%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV076^5 : 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 : n007.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 08:37:36 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV076^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n007.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 15:04:42 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.24/0.29 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
% 0.24/0.33 % (3479521)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.33 % (3479528)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2734471740:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.33 % (3479528) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3479521-3479528"...
% 0.24/0.33 % (3479528)...printing done.
% 0.24/0.33 % (3479528)Refutation found. Thanks to Tanya!
% 0.24/0.33 % SZS status Theorem for theBenchmark
% 0.24/0.33 % SZS output start Proof for theBenchmark
% 0.24/0.33 thf(type_def_5, type, a: $tType).
% 0.24/0.33 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.33 thf(func_def_3, type, sK0: ((a > $o) > a)).
% 0.24/0.33 thf(func_def_4, type, sK1: (a > a > $o)).
% 0.24/0.33 thf(func_def_5, type, sK2: (a > (a > $o) > a)).
% 0.24/0.33 thf(func_def_6, type, sK3: (a > $o)).
% 0.24/0.33 thf(func_def_7, type, sK4: (a > a)).
% 0.24/0.33 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.24/0.33 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.33 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.33 thf(f1,conjecture,(
% 0.24/0.33 ! [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,X3 : a,X4 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4))) => ! [X5 : (a > $o)] : ? [X8 : a] : ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ X8)))),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM401B_pme)).
% 0.24/0.33 thf(f2,negated_conjecture,(
% 0.24/0.33 ~ ! [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,X3 : a,X4 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4))) => ! [X5 : (a > $o)] : ? [X8 : a] : ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ X8)))),
% 0.24/0.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.33 thf(f3,plain,(
% 0.24/0.33 ~ ! [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 @ X6 @ X7) & (X1 @ X7 @ X8)) => (X1 @ X6 @ X8))) => ! [X9 : (a > $o)] : ? [X10 : a] : ! [X11 : a] : ((X9 @ X11) => (X1 @ X11 @ X10)))),
% 0.24/0.33 inference(rectify,[],[f2])).
% 0.24/0.33 thf(f4,plain,(
% 0.24/0.33 ~ ! [X1 : (a > a > $o),X0 : ((a > $o) > a)] : ((! [X8 : a,X6 : a,X7 : a] : ((($true = ((X1 @ X6 @ X7))) & ($true = ((X1 @ X7 @ X8)))) => ($true = ((X1 @ X6 @ X8)))) & ! [X2 : (a > $o)] : (! [X3 : a] : (! [X4 : a] : (($true = ((X2 @ X4))) => ($true = ((X1 @ X4 @ X3)))) => ($true = ((X1 @ (X0 @ X2) @ X3)))) & ! [X5 : a] : (($true = ((X2 @ X5))) => ($true = ((X1 @ X5 @ (X0 @ X2))))))) => ! [X9 : (a > $o)] : ? [X10 : a] : ! [X11 : a] : (($true = ((X9 @ X11))) => (((X1 @ X11 @ X10)) = $true)))),
% 0.24/0.33 inference(fool_elimination,[],[f3])).
% 0.24/0.33 thf(f5,plain,(
% 0.24/0.33 ? [X1 : (a > a > $o),X0 : ((a > $o) > a)] : (? [X9 : (a > $o)] : ! [X10 : a] : ? [X11 : a] : ((((X1 @ X11 @ X10)) != $true) & ($true = ((X9 @ X11)))) & (! [X8 : a,X6 : a,X7 : a] : (($true = ((X1 @ X6 @ X8))) | (($true != ((X1 @ X6 @ X7))) | ($true != ((X1 @ X7 @ X8))))) & ! [X2 : (a > $o)] : (! [X5 : a] : (($true != ((X2 @ X5))) | ($true = ((X1 @ X5 @ (X0 @ X2))))) & ! [X3 : a] : (? [X4 : a] : (($true = ((X2 @ X4))) & ($true != ((X1 @ X4 @ X3)))) | ($true = ((X1 @ (X0 @ X2) @ X3)))))))),
% 0.24/0.33 inference(ennf_transformation,[],[f4])).
% 0.24/0.33 thf(f6,plain,(
% 0.24/0.33 ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (! [X2 : (a > $o)] : (! [X5 : a] : (($true != ((X2 @ X5))) | ($true = ((X1 @ X5 @ (X0 @ X2))))) & ! [X3 : a] : (? [X4 : a] : (($true = ((X2 @ X4))) & ($true != ((X1 @ X4 @ X3)))) | ($true = ((X1 @ (X0 @ X2) @ X3))))) & ! [X7 : a,X6 : a,X8 : a] : (($true != ((X1 @ X7 @ X8))) | ($true = ((X1 @ X6 @ X8))) | ($true != ((X1 @ X6 @ X7)))) & ? [X9 : (a > $o)] : ! [X10 : a] : ? [X11 : a] : ((((X1 @ X11 @ X10)) != $true) & ($true = ((X9 @ X11)))))),
% 0.24/0.33 inference(flattening,[],[f5])).
