%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV054^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:37:33 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV054^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:08:28 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
% 0.08/0.24 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
% 0.21/0.28 % (715679)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (715685)lrs+10_16_si=on:nwc=1.5:random_seed=1248200702:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (715685) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-715679-715685"...
% 0.21/0.28 % (715685)...printing done.
% 0.21/0.28 % (715685)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, a: $tType).
% 0.21/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_3, type, sK0: ((a > $o) > a)).
% 0.21/0.28 thf(func_def_4, type, sK1: (a > a > $o)).
% 0.21/0.28 thf(func_def_5, type, sK2: (a > (a > $o) > a)).
% 0.21/0.28 thf(func_def_6, type, sK3: (a > a)).
% 0.21/0.28 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ! [X1 : ((a > $o) > a),X0 : (a > a > $o)] : ((! [X5 : (a > $o)] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)) & ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5)))) & ! [X2 : a,X4 : a,X3 : a] : (((X0 @ X3 @ X4) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X4))) => ! [X8 : (a > a)] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ (X8 @ X9) @ X9)))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM403_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ ! [X1 : ((a > $o) > a),X0 : (a > a > $o)] : ((! [X5 : (a > $o)] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)) & ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5)))) & ! [X2 : a,X4 : a,X3 : a] : (((X0 @ X3 @ X4) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X4))) => ! [X8 : (a > a)] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ (X8 @ X9) @ X9)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~ ! [X0 : ((a > $o) > a),X1 : (a > a > $o)] : ((! [X2 : (a > $o)] : (! [X3 : a] : (! [X4 : a] : ((X2 @ X4) => (X1 @ X4 @ X3)) => (X1 @ (X0 @ X2) @ X3)) & ! [X5 : a] : ((X2 @ X5) => (X1 @ X5 @ (X0 @ X2)))) & ! [X6 : a,X7 : a,X8 : a] : (((X1 @ X8 @ X7) & (X1 @ X6 @ X8)) => (X1 @ X6 @ X7))) => ! [X9 : (a > a)] : (! [X10 : a,X11 : a] : ((X1 @ X11 @ X10) => (X1 @ (X9 @ X11) @ (X9 @ X10))) => ? [X12 : a] : (X1 @ (X9 @ X12) @ X12)))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~ ! [X0 : ((a > $o) > a),X1 : (a > a > $o)] : ((! [X7 : a,X6 : a,X8 : a] : ((($true = ((X1 @ X6 @ X8))) & (((X1 @ X8 @ X7)) = $true)) => (((X1 @ X6 @ X7)) = $true)) & ! [X2 : (a > $o)] : (! [X5 : a] : ((((X2 @ X5)) = $true) => (((X1 @ X5 @ (X0 @ X2))) = $true)) & ! [X3 : a] : (! [X4 : a] : ((((X2 @ X4)) = $true) => (((X1 @ X4 @ X3)) = $true)) => (((X1 @ (X0 @ X2) @ X3)) = $true)))) => ! [X9 : (a > a)] : (! [X10 : a,X11 : a] : (($true = ((X1 @ X11 @ X10))) => (((X1 @ (X9 @ X11) @ (X9 @ X10))) = $true)) => ? [X12 : a] : (((X1 @ (X9 @ X12) @ X12)) = $true)))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (? [X9 : (a > a)] : (! [X12 : a] : (((X1 @ (X9 @ X12) @ X12)) != $true) & ! [X11 : a,X10 : a] : (($true != ((X1 @ X11 @ X10))) | (((X1 @ (X9 @ X11) @ (X9 @ X10))) = $true))) & (! [X7 : a,X6 : a,X8 : a] : ((((X1 @ X6 @ X7)) = $true) | (($true != ((X1 @ X6 @ X8))) | (((X1 @ X8 @ X7)) != $true))) & ! [X2 : (a > $o)] : (! [X5 : a] : ((((X2 @ X5)) != $true) | (((X1 @ X5 @ (X0 @ X2))) = $true)) & ! [X3 : a] : (? [X4 : a] : ((((X1 @ X4 @ X3)) != $true) & (((X2 @ X4)) = $true)) | (((X1 @ (X0 @ X2) @ X3)) = $true)))))),
