%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM658^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:18:26 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM658^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 12:34:56 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25 % (14435)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.25 % (14445)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=679189212:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.25 % (14445) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-14435-14445"...
% 0.08/0.25 % (14445)...printing done.
% 0.08/0.25 % (14445)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% 0.08/0.25 thf(type_def_5, type, nat: $tType).
% 0.08/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.25 thf(func_def_0, type, x: nat).
% 0.08/0.25 thf(func_def_1, type, y: nat).
% 0.08/0.25 thf(func_def_2, type, more: (nat > nat > $o)).
% 0.08/0.25 thf(func_def_4, type, less: (nat > nat > $o)).
% 0.08/0.25 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.08/0.25 thf(f1,axiom,(
% 0.08/0.25 ~(~(more @ x @ y) => (x = y))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n)).
% 0.08/0.25 thf(f2,axiom,(
% 0.08/0.25 ! [X1 : nat,X0 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a)).
% 0.08/0.25 thf(f4,conjecture,(
% 0.08/0.25 (less @ x @ y)),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10j)).
% 0.08/0.25 thf(f5,negated_conjecture,(
% 0.08/0.25 ~(less @ x @ y)),
% 0.08/0.25 inference(negated_conjecture,[status(cth)],[f4])).
% 0.08/0.25 thf(f8,plain,(
% 0.08/0.25 ~(~(more @ x @ y) => (x = y))),
% 0.08/0.25 inference(rectify,[],[f1])).
% 0.08/0.25 thf(f9,plain,(
% 0.08/0.25 ~(~ (((more @ x @ y)) = $true) => (x = y))),
% 0.08/0.25 inference(fool_elimination,[],[f8])).
% 0.08/0.25 thf(f10,plain,(
% 0.08/0.25 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X1 @ X0) => (less @ X1 @ X0)))),
% 0.08/0.25 inference(rectify,[],[f2])).
% 0.08/0.25 thf(f11,plain,(
% 0.08/0.25 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ ($true = ((more @ X1 @ X0))) => ($true = ((less @ X1 @ X0)))))),
% 0.08/0.25 inference(fool_elimination,[],[f10])).
% 0.08/0.25 thf(f12,plain,(
% 0.08/0.25 ~(less @ x @ y)),
% 0.08/0.25 inference(rectify,[],[f5])).
% 0.08/0.25 thf(f13,plain,(
% 0.08/0.25 ~ (((less @ x @ y)) = $true)),
% 0.08/0.25 inference(fool_elimination,[],[f12])).
% 0.08/0.25 thf(f15,plain,(
% 0.08/0.25 ~((((more @ x @ y)) != $true) => (x = y))),
% 0.08/0.25 inference(flattening,[],[f9])).
% 0.08/0.25 thf(f16,plain,(
% 0.08/0.25 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (($true != ((more @ X1 @ X0))) => ($true = ((less @ X1 @ X0)))))),
% 0.08/0.25 inference(flattening,[],[f11])).
% 0.08/0.25 thf(f17,plain,(
% 0.08/0.25 (((less @ x @ y)) != $true)),
% 0.08/0.25 inference(flattening,[],[f13])).
% 0.08/0.25 thf(f19,plain,(
% 0.08/0.25 (((more @ x @ y)) != $true) & (x != y)),
% 0.08/0.25 inference(ennf_transformation,[],[f15])).
% 0.08/0.25 thf(f20,plain,(
% 0.08/0.25 ! [X0 : nat,X1 : nat] : ((($true = ((less @ X1 @ X0))) | ($true = ((more @ X1 @ X0)))) | (X0 = X1))),
% 0.08/0.25 inference(ennf_transformation,[],[f16])).
% 0.08/0.25 thf(f21,plain,(
% 0.08/0.25 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = ((less @ X1 @ X0))) | ($true = ((more @ X1 @ X0))))),
% 0.08/0.25 inference(flattening,[],[f20])).
% 0.08/0.25 thf(f23,plain,(
% 0.08/0.25 (((less @ x @ y)) != $true)),
% 0.08/0.25 inference(cnf_transformation,[],[f17])).
% 0.08/0.25 thf(f24,plain,(
% 0.08/0.25 ( ! [X0 : nat,X1 : nat] : (($true = ((more @ X1 @ X0))) | ($true = ((less @ X1 @ X0))) | (X0 = X1)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f21])).
% 0.08/0.25 thf(f25,plain,(
% 0.08/0.25 (x != y)),
% 0.08/0.25 inference(cnf_transformation,[],[f19])).
% 0.08/0.25 thf(f26,plain,(
% 0.08/0.25 (((more @ x @ y)) != $true)),
% 0.08/0.25 inference(cnf_transformation,[],[f19])).
% 0.08/0.25 thf(f28,definition,(
% 0.08/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.25 thf(f32,plain,(
% 0.08/0.25 ($true != $true) | (((less @ x @ y)) = $false)),
% 0.08/0.25 inference(constrained_superposition,[],[f23,f28])).
% 0.08/0.25 thf(f33,plain,(
% 0.08/0.25 (((more @ x @ y)) = $false) | ($true != $true)),
% 0.08/0.25 inference(constrained_superposition,[],[f26,f28])).
% 0.08/0.25 thf(f35,plain,(
% 0.08/0.25 (((more @ x @ y)) = $false)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f33])).
% 0.08/0.25 thf(f36,plain,(
% 0.08/0.25 (((less @ x @ y)) = $false)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f32])).
% 0.08/0.25 thf(f46,plain,(
% 0.08/0.25 ($true = $false) | (x = y) | (((less @ x @ y)) = $true)),
% 0.08/0.25 inference(constrained_superposition,[],[f35,f24])).
% 0.08/0.25 thf(f48,plain,(
% 0.08/0.25 (((less @ x @ y)) = $true) | (x = y)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f46])).
% 0.08/0.25 thf(f51,plain,(
% 0.08/0.25 (((less @ x @ y)) = $true)),
% 0.08/0.25 inference(forward_subsumption_resolution,[],[f48,f25])).
% 0.08/0.25 thf(f53,plain,(
% 0.08/0.25 ($true = $false)),
% 0.08/0.25 inference(forward_demodulation,[],[f51,f36])).
% 0.08/0.25 thf(f54,plain,(
% 0.08/0.25 $false),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f53])).
% 0.08/0.25 % SZS output end Proof for theBenchmark
% 0.08/0.25 % (14445)------------------------------
% 0.08/0.25 % (14445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (14445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (14445)CaDiCaL version: 2.1.3
% 0.08/0.25 % (14445)Termination reason: Refutation
% 0.08/0.25 % (14445)Time elapsed: 0.002 s
% 0.08/0.25 % (14445)Peak memory usage: 13 MB
% 0.08/0.25 % (14445)Instructions burned: 2 (million)
% 0.08/0.25 % (14435)Success in time 0.025 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------