%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM791^1 : 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 : n009.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 08:19:32 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM791^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 12:57:15 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.24 % (3944104)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (3944115)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3271241499:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.24 % (3944115) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3944104-3944115"...
% 0.07/0.24 % (3944115)...printing done.
% 0.07/0.24 % (3944110)% WARNING: option uhcvi not known.
% 0.07/0.24 % (3944115)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% 0.07/0.24 thf(type_def_5, type, rat: $tType).
% 0.07/0.24 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.24 thf(func_def_0, type, x0: rat).
% 0.07/0.24 thf(func_def_1, type, y0: rat).
% 0.07/0.24 thf(func_def_2, type, less: (rat > rat > $o)).
% 0.07/0.24 thf(func_def_3, type, is: (rat > rat > $o)).
% 0.07/0.24 thf(func_def_5, type, more: (rat > rat > $o)).
% 0.07/0.24 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.07/0.24 thf(f1,axiom,(
% 0.07/0.24 ~(~(less @ x0 @ y0) => (is @ x0 @ y0))),
% 0.07/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n)).
% 0.07/0.24 thf(f3,axiom,(
% 0.07/0.24 ! [X0 : rat,X1 : rat] : (~(is @ X0 @ X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.07/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81a)).
% 0.07/0.24 thf(f4,conjecture,(
% 0.07/0.24 (more @ x0 @ y0)),
% 0.07/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81k)).
% 0.07/0.24 thf(f5,negated_conjecture,(
% 0.07/0.24 ~(more @ x0 @ y0)),
% 0.07/0.24 inference(negated_conjecture,[status(cth)],[f4])).
% 0.07/0.24 thf(f6,plain,(
% 0.07/0.24 ~(~(less @ x0 @ y0) => (is @ x0 @ y0))),
% 0.07/0.24 inference(rectify,[],[f1])).
% 0.07/0.24 thf(f7,plain,(
% 0.07/0.24 ~(~ (((less @ x0 @ y0)) = $true) => (((is @ x0 @ y0)) = $true))),
% 0.07/0.24 inference(fool_elimination,[],[f6])).
% 0.07/0.24 thf(f10,plain,(
% 0.07/0.24 ! [X0 : rat,X1 : rat] : (~(is @ X0 @ X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.07/0.24 inference(rectify,[],[f3])).
% 0.07/0.24 thf(f11,plain,(
% 0.07/0.24 ! [X0 : rat,X1 : rat] : (~ (((is @ X0 @ X1)) = $true) => (~ (((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) = $true)))),
% 0.07/0.24 inference(fool_elimination,[],[f10])).
% 0.07/0.24 thf(f12,plain,(
% 0.07/0.24 ~(more @ x0 @ y0)),
% 0.07/0.24 inference(rectify,[],[f5])).
% 0.07/0.24 thf(f13,plain,(
% 0.07/0.24 ~ (((more @ x0 @ y0)) = $true)),
% 0.07/0.24 inference(fool_elimination,[],[f12])).
% 0.07/0.24 thf(f14,plain,(
% 0.07/0.24 ~((((less @ x0 @ y0)) != $true) => (((is @ x0 @ y0)) = $true))),
% 0.07/0.24 inference(flattening,[],[f7])).
% 0.07/0.24 thf(f16,plain,(
% 0.07/0.24 ! [X0 : rat,X1 : rat] : ((((is @ X0 @ X1)) != $true) => ((((more @ X0 @ X1)) != $true) => (((less @ X0 @ X1)) = $true)))),
% 0.07/0.24 inference(flattening,[],[f11])).
% 0.07/0.24 thf(f17,plain,(
% 0.07/0.24 (((more @ x0 @ y0)) != $true)),
% 0.07/0.24 inference(flattening,[],[f13])).
% 0.07/0.24 thf(f18,plain,(
% 0.07/0.24 (((is @ x0 @ y0)) != $true) & (((less @ x0 @ y0)) != $true)),
% 0.07/0.24 inference(ennf_transformation,[],[f14])).
% 0.07/0.24 thf(f20,plain,(
% 0.07/0.24 ! [X0 : rat,X1 : rat] : (((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true)) | (((is @ X0 @ X1)) = $true))),
% 0.07/0.24 inference(ennf_transformation,[],[f16])).
% 0.07/0.24 thf(f21,plain,(
% 0.07/0.24 ! [X0 : rat,X1 : rat] : ((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true) | (((is @ X0 @ X1)) = $true))),
% 0.07/0.24 inference(flattening,[],[f20])).
% 0.07/0.24 thf(f22,plain,(
% 0.07/0.24 (((less @ x0 @ y0)) != $true)),
% 0.07/0.24 inference(cnf_transformation,[],[f18])).
% 0.07/0.24 thf(f23,plain,(
% 0.07/0.24 (((is @ x0 @ y0)) != $true)),
% 0.07/0.24 inference(cnf_transformation,[],[f18])).
