%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO552^1 : 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 : n017.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 08:48:24 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO552^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:09:52 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.26 % (624610)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (624617)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1901591017:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.26 % (624617) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-624610-624617"...
% 0.19/0.26 % (624617)...printing done.
% 0.19/0.26 % (624617)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% 0.19/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.26 thf(func_def_1, type, sK0: (($i > $i > $i) > $i)).
% 0.19/0.26 thf(func_def_2, type, sK1: (($i > $i > $i) > $i)).
% 0.19/0.26 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_4, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_5, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.26 thf(f1,conjecture,(
% 0.19/0.26 ? [X0 : ($i > $i > $i)] : ! [X1 : $i,X2 : $i] : (((X0 @ X1 @ X2)) = X1)),
% 0.19/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim)).
% 0.19/0.26 thf(f2,negated_conjecture,(
% 0.19/0.26 ~ ? [X0 : ($i > $i > $i)] : ! [X1 : $i,X2 : $i] : (((X0 @ X1 @ X2)) = X1)),
% 0.19/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.26 thf(f3,plain,(
% 0.19/0.26 ~ ? [X0 : ($i > $i > $i)] : ! [X2 : $i,X1 : $i] : (((X0 @ X1 @ X2)) = X1)),
% 0.19/0.26 inference(fool_elimination,[],[f2])).
% 0.19/0.26 thf(f4,plain,(
% 0.19/0.26 ! [X0 : ($i > $i > $i)] : ? [X2 : $i,X1 : $i] : (((X0 @ X1 @ X2)) != X1)),
% 0.19/0.26 inference(ennf_transformation,[],[f3])).
% 0.19/0.26 thf(f5,plain,(
% 0.19/0.26 ! [X0 : ($i > $i > $i)] : ? [X1 : $i,X2 : $i] : (((X0 @ X2 @ X1)) != X2)),
% 0.19/0.26 inference(rectify,[],[f4])).
% 0.19/0.26 thf(f6,plain,(
% 0.19/0.26 ! [X0 : ($i > $i > $i)] : (((sK1 @ X0)) != ((X0 @ (sK1 @ X0) @ (sK0 @ X0))))),
% 0.19/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f5])).
% 0.19/0.26 thf(f7,plain,(
% 0.19/0.26 ( ! [X0 : ($i > $i > $i)] : ((((sK1 @ X0)) != ((X0 @ (sK1 @ X0) @ (sK0 @ X0))))) )),
% 0.19/0.26 inference(cnf_transformation,[],[f6])).
% 0.19/0.26 thf(f9,plain,(
% 0.19/0.26 ((((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0))))) @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0))))))) != ((sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))))))),
% 0.19/0.27 inference(projection,[],[f7])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 (((sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))))) != ((sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))))))),
% 0.19/0.27 inference(beta-eta_normalization,[],[f9])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f10])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (624617)------------------------------
% 0.19/0.27 % (624617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (624617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (624617)CaDiCaL version: 2.1.3
% 0.19/0.27 % (624617)Termination reason: Refutation
% 0.19/0.27 % (624617)Time elapsed: 0.001 s
% 0.19/0.27 % (624617)Peak memory usage: 12 MB
% 0.19/0.27 % (624610)Success in time 0.023 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------