%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN996^1 : 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 : n020.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 08:41:47 AM UTC 2026
% Result : Theorem 0.25s 0.37s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN996^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n020.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 16:21:19 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.25/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running higher-order theorem proving
% 0.25/0.33 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
% 0.25/0.37 % (1243238)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.37 % (1243244)lrs+10_16_si=on:nwc=1.5:random_seed=2878080464:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.37 % (1243244) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1243238-1243244"...
% 0.25/0.37 % (1243244)...printing done.
% 0.25/0.37 % (1243244)Refutation found. Thanks to Tanya!
% 0.25/0.37 % SZS status Theorem for theBenchmark
% 0.25/0.37 % SZS output start Proof for theBenchmark
% 0.25/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.37 thf(func_def_0, type, r: ($i > $i > $o)).
% 0.25/0.37 thf(func_def_4, type, sK0: (($i > $i) > $i)).
% 0.25/0.37 thf(func_def_5, type, sK1: ($i > $i)).
% 0.25/0.37 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.25/0.37 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.25/0.37 thf(f1,conjecture,(
% 0.25/0.37 ! [X0 : $i] : ? [X1 : $i] : (r @ X0 @ X1) => ? [X2 : ($i > $i)] : ! [X0 : $i] : (r @ X0 @ (X2 @ X0))),
% 0.25/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.25/0.37 thf(f2,negated_conjecture,(
% 0.25/0.37 ~(! [X0 : $i] : ? [X1 : $i] : (r @ X0 @ X1) => ? [X2 : ($i > $i)] : ! [X0 : $i] : (r @ X0 @ (X2 @ X0)))),
% 0.25/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/0.38 thf(f3,plain,(
% 0.25/0.38 ~(! [X0 : $i] : ? [X1 : $i] : (r @ X0 @ X1) => ? [X2 : ($i > $i)] : ! [X3 : $i] : (r @ X3 @ (X2 @ X3)))),
% 0.25/0.38 inference(rectify,[],[f2])).
% 0.25/0.38 thf(f4,plain,(
% 0.25/0.38 ~(! [X0 : $i] : ? [X1 : $i] : (((r @ X0 @ X1)) = $true) => ? [X2 : ($i > $i)] : ! [X3 : $i] : ($true = ((r @ X3 @ (X2 @ X3)))))),
% 0.25/0.38 inference(fool_elimination,[],[f3])).
% 0.25/0.38 thf(f5,plain,(
% 0.25/0.38 ! [X2 : ($i > $i)] : ? [X3 : $i] : ($true != ((r @ X3 @ (X2 @ X3)))) & ! [X0 : $i] : ? [X1 : $i] : (((r @ X0 @ X1)) = $true)),
% 0.25/0.38 inference(ennf_transformation,[],[f4])).
% 0.25/0.38 thf(f6,plain,(
% 0.25/0.38 ! [X0 : ($i > $i)] : ? [X1 : $i] : (((r @ X1 @ (X0 @ X1))) != $true) & ! [X2 : $i] : ? [X3 : $i] : (((r @ X2 @ X3)) = $true)),
% 0.25/0.38 inference(rectify,[],[f5])).
% 0.25/0.38 thf(f7,plain,(
% 0.25/0.38 ! [X0 : ($i > $i)] : (((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))) != $true) & ! [X2 : $i] : ($true = ((r @ X2 @ (sK1 @ X2))))),
% 0.25/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK1 @ X2),skolemize(X3,sK1 @ X2)],[f6])).
% 0.25/0.38 thf(f8,plain,(
% 0.25/0.38 ( ! [X2 : $i] : (($true = ((r @ X2 @ (sK1 @ X2))))) )),
% 0.25/0.38 inference(cnf_transformation,[],[f7])).
% 0.25/0.38 thf(f9,plain,(
% 0.25/0.38 ( ! [X0 : ($i > $i)] : ((((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))) != $true)) )),
% 0.25/0.38 inference(cnf_transformation,[],[f7])).
% 0.25/0.38 thf(f12,plain,(
% 0.25/0.38 ($true != $true) | ((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0))) != sK1)),
% 0.25/0.38 inference(constrained_superposition,[],[f9,f8])).
% 0.25/0.38 thf(f14,plain,(
% 0.25/0.38 ((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0))) != sK1)),
% 0.25/0.38 inference(trivial_inequality_removal,[],[f12])).
% 0.25/0.38 thf(f15,plain,(
% 0.25/0.38 (sK1 != sK1)),
% 0.25/0.38 inference(beta-eta_normalization,[],[f14])).
% 0.25/0.38 thf(f16,plain,(
% 0.25/0.38 $false),
% 0.25/0.38 inference(trivial_inequality_removal,[],[f15])).
% 0.25/0.38 % SZS output end Proof for theBenchmark
% 0.25/0.38 % (1243244)------------------------------
% 0.25/0.38 % (1243244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (1243244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (1243244)CaDiCaL version: 2.1.3
% 0.25/0.38 % (1243244)Termination reason: Refutation
% 0.25/0.38 % (1243244)Time elapsed: 0.002 s
% 0.25/0.38 % (1243244)Peak memory usage: 12 MB
% 0.25/0.38 % (1243244)Instructions burned: 1 (million)
% 0.25/0.38 % (1243238)Success in time 0.026 s
% 0.25/0.38 % Vampire exiting
%------------------------------------------------------------------------------