%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV049^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:37:33 AM UTC 2026
% Result : Theorem 0.24s 0.37s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV049^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n017.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.24/0.27 % CPULimit : 300
% 0.24/0.27 % WCLimit : 300
% 0.24/0.27 % DateTime : Tue Sep 29 15:00:52 UTC 2026
% 0.24/0.27 % CPUTime :
% 0.24/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running higher-order theorem proving
% 0.24/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.37 % (436708)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.37 % (436718)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=122763771:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.37 % (436718) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-436708-436718"...
% 0.24/0.37 % (436718)...printing done.
% 0.24/0.37 % (436718)Refutation found. Thanks to Tanya!
% 0.24/0.37 % SZS status Theorem for theBenchmark
% 0.24/0.37 % SZS output start Proof for theBenchmark
% 0.24/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.37 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.37 thf(func_def_4, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.24/0.37 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.24/0.37 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.24/0.37 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.24/0.37 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.37 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.24/0.37 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.24/0.37 thf(f1,conjecture,(
% 0.24/0.37 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))) & ! [X2 : ($i > $o),X1 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))),
% 0.24/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120A_pme)).
% 0.24/0.37 thf(f2,negated_conjecture,(
% 0.24/0.37 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))) & ! [X2 : ($i > $o),X1 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))),
% 0.24/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.37 thf(f3,plain,(
% 0.24/0.37 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~(X0 @ (^[X1 : $i] : ($true)) @ (^[X2 : $i] : ($false))) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X4 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X4 @ X5)))),
% 0.24/0.37 inference(rectify,[],[f2])).
% 0.24/0.37 thf(f4,plain,(
% 0.24/0.37 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~ (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X4 @ X3)) = $true) & (((X0 @ X3 @ X5)) = $true)) => (((X0 @ X4 @ X5)) = $true)))),
% 0.24/0.37 inference(fool_elimination,[],[f3])).
% 0.24/0.37 thf(f5,plain,(
% 0.24/0.37 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~ (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) & ! [X3 : ($i > $o),X2 : ($i > $o),X1 : ($i > $o)] : (((((X0 @ X1 @ X3)) = $true) & (((X0 @ X2 @ X1)) = $true)) => (((X0 @ X2 @ X3)) = $true)))),
% 0.24/0.37 inference(rectify,[],[f4])).
% 0.24/0.37 thf(f6,plain,(
% 0.24/0.37 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X3 : ($i > $o),X2 : ($i > $o),X1 : ($i > $o)] : (((((X0 @ X1 @ X3)) = $true) & (((X0 @ X2 @ X1)) = $true)) => (((X0 @ X2 @ X3)) = $true)) & (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) != $true))),
% 0.24/0.37 inference(flattening,[],[f5])).
% 0.24/0.37 thf(f7,plain,(
% 0.24/0.37 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X3 : ($i > $o),X2 : ($i > $o),X1 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & ((((X0 @ X1 @ X3)) = $true) & (((X0 @ X2 @ X1)) = $true))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true))),
% 0.24/0.37 inference(ennf_transformation,[],[f6])).
% 0.24/0.37 thf(f8,plain,(
% 0.24/0.37 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ? [X2 : ($i > $o),X1 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & (((X0 @ X1 @ X3)) = $true) & (((X0 @ X2 @ X1)) = $true)))),
% 0.24/0.37 inference(flattening,[],[f7])).
% 0.24/0.37 thf(f9,plain,(
% 0.24/0.37 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) != $true) & (((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)))),
% 0.24/0.37 inference(rectify,[],[f8])).
% 0.24/0.37 thf(f10,plain,(
% 0.24/0.37 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ((((X0 @ (sK0 @ X0) @ (sK2 @ X0))) != $true) & (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $true) & (((X0 @ (sK0 @ X0) @ (sK1 @ X0))) = $true)))),
% 0.24/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK2 @ X0),skolemize(X3,sK2 @ X0),skolemize(X3,sK2 @ X0)],[f9])).
% 0.24/0.37 thf(f11,plain,(
% 0.24/0.37 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK0 @ X0) @ (sK1 @ X0))) = $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.24/0.37 inference(cnf_transformation,[],[f10])).
% 0.24/0.37 thf(f19,plain,(
% 0.24/0.37 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)),
% 0.24/0.37 inference(primitive_instantiation,[],[f11])).
% 0.24/0.37 thf(f29,plain,(
% 0.24/0.37 ($false = $true) | ($false = $true)),
% 0.24/0.37 inference(beta-eta_normalization,[],[f19])).
% 0.24/0.37 thf(f30,plain,(
% 0.24/0.37 ($false = $true)),
% 0.24/0.37 inference(duplicate_literal_removal,[],[f29])).
% 0.24/0.37 thf(f31,plain,(
% 0.24/0.37 $false),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f30])).
% 0.24/0.37 % SZS output end Proof for theBenchmark
% 0.24/0.37 % (436718)------------------------------
% 0.24/0.37 % (436718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (436718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (436718)CaDiCaL version: 2.1.3
% 0.24/0.37 % (436718)Termination reason: Refutation
% 0.24/0.37 % (436718)Time elapsed: 0.003 s
% 0.24/0.37 % (436718)Peak memory usage: 12 MB
% 0.24/0.37 % (436718)Instructions burned: 3 (million)
% 0.24/0.37 % (436708)Success in time 0.027 s
% 0.24/0.37 % Vampire exiting
%------------------------------------------------------------------------------