%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM786^1 : 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 : n007.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 08:18:52 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM786^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:54:26 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.07/0.26 % (3317949)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (3317959)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1041642518:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.07/0.26 % (3317959) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3317949-3317959"...
% 0.07/0.26 % (3317959)...printing done.
% 0.07/0.26 % (3317959)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% 0.07/0.26 thf(type_def_5, type, rat: $tType).
% 0.07/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.26 thf(func_def_0, type, x0: rat).
% 0.07/0.26 thf(func_def_1, type, y0: rat).
% 0.07/0.26 thf(func_def_2, type, more: (rat > rat > $o)).
% 0.07/0.26 thf(func_def_4, type, less: (rat > rat > $o)).
% 0.07/0.26 thf(func_def_5, type, is: (rat > rat > $o)).
% 0.07/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.07/0.26 thf(f1,axiom,(
% 0.07/0.26 ~(more @ x0 @ y0)),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n)).
% 0.07/0.26 thf(f3,axiom,(
% 0.07/0.26 ! [X1 : rat,X0 : rat] : (~(is @ X0 @ X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81a)).
% 0.07/0.26 thf(f4,conjecture,(
% 0.07/0.26 ~(less @ x0 @ y0) => (is @ x0 @ y0)),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81e)).
% 0.07/0.26 thf(f5,negated_conjecture,(
% 0.07/0.26 ~(~(less @ x0 @ y0) => (is @ x0 @ y0))),
% 0.07/0.26 inference(negated_conjecture,[status(cth)],[f4])).
% 0.07/0.26 thf(f6,plain,(
% 0.07/0.26 ~(more @ x0 @ y0)),
% 0.07/0.26 inference(rectify,[],[f1])).
% 0.07/0.26 thf(f7,plain,(
% 0.07/0.26 ~ (((more @ x0 @ y0)) = $true)),
% 0.07/0.26 inference(fool_elimination,[],[f6])).
% 0.07/0.26 thf(f8,plain,(
% 0.07/0.26 ~(~(less @ x0 @ y0) => (is @ x0 @ y0))),
% 0.07/0.26 inference(rectify,[],[f5])).
% 0.07/0.26 thf(f9,plain,(
% 0.07/0.26 ~(~ (((less @ x0 @ y0)) = $true) => (((is @ x0 @ y0)) = $true))),
% 0.07/0.26 inference(fool_elimination,[],[f8])).
% 0.07/0.26 thf(f10,plain,(
% 0.07/0.26 ! [X0 : rat,X1 : rat] : (~(is @ X1 @ X0) => (~(more @ X1 @ X0) => (less @ X1 @ X0)))),
% 0.07/0.26 inference(rectify,[],[f3])).
% 0.07/0.26 thf(f11,plain,(
% 0.07/0.26 ! [X0 : rat,X1 : rat] : (~ ($true = ((is @ X1 @ X0))) => (~ (((more @ X1 @ X0)) = $true) => (((less @ X1 @ X0)) = $true)))),
% 0.07/0.26 inference(fool_elimination,[],[f10])).
% 0.07/0.26 thf(f14,plain,(
% 0.07/0.26 (((more @ x0 @ y0)) != $true)),
% 0.07/0.26 inference(flattening,[],[f7])).
% 0.07/0.26 thf(f15,plain,(
% 0.07/0.26 ~((((less @ x0 @ y0)) != $true) => (((is @ x0 @ y0)) = $true))),
% 0.07/0.26 inference(flattening,[],[f9])).
% 0.07/0.26 thf(f16,plain,(
% 0.07/0.26 ! [X0 : rat,X1 : rat] : (($true != ((is @ X1 @ X0))) => ((((more @ X1 @ X0)) != $true) => (((less @ X1 @ X0)) = $true)))),
% 0.07/0.26 inference(flattening,[],[f11])).
% 0.07/0.26 thf(f18,plain,(
% 0.07/0.26 (((less @ x0 @ y0)) != $true) & (((is @ x0 @ y0)) != $true)),
% 0.07/0.26 inference(ennf_transformation,[],[f15])).
% 0.07/0.26 thf(f20,plain,(
% 0.07/0.26 ! [X0 : rat,X1 : rat] : (((((less @ X1 @ X0)) = $true) | (((more @ X1 @ X0)) = $true)) | ($true = ((is @ X1 @ X0))))),
% 0.07/0.26 inference(ennf_transformation,[],[f16])).
