%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV055^5 : 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 : n013.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 0.25s 0.37s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV055^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n013.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 15:05:06 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.32 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
% 0.25/0.37 % (2227939)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.37 % (2227944)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1805481106:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.37 % (2227944) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2227939-2227944"...
% 0.25/0.37 % (2227944)...printing done.
% 0.25/0.37 % (2227944)Refutation found. Thanks to Tanya!
% 0.25/0.37 % SZS status Theorem for theBenchmark
% 0.25/0.37 % SZS output start Proof for theBenchmark
% 0.25/0.37 thf(type_def_5, type, a: $tType).
% 0.25/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.37 thf(func_def_3, type, sK0: ((a > $o) > a)).
% 0.25/0.37 thf(func_def_4, type, sK1: (a > a > $o)).
% 0.25/0.37 thf(func_def_5, type, sK2: (a > (a > $o) > a)).
% 0.25/0.37 thf(func_def_6, type, sK3: (a > a)).
% 0.25/0.37 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.25/0.37 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.25/0.37 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.25/0.37 thf(f1,conjecture,(
% 0.25/0.37 ! [X1 : ((a > $o) > a),X0 : (a > a > $o)] : ((! [X3 : a,X2 : a,X4 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4)) & ! [X5 : (a > $o)] : (! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5))) & ! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)))) => ! [X8 : (a > a)] : (! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ X9 @ (X8 @ X9))))),
% 0.25/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM402_pme)).
% 0.25/0.37 thf(f2,negated_conjecture,(
% 0.25/0.37 ~ ! [X1 : ((a > $o) > a),X0 : (a > a > $o)] : ((! [X3 : a,X2 : a,X4 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4)) & ! [X5 : (a > $o)] : (! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5))) & ! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)))) => ! [X8 : (a > a)] : (! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ X9 @ (X8 @ X9))))),
% 0.25/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/0.37 thf(f3,plain,(
% 0.25/0.37 ~ ! [X0 : ((a > $o) > a),X1 : (a > a > $o)] : ((! [X2 : a,X3 : a,X4 : a] : (((X1 @ X3 @ X2) & (X1 @ X2 @ X4)) => (X1 @ X3 @ X4)) & ! [X5 : (a > $o)] : (! [X6 : a] : ((X5 @ X6) => (X1 @ X6 @ (X0 @ X5))) & ! [X7 : a] : (! [X8 : a] : ((X5 @ X8) => (X1 @ X8 @ X7)) => (X1 @ (X0 @ X5) @ X7)))) => ! [X9 : (a > a)] : (! [X10 : a,X11 : a] : ((X1 @ X10 @ X11) => (X1 @ (X9 @ X10) @ (X9 @ X11))) => ? [X12 : a] : (X1 @ X12 @ (X9 @ X12))))),
% 0.25/0.37 inference(rectify,[],[f2])).
% 0.25/0.37 thf(f4,plain,(
% 0.25/0.37 ~ ! [X1 : (a > a > $o),X0 : ((a > $o) > a)] : ((! [X5 : (a > $o)] : (! [X7 : a] : (! [X8 : a] : ((((X5 @ X8)) = $true) => (((X1 @ X8 @ X7)) = $true)) => (((X1 @ (X0 @ X5) @ X7)) = $true)) & ! [X6 : a] : ((((X5 @ X6)) = $true) => (((X1 @ X6 @ (X0 @ X5))) = $true))) & ! [X2 : a,X3 : a,X4 : a] : (((((X1 @ X3 @ X2)) = $true) & ($true = ((X1 @ X2 @ X4)))) => ($true = ((X1 @ X3 @ X4))))) => ! [X9 : (a > a)] : (! [X10 : a,X11 : a] : (($true = ((X1 @ X10 @ X11))) => ($true = ((X1 @ (X9 @ X10) @ (X9 @ X11))))) => ? [X12 : a] : (((X1 @ X12 @ (X9 @ X12))) = $true)))),
% 0.25/0.37 inference(fool_elimination,[],[f3])).
% 0.25/0.37 thf(f5,plain,(
% 0.25/0.37 ? [X1 : (a > a > $o),X0 : ((a > $o) > a)] : (? [X9 : (a > a)] : (! [X12 : a] : (((X1 @ X12 @ (X9 @ X12))) != $true) & ! [X10 : a,X11 : a] : (($true != ((X1 @ X10 @ X11))) | ($true = ((X1 @ (X9 @ X10) @ (X9 @ X11)))))) & (! [X5 : (a > $o)] : (! [X6 : a] : ((((X1 @ X6 @ (X0 @ X5))) = $true) | (((X5 @ X6)) != $true)) & ! [X7 : a] : (? [X8 : a] : ((((X5 @ X8)) = $true) & (((X1 @ X8 @ X7)) != $true)) | (((X1 @ (X0 @ X5) @ X7)) = $true))) & ! [X2 : a,X3 : a,X4 : a] : (($true = ((X1 @ X3 @ X4))) | ((((X1 @ X3 @ X2)) != $true) | ($true != ((X1 @ X2 @ X4)))))))),
% 0.25/0.37 inference(ennf_transformation,[],[f4])).
