%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM795^1 : 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 : n004.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 08:19:33 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM795^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:59:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.27 % (1239960)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (1239976)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2144447168:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (1239976)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (1239973)% WARNING: option uhcvi not known.
% 0.19/0.27 % (1239976) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1239960-1239976"...
% 0.19/0.27 % (1239976)...printing done.
% 0.19/0.27 % (1239976)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, rat: $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, x0: rat).
% 0.19/0.27 thf(func_def_1, type, y0: rat).
% 0.19/0.27 thf(func_def_2, type, z0: rat).
% 0.19/0.27 thf(func_def_3, type, u0: rat).
% 0.19/0.27 thf(func_def_4, type, lessis: (rat > rat > $o)).
% 0.19/0.27 thf(func_def_6, type, less: (rat > rat > $o)).
% 0.19/0.27 thf(func_def_7, type, pl: (rat > rat > rat)).
% 0.19/0.27 thf(func_def_8, type, more: (rat > rat > $o)).
% 0.19/0.27 thf(func_def_9, type, moreis: (rat > rat > $o)).
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 (lessis @ x0 @ y0)),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l)).
% 0.19/0.27 thf(f2,axiom,(
% 0.19/0.27 (less @ z0 @ u0)),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',k)).
% 0.19/0.27 thf(f3,axiom,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz82)).
% 0.19/0.27 thf(f4,axiom,(
% 0.19/0.27 ! [X0 : rat,X1 : rat,X2 : rat,X3 : rat] : ((moreis @ X0 @ X1) => ((more @ X2 @ X3) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz99a)).
% 0.19/0.27 thf(f5,axiom,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz85)).
% 0.19/0.27 thf(f6,axiom,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((less @ X0 @ X1) => (more @ X1 @ X0))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz83)).
% 0.19/0.27 thf(f7,conjecture,(
% 0.19/0.27 (less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz99c)).
% 0.19/0.27 thf(f8,negated_conjecture,(
% 0.19/0.27 ~(less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 (lessis @ x0 @ y0)),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 (((lessis @ x0 @ y0)) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f9])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 (less @ z0 @ u0)),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 (((less @ z0 @ u0)) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f11])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 0.19/0.27 inference(rectify,[],[f3])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((((more @ X0 @ X1)) = $true) => (((less @ X1 @ X0)) = $true))),
% 0.19/0.27 inference(fool_elimination,[],[f13])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat,X2 : rat,X3 : rat] : ((moreis @ X0 @ X1) => ((more @ X2 @ X3) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))))),
% 0.19/0.27 inference(rectify,[],[f4])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat,X2 : rat,X3 : rat] : ((((moreis @ X0 @ X1)) = $true) => ((((more @ X2 @ X3)) = $true) => (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f15])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 0.19/0.27 inference(rectify,[],[f5])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((((lessis @ X0 @ X1)) = $true) => (((moreis @ X1 @ X0)) = $true))),
% 0.19/0.27 inference(fool_elimination,[],[f17])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((less @ X0 @ X1) => (more @ X1 @ X0))),
% 0.19/0.27 inference(rectify,[],[f6])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((((less @ X0 @ X1)) = $true) => (((more @ X1 @ X0)) = $true))),
% 0.19/0.27 inference(fool_elimination,[],[f19])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ~(less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))),
% 0.19/0.27 inference(rectify,[],[f8])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ~ (((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f21])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 (((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))) != $true)),
% 0.19/0.27 inference(flattening,[],[f22])).
% 0.19/0.27 thf(f24,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((((less @ X1 @ X0)) = $true) | (((more @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f14])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat,X2 : rat,X3 : rat] : (((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true)) | (((moreis @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f16])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat,X2 : rat,X3 : rat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true) | (((moreis @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(flattening,[],[f25])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((((moreis @ X1 @ X0)) = $true) | (((lessis @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f18])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 ! [X0 : rat,X1 : rat] : ((((more @ X1 @ X0)) = $true) | (((less @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f20])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 (((lessis @ x0 @ y0)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f10])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 (((less @ z0 @ u0)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f12])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 ( ! [X0 : rat,X1 : rat] : ((((less @ X1 @ X0)) = $true) | (((more @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f24])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 ( ! [X2 : rat,X3 : rat,X0 : rat,X1 : rat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true) | (((moreis @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f26])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ( ! [X0 : rat,X1 : rat] : ((((moreis @ X1 @ X0)) = $true) | (((lessis @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f27])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 ( ! [X0 : rat,X1 : rat] : ((((more @ X1 @ X0)) = $true) | (((less @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f28])).
