%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL454+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:33:19 EDT 2023

% Result   : Theorem 0.35s 1.33s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : LCL454+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.09  % Command  : nanocop.sh %s %d
% 0.09/0.29  % Computer : n006.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Thu May 18 16:12:21 EDT 2023
% 0.09/0.29  % CPUTime  : 
% 0.35/1.33  
% 0.35/1.33  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.35/1.33  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/1.33  %-----------------------------------------------------
% 0.35/1.33  ncf(matrix, plain, [(533 ^ _64585) ^ [] : [r1], (20 ^ _64585) ^ [_65333, _65335] : [-(is_a_theorem(_65333)), _65335 = _65333, is_a_theorem(_65335)], (2 ^ _64585) ^ [_64729] : [-(_64729 = _64729)], (4 ^ _64585) ^ [_64836, _64838] : [_64838 = _64836, -(_64836 = _64838)], (10 ^ _64585) ^ [_65040, _65042, _65044] : [-(_65044 = _65040), _65044 = _65042, _65042 = _65040], (30 ^ _64585) ^ [_65658, _65660, _65662, _65664] : [-(or(_65664, _65660) = or(_65662, _65658)), _65664 = _65662, _65660 = _65658], (40 ^ _64585) ^ [_65989, _65991] : [_65991 = _65989, -((not _65991) = (not _65989))], (46 ^ _64585) ^ [_66235, _66237, _66239, _66241] : [-(equiv(_66241, _66237) = equiv(_66239, _66235)), _66241 = _66239, _66237 = _66235], (56 ^ _64585) ^ [_66594, _66596, _66598, _66600] : [-(and(_66600, _66596) = and(_66598, _66594)), _66600 = _66598, _66596 = _66594], (66 ^ _64585) ^ [_66933, _66935, _66937, _66939] : [-(implies(_66939, _66935) = implies(_66937, _66933)), _66939 = _66937, _66935 = _66933], (491 ^ _64585) ^ [] : [-(op_or)], (493 ^ _64585) ^ [] : [-(op_implies_and)], (495 ^ _64585) ^ [] : [-(op_equiv)], (497 ^ _64585) ^ [] : [-(modus_ponens)], (499 ^ _64585) ^ [] : [-(modus_tollens)], (501 ^ _64585) ^ [] : [-(implies_1)], (503 ^ _64585) ^ [] : [-(implies_2)], (505 ^ _64585) ^ [] : [-(implies_3)], (507 ^ _64585) ^ [] : [-(and_1)], (509 ^ _64585) ^ [] : [-(and_2)], (511 ^ _64585) ^ [] : [-(and_3)], (513 ^ _64585) ^ [] : [-(or_1)], (515 ^ _64585) ^ [] : [-(or_2)], (517 ^ _64585) ^ [] : [-(or_3)], (519 ^ _64585) ^ [] : [-(equivalence_1)], (521 ^ _64585) ^ [] : [-(equivalence_2)], (523 ^ _64585) ^ [] : [-(equivalence_3)], (525 ^ _64585) ^ [] : [-(substitution_of_equivalents)], (527 ^ _64585) ^ [] : [-(op_implies_or)], (529 ^ _64585) ^ [] : [-(op_and)], (531 ^ _64585) ^ [] : [-(op_equiv)], (461 ^ _64585) ^ [] : [op_or, 464 ^ _64585 : [(465 ^ _64585) ^ [_78587, _78589] : [-(or(_78589, _78587) = (not and(not _78589, not _78587)))]]], (467 ^ _64585) ^ [] : [op_and, 470 ^ _64585 : [(471 ^ _64585) ^ [_78760, _78762] : [-(and(_78762, _78760) = (not or(not _78762, not _78760)))]]], (473 ^ _64585) ^ [] : [op_implies_and, 476 ^ _64585 : [(477 ^ _64585) ^ [_78933, _78935] : [-(implies(_78935, _78933) = (not and(_78935, not _78933)))]]], (479 ^ _64585) ^ [] : [op_implies_or, 482 ^ _64585 : [(483 ^ _64585) ^ [_79104, _79106] : [-(implies(_79106, _79104) = or(not _79106, _79104))]]], (485 ^ _64585) ^ [] : [op_equiv, 488 ^ _64585 : [(489 ^ _64585) ^ [_79253, _79255] : [-(equiv(_79255, _79253) = and(implies(_79255, _79253), implies(_79253, _79255)))]]], (90 ^ _64585) ^ [] : [93 ^ _64585 : [(94 ^ _64585) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _64585) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _64585) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _64585) ^ [] : [modus_ponens, 79 ^ _64585 : [(80 ^ _64585) ^ [_67391, _67393] : [-(is_a_theorem(_67391)), is_a_theorem(_67393), is_a_theorem(implies(_67393, _67391))]]], (112 ^ _64585) ^ [] : [115 ^ _64585 : [(116 ^ _64585) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _64585) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _64585) ^ [] : [substitution_of_equivalents, 105 ^ _64585 : [(106 ^ _64585) ^ [_68101, _68103] : [is_a_theorem(equiv(_68103, _68101)), -(_68103 = _68101)]]], (122 ^ _64585) ^ [] : [modus_tollens, 125 ^ _64585 : [(126 ^ _64585) ^ [_68648, _68650] : [-(is_a_theorem(implies(implies(not _68648, not _68650), implies(_68650, _68648))))]]], (128 ^ _64585) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _64585) ^ [] : [implies_1, 139 ^ _64585 : [(140 ^ _64585) ^ [_69052, _69054] : [-(is_a_theorem(implies(_69054, implies(_69052, _69054))))]]], (142 ^ _64585) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _64585) ^ [] : [implies_2, 153 ^ _64585 : [(154 ^ _64585) ^ [_69437, _69439] : [-(is_a_theorem(implies(implies(_69439, implies(_69439, _69437)), implies(_69439, _69437))))]]], (156 ^ _64585) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _64585) ^ [] : [implies_3, 167 ^ _64585 : [(168 ^ _64585) ^ [_69854, _69856, _69858] : [-(is_a_theorem(implies(implies(_69858, _69856), implies(implies(_69856, _69854), implies(_69858, _69854)))))]]], (170 ^ _64585) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _64585) ^ [] : [and_1, 182 ^ _64585 : [(183 ^ _64585) ^ [_70326, _70328] : [-(is_a_theorem(implies(and(_70328, _70326), _70328)))]]], (185 ^ _64585) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _64585) ^ [] : [and_2, 196 ^ _64585 : [(197 ^ _64585) ^ [_70711, _70713] : [-(is_a_theorem(implies(and(_70713, _70711), _70711)))]]], (199 ^ _64585) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _64585) ^ [] : [and_3, 210 ^ _64585 : [(211 ^ _64585) ^ [_71096, _71098] : [-(is_a_theorem(implies(_71098, implies(_71096, and(_71098, _71096)))))]]], (213 ^ _64585) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _64585) ^ [] : [or_1, 224 ^ _64585 : [(225 ^ _64585) ^ [_71490, _71492] : [-(is_a_theorem(implies(_71492, or(_71492, _71490))))]]], (227 ^ _64585) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _64585) ^ [] : [or_2, 238 ^ _64585 : [(239 ^ _64585) ^ [_71875, _71877] : [-(is_a_theorem(implies(_71875, or(_71877, _71875))))]]], (241 ^ _64585) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _64585) ^ [] : [or_3, 252 ^ _64585 : [(253 ^ _64585) ^ [_72274, _72276, _72278] : [-(is_a_theorem(implies(implies(_72278, _72274), implies(implies(_72276, _72274), implies(or(_72278, _72276), _72274)))))]]], (255 ^ _64585) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _64585) ^ [] : [equivalence_1, 267 ^ _64585 : [(268 ^ _64585) ^ [_72758, _72760] : [-(is_a_theorem(implies(equiv(_72760, _72758), implies(_72760, _72758))))]]], (270 ^ _64585) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _64585) ^ [] : [equivalence_2, 281 ^ _64585 : [(282 ^ _64585) ^ [_73152, _73154] : [-(is_a_theorem(implies(equiv(_73154, _73152), implies(_73152, _73154))))]]], (284 ^ _64585) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _64585) ^ [] : [equivalence_3, 295 ^ _64585 : [(296 ^ _64585) ^ [_73546, _73548] : [-(is_a_theorem(implies(implies(_73548, _73546), implies(implies(_73546, _73548), equiv(_73548, _73546)))))]]], (298 ^ _64585) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _64585) ^ [] : [kn1, 309 ^ _64585 : [(310 ^ _64585) ^ [_73944] : [-(is_a_theorem(implies(_73944, and(_73944, _73944))))]]], (312 ^ _64585) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _64585) ^ [] : [kn2, 322 ^ _64585 : [(323 ^ _64585) ^ [_74280, _74282] : [-(is_a_theorem(implies(and(_74282, _74280), _74282)))]]], (325 ^ _64585) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _64585) ^ [] : [kn3, 336 ^ _64585 : [(337 ^ _64585) ^ [_74679, _74681, _74683] : [-(is_a_theorem(implies(implies(_74683, _74681), implies(not and(_74681, _74679), not and(_74679, _74683)))))]]], (339 ^ _64585) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _64585) ^ [] : [cn1, 351 ^ _64585 : [(352 ^ _64585) ^ [_75181, _75183, _75185] : [-(is_a_theorem(implies(implies(_75185, _75183), implies(implies(_75183, _75181), implies(_75185, _75181)))))]]], (354 ^ _64585) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _64585) ^ [] : [cn2, 366 ^ _64585 : [(367 ^ _64585) ^ [_75653, _75655] : [-(is_a_theorem(implies(_75655, implies(not _75655, _75653))))]]], (369 ^ _64585) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _64585) ^ [] : [cn3, 380 ^ _64585 : [(381 ^ _64585) ^ [_76028] : [-(is_a_theorem(implies(implies(not _76028, _76028), _76028)))]]], (383 ^ _64585) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _64585) ^ [] : [r1, 393 ^ _64585 : [(394 ^ _64585) ^ [_76354] : [-(is_a_theorem(implies(or(_76354, _76354), _76354)))]]], (396 ^ _64585) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _64585) ^ [] : [r2, 406 ^ _64585 : [(407 ^ _64585) ^ [_76690, _76692] : [-(is_a_theorem(implies(_76690, or(_76692, _76690))))]]], (409 ^ _64585) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _64585) ^ [] : [r3, 420 ^ _64585 : [(421 ^ _64585) ^ [_77075, _77077] : [-(is_a_theorem(implies(or(_77077, _77075), or(_77075, _77077))))]]], (423 ^ _64585) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _64585) ^ [] : [r4, 434 ^ _64585 : [(435 ^ _64585) ^ [_77483, _77485, _77487] : [-(is_a_theorem(implies(or(_77487, or(_77485, _77483)), or(_77485, or(_77487, _77483)))))]]], (437 ^ _64585) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _64585) ^ [] : [r5, 449 ^ _64585 : [(450 ^ _64585) ^ [_77952, _77954, _77956] : [-(is_a_theorem(implies(implies(_77954, _77952), implies(or(_77956, _77954), or(_77956, _77952)))))]]], (452 ^ _64585) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 0.35/1.33  ncf('1',plain,[r1],start(533 ^ 0)).
