%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO527^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:48:11 AM UTC 2026
% Result : Theorem 0.17s 0.26s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO527^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n016.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 17:17:50 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.22 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
% 0.17/0.26 % (639654)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.17/0.26 % (639660)lrs+10_16_si=on:nwc=1.5:random_seed=3098850177:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.17/0.26 % (639660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-639654-639660"...
% 0.17/0.26 % (639660)...printing done.
% 0.17/0.26 % (639660)Refutation found. Thanks to Tanya!
% 0.17/0.26 % SZS status Theorem for theBenchmark
% 0.17/0.26 % SZS output start Proof for theBenchmark
% 0.17/0.26 thf(type_def_5, type, a: $tType).
% 0.17/0.26 thf(type_def_6, type, b: $tType).
% 0.17/0.26 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.17/0.26 thf(func_def_0, type, r: (a > b > $o)).
% 0.17/0.26 thf(func_def_4, type, sK0: (a > b)).
% 0.17/0.26 thf(func_def_5, type, sK1: ((a > b) > a)).
% 0.17/0.26 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.17/0.26 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.17/0.26 thf(f1,axiom,(
% 0.17/0.26 ! [X0 : a] : ? [X1 : b] : (r @ X0 @ X1)),
% 0.17/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rtotal)).
% 0.17/0.26 thf(f2,conjecture,(
% 0.17/0.26 ? [X0 : (a > b)] : ! [X1 : a] : (r @ X1 @ (X0 @ X1))),
% 0.17/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',skolem)).
% 0.17/0.26 thf(f3,negated_conjecture,(
% 0.17/0.26 ~ ? [X0 : (a > b)] : ! [X1 : a] : (r @ X1 @ (X0 @ X1))),
% 0.17/0.26 inference(negated_conjecture,[status(cth)],[f2])).
% 0.17/0.26 thf(f4,plain,(
% 0.17/0.26 ~ ? [X0 : (a > b)] : ! [X1 : a] : (r @ X1 @ (X0 @ X1))),
% 0.17/0.26 inference(rectify,[],[f3])).
% 0.17/0.26 thf(f5,plain,(
% 0.17/0.26 ~ ? [X0 : (a > b)] : ! [X1 : a] : (((r @ X1 @ (X0 @ X1))) = $true)),
% 0.17/0.26 inference(fool_elimination,[],[f4])).
% 0.17/0.26 thf(f6,plain,(
% 0.17/0.26 ! [X0 : a] : ? [X1 : b] : (r @ X0 @ X1)),
% 0.17/0.26 inference(rectify,[],[f1])).
% 0.17/0.26 thf(f7,plain,(
% 0.17/0.26 ! [X0 : a] : ? [X1 : b] : (((r @ X0 @ X1)) = $true)),
% 0.17/0.26 inference(fool_elimination,[],[f6])).
% 0.17/0.26 thf(f8,plain,(
% 0.17/0.26 ! [X0 : (a > b)] : ? [X1 : a] : (((r @ X1 @ (X0 @ X1))) != $true)),
% 0.17/0.26 inference(ennf_transformation,[],[f5])).
% 0.17/0.26 thf(f9,plain,(
% 0.17/0.26 ! [X0 : a] : ($true = ((r @ X0 @ (sK0 @ X0))))),
% 0.17/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f7])).
% 0.17/0.26 thf(f10,plain,(
% 0.17/0.26 ! [X0 : (a > b)] : (((r @ (sK1 @ X0) @ (X0 @ (sK1 @ X0)))) != $true)),
% 0.17/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f8])).
% 0.17/0.26 thf(f11,plain,(
% 0.17/0.26 ( ! [X0 : a] : (($true = ((r @ X0 @ (sK0 @ X0))))) )),
% 0.17/0.26 inference(cnf_transformation,[],[f9])).
% 0.17/0.26 thf(f12,plain,(
% 0.17/0.26 ( ! [X0 : (a > b)] : ((((r @ (sK1 @ X0) @ (X0 @ (sK1 @ X0)))) != $true)) )),
% 0.17/0.26 inference(cnf_transformation,[],[f10])).
% 0.17/0.26 thf(f15,plain,(
% 0.17/0.26 ($true != $true) | ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))) != sK0)),
% 0.17/0.26 inference(constrained_superposition,[],[f12,f11])).
% 0.17/0.26 thf(f17,plain,(
% 0.17/0.26 ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))) != sK0)),
% 0.17/0.26 inference(trivial_inequality_removal,[],[f15])).
% 0.17/0.26 thf(f18,plain,(
% 0.17/0.26 (sK0 != sK0)),
% 0.17/0.26 inference(beta-eta_normalization,[],[f17])).
% 0.17/0.26 thf(f19,plain,(
% 0.17/0.26 $false),
% 0.17/0.26 inference(trivial_inequality_removal,[],[f18])).
% 0.17/0.26 % SZS output end Proof for theBenchmark
% 0.17/0.26 % (639660)------------------------------
% 0.17/0.26 % (639660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.26 % (639660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.26 % (639660)CaDiCaL version: 2.1.3
% 0.17/0.26 % (639660)Termination reason: Refutation
% 0.17/0.26 % (639660)Time elapsed: 0.001 s
% 0.17/0.26 % (639660)Peak memory usage: 12 MB
% 0.17/0.26 % (639660)Instructions burned: 1 (million)
% 0.17/0.26 % (639654)Success in time 0.032 s
% 0.17/0.26 % Vampire exiting
%------------------------------------------------------------------------------