%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL452+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n012.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 1.08s 1.36s
% Output   : Proof 1.08s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : LCL452+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n012.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 16:26:17 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.08/1.36  
% 1.08/1.36  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.08/1.36  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/1.36  %-----------------------------------------------------
% 1.08/1.36  ncf(matrix, plain, [(533 ^ _63568) ^ [] : [cn2], (20 ^ _63568) ^ [_64316, _64318] : [-(is_a_theorem(_64316)), _64318 = _64316, is_a_theorem(_64318)], (2 ^ _63568) ^ [_63712] : [-(_63712 = _63712)], (4 ^ _63568) ^ [_63819, _63821] : [_63821 = _63819, -(_63819 = _63821)], (10 ^ _63568) ^ [_64023, _64025, _64027] : [-(_64027 = _64023), _64027 = _64025, _64025 = _64023], (30 ^ _63568) ^ [_64641, _64643, _64645, _64647] : [-(or(_64647, _64643) = or(_64645, _64641)), _64647 = _64645, _64643 = _64641], (40 ^ _63568) ^ [_64972, _64974] : [_64974 = _64972, -((not _64974) = (not _64972))], (46 ^ _63568) ^ [_65218, _65220, _65222, _65224] : [-(equiv(_65224, _65220) = equiv(_65222, _65218)), _65224 = _65222, _65220 = _65218], (56 ^ _63568) ^ [_65577, _65579, _65581, _65583] : [-(and(_65583, _65579) = and(_65581, _65577)), _65583 = _65581, _65579 = _65577], (66 ^ _63568) ^ [_65916, _65918, _65920, _65922] : [-(implies(_65922, _65918) = implies(_65920, _65916)), _65922 = _65920, _65918 = _65916], (491 ^ _63568) ^ [] : [-(op_or)], (493 ^ _63568) ^ [] : [-(op_implies_and)], (495 ^ _63568) ^ [] : [-(op_equiv)], (497 ^ _63568) ^ [] : [-(modus_ponens)], (499 ^ _63568) ^ [] : [-(modus_tollens)], (501 ^ _63568) ^ [] : [-(implies_1)], (503 ^ _63568) ^ [] : [-(implies_2)], (505 ^ _63568) ^ [] : [-(implies_3)], (507 ^ _63568) ^ [] : [-(and_1)], (509 ^ _63568) ^ [] : [-(and_2)], (511 ^ _63568) ^ [] : [-(and_3)], (513 ^ _63568) ^ [] : [-(or_1)], (515 ^ _63568) ^ [] : [-(or_2)], (517 ^ _63568) ^ [] : [-(or_3)], (519 ^ _63568) ^ [] : [-(equivalence_1)], (521 ^ _63568) ^ [] : [-(equivalence_2)], (523 ^ _63568) ^ [] : [-(equivalence_3)], (525 ^ _63568) ^ [] : [-(substitution_of_equivalents)], (527 ^ _63568) ^ [] : [-(op_or)], (529 ^ _63568) ^ [] : [-(op_implies)], (531 ^ _63568) ^ [] : [-(op_equiv)], (461 ^ _63568) ^ [] : [op_or, 464 ^ _63568 : [(465 ^ _63568) ^ [_77570, _77572] : [-(or(_77572, _77570) = (not and(not _77572, not _77570)))]]], (467 ^ _63568) ^ [] : [op_and, 470 ^ _63568 : [(471 ^ _63568) ^ [_77743, _77745] : [-(and(_77745, _77743) = (not or(not _77745, not _77743)))]]], (473 ^ _63568) ^ [] : [op_implies_and, 476 ^ _63568 : [(477 ^ _63568) ^ [_77916, _77918] : [-(implies(_77918, _77916) = (not and(_77918, not _77916)))]]], (479 ^ _63568) ^ [] : [op_implies_or, 482 ^ _63568 : [(483 ^ _63568) ^ [_78087, _78089] : [-(implies(_78089, _78087) = or(not _78089, _78087))]]], (485 ^ _63568) ^ [] : [op_equiv, 488 ^ _63568 : [(489 ^ _63568) ^ [_78236, _78238] : [-(equiv(_78238, _78236) = and(implies(_78238, _78236), implies(_78236, _78238)))]]], (90 ^ _63568) ^ [] : [93 ^ _63568 : [(94 ^ _63568) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _63568) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _63568) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _63568) ^ [] : [modus_ponens, 79 ^ _63568 : [(80 ^ _63568) ^ [_66374, _66376] : [-(is_a_theorem(_66374)), is_a_theorem(_66376), is_a_theorem(implies(_66376, _66374))]]], (112 ^ _63568) ^ [] : [115 ^ _63568 : [(116 ^ _63568) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _63568) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _63568) ^ [] : [substitution_of_equivalents, 105 ^ _63568 : [(106 ^ _63568) ^ [_67084, _67086] : [is_a_theorem(equiv(_67086, _67084)), -(_67086 = _67084)]]], (122 ^ _63568) ^ [] : [modus_tollens, 125 ^ _63568 : [(126 ^ _63568) ^ [_67631, _67633] : [-(is_a_theorem(implies(implies(not _67631, not _67633), implies(_67633, _67631))))]]], (128 ^ _63568) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _63568) ^ [] : [implies_1, 139 ^ _63568 : [(140 ^ _63568) ^ [_68035, _68037] : [-(is_a_theorem(implies(_68037, implies(_68035, _68037))))]]], (142 ^ _63568) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _63568) ^ [] : [implies_2, 153 ^ _63568 : [(154 ^ _63568) ^ [_68420, _68422] : [-(is_a_theorem(implies(implies(_68422, implies(_68422, _68420)), implies(_68422, _68420))))]]], (156 ^ _63568) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _63568) ^ [] : [implies_3, 167 ^ _63568 : [(168 ^ _63568) ^ [_68837, _68839, _68841] : [-(is_a_theorem(implies(implies(_68841, _68839), implies(implies(_68839, _68837), implies(_68841, _68837)))))]]], (170 ^ _63568) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _63568) ^ [] : [and_1, 182 ^ _63568 : [(183 ^ _63568) ^ [_69309, _69311] : [-(is_a_theorem(implies(and(_69311, _69309), _69311)))]]], (185 ^ _63568) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _63568) ^ [] : [and_2, 196 ^ _63568 : [(197 ^ _63568) ^ [_69694, _69696] : [-(is_a_theorem(implies(and(_69696, _69694), _69694)))]]], (199 ^ _63568) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _63568) ^ [] : [and_3, 210 ^ _63568 : [(211 ^ _63568) ^ [_70079, _70081] : [-(is_a_theorem(implies(_70081, implies(_70079, and(_70081, _70079)))))]]], (213 ^ _63568) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _63568) ^ [] : [or_1, 224 ^ _63568 : [(225 ^ _63568) ^ [_70473, _70475] : [-(is_a_theorem(implies(_70475, or(_70475, _70473))))]]], (227 ^ _63568) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _63568) ^ [] : [or_2, 238 ^ _63568 : [(239 ^ _63568) ^ [_70858, _70860] : [-(is_a_theorem(implies(_70858, or(_70860, _70858))))]]], (241 ^ _63568) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _63568) ^ [] : [or_3, 252 ^ _63568 : [(253 ^ _63568) ^ [