0.00/0.02	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.10/0.37	% Computer : n026.cluster.edu
0.10/0.37	% Model    : x86_64 x86_64
0.10/0.37	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.37	% Memory   : 8046.5625MB
0.10/0.37	% OS       : Linux 6.8.0-71-generic
0.10/0.37	% CPULimit : 1440
0.10/0.37	% WCLimit  : 180
0.10/0.37	% DateTime : Mon Jul 27 08:57:57 UTC 2026
0.10/0.37	% CPUTime  : 
0.10/0.37	Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.10/0.41	Running higher-order theorem proving
0.10/0.43	Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p
0.17/0.47	% (2501538)Detected a higher-order problem, will run a greedy HOL sequence.
0.17/0.47	% (2501543)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3710543414:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.17/0.47	% (2501543) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2501538-2501543"...
0.17/0.47	% (2501543)...printing done.
0.17/0.47	% (2501543)Refutation found. Thanks to Tanya!
0.17/0.47	% SZS status Theorem for theBenchmark
0.17/0.47	% SZS output start Proof for theBenchmark
0.17/0.47	thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
0.17/0.47	thf(func_def_1, type, cS: ($i > $i)).
0.17/0.47	thf(func_def_2, type, cIND: $o).
0.17/0.47	thf(func_def_6, type, sK0: (($i > $o) > $i)).
0.17/0.47	thf(func_def_7, type, sK1: ($i > $o)).
0.17/0.47	thf(func_def_10, type, vNOT: ($o > $o)).
0.17/0.47	thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.17/0.47	thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
0.17/0.47	thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.17/0.47	thf(f1,axiom,(
0.17/0.47	  (! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X1 : $i] : (X0 @ X1)) = cIND)),
0.17/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cIND_def)).
0.17/0.47	thf(f2,conjecture,(
0.17/0.47	  cIND => ! [X0 : $i] : ((X0 = c0) | ? [X1 : $i] : (X0 = ((cS @ X1))))),
0.17/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM578)).
0.17/0.47	thf(f3,negated_conjecture,(
0.17/0.47	  ~(cIND => ! [X0 : $i] : ((X0 = c0) | ? [X1 : $i] : (X0 = ((cS @ X1)))))),
0.17/0.47	  inference(negated_conjecture,[status(cth)],[f2])).
0.17/0.47	thf(f4,plain,(
0.17/0.47	  ~(cIND => ! [X0 : $i] : ((X0 = c0) | ? [X1 : $i] : (X0 = ((cS @ X1)))))),
0.17/0.47	  inference(rectify,[],[f3])).
0.17/0.47	thf(f5,plain,(
0.17/0.47	  ~((cIND = $true) => ! [X0 : $i] : (? [X1 : $i] : (((cS @ X1)) = X0) | (c0 = X0)))),
0.17/0.47	  inference(fool_elimination,[],[f4])).
0.17/0.47	thf(f6,plain,(
0.17/0.47	  (! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X2 : $i] : (X0 @ X2)) = cIND)),
0.17/0.47	  inference(rectify,[],[f1])).
0.17/0.47	thf(f7,plain,(
0.17/0.47	  ! [X0 : ($i > $o)] : (((((X0 @ c0)) = $true) & ! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (cS @ X1))) = $true))) => ! [X2 : $i] : ($true = ((X0 @ X2)))) <=> (cIND = $true)),
0.17/0.47	  inference(fool_elimination,[],[f6])).
0.17/0.47	thf(f8,plain,(
0.17/0.47	  ! [X0 : ($i > $o)] : (! [X2 : $i] : ($true = ((X0 @ X2))) | ((((X0 @ c0)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (cS @ X1))) != $true)))) <=> (cIND = $true)),
0.17/0.47	  inference(ennf_transformation,[],[f7])).
0.17/0.47	thf(f9,plain,(
0.17/0.47	  ! [X0 : ($i > $o)] : (! [X2 : $i] : ($true = ((X0 @ X2))) | (((X0 @ c0)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (cS @ X1))) != $true))) <=> (cIND = $true)),
0.17/0.47	  inference(flattening,[],[f8])).
0.17/0.47	thf(f10,plain,(
0.17/0.47	  ? [X0 : $i] : ((c0 != X0) & ! [X1 : $i] : (((cS @ X1)) != X0)) & (cIND = $true)),
0.17/0.47	  inference(ennf_transformation,[],[f5])).
0.17/0.47	thf(f11,plain,(
0.17/0.47	  (! [X0 : ($i > $o)] : (! [X2 : $i] : ($true = ((X0 @ X2))) | (((X0 @ c0)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (cS @ X1))) != $true))) | (cIND != $true)) & ((cIND = $true) | ? [X0 : ($i > $o)] : (? [X2 : $i] : ($true != ((X0 @ X2))) & (((X0 @ c0)) = $true) & ! [X1 : $i] : ((((X0 @ X1)) != $true) | (((X0 @ (cS @ X1))) = $true))))),
0.17/0.47	  inference(nnf_transformation,[],[f9])).
