%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM743^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:19:26 AM UTC 2026
% Result : Theorem 0.18s 0.32s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM743^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 % Computer : n015.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Tue Sep 29 12:52:17 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.29 Running first-order model finding
% 0.18/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.32 % (3472061)Will run a generic schedule for satisfiability detection.
% 0.18/0.32 % (3472069)dis+10_1_sil=32000:sp=arity:random_seed=3464052401:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.32 % (3472069) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3472061-3472069"...
% 0.18/0.32 % (3472067)% WARNING: option uhcvi not known.
% 0.18/0.32 % (3472069)...printing done.
% 0.18/0.32 % (3472069)Refutation found. Thanks to Tanya!
% 0.18/0.32 % SZS status Theorem for theBenchmark
% 0.18/0.32 % SZS output start Proof for theBenchmark
% 0.18/0.32 thf(type_def_5, type, frac: $tType).
% 0.18/0.32 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.32 thf(func_def_0, type, x: frac).
% 0.18/0.32 thf(func_def_1, type, y: frac).
% 0.18/0.32 thf(func_def_2, type, z: frac).
% 0.18/0.32 thf(func_def_3, type, lessf: (frac > frac > $o)).
% 0.18/0.32 thf(func_def_5, type, eq: (frac > frac > $o)).
% 0.18/0.32 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.18/0.32 thf(f1,axiom,(
% 0.18/0.32 (lessf @ x @ y)),
% 0.18/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l)).
% 0.18/0.32 thf(f2,axiom,(
% 0.18/0.32 ~(lessf @ y @ z) => (eq @ y @ z)),
% 0.18/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',k)).
% 0.18/0.32 thf(f4,axiom,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((lessf @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (lessf @ X2 @ X3))))),
% 0.18/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz45)).
% 0.18/0.32 thf(f5,axiom,(
% 0.18/0.32 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.18/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37)).
% 0.18/0.32 thf(f6,axiom,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X0 @ X1) => ((lessf @ X1 @ X2) => (lessf @ X0 @ X2)))),
% 0.18/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz50)).
% 0.18/0.32 thf(f7,conjecture,(
% 0.18/0.32 (lessf @ x @ z)),
% 0.18/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51b)).
% 0.18/0.32 thf(f8,negated_conjecture,(
% 0.18/0.32 ~(lessf @ x @ z)),
% 0.18/0.32 inference(negated_conjecture,[status(cth)],[f7])).
% 0.18/0.32 thf(f9,plain,(
% 0.18/0.32 (lessf @ x @ y)),
% 0.18/0.32 inference(rectify,[],[f1])).
% 0.18/0.32 thf(f10,plain,(
% 0.18/0.32 (((lessf @ x @ y)) = $true)),
% 0.18/0.32 inference(fool_elimination,[],[f9])).
% 0.18/0.32 thf(f11,plain,(
% 0.18/0.32 ~(lessf @ y @ z) => (eq @ y @ z)),
% 0.18/0.32 inference(rectify,[],[f2])).
% 0.18/0.32 thf(f12,plain,(
% 0.18/0.32 ~ (((lessf @ y @ z)) = $true) => (((eq @ y @ z)) = $true)),
% 0.18/0.32 inference(fool_elimination,[],[f11])).
% 0.18/0.32 thf(f15,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((lessf @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (lessf @ X2 @ X3))))),
% 0.18/0.32 inference(rectify,[],[f4])).
% 0.18/0.32 thf(f16,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((lessf @ X0 @ X1)) = $true) => ((((eq @ X0 @ X2)) = $true) => ((((eq @ X1 @ X3)) = $true) => (((lessf @ X2 @ X3)) = $true))))),
% 0.18/0.32 inference(fool_elimination,[],[f15])).
% 0.18/0.32 thf(f17,plain,(
% 0.18/0.32 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.18/0.32 inference(rectify,[],[f5])).
% 0.18/0.32 thf(f18,plain,(
% 0.18/0.32 ! [X0 : frac] : (((eq @ X0 @ X0)) = $true)),
% 0.18/0.32 inference(fool_elimination,[],[f17])).
% 0.18/0.32 thf(f19,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X0 @ X1) => ((lessf @ X1 @ X2) => (lessf @ X0 @ X2)))),
% 0.18/0.32 inference(rectify,[],[f6])).
% 0.18/0.32 thf(f20,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac] : ((((lessf @ X0 @ X1)) = $true) => ((((lessf @ X1 @ X2)) = $true) => (((lessf @ X0 @ X2)) = $true)))),
% 0.18/0.32 inference(fool_elimination,[],[f19])).
% 0.18/0.32 thf(f21,plain,(
% 0.18/0.32 ~(lessf @ x @ z)),
% 0.18/0.32 inference(rectify,[],[f8])).
% 0.18/0.32 thf(f22,plain,(
% 0.18/0.32 ~ (((lessf @ x @ z)) = $true)),
% 0.18/0.32 inference(fool_elimination,[],[f21])).
