%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV056^5 : 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 : n006.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 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV056^5 : 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 : n006.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
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:05:24 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
% 0.08/0.23 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
% 0.20/0.27 % (839567)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (839575)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=1978943588: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)
% 0.20/0.27 % (839575) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-839567-839575"...
% 0.20/0.27 % (839575)...printing done.
% 0.20/0.27 % (839575)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, a: $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_3, type, sK0: (a > a > $o)).
% 0.20/0.27 thf(func_def_4, type, sK1: ((a > a > $o) > a)).
% 0.20/0.27 thf(func_def_5, type, sK2: ((a > a > $o) > a)).
% 0.20/0.27 thf(func_def_6, type, sK3: ((a > a > $o) > a)).
% 0.20/0.27 thf(func_def_7, type, sK4: ((a > a > $o) > a)).
% 0.20/0.27 thf(func_def_8, type, sK5: ((a > a > $o) > a)).
% 0.20/0.27 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.20/0.27 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.27 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.27 thf(f1,conjecture,(
% 0.20/0.27 ! [X0 : (a > a > $o)] : ? [X1 : (a > a > $o)] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)) & ! [X3 : a,X2 : a,X4 : a] : (((X1 @ X3 @ X4) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X4)))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM275_pme)).
% 0.20/0.27 thf(f2,negated_conjecture,(
% 0.20/0.27 ~ ! [X0 : (a > a > $o)] : ? [X1 : (a > a > $o)] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)) & ! [X3 : a,X2 : a,X4 : a] : (((X1 @ X3 @ X4) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X4)))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.27 thf(f3,plain,(
% 0.20/0.27 ~ ! [X0 : (a > a > $o)] : ? [X1 : (a > a > $o)] : (! [X2 : a,X3 : a] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)) & ! [X4 : a,X5 : a,X6 : a] : (((X1 @ X4 @ X6) & (X1 @ X5 @ X4)) => (X1 @ X5 @ X6)))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~ ! [X0 : (a > a > $o)] : ? [X1 : (a > a > $o)] : (! [X6 : a,X5 : a,X4 : a] : (((((X1 @ X5 @ X4)) = $true) & ($true = ((X1 @ X4 @ X6)))) => (((X1 @ X5 @ X6)) = $true)) & ! [X3 : a,X2 : a] : (($true = ((X0 @ X3 @ X2))) => ($true = ((X1 @ X3 @ X2)))))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ? [X0 : (a > a > $o)] : ! [X1 : (a > a > $o)] : (? [X6 : a,X5 : a,X4 : a] : ((((X1 @ X5 @ X6)) != $true) & ((((X1 @ X5 @ X4)) = $true) & ($true = ((X1 @ X4 @ X6))))) | ? [X2 : a,X3 : a] : (($true != ((X1 @ X3 @ X2))) & ($true = ((X0 @ X3 @ X2)))))),
% 0.20/0.27 inference(ennf_transformation,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ? [X0 : (a > a > $o)] : ! [X1 : (a > a > $o)] : (? [X4 : a,X6 : a,X5 : a] : ((((X1 @ X5 @ X4)) = $true) & (((X1 @ X5 @ X6)) != $true) & ($true = ((X1 @ X4 @ X6)))) | ? [X2 : a,X3 : a] : (($true != ((X1 @ X3 @ X2))) & ($true = ((X0 @ X3 @ X2)))))),
% 0.20/0.27 inference(flattening,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ? [X0 : (a > a > $o)] : ! [X1 : (a > a > $o)] : (? [X2 : a,X3 : a,X4 : a] : (($true = ((X1 @ X4 @ X2))) & ($true != ((X1 @ X4 @ X3))) & (((X1 @ X2 @ X3)) = $true)) | ? [X5 : a,X6 : a] : (($true != ((X1 @ X6 @ X5))) & ($true = ((X0 @ X6 @ X5)))))),
% 0.20/0.27 inference(rectify,[],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ! [X1 : (a > a > $o)] : ((($true = ((X1 @ (sK3 @ X1) @ (sK1 @ X1)))) & ($true != ((X1 @ (sK3 @ X1) @ (sK2 @ X1)))) & ($true = ((X1 @ (sK1 @ X1) @ (sK2 @ X1))))) | (($true != ((X1 @ (sK5 @ X1) @ (sK4 @ X1)))) & ($true = ((sK0 @ (sK5 @ X1) @ (sK4 @ X1))))))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X6,sK5 @ X1),skolemize(X6,sK5 @ X1),skolemize(X6,sK5 @ X1),skolemize(X6,sK5 @ X1),skolemize(X6,sK5 @ X1)],[f7])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 ( ! [X1 : (a > a > $o)] : (($true != ((X1 @ (sK5 @ X1) @ (sK4 @ X1)))) | ($true != ((X1 @ (sK3 @ X1) @ (sK2 @ X1))))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f8])).
% 0.20/0.27 thf(f57,plain,(
% 0.20/0.27 ($true != (((^[Y0 : a]: ((^[Y1 : a]: ($true)))) @ (sK3 @ (^[Y0 : a]: ((^[Y1 : a]: ($true))))) @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a]: ($true)))))))) | ((((^[Y0 : a]: ((^[Y1 : a]: ($true)))) @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: ($true))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: ($true))))))) != $true)),
% 0.20/0.27 inference(imitation,[],[f12])).
% 0.20/0.27 thf(f61,plain,(
% 0.20/0.27 ($true != $true) | ($true != $true)),
% 0.20/0.27 inference(beta-eta_normalization,[],[f57])).
% 0.20/0.27 thf(f62,plain,(
% 0.20/0.27 ($true != $true)),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f61])).
% 0.20/0.27 thf(f63,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f62])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (839575)------------------------------
% 0.20/0.27 % (839575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (839575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (839575)CaDiCaL version: 2.1.3
% 0.20/0.27 % (839575)Termination reason: Refutation
% 0.20/0.27 % (839575)Time elapsed: 0.002 s
% 0.20/0.27 % (839575)Peak memory usage: 12 MB
% 0.20/0.27 % (839575)Instructions burned: 5 (million)
% 0.20/0.27 % (839567)Success in time 0.03 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------