%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO032^1 : 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 : 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 08:46:19 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO032^1 : 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 : n004.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 16:23:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 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
% 0.22/0.28 % (1504177)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1504186)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2020273225:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (1504186) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1504177-1504186"...
% 0.22/0.28 % (1504186)...printing done.
% 0.22/0.28 % (1504186)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_3, type, sK0: (($o > $o > $o) > $o)).
% 0.22/0.28 thf(func_def_4, type, sK1: (($o > $o > $o) > $o)).
% 0.22/0.28 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.22/0.28 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.28 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.28 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.28 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.28 thf(func_def_10, type, vOR: ($o > $o > $o)).
% 0.22/0.28 thf(func_def_11, type, vAND: ($o > $o > $o)).
% 0.22/0.28 thf(f1,conjecture,(
% 0.22/0.28 ? [X0 : ($o > $o > $o)] : ! [X1 : $o,X2 : $o] : ((X0 @ X1 @ X2) <=> (X1 | X2))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.22/0.28 thf(f2,negated_conjecture,(
% 0.22/0.28 ~ ? [X0 : ($o > $o > $o)] : ! [X1 : $o,X2 : $o] : ((X0 @ X1 @ X2) <=> (X1 | X2))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.28 thf(f3,plain,(
% 0.22/0.28 ~ ? [X0 : ($o > $o > $o)] : ! [X1 : $o,X2 : $o] : ((X0 @ X1 @ X2) <=> (X1 | X2))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f4,plain,(
% 0.22/0.28 ~ ? [X0 : ($o > $o > $o)] : ! [X2 : $o,X1 : $o] : ((((X0 @ X1 @ X2)) = $true) <=> (($true = X2) | ($true = X1)))),
% 0.22/0.28 inference(fool_elimination,[],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 ! [X0 : ($o > $o > $o)] : ? [X1 : $o,X2 : $o] : ((($true = X2) | ($true = X1)) <~> (((X0 @ X1 @ X2)) = $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 ! [X0 : ($o > $o > $o)] : ? [X1 : $o,X2 : $o] : (((((X0 @ X1 @ X2)) != $true) | (($true != X2) & ($true != X1))) & ((((X0 @ X1 @ X2)) = $true) | (($true = X2) | ($true = X1))))),
% 0.22/0.28 inference(nnf_transformation,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ! [X0 : ($o > $o > $o)] : ? [X1 : $o,X2 : $o] : (((((X0 @ X1 @ X2)) != $true) | (($true != X2) & ($true != X1))) & ((((X0 @ X1 @ X2)) = $true) | ($true = X2) | ($true = X1)))),
% 0.22/0.28 inference(flattening,[],[f6])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ! [X0 : ($o > $o > $o)] : ((($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (($true != ((sK1 @ X0))) & (((sK0 @ X0)) != $true))) & (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | ($true = ((sK1 @ X0))) | (((sK0 @ X0)) = $true)))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ( ! [X0 : ($o > $o > $o)] : (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (((sK0 @ X0)) = $true) | ($true = ((sK1 @ X0)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ( ! [X0 : ($o > $o > $o)] : (($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (((sK0 @ X0)) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ( ! [X0 : ($o > $o > $o)] : (($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | ($true != ((sK1 @ X0)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f85,plain,(
% 0.22/0.28 (((sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1)))))) = $true) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1)))) @ (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1))))) @ (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1)))))))) | (((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1)))))) = $true)),
% 0.22/0.28 inference(primitive_instantiation,[],[f9])).
% 0.22/0.28 thf(f100,plain,(
% 0.22/0.28 ($true = (((sK0 @ |) | (sK1 @ |)))) | ($true = ((sK0 @ |))) | (((sK1 @ |)) = $true)),
% 0.22/0.28 inference(beta-eta_normalization,[],[f85])).
% 0.22/0.28 thf(f101,plain,(
% 0.22/0.28 (((sK1 @ |)) = $true) | ($true = ((sK0 @ |))) | (((sK1 @ |)) = $true) | ($true = ((sK0 @ |)))),
% 0.22/0.28 inference(or_proxy_clausification,[],[f100])).
% 0.22/0.28 thf(f102,plain,(
% 0.22/0.28 ($true = ((sK0 @ |))) | (((sK1 @ |)) = $true)),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f101])).
% 0.22/0.28 thf(f138,plain,(
% 0.22/0.28 (((sK1 @ |)) = $true) | ((($true | (sK1 @ |))) != $true) | ($true != $true)),
% 0.22/0.28 inference(superposition,[],[f10,f102])).
% 0.22/0.28 thf(f140,plain,(
% 0.22/0.28 ($true != $true) | (((sK1 @ |)) = $true) | ($false = $true)),
% 0.22/0.28 inference(or_proxy_clausification,[],[f138])).
% 0.22/0.28 thf(f141,plain,(
% 0.22/0.28 (((sK1 @ |)) = $true)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f140])).
% 0.22/0.28 thf(f147,plain,(
% 0.22/0.28 ($true != $true) | ($true != (((sK0 @ |) | $true)))),
% 0.22/0.28 inference(superposition,[],[f11,f141])).
% 0.22/0.28 thf(f152,plain,(
% 0.22/0.28 ($true != $true) | ($false = $true)),
% 0.22/0.28 inference(or_proxy_clausification,[],[f147])).
% 0.22/0.28 thf(f155,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f152])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (1504186)------------------------------
% 0.22/0.28 % (1504186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1504186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1504186)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1504186)Termination reason: Refutation
% 0.22/0.28 % (1504186)Time elapsed: 0.002 s
% 0.22/0.28 % (1504186)Peak memory usage: 12 MB
% 0.22/0.28 % (1504186)Instructions burned: 6 (million)
% 0.22/0.28 % (1504177)Success in time 0.032 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------