% 0.07/0.26 thf(f21,plain,(
% 0.07/0.26 ! [X0 : rat,X1 : rat] : (($true = ((is @ X1 @ X0))) | (((more @ X1 @ X0)) = $true) | (((less @ X1 @ X0)) = $true))),
% 0.07/0.26 inference(flattening,[],[f20])).
% 0.07/0.26 thf(f23,plain,(
% 0.07/0.26 (((is @ x0 @ y0)) != $true)),
% 0.07/0.26 inference(cnf_transformation,[],[f18])).
% 0.07/0.26 thf(f24,plain,(
% 0.07/0.26 (((less @ x0 @ y0)) != $true)),
% 0.07/0.26 inference(cnf_transformation,[],[f18])).
% 0.07/0.26 thf(f25,plain,(
% 0.07/0.26 (((more @ x0 @ y0)) != $true)),
% 0.07/0.26 inference(cnf_transformation,[],[f14])).
% 0.07/0.26 thf(f26,plain,(
% 0.07/0.26 ( ! [X0 : rat,X1 : rat] : ((((more @ X1 @ X0)) = $true) | (((less @ X1 @ X0)) = $true) | ($true = ((is @ X1 @ X0)))) )),
% 0.07/0.26 inference(cnf_transformation,[],[f21])).
% 0.07/0.26 thf(f28,definition,(
% 0.07/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.26 thf(f32,plain,(
% 0.07/0.26 (((is @ x0 @ y0)) = $false) | ($true != $true)),
% 0.07/0.26 inference(constrained_superposition,[],[f23,f28])).
% 0.07/0.26 thf(f33,plain,(
% 0.07/0.26 ($true != $true) | (((less @ x0 @ y0)) = $false)),
% 0.07/0.26 inference(constrained_superposition,[],[f24,f28])).
% 0.07/0.26 thf(f34,plain,(
% 0.07/0.26 ($true != $true) | (((more @ x0 @ y0)) = $false)),
% 0.07/0.26 inference(constrained_superposition,[],[f25,f28])).
% 0.07/0.26 thf(f36,plain,(
% 0.07/0.26 (((more @ x0 @ y0)) = $false)),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f34])).
% 0.07/0.26 thf(f37,plain,(
% 0.07/0.26 (((is @ x0 @ y0)) = $false)),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f32])).
% 0.07/0.26 thf(f38,plain,(
% 0.07/0.26 (((less @ x0 @ y0)) = $false)),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f33])).
% 0.07/0.26 thf(f51,plain,(
% 0.07/0.26 (((is @ x0 @ y0)) = $true) | (((less @ x0 @ y0)) = $true) | ($false = $true)),
% 0.07/0.26 inference(constrained_superposition,[],[f36,f26])).
% 0.07/0.26 thf(f53,plain,(
% 0.07/0.26 (((less @ x0 @ y0)) = $true) | (((is @ x0 @ y0)) = $true)),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f51])).
% 0.07/0.26 thf(f56,plain,(
% 0.07/0.26 ($false = $true) | (((is @ x0 @ y0)) = $true)),
% 0.07/0.26 inference(forward_demodulation,[],[f53,f38])).
% 0.07/0.26 thf(f57,plain,(
% 0.07/0.26 (((is @ x0 @ y0)) = $true)),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f56])).
% 0.07/0.26 thf(f60,plain,(
% 0.07/0.26 ($false = $true)),
% 0.07/0.26 inference(forward_demodulation,[],[f57,f37])).
% 0.07/0.26 thf(f61,plain,(
% 0.07/0.26 $false),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f60])).
% 0.07/0.26 % SZS output end Proof for theBenchmark
% 0.07/0.26 % (3317959)------------------------------
% 0.07/0.26 % (3317959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3317959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3317959)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3317959)Termination reason: Refutation
% 0.07/0.26 % (3317959)Time elapsed: 0.002 s
% 0.07/0.26 % (3317959)Peak memory usage: 12 MB
% 0.07/0.26 % (3317959)Instructions burned: 3 (million)
% 0.07/0.26 % (3317949)Success in time 0.025 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------