% 0.19/0.27 thf(f35,plain,(
% 0.19/0.27 (((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))) != $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f23])).
% 0.19/0.27 thf(f37,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f40,plain,(
% 0.19/0.27 ($true != $true) | (((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))) = $false)),
% 0.19/0.27 inference(constrained_superposition,[],[f35,f37])).
% 0.19/0.27 thf(f42,plain,(
% 0.19/0.27 (((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))) = $false)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f40])).
% 0.19/0.27 thf(f58,plain,(
% 0.19/0.27 ( ! [X2 : rat,X3 : rat,X0 : rat,X1 : rat] : (($true != $true) | ($true = ((less @ (pl @ X2 @ X3) @ (pl @ X0 @ X1)))) | ($true != ((more @ X1 @ X3))) | ($true != ((moreis @ X0 @ X2)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f31,f32])).
% 0.19/0.27 thf(f59,plain,(
% 0.19/0.27 ( ! [X2 : rat,X3 : rat,X0 : rat,X1 : rat] : (($true = ((less @ (pl @ X2 @ X3) @ (pl @ X0 @ X1)))) | ($true != ((more @ X1 @ X3))) | ($true != ((moreis @ X0 @ X2)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f58])).
% 0.19/0.27 thf(f92,plain,(
% 0.19/0.27 ($true = $false) | ($true != ((more @ u0 @ z0))) | ($true != ((moreis @ y0 @ x0)))),
% 0.19/0.27 inference(constrained_superposition,[],[f59,f42])).
% 0.19/0.27 thf(f103,plain,(
% 0.19/0.27 ($true != ((more @ u0 @ z0))) | ($true != ((moreis @ y0 @ x0)))),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f92])).
% 0.19/0.27 thf(f105,definition,(
% 0.19/0.27 spl0_1 <=> ($true = ((moreis @ y0 @ x0)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.19/0.27 thf(f107,plain,(
% 0.19/0.27 ($true != ((moreis @ y0 @ x0))) | spl0_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f105])).
% 0.19/0.27 thf(f109,definition,(
% 0.19/0.27 spl0_2 <=> ($true = ((more @ u0 @ z0)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.19/0.27 thf(f111,plain,(
% 0.19/0.27 ($true != ((more @ u0 @ z0))) | spl0_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f109])).
% 0.19/0.27 thf(f114,plain,(
% 0.19/0.27 ~spl0_1 | ~spl0_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f103,f109,f105])).
% 0.19/0.27 thf(f117,plain,(
% 0.19/0.27 ($true != $true) | (((lessis @ x0 @ y0)) != $true) | spl0_1),
% 0.19/0.27 inference(constrained_superposition,[],[f107,f33])).
% 0.19/0.27 thf(f118,plain,(
% 0.19/0.27 (((lessis @ x0 @ y0)) != $true) | spl0_1),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f117])).
% 0.19/0.27 thf(f121,plain,(
% 0.19/0.27 $false | spl0_1),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f118,f29])).
% 0.19/0.27 thf(f122,plain,(
% 0.19/0.27 spl0_1),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f121])).
% 0.19/0.27 thf(f126,plain,(
% 0.19/0.27 ($true != $true) | (((less @ z0 @ u0)) != $true) | spl0_2),
% 0.19/0.27 inference(constrained_superposition,[],[f111,f34])).
% 0.19/0.27 thf(f127,plain,(
% 0.19/0.27 (((less @ z0 @ u0)) != $true) | spl0_2),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f126])).
% 0.19/0.27 thf(f130,plain,(
% 0.19/0.27 $false | spl0_2),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f127,f30])).
% 0.19/0.27 thf(f131,plain,(
% 0.19/0.27 spl0_2),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f130])).
% 0.19/0.27 cnf(s3, plain, ~spl0_1 | ~spl0_2, inference(sat_conversion,[],[f114])).
% 0.19/0.27 cnf(s4, plain, spl0_1, inference(sat_conversion,[],[f122])).
% 0.19/0.27 cnf(s5, plain, spl0_2, inference(sat_conversion,[],[f131])).
% 0.19/0.27 cnf(s6, plain, $false, inference(rat,[],[s3,s5,s4])).
% 0.19/0.27 thf(f132,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s6])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (1239976)------------------------------
% 0.19/0.27 % (1239976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1239976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1239976)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1239976)Termination reason: Refutation
% 0.19/0.27 % (1239976)Time elapsed: 0.004 s
% 0.19/0.27 % (1239976)Peak memory usage: 12 MB
% 0.19/0.27 % (1239976)Instructions burned: 10 (million)
% 0.19/0.27 % (1239960)Success in time 0.04 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------