% 0.18/0.32 thf(f23,plain,(
% 0.18/0.32 (((lessf @ y @ z)) != $true) => (((eq @ y @ z)) = $true)),
% 0.18/0.32 inference(flattening,[],[f12])).
% 0.18/0.32 thf(f25,plain,(
% 0.18/0.32 (((lessf @ x @ z)) != $true)),
% 0.18/0.32 inference(flattening,[],[f22])).
% 0.18/0.32 thf(f26,plain,(
% 0.18/0.32 (((eq @ y @ z)) = $true) | (((lessf @ y @ z)) = $true)),
% 0.18/0.32 inference(ennf_transformation,[],[f23])).
% 0.18/0.32 thf(f28,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((((lessf @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true)) | (((eq @ X0 @ X2)) != $true)) | (((lessf @ X0 @ X1)) != $true))),
% 0.18/0.32 inference(ennf_transformation,[],[f16])).
% 0.18/0.32 thf(f29,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((lessf @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true) | (((eq @ X0 @ X2)) != $true) | (((lessf @ X0 @ X1)) != $true))),
% 0.18/0.32 inference(flattening,[],[f28])).
% 0.18/0.32 thf(f30,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac] : (((((lessf @ X0 @ X2)) = $true) | (((lessf @ X1 @ X2)) != $true)) | (((lessf @ X0 @ X1)) != $true))),
% 0.18/0.32 inference(ennf_transformation,[],[f20])).
% 0.18/0.32 thf(f31,plain,(
% 0.18/0.32 ! [X0 : frac,X1 : frac,X2 : frac] : ((((lessf @ X0 @ X2)) = $true) | (((lessf @ X1 @ X2)) != $true) | (((lessf @ X0 @ X1)) != $true))),
% 0.18/0.32 inference(flattening,[],[f30])).
% 0.18/0.32 thf(f32,plain,(
% 0.18/0.32 (((lessf @ x @ y)) = $true)),
% 0.18/0.32 inference(cnf_transformation,[],[f10])).
% 0.18/0.32 thf(f33,plain,(
% 0.18/0.32 (((eq @ y @ z)) = $true) | (((lessf @ y @ z)) = $true)),
% 0.18/0.32 inference(cnf_transformation,[],[f26])).
% 0.18/0.32 thf(f35,plain,(
% 0.18/0.32 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X1 @ X3)) != $true) | (((lessf @ X2 @ X3)) = $true) | (((eq @ X0 @ X2)) != $true) | (((lessf @ X0 @ X1)) != $true)) )),
% 0.18/0.32 inference(cnf_transformation,[],[f29])).
% 0.18/0.32 thf(f36,plain,(
% 0.18/0.32 ( ! [X0 : frac] : ((((eq @ X0 @ X0)) = $true)) )),
% 0.18/0.32 inference(cnf_transformation,[],[f18])).
% 0.18/0.32 thf(f37,plain,(
% 0.18/0.32 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((lessf @ X1 @ X2)) != $true) | (((lessf @ X0 @ X2)) = $true) | (((lessf @ X0 @ X1)) != $true)) )),
% 0.18/0.32 inference(cnf_transformation,[],[f31])).
% 0.18/0.32 thf(f38,plain,(
% 0.18/0.32 (((lessf @ x @ z)) != $true)),
% 0.18/0.32 inference(cnf_transformation,[],[f25])).
% 0.18/0.32 thf(f40,definition,(
% 0.18/0.32 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.32 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.32 thf(f43,definition,(
% 0.18/0.32 spl0_1 <=> (((lessf @ y @ z)) = $true)),
% 0.18/0.32 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.18/0.32 thf(f45,plain,(
% 0.18/0.32 (((lessf @ y @ z)) = $true) | ~spl0_1),
% 0.18/0.32 inference(avatar_component_clause,[],[f43])).
% 0.18/0.32 thf(f47,definition,(
% 0.18/0.32 spl0_2 <=> (((eq @ y @ z)) = $true)),
% 0.18/0.32 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.18/0.32 thf(f49,plain,(
% 0.18/0.32 (((eq @ y @ z)) = $true) | ~spl0_2),
% 0.18/0.32 inference(avatar_component_clause,[],[f47])).
% 0.18/0.32 thf(f50,plain,(
% 0.18/0.32 spl0_1 | spl0_2),
% 0.18/0.32 inference(avatar_split_clause,[],[f33,f47,f43])).
% 0.18/0.32 thf(f63,plain,(
% 0.18/0.32 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((lessf @ X2 @ X1))) | ($true != ((lessf @ X2 @ X0))) | (((lessf @ X0 @ X1)) = $false)) )),
% 0.18/0.32 inference(constrained_superposition,[],[f37,f40])).
% 0.18/0.32 thf(f67,plain,(
% 0.18/0.32 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((lessf @ X2 @ X0))) | ($true = ((lessf @ X2 @ X1))) | (((lessf @ X0 @ X1)) = $false)) )),
% 0.18/0.32 inference(trivial_inequality_removal,[],[f63])).
