%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV228^5 : 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 : n015.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 08:38:04 AM UTC 2026
% Result : Theorem 0.10s 0.30s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV228^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:26:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.10/0.30 % (3657943)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.30 % (3657949)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1938304112:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.10/0.30 % (3657949) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3657943-3657949"...
% 0.10/0.30 % (3657949)...printing done.
% 0.10/0.30 % (3657952)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2599237554:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.10/0.30 % (3657949)Refutation found. Thanks to Tanya!
% 0.10/0.30 % SZS status Theorem for theBenchmark
% 0.10/0.30 % SZS output start Proof for theBenchmark
% 0.10/0.30 thf(type_def_5, type, a: $tType).
% 0.10/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.30 thf(func_def_0, type, cS: (a > $o)).
% 0.10/0.30 thf(func_def_4, type, sK0: a).
% 0.10/0.30 thf(func_def_5, type, sK1: ((a > $o) > a)).
% 0.10/0.30 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.10/0.30 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.10/0.30 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.10/0.30 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.10/0.30 thf(f1,conjecture,(
% 0.10/0.30 ! [X0 : a] : ((cS @ X0) => ? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : a] : ((X1 @ X2) => (cS @ X2))))),
% 0.10/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM91A_pme)).
% 0.10/0.30 thf(f2,negated_conjecture,(
% 0.10/0.30 ~ ! [X0 : a] : ((cS @ X0) => ? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : a] : ((X1 @ X2) => (cS @ X2))))),
% 0.10/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.30 thf(f3,plain,(
% 0.10/0.30 ~ ! [X0 : a] : ((cS @ X0) => ? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : a] : ((X1 @ X2) => (cS @ X2))))),
% 0.10/0.30 inference(rectify,[],[f2])).
% 0.10/0.30 thf(f4,plain,(
% 0.10/0.30 ~ ! [X0 : a] : ((((cS @ X0)) = $true) => ? [X1 : (a > $o)] : (! [X2 : a] : ((((X1 @ X2)) = $true) => (((cS @ X2)) = $true)) & (((X1 @ X0)) = $true)))),
% 0.10/0.30 inference(fool_elimination,[],[f3])).
% 0.10/0.30 thf(f5,plain,(
% 0.10/0.30 ? [X0 : a] : ((((cS @ X0)) = $true) & ! [X1 : (a > $o)] : (? [X2 : a] : ((((cS @ X2)) != $true) & (((X1 @ X2)) = $true)) | (((X1 @ X0)) != $true)))),
% 0.10/0.30 inference(ennf_transformation,[],[f4])).
% 0.10/0.30 thf(f6,plain,(
% 0.10/0.30 ($true = ((cS @ sK0))) & ! [X1 : (a > $o)] : ((($true != ((cS @ (sK1 @ X1)))) & (((X1 @ (sK1 @ X1))) = $true)) | ($true != ((X1 @ sK0))))),
% 0.10/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X2,sK1 @ X1)],[f5])).
% 0.10/0.30 thf(f7,plain,(
% 0.10/0.30 ( ! [X1 : (a > $o)] : (($true != ((X1 @ sK0))) | (((X1 @ (sK1 @ X1))) = $true)) )),
% 0.10/0.30 inference(cnf_transformation,[],[f6])).
% 0.10/0.30 thf(f8,plain,(
% 0.10/0.30 ( ! [X1 : (a > $o)] : (($true != ((cS @ (sK1 @ X1)))) | ($true != ((X1 @ sK0)))) )),
% 0.10/0.30 inference(cnf_transformation,[],[f6])).
% 0.10/0.30 thf(f9,plain,(
% 0.10/0.30 ($true = ((cS @ sK0)))),
% 0.10/0.30 inference(cnf_transformation,[],[f6])).
% 0.10/0.30 thf(f12,plain,(
% 0.10/0.30 (((sK1 @ (= @ sK0))) = sK0)),
% 0.10/0.30 inference(leibniz_equality_elimination,[],[f7])).
% 0.10/0.30 thf(f25,plain,(
% 0.10/0.30 (((sK0 = sK0)) != $true) | ($true != ((cS @ sK0)))),
% 0.10/0.30 inference(constrained_superposition,[],[f8,f12])).
% 0.10/0.30 thf(f27,plain,(
% 0.10/0.30 (sK0 != sK0) | ($true != ((cS @ sK0)))),
% 0.10/0.30 inference(equality_proxy_clausification,[],[f25])).
% 0.10/0.30 thf(f28,plain,(
% 0.10/0.30 ($true != ((cS @ sK0)))),
% 0.10/0.30 inference(trivial_inequality_removal,[],[f27])).
% 0.10/0.30 thf(f30,plain,(
% 0.10/0.30 $false),
% 0.10/0.30 inference(forward_subsumption_resolution,[],[f28,f9])).
% 0.10/0.30 % SZS output end Proof for theBenchmark
% 0.10/0.30 % (3657949)------------------------------
% 0.10/0.30 % (3657949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.30 % (3657949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.30 % (3657949)CaDiCaL version: 2.1.3
% 0.10/0.30 % (3657949)Termination reason: Refutation
% 0.10/0.30 % (3657949)Time elapsed: 0.002 s
% 0.10/0.30 % (3657949)Peak memory usage: 12 MB
% 0.10/0.30 % (3657949)Instructions burned: 1 (million)
% 0.10/0.30 % (3657943)Success in time 0.039 s
% 0.10/0.30 % Vampire exiting
%------------------------------------------------------------------------------