%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM654^1 : 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 : 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 08:19:13 AM UTC 2026
% Result : Theorem 0.09s 0.29s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM654^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n015.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 12:35:33 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 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
% 0.09/0.29 % (3455228)Will run a generic schedule for satisfiability detection.
% 0.09/0.29 % (3455240)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2257959036:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.09/0.29 % (3455240) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3455228-3455240"...
% 0.09/0.29 % (3455240)...printing done.
% 0.09/0.29 % (3455240)Refutation found. Thanks to Tanya!
% 0.09/0.29 % SZS status Theorem for theBenchmark
% 0.09/0.29 % SZS output start Proof for theBenchmark
% 0.09/0.29 thf(type_def_5, type, nat: $tType).
% 0.09/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.29 thf(func_def_0, type, x: nat).
% 0.09/0.29 thf(func_def_1, type, y: nat).
% 0.09/0.29 thf(func_def_2, type, more: (nat > nat > $o)).
% 0.09/0.29 thf(func_def_4, type, less: (nat > nat > $o)).
% 0.09/0.29 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.09/0.29 thf(f1,axiom,(
% 0.09/0.29 ~(more @ x @ y)),
% 0.09/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n)).
% 0.09/0.29 thf(f3,axiom,(
% 0.09/0.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.09/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a)).
% 0.09/0.29 thf(f4,conjecture,(
% 0.09/0.29 ~(less @ x @ y) => (x = y)),
% 0.09/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10e)).
% 0.09/0.29 thf(f5,negated_conjecture,(
% 0.09/0.29 ~(~(less @ x @ y) => (x = y))),
% 0.09/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.09/0.29 thf(f6,plain,(
% 0.09/0.29 ~(more @ x @ y)),
% 0.09/0.29 inference(rectify,[],[f1])).
% 0.09/0.29 thf(f7,plain,(
% 0.09/0.29 ~ (((more @ x @ y)) = $true)),
% 0.09/0.29 inference(fool_elimination,[],[f6])).
% 0.09/0.29 thf(f10,plain,(
% 0.09/0.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.09/0.29 inference(rectify,[],[f3])).
% 0.09/0.29 thf(f11,plain,(
% 0.09/0.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ (((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) = $true)))),
% 0.09/0.29 inference(fool_elimination,[],[f10])).
% 0.09/0.29 thf(f12,plain,(
% 0.09/0.29 ~(~(less @ x @ y) => (x = y))),
% 0.09/0.29 inference(rectify,[],[f5])).
% 0.09/0.29 thf(f13,plain,(
% 0.09/0.29 ~(~ (((less @ x @ y)) = $true) => (x = y))),
% 0.09/0.29 inference(fool_elimination,[],[f12])).
% 0.09/0.29 thf(f14,plain,(
% 0.09/0.29 (((more @ x @ y)) != $true)),
% 0.09/0.29 inference(flattening,[],[f7])).
% 0.09/0.29 thf(f16,plain,(
% 0.09/0.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) => ((((more @ X0 @ X1)) != $true) => (((less @ X0 @ X1)) = $true)))),
% 0.09/0.29 inference(flattening,[],[f11])).
% 0.09/0.29 thf(f17,plain,(
% 0.09/0.29 ~((((less @ x @ y)) != $true) => (x = y))),
% 0.09/0.29 inference(flattening,[],[f13])).
% 0.09/0.29 thf(f19,plain,(
% 0.09/0.29 ! [X0 : nat,X1 : nat] : (((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true)) | (X0 = X1))),
% 0.09/0.29 inference(ennf_transformation,[],[f16])).
% 0.09/0.29 thf(f20,plain,(
% 0.09/0.29 ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true) | (X0 = X1))),
% 0.09/0.29 inference(flattening,[],[f19])).
% 0.09/0.29 thf(f21,plain,(
% 0.09/0.29 (x != y) & (((less @ x @ y)) != $true)),
% 0.09/0.29 inference(ennf_transformation,[],[f17])).
% 0.09/0.29 thf(f22,plain,(
% 0.09/0.29 (((more @ x @ y)) != $true)),
% 0.09/0.29 inference(cnf_transformation,[],[f14])).
% 0.09/0.29 thf(f24,plain,(
% 0.09/0.29 ( ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 0.09/0.29 inference(cnf_transformation,[],[f20])).
% 0.09/0.29 thf(f25,plain,(
% 0.09/0.29 (((less @ x @ y)) != $true)),
% 0.09/0.29 inference(cnf_transformation,[],[f21])).
% 0.09/0.29 thf(f26,plain,(
% 0.09/0.29 (x != y)),
% 0.09/0.29 inference(cnf_transformation,[],[f21])).