% 0.24/0.33 thf(f7,plain,(
% 0.24/0.33 ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (! [X2 : (a > $o)] : (! [X3 : a] : (($true != ((X2 @ X3))) | ($true = ((X1 @ X3 @ (X0 @ X2))))) & ! [X4 : a] : (? [X5 : a] : (($true = ((X2 @ X5))) & (((X1 @ X5 @ X4)) != $true)) | ($true = ((X1 @ (X0 @ X2) @ X4))))) & ! [X6 : a,X7 : a,X8 : a] : (($true != ((X1 @ X6 @ X8))) | ($true = ((X1 @ X7 @ X8))) | ($true != ((X1 @ X7 @ X6)))) & ? [X9 : (a > $o)] : ! [X10 : a] : ? [X11 : a] : ((((X1 @ X11 @ X10)) != $true) & ($true = ((X9 @ X11)))))),
% 0.24/0.33 inference(rectify,[],[f6])).
% 0.24/0.33 thf(f8,plain,(
% 0.24/0.33 ! [X2 : (a > $o)] : (! [X3 : a] : (($true != ((X2 @ X3))) | ($true = ((sK1 @ X3 @ (sK0 @ X2))))) & ! [X4 : a] : ((($true = ((X2 @ (sK2 @ X4 @ X2)))) & ($true != ((sK1 @ (sK2 @ X4 @ X2) @ X4)))) | ($true = ((sK1 @ (sK0 @ X2) @ X4))))) & ! [X6 : a,X7 : a,X8 : a] : (($true != ((sK1 @ X6 @ X8))) | ($true = ((sK1 @ X7 @ X8))) | ($true != ((sK1 @ X7 @ X6)))) & ! [X10 : a] : (($true != ((sK1 @ (sK4 @ X10) @ X10))) & (((sK3 @ (sK4 @ X10))) = $true))),
% 0.24/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X11,sK4 @ X10),skolemize(X9,sK3),skolemize(X11,sK4 @ X10)],[f7])).
% 0.24/0.33 thf(f10,plain,(
% 0.24/0.33 ( ! [X10 : a] : (($true != ((sK1 @ (sK4 @ X10) @ X10)))) )),
% 0.24/0.33 inference(cnf_transformation,[],[f8])).
% 0.24/0.33 thf(f14,plain,(
% 0.24/0.33 ( ! [X2 : (a > $o),X3 : a] : (($true != ((X2 @ X3))) | ($true = ((sK1 @ X3 @ (sK0 @ X2))))) )),
% 0.24/0.33 inference(cnf_transformation,[],[f8])).
% 0.24/0.33 thf(f20,plain,(
% 0.24/0.33 ( ! [X3 : a] : (($true != (((^[Y0 : a]: ($true)) @ X3))) | ($true = ((sK1 @ X3 @ (sK0 @ (^[Y0 : a]: ($true))))))) )),
% 0.24/0.33 inference(imitation,[],[f14])).
% 0.24/0.33 thf(f22,plain,(
% 0.24/0.33 ( ! [X3 : a] : (($true != $true) | ($true = ((sK1 @ X3 @ (sK0 @ (^[Y0 : a]: ($true))))))) )),
% 0.24/0.33 inference(beta-eta_normalization,[],[f20])).
% 0.24/0.33 thf(f23,plain,(
% 0.24/0.33 ( ! [X3 : a] : (($true = ((sK1 @ X3 @ (sK0 @ (^[Y0 : a]: ($true))))))) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f22])).
% 0.24/0.33 thf(f29,plain,(
% 0.24/0.33 ($true != $true)),
% 0.24/0.33 inference(constrained_superposition,[],[f10,f23])).
% 0.24/0.33 thf(f32,plain,(
% 0.24/0.33 $false),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f29])).
% 0.24/0.33 % SZS output end Proof for theBenchmark
% 0.24/0.33 % (3479528)------------------------------
% 0.24/0.33 % (3479528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (3479528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (3479528)CaDiCaL version: 2.1.3
% 0.24/0.33 % (3479528)Termination reason: Refutation
% 0.24/0.33 % (3479528)Time elapsed: 0.003 s
% 0.24/0.33 % (3479528)Peak memory usage: 12 MB
% 0.24/0.33 % (3479528)Instructions burned: 3 (million)
% 0.24/0.33 % (3479521)Success in time 0.025 s
% 0.24/0.33 % Vampire exiting
%------------------------------------------------------------------------------