% 0.18/0.32 thf(f72,plain,(
% 0.18/0.32 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ($true = ((lessf @ X0 @ z))) | ($true != ((eq @ X1 @ X0))) | ($true != ((lessf @ X1 @ y)))) ) | ~spl0_2),
% 0.18/0.32 inference(constrained_superposition,[],[f35,f49])).
% 0.18/0.32 thf(f73,plain,(
% 0.18/0.32 ( ! [X0 : frac,X1 : frac] : (($true != ((eq @ X1 @ X0))) | ($true = ((lessf @ X0 @ z))) | ($true != ((lessf @ X1 @ y)))) ) | ~spl0_2),
% 0.18/0.32 inference(trivial_inequality_removal,[],[f72])).
% 0.18/0.32 thf(f79,plain,(
% 0.18/0.32 ( ! [X0 : frac] : (($true != $true) | ($true = ((lessf @ x @ X0))) | ($false = ((lessf @ y @ X0)))) )),
% 0.18/0.32 inference(constrained_superposition,[],[f67,f32])).
% 0.18/0.32 thf(f83,plain,(
% 0.18/0.32 ( ! [X0 : frac] : (($false = ((lessf @ y @ X0))) | ($true = ((lessf @ x @ X0)))) )),
% 0.18/0.32 inference(trivial_inequality_removal,[],[f79])).
% 0.18/0.32 thf(f95,plain,(
% 0.18/0.32 ( ! [X0 : frac] : (($true != $true) | ($true = ((lessf @ X0 @ z))) | ($true != ((lessf @ X0 @ y)))) ) | ~spl0_2),
% 0.18/0.32 inference(constrained_superposition,[],[f73,f36])).
% 0.18/0.32 thf(f98,plain,(
% 0.18/0.32 ( ! [X0 : frac] : (($true != ((lessf @ X0 @ y))) | ($true = ((lessf @ X0 @ z)))) ) | ~spl0_2),
% 0.18/0.32 inference(trivial_inequality_removal,[],[f95])).
% 0.18/0.32 thf(f140,plain,(
% 0.18/0.32 ($true != $true) | (((lessf @ x @ z)) = $true) | ~spl0_2),
% 0.18/0.32 inference(constrained_superposition,[],[f98,f32])).
% 0.18/0.32 thf(f145,plain,(
% 0.18/0.32 (((lessf @ x @ z)) = $true) | ~spl0_2),
% 0.18/0.32 inference(trivial_inequality_removal,[],[f140])).
% 0.18/0.32 thf(f147,plain,(
% 0.18/0.32 $false | ~spl0_2),
% 0.18/0.32 inference(forward_subsumption_resolution,[],[f145,f38])).
% 0.18/0.32 thf(f148,plain,(
% 0.18/0.32 ~spl0_2),
% 0.18/0.32 inference(avatar_contradiction_clause,[],[f147])).
% 0.18/0.32 thf(f149,plain,(
% 0.18/0.32 ($true = $false) | (((lessf @ x @ z)) = $true) | ~spl0_1),
% 0.18/0.32 inference(constrained_superposition,[],[f45,f83])).
% 0.18/0.32 thf(f156,plain,(
% 0.18/0.32 (((lessf @ x @ z)) = $true) | ~spl0_1),
% 0.18/0.32 inference(trivial_inequality_removal,[],[f149])).
% 0.18/0.32 thf(f159,plain,(
% 0.18/0.32 $false | ~spl0_1),
% 0.18/0.32 inference(forward_subsumption_resolution,[],[f156,f38])).
% 0.18/0.32 thf(f160,plain,(
% 0.18/0.32 ~spl0_1),
% 0.18/0.32 inference(avatar_contradiction_clause,[],[f159])).
% 0.18/0.32 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f50])).
% 0.18/0.32 cnf(s3, plain, ~spl0_2, inference(sat_conversion,[],[f148])).
% 0.18/0.32 cnf(s5, plain, ~spl0_1, inference(sat_conversion,[],[f160])).
% 0.18/0.32 cnf(s6, plain, $false, inference(rat,[],[s1,s3,s5])).
% 0.18/0.32 thf(f161,plain,(
% 0.18/0.32 $false),
% 0.18/0.32 inference(avatar_sat_refutation,[],[s6])).
% 0.18/0.32 % SZS output end Proof for theBenchmark
% 0.18/0.32 % (3472069)------------------------------
% 0.18/0.32 % (3472069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.32 % (3472069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.32 % (3472069)CaDiCaL version: 2.1.3
% 0.18/0.32 % (3472069)Termination reason: Refutation
% 0.18/0.32 % (3472069)Time elapsed: 0.004 s
% 0.18/0.32 % (3472069)Peak memory usage: 12 MB
% 0.18/0.32 % (3472069)Instructions burned: 10 (million)
% 0.18/0.32 % (3472061)Success in time 0.024 s
% 0.18/0.32 % Vampire exiting
%------------------------------------------------------------------------------