% 0.21/0.28 inference(ennf_transformation,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (! [X2 : (a > $o)] : (! [X5 : a] : ((((X2 @ X5)) != $true) | (((X1 @ X5 @ (X0 @ X2))) = $true)) & ! [X3 : a] : (? [X4 : a] : ((((X1 @ X4 @ X3)) != $true) & (((X2 @ X4)) = $true)) | (((X1 @ (X0 @ X2) @ X3)) = $true))) & ? [X9 : (a > a)] : (! [X12 : a] : (((X1 @ (X9 @ X12) @ X12)) != $true) & ! [X11 : a,X10 : a] : (($true != ((X1 @ X11 @ X10))) | (((X1 @ (X9 @ X11) @ (X9 @ X10))) = $true))) & ! [X8 : a,X7 : a,X6 : a] : (($true != ((X1 @ X6 @ X8))) | (((X1 @ X8 @ X7)) != $true) | (((X1 @ X6 @ X7)) = $true)))),
% 0.21/0.28 inference(flattening,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (! [X2 : (a > $o)] : (! [X3 : a] : ((((X2 @ X3)) != $true) | ($true = ((X1 @ X3 @ (X0 @ X2))))) & ! [X4 : a] : (? [X5 : a] : ((((X1 @ X5 @ X4)) != $true) & (((X2 @ X5)) = $true)) | (((X1 @ (X0 @ X2) @ X4)) = $true))) & ? [X6 : (a > a)] : (! [X7 : a] : (((X1 @ (X6 @ X7) @ X7)) != $true) & ! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9)) != $true) | ($true = ((X1 @ (X6 @ X8) @ (X6 @ X9)))))) & ! [X10 : a,X11 : a,X12 : a] : (($true != ((X1 @ X12 @ X10))) | (((X1 @ X10 @ X11)) != $true) | ($true = ((X1 @ X12 @ X11)))))),
% 0.21/0.28 inference(rectify,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ! [X2 : (a > $o)] : (! [X3 : a] : ((((X2 @ X3)) != $true) | (((sK1 @ X3 @ (sK0 @ X2))) = $true)) & ! [X4 : a] : (((((sK1 @ (sK2 @ X4 @ X2) @ X4)) != $true) & (((X2 @ (sK2 @ X4 @ X2))) = $true)) | (((sK1 @ (sK0 @ X2) @ X4)) = $true))) & (! [X7 : a] : (((sK1 @ (sK3 @ X7) @ X7)) != $true) & ! [X8 : a,X9 : a] : ((((sK1 @ X8 @ X9)) != $true) | (((sK1 @ (sK3 @ X8) @ (sK3 @ X9))) = $true))) & ! [X10 : a,X11 : a,X12 : a] : ((((sK1 @ X12 @ X10)) != $true) | (((sK1 @ X10 @ X11)) != $true) | (((sK1 @ X12 @ X11)) = $true))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X2),skolemize(X6,sK3)],[f7])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ( ! [X7 : a] : ((((sK1 @ (sK3 @ X7) @ X7)) != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f8])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ( ! [X2 : (a > $o),X3 : a] : ((((X2 @ X3)) != $true) | (((sK1 @ X3 @ (sK0 @ X2))) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f8])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ( ! [X3 : a] : (($true = ((sK1 @ X3 @ (sK0 @ (^[Y0 : a]: ($true)))))) | ($true != (((^[Y0 : a]: ($true)) @ X3)))) )),
% 0.21/0.28 inference(primitive_instantiation,[],[f14])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ( ! [X3 : a] : (($true != $true) | ($true = ((sK1 @ X3 @ (sK0 @ (^[Y0 : a]: ($true))))))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f17])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 ( ! [X3 : a] : (($true = ((sK1 @ X3 @ (sK0 @ (^[Y0 : a]: ($true))))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f21])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 ($true != $true)),
% 0.21/0.28 inference(constrained_superposition,[],[f11,f22])).
% 0.21/0.28 thf(f29,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f26])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (715685)------------------------------
% 0.21/0.28 % (715685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (715685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (715685)CaDiCaL version: 2.1.3
% 0.21/0.28 % (715685)Termination reason: Refutation
% 0.21/0.28 % (715685)Time elapsed: 0.002 s
% 0.21/0.28 % (715685)Peak memory usage: 12 MB
% 0.21/0.28 % (715685)Instructions burned: 4 (million)
% 0.21/0.28 % (715679)Success in time 0.034 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------