 % (3097237)CaDiCaL version: 2.1.3
% 0.26/0.35 % (3097237)Termination reason: Refutation
% 0.26/0.35 % (3097237)Time elapsed: 0.009 s
% 0.26/0.35 % (3097237)Peak memory usage: 12 MB
% 0.26/0.35 % (3097237)Instructions burned: 15 (million)
% 0.26/0.35 % (3097231)Success in time 0.03 s
% 0.26/0.35 % Vampire exiting
%------------------------------------------------------------------------------