% 0.25/0.37 thf(f6,plain,(
% 0.25/0.37 ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (! [X4 : a,X3 : a,X2 : a] : ((((X1 @ X3 @ X2)) != $true) | ($true = ((X1 @ X3 @ X4))) | ($true != ((X1 @ X2 @ X4)))) & ! [X5 : (a > $o)] : (! [X6 : a] : ((((X1 @ X6 @ (X0 @ X5))) = $true) | (((X5 @ X6)) != $true)) & ! [X7 : a] : (? [X8 : a] : ((((X5 @ X8)) = $true) & (((X1 @ X8 @ X7)) != $true)) | (((X1 @ (X0 @ X5) @ X7)) = $true))) & ? [X9 : (a > a)] : (! [X12 : a] : (((X1 @ X12 @ (X9 @ X12))) != $true) & ! [X10 : a,X11 : a] : (($true != ((X1 @ X10 @ X11))) | ($true = ((X1 @ (X9 @ X10) @ (X9 @ X11)))))))),
% 0.25/0.37 inference(flattening,[],[f5])).
% 0.25/0.37 thf(f7,plain,(
% 0.25/0.37 ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (! [X2 : a,X3 : a,X4 : a] : (($true != ((X1 @ X3 @ X4))) | (((X1 @ X3 @ X2)) = $true) | (((X1 @ X4 @ X2)) != $true)) & ! [X5 : (a > $o)] : (! [X6 : a] : ((((X1 @ X6 @ (X0 @ X5))) = $true) | (((X5 @ X6)) != $true)) & ! [X7 : a] : (? [X8 : a] : ((((X5 @ X8)) = $true) & (((X1 @ X8 @ X7)) != $true)) | (((X1 @ (X0 @ X5) @ X7)) = $true))) & ? [X9 : (a > a)] : (! [X10 : a] : (((X1 @ X10 @ (X9 @ X10))) != $true) & ! [X11 : a,X12 : a] : ((((X1 @ X11 @ X12)) != $true) | (((X1 @ (X9 @ X11) @ (X9 @ X12))) = $true))))),
% 0.25/0.37 inference(rectify,[],[f6])).
% 0.25/0.37 thf(f8,plain,(
% 0.25/0.37 ! [X2 : a,X3 : a,X4 : a] : ((((sK1 @ X3 @ X4)) != $true) | (((sK1 @ X3 @ X2)) = $true) | (((sK1 @ X4 @ X2)) != $true)) & ! [X5 : (a > $o)] : (! [X6 : a] : ((((sK1 @ X6 @ (sK0 @ X5))) = $true) | (((X5 @ X6)) != $true)) & ! [X7 : a] : (((((X5 @ (sK2 @ X7 @ X5))) = $true) & ($true != ((sK1 @ (sK2 @ X7 @ X5) @ X7)))) | (((sK1 @ (sK0 @ X5) @ X7)) = $true))) & (! [X10 : a] : ($true != ((sK1 @ X10 @ (sK3 @ X10)))) & ! [X11 : a,X12 : a] : (($true != ((sK1 @ X11 @ X12))) | (((sK1 @ (sK3 @ X11) @ (sK3 @ X12))) = $true)))),
% 0.25/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X8,sK2 @ X7 @ X5),skolemize(X9,sK3)],[f7])).
% 0.25/0.37 thf(f10,plain,(
% 0.25/0.37 ( ! [X10 : a] : (($true != ((sK1 @ X10 @ (sK3 @ X10))))) )),
% 0.25/0.37 inference(cnf_transformation,[],[f8])).
% 0.25/0.37 thf(f12,plain,(
% 0.25/0.37 ( ! [X7 : a,X5 : (a > $o)] : ((((X5 @ (sK2 @ X7 @ X5))) = $true) | (((sK1 @ (sK0 @ X5) @ X7)) = $true)) )),
% 0.25/0.37 inference(cnf_transformation,[],[f8])).
% 0.25/0.37 thf(f72,plain,(
% 0.25/0.37 ( ! [X7 : a] : ((((sK1 @ (sK0 @ (^[Y0 : a]: ($false))) @ X7)) = $true) | ((((^[Y0 : a]: ($false)) @ (sK2 @ X7 @ (^[Y0 : a]: ($false))))) = $true)) )),
% 0.25/0.37 inference(primitive_instantiation,[],[f12])).
% 0.25/0.37 thf(f78,plain,(
% 0.25/0.37 ( ! [X7 : a] : ((((sK1 @ (sK0 @ (^[Y0 : a]: ($false))) @ X7)) = $true) | ($false = $true)) )),
% 0.25/0.38 inference(beta-eta_normalization,[],[f72])).
% 0.25/0.38 thf(f79,plain,(
% 0.25/0.38 ( ! [X7 : a] : ((((sK1 @ (sK0 @ (^[Y0 : a]: ($false))) @ X7)) = $true)) )),
% 0.25/0.38 inference(trivial_inequality_removal,[],[f78])).
% 0.25/0.38 thf(f85,plain,(
% 0.25/0.38 ($true != $true)),
% 0.25/0.38 inference(constrained_superposition,[],[f10,f79])).
% 0.25/0.38 thf(f91,plain,(
% 0.25/0.38 $false),
% 0.25/0.38 inference(trivial_inequality_removal,[],[f85])).
% 0.25/0.38 % SZS output end Proof for theBenchmark
% 0.25/0.38 % (2227944)------------------------------
% 0.25/0.38 % (2227944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (2227944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (2227944)CaDiCaL version: 2.1.3
% 0.25/0.38 % (2227944)Termination reason: Refutation
% 0.25/0.38 % (2227944)Time elapsed: 0.006 s
% 0.25/0.38 % (2227944)Peak memory usage: 12 MB
% 0.25/0.38 % (2227944)Instructions burned: 9 (million)
% 0.25/0.38 % (2227939)Success in time 0.04 s
% 0.25/0.38 % Vampire exiting
%------------------------------------------------------------------------------