% 0.09/0.29 thf(f28,definition,(
% 0.09/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.29 thf(f32,plain,(
% 0.09/0.29 ($true != $true) | (((less @ x @ y)) = $false)),
% 0.09/0.29 inference(constrained_superposition,[],[f25,f28])).
% 0.09/0.29 thf(f34,plain,(
% 0.09/0.29 (((less @ x @ y)) = $false)),
% 0.09/0.29 inference(trivial_inequality_removal,[],[f32])).
% 0.09/0.29 thf(f42,plain,(
% 0.09/0.29 ($true != $true) | (((more @ x @ y)) = $false)),
% 0.09/0.29 inference(constrained_superposition,[],[f22,f28])).
% 0.09/0.29 thf(f43,plain,(
% 0.09/0.29 (((more @ x @ y)) = $false)),
% 0.09/0.29 inference(trivial_inequality_removal,[],[f42])).
% 0.09/0.29 thf(f47,plain,(
% 0.09/0.29 ($true = $false) | (((more @ x @ y)) = $true) | (x = y)),
% 0.09/0.29 inference(constrained_superposition,[],[f24,f34])).
% 0.09/0.29 thf(f52,plain,(
% 0.09/0.29 (((more @ x @ y)) = $true) | (x = y)),
% 0.09/0.29 inference(trivial_inequality_removal,[],[f47])).
% 0.09/0.29 thf(f54,definition,(
% 0.09/0.29 spl0_1 <=> (x = y)),
% 0.09/0.29 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.09/0.29 thf(f56,plain,(
% 0.09/0.29 (x = y) | ~spl0_1),
% 0.09/0.29 inference(avatar_component_clause,[],[f54])).
% 0.09/0.29 thf(f58,definition,(
% 0.09/0.29 spl0_2 <=> (((more @ x @ y)) = $true)),
% 0.09/0.29 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.09/0.29 thf(f60,plain,(
% 0.09/0.29 (((more @ x @ y)) = $true) | ~spl0_2),
% 0.09/0.29 inference(avatar_component_clause,[],[f58])).
% 0.09/0.29 thf(f63,plain,(
% 0.09/0.29 spl0_1 | spl0_2),
% 0.09/0.29 inference(avatar_split_clause,[],[f52,f58,f54])).
% 0.09/0.29 thf(f64,plain,(
% 0.09/0.29 ($true = $false) | ~spl0_2),
% 0.09/0.29 inference(constrained_superposition,[],[f60,f43])).
% 0.09/0.29 thf(f71,plain,(
% 0.09/0.29 $false | ~spl0_2),
% 0.09/0.29 inference(trivial_inequality_removal,[],[f64])).
% 0.09/0.29 thf(f72,plain,(
% 0.09/0.29 ~spl0_2),
% 0.09/0.29 inference(avatar_contradiction_clause,[],[f71])).
% 0.09/0.29 thf(f77,plain,(
% 0.09/0.29 (x != x) | ~spl0_1),
% 0.09/0.29 inference(constrained_superposition,[],[f26,f56])).
% 0.09/0.29 thf(f78,plain,(
% 0.09/0.29 $false | ~spl0_1),
% 0.09/0.29 inference(trivial_inequality_removal,[],[f77])).
% 0.09/0.29 thf(f79,plain,(
% 0.09/0.29 ~spl0_1),
% 0.09/0.29 inference(avatar_contradiction_clause,[],[f78])).
% 0.09/0.29 cnf(s3, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f63])).
% 0.09/0.29 cnf(s6, plain, ~spl0_2, inference(sat_conversion,[],[f72])).
% 0.09/0.29 cnf(s7, plain, ~spl0_1, inference(sat_conversion,[],[f79])).
% 0.09/0.29 cnf(s8, plain, $false, inference(rat,[],[s3,s6,s7])).
% 0.09/0.29 thf(f80,plain,(
% 0.09/0.29 $false),
% 0.09/0.29 inference(avatar_sat_refutation,[],[s8])).
% 0.09/0.29 % SZS output end Proof for theBenchmark
% 0.09/0.29 % (3455240)------------------------------
% 0.09/0.29 % (3455240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.29 % (3455240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.29 % (3455240)CaDiCaL version: 2.1.3
% 0.09/0.29 % (3455240)Termination reason: Refutation
% 0.09/0.29 % (3455240)Time elapsed: 0.003 s
% 0.09/0.29 % (3455240)Peak memory usage: 13 MB
% 0.09/0.29 % (3455240)Instructions burned: 3 (million)
% 0.09/0.29 % (3455228)Success in time 0.025 s
% 0.09/0.29 % Vampire exiting
%------------------------------------------------------------------------------