% 0.35/1.33  ncf('1.1',plain,[-(r1), is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ []))],extension(396 ^ 1)).
% 0.35/1.33  ncf('1.1.1',plain,[-(is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ []))), 80 : is_a_theorem(implies(397 ^ [], 397 ^ [])), 80 : is_a_theorem(implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ []))), 80 : modus_ponens],extension(76 ^ 2,bind([[_67391, _67393], [implies(or(397 ^ [], 397 ^ []), 397 ^ []), implies(397 ^ [], 397 ^ [])]]))).
% 0.35/1.33  ncf('1.1.1.1',plain,[-(is_a_theorem(implies(397 ^ [], 397 ^ []))), is_a_theorem(implies(397 ^ [], implies(397 ^ [], 397 ^ []))), is_a_theorem(implies(implies(397 ^ [], implies(397 ^ [], 397 ^ [])), implies(397 ^ [], 397 ^ [])))],extension(80 ^ 5,bind([[_67391, _67393], [implies(397 ^ [], 397 ^ []), implies(397 ^ [], implies(397 ^ [], 397 ^ []))]]))).
% 0.35/1.33  ncf('1.1.1.1.1',plain,[-(is_a_theorem(implies(397 ^ [], implies(397 ^ [], 397 ^ [])))), implies_1],extension(136 ^ 6,bind([[_69052, _69054], [397 ^ [], 397 ^ []]]))).
% 0.35/1.33  ncf('1.1.1.1.1.1',plain,[-(implies_1)],extension(501 ^ 7)).
% 0.35/1.33  ncf('1.1.1.1.2',plain,[-(is_a_theorem(implies(implies(397 ^ [], implies(397 ^ [], 397 ^ [])), implies(397 ^ [], 397 ^ [])))), implies_2],extension(150 ^ 6,bind([[_69437, _69439], [397 ^ [], 397 ^ []]]))).
% 0.35/1.33  ncf('1.1.1.1.2.1',plain,[-(implies_2)],extension(503 ^ 7)).
% 0.35/1.33  ncf('1.1.1.2',plain,[-(is_a_theorem(implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ [])))), is_a_theorem(implies(implies(397 ^ [], 397 ^ []), implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ [])))), is_a_theorem(implies(implies(implies(397 ^ [], 397 ^ []), implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ []))), implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ []))))],extension(80 ^ 5,bind([[_67391, _67393], [implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ [])), implies(implies(397 ^ [], 397 ^ []), implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ [])))]]))).
% 0.35/1.33  ncf('1.1.1.2.1',plain,[-(is_a_theorem(implies(implies(397 ^ [], 397 ^ []), implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ []))))), or_3],extension(249 ^ 6,bind([[_72274, _72276, _72278], [397 ^ [], 397 ^ [], 397 ^ []]]))).
% 0.35/1.33  ncf('1.1.1.2.1.1',plain,[-(or_3)],extension(517 ^ 7)).
% 0.35/1.33  ncf('1.1.1.2.2',plain,[-(is_a_theorem(implies(implies(implies(397 ^ [], 397 ^ []), implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ []))), implies(implies(397 ^ [], 397 ^ []), implies(or(397 ^ [], 397 ^ []), 397 ^ []))))), implies_2],extension(150 ^ 6,bind([[_69437, _69439], [implies(or(397 ^ [], 397 ^ []), 397 ^ []), implies(397 ^ [], 397 ^ [])]]))).
% 0.35/1.33  ncf('1.1.1.2.2.1',plain,[-(implies_2)],extension(503 ^ 7)).
% 0.35/1.33  ncf('1.1.1.3',plain,[-(modus_ponens)],extension(497 ^ 3)).
% 0.35/1.33  %-----------------------------------------------------
% 0.35/1.33  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------