% 0.07/0.24 thf(f25,plain,(
% 0.07/0.24 ( ! [X0 : rat,X1 : rat] : ((((more @ X0 @ X1)) = $true) | (((less @ X0 @ X1)) = $true) | (((is @ X0 @ X1)) = $true)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f21])).
% 0.07/0.24 thf(f26,plain,(
% 0.07/0.24 (((more @ x0 @ y0)) != $true)),
% 0.07/0.24 inference(cnf_transformation,[],[f17])).
% 0.07/0.24 thf(f28,definition,(
% 0.07/0.24 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.24 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.24 thf(f32,plain,(
% 0.07/0.24 ($true != $true) | (((more @ x0 @ y0)) = $false)),
% 0.07/0.24 inference(constrained_superposition,[],[f26,f28])).
% 0.07/0.24 thf(f34,plain,(
% 0.07/0.24 (((more @ x0 @ y0)) = $false)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f32])).
% 0.07/0.24 thf(f42,plain,(
% 0.07/0.24 ($true != $true) | (((less @ x0 @ y0)) = $false)),
% 0.07/0.24 inference(constrained_superposition,[],[f22,f28])).
% 0.07/0.24 thf(f43,plain,(
% 0.07/0.24 (((less @ x0 @ y0)) = $false)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f42])).
% 0.07/0.24 thf(f44,plain,(
% 0.07/0.24 ($true != $true) | (((is @ x0 @ y0)) = $false)),
% 0.07/0.24 inference(constrained_superposition,[],[f23,f28])).
% 0.07/0.24 thf(f45,plain,(
% 0.07/0.24 (((is @ x0 @ y0)) = $false)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f44])).
% 0.07/0.24 thf(f52,plain,(
% 0.07/0.24 ($true = $false) | (((less @ x0 @ y0)) = $true) | (((is @ x0 @ y0)) = $true)),
% 0.07/0.24 inference(constrained_superposition,[],[f25,f34])).
% 0.07/0.24 thf(f57,plain,(
% 0.07/0.24 (((less @ x0 @ y0)) = $true) | (((is @ x0 @ y0)) = $true)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f52])).
% 0.07/0.24 thf(f59,definition,(
% 0.07/0.24 spl0_1 <=> (((is @ x0 @ y0)) = $true)),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.07/0.24 thf(f61,plain,(
% 0.07/0.24 (((is @ x0 @ y0)) = $true) | ~spl0_1),
% 0.07/0.24 inference(avatar_component_clause,[],[f59])).
% 0.07/0.24 thf(f63,definition,(
% 0.07/0.24 spl0_2 <=> (((less @ x0 @ y0)) = $true)),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.07/0.24 thf(f65,plain,(
% 0.07/0.24 (((less @ x0 @ y0)) = $true) | ~spl0_2),
% 0.07/0.24 inference(avatar_component_clause,[],[f63])).
% 0.07/0.24 thf(f68,plain,(
% 0.07/0.24 spl0_1 | spl0_2),
% 0.07/0.24 inference(avatar_split_clause,[],[f57,f63,f59])).
% 0.07/0.24 thf(f69,plain,(
% 0.07/0.24 ($true = $false) | ~spl0_2),
% 0.07/0.24 inference(constrained_superposition,[],[f65,f43])).
% 0.07/0.24 thf(f76,plain,(
% 0.07/0.24 $false | ~spl0_2),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f69])).
% 0.07/0.24 thf(f77,plain,(
% 0.07/0.24 ~spl0_2),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f76])).
% 0.07/0.24 thf(f78,plain,(
% 0.07/0.24 ($true = $false) | ~spl0_1),
% 0.07/0.24 inference(constrained_superposition,[],[f61,f45])).
% 0.07/0.24 thf(f85,plain,(
% 0.07/0.24 $false | ~spl0_1),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f78])).
% 0.07/0.24 thf(f86,plain,(
% 0.07/0.24 ~spl0_1),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f85])).
% 0.07/0.24 cnf(s3, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f68])).
% 0.07/0.24 cnf(s6, plain, ~spl0_2, inference(sat_conversion,[],[f77])).
% 0.07/0.24 cnf(s9, plain, ~spl0_1, inference(sat_conversion,[],[f86])).
% 0.07/0.24 cnf(s10, plain, $false, inference(rat,[],[s3,s6,s9])).
% 0.07/0.24 thf(f87,plain,(
% 0.07/0.24 $false),
% 0.07/0.24 inference(avatar_sat_refutation,[],[s10])).
% 0.07/0.24 % SZS output end Proof for theBenchmark
% 0.07/0.24 % (3944115)------------------------------
% 0.07/0.24 % (3944115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (3944115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (3944115)CaDiCaL version: 2.1.3
% 0.07/0.24 % (3944115)Termination reason: Refutation
% 0.07/0.24 % (3944115)Time elapsed: 0.002 s
% 0.07/0.24 % (3944115)Peak memory usage: 13 MB
% 0.07/0.24 % (3944115)Instructions burned: 3 (million)
% 0.07/0.24 % (3944104)Success in time 0.024 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------