%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV088^5 : 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 : n014.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 08:37:37 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV088^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:07:00 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
% 0.23/0.28 % (2782318)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (2782325)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3063651415:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.28 % (2782325) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2782318-2782325"...
% 0.23/0.28 % (2782325)...printing done.
% 0.23/0.28 % (2782325)Refutation found. Thanks to Tanya!
% 0.23/0.28 % SZS status Theorem for theBenchmark
% 0.23/0.28 % SZS output start Proof for theBenchmark
% 0.23/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.28 thf(func_def_3, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.28 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.23/0.28 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.28 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.28 thf(func_def_7, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.28 thf(func_def_8, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.23/0.28 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.23/0.28 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.28 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.28 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.28 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.28 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.28 thf(f1,conjecture,(
% 0.23/0.28 ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X3 : ($i > $o),X2 : ($i > $o),X4 : ($i > $o)] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))) & ! [X2 : ($i > $o),X5 : $i] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)))),
% 0.23/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120G_pme)).
% 0.23/0.28 thf(f2,negated_conjecture,(
% 0.23/0.28 ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X3 : ($i > $o),X2 : ($i > $o),X4 : ($i > $o)] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))) & ! [X2 : ($i > $o),X5 : $i] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)))),
% 0.23/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.28 thf(f3,plain,(
% 0.23/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((! [X5 : $i] : ((X0 @ X3 @ X2 @ X5) | (X1 @ X3 @ X2 @ X5)) & ! [X6 : $i] : ((X1 @ X2 @ X4 @ X6) | (X0 @ X2 @ X4 @ X6))) => ! [X7 : $i] : ((X1 @ X3 @ X4 @ X7) | (X0 @ X3 @ X4 @ X7))) & ! [X8 : ($i > $o),X9 : $i] : ((X1 @ X8 @ X8 @ X9) | (X0 @ X8 @ X8 @ X9)))),
% 0.23/0.28 inference(rectify,[],[f2])).
% 0.23/0.28 thf(f4,plain,(
% 0.23/0.28 ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((! [X6 : $i] : (($true = ((X0 @ X2 @ X4 @ X6))) | ($true = ((X1 @ X2 @ X4 @ X6)))) & ! [X5 : $i] : ((((X1 @ X3 @ X2 @ X5)) = $true) | ($true = ((X0 @ X3 @ X2 @ X5))))) => ! [X7 : $i] : ((((X1 @ X3 @ X4 @ X7)) = $true) | ($true = ((X0 @ X3 @ X4 @ X7))))) & ! [X9 : $i,X8 : ($i > $o)] : (($true = ((X0 @ X8 @ X8 @ X9))) | ($true = ((X1 @ X8 @ X8 @ X9)))))),
% 0.23/0.28 inference(fool_elimination,[],[f3])).
% 0.23/0.28 thf(f5,plain,(
% 0.23/0.28 ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : (? [X7 : $i] : (($true != ((X0 @ X3 @ X4 @ X7))) & (((X1 @ X3 @ X4 @ X7)) != $true)) & (! [X6 : $i] : (($true = ((X0 @ X2 @ X4 @ X6))) | ($true = ((X1 @ X2 @ X4 @ X6)))) & ! [X5 : $i] : ((((X1 @ X3 @ X2 @ X5)) = $true) | ($true = ((X0 @ X3 @ X2 @ X5)))))) | ? [X8 : ($i > $o),X9 : $i] : (($true != ((X0 @ X8 @ X8 @ X9))) & ($true != ((X1 @ X8 @ X8 @ X9)))))),
% 0.23/0.28 inference(ennf_transformation,[],[f4])).
% 0.23/0.28 thf(f6,plain,(
% 0.23/0.28 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X8 : ($i > $o),X9 : $i] : (($true != ((X0 @ X8 @ X8 @ X9))) & ($true != ((X1 @ X8 @ X8 @ X9)))) | ? [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : (! [X6 : $i] : (($true = ((X0 @ X2 @ X4 @ X6))) | ($true = ((X1 @ X2 @ X4 @ X6)))) & ! [X5 : $i] : ((((X1 @ X3 @ X2 @ X5)) = $true) | ($true = ((X0 @ X3 @ X2 @ X5)))) & ? [X7 : $i] : (($true != ((X0 @ X3 @ X4 @ X7))) & (((X1 @ X3 @ X4 @ X7)) != $true))))),
% 0.23/0.28 inference(flattening,[],[f5])).
% 0.23/0.28 thf(f7,plain,(
% 0.23/0.28 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : $i] : (($true != ((X0 @ X2 @ X2 @ X3))) & ($true != ((X1 @ X2 @ X2 @ X3)))) | ? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (! [X7 : $i] : (($true = ((X0 @ X4 @ X5 @ X7))) | (((X1 @ X4 @ X5 @ X7)) = $true)) & ! [X8 : $i] : (($true = ((X1 @ X6 @ X4 @ X8))) | ($true = ((X0 @ X6 @ X4 @ X8)))) & ? [X9 : $i] : (($true != ((X0 @ X6 @ X5 @ X9))) & (((X1 @ X6 @ X5 @ X9)) != $true))))),
% 0.23/0.28 inference(rectify,[],[f6])).
% 0.23/0.28 thf(f8,plain,(
% 0.23/0.28 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (((((X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) != $true) & ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))))) | (! [X7 : $i] : (($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7)))) & ! [X8 : $i] : (($true = ((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) | (((X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8)) = $true)) & ((((X0 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) & ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)))))))),
% 0.23/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0)],[f7])).
% 0.23/0.28 thf(f9,plain,(
% 0.23/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))))) )),
% 0.23/0.28 inference(cnf_transformation,[],[f8])).
% 0.23/0.28 thf(f24,plain,(
% 0.23/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o)] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ X0))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ X0))) != $true)) )),
% 0.23/0.28 inference(imitation,[],[f9])).
% 0.23/0.28 thf(f33,plain,(
% 0.23/0.28 ($true != $true) | ($true != $true)),
% 0.23/0.28 inference(beta-eta_normalization,[],[f24])).
% 0.23/0.28 thf(f34,plain,(
% 0.23/0.28 ($true != $true)),
% 0.23/0.28 inference(duplicate_literal_removal,[],[f33])).
% 0.23/0.28 thf(f35,plain,(
% 0.23/0.28 $false),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f34])).
% 0.23/0.28 % SZS output end Proof for theBenchmark
% 0.23/0.28 % (2782325)------------------------------
% 0.23/0.28 % (2782325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (2782325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (2782325)CaDiCaL version: 2.1.3
% 0.23/0.28 % (2782325)Termination reason: Refutation
% 0.23/0.28 % (2782325)Time elapsed: 0.002 s
% 0.23/0.28 % (2782325)Peak memory usage: 12 MB
% 0.23/0.28 % (2782325)Instructions burned: 7 (million)
% 0.23/0.28 % (2782318)Success in time 0.032 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------