0.17/0.47	thf(f12,plain,(
0.17/0.47	  (! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | (((X0 @ c0)) != $true) | ? [X2 : $i] : (($true = ((X0 @ X2))) & ($true != ((X0 @ (cS @ X2)))))) | (cIND != $true)) & ((cIND = $true) | ? [X3 : ($i > $o)] : (? [X4 : $i] : (((X3 @ X4)) != $true) & (((X3 @ c0)) = $true) & ! [X5 : $i] : ((((X3 @ X5)) != $true) | ($true = ((X3 @ (cS @ X5)))))))),
0.17/0.47	  inference(rectify,[],[f11])).
0.17/0.47	thf(f13,plain,(
0.17/0.47	  (! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | (((X0 @ c0)) != $true) | ((((X0 @ (sK0 @ X0))) = $true) & ($true != ((X0 @ (cS @ (sK0 @ X0))))))) | (cIND != $true)) & ((cIND = $true) | ((((sK1 @ sK2)) != $true) & (((sK1 @ c0)) = $true) & ! [X5 : $i] : ((((sK1 @ X5)) != $true) | ($true = ((sK1 @ (cS @ X5)))))))),
0.17/0.47	  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f12])).
0.17/0.47	thf(f14,plain,(
0.17/0.47	  ((c0 != sK3) & ! [X1 : $i] : (((cS @ X1)) != sK3)) & (cIND = $true)),
0.17/0.47	  inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f10])).
0.17/0.47	thf(f18,plain,(
0.17/0.47	  ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) = $true) | (((X0 @ c0)) != $true) | ($true != ((X0 @ (cS @ (sK0 @ X0))))) | (cIND != $true)) )),
0.17/0.47	  inference(cnf_transformation,[],[f13])).
0.17/0.47	thf(f20,plain,(
0.17/0.47	  (cIND = $true)),
0.17/0.47	  inference(cnf_transformation,[],[f14])).
0.17/0.47	thf(f21,plain,(
0.17/0.47	  ( ! [X1 : $i] : ((((cS @ X1)) != sK3)) )),
0.17/0.47	  inference(cnf_transformation,[],[f14])).
0.17/0.47	thf(f22,plain,(
0.17/0.47	  (c0 != sK3)),
0.17/0.47	  inference(cnf_transformation,[],[f14])).
0.17/0.47	thf(f26,plain,(
0.17/0.47	  ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ c0)) != $true) | (((X0 @ X1)) = $true) | ($true != ((X0 @ (cS @ (sK0 @ X0))))) | ($true != $true)) )),
0.17/0.47	  inference(definition_unfolding,[],[f18,f20])).
0.17/0.47	thf(f30,plain,(
0.17/0.47	  ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (cS @ (sK0 @ X0))))) | (((X0 @ c0)) != $true) | (((X0 @ X1)) = $true)) )),
0.17/0.47	  inference(trivial_inequality_removal,[],[f26])).
0.17/0.47	thf(f67,plain,(
0.17/0.47	  ( ! [X0 : $i] : (((((^[Y0 : $i]: (~ (Y0 = X0))) @ c0)) != $true) | (((cS @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
0.17/0.47	  inference(leibniz_equality_elimination,[],[f30])).
0.17/0.47	thf(f75,plain,(
0.17/0.47	  ( ! [X0 : $i] : ((((cS @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (((~ (c0 = X0))) != $true)) )),
0.17/0.47	  inference(beta-eta_normalization,[],[f67])).
0.17/0.47	thf(f76,plain,(
0.17/0.47	  ( ! [X0 : $i] : ((((cS @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (((c0 = X0)) = $true)) )),
0.17/0.47	  inference(not_proxy_clausification,[],[f75])).
0.17/0.47	thf(f77,plain,(
0.17/0.47	  ( ! [X0 : $i] : ((((cS @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (c0 = X0)) )),
0.17/0.47	  inference(equality_proxy_clausification,[],[f76])).
0.17/0.47	thf(f96,plain,(
0.17/0.47	  ( ! [X0 : $i] : ((sK3 != X0) | (c0 = X0)) )),
0.17/0.47	  inference(constrained_superposition,[],[f21,f77])).
0.17/0.47	thf(f106,plain,(
0.17/0.47	  (sK3 != sK3) | (c0 = sK3)),
0.17/0.47	  inference(imitation,[],[f96])).
0.17/0.47	thf(f108,plain,(
0.17/0.47	  (c0 = sK3)),
0.17/0.47	  inference(trivial_inequality_removal,[],[f106])).
0.17/0.47	thf(f109,plain,(
0.17/0.47	  $false),
0.17/0.47	  inference(forward_subsumption_resolution,[],[f108,f22])).
0.17/0.47	% SZS output end Proof for theBenchmark
0.17/0.47	% (2501543)------------------------------
0.17/0.47	% (2501543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.17/0.47	% (2501543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.17/0.47	% (2501543)CaDiCaL version: 2.1.3
0.17/0.47	% (2501543)Termination reason: Refutation
0.17/0.47	% (2501543)Time elapsed: 0.002 s
0.17/0.47	% (2501543)Peak memory usage: 12 MB
0.17/0.47	% (2501543)Instructions burned: 4 (million)
0.17/0.47	% (2501538)Success in time 0.027 s
0.17/0.47	% Vampire exiting
0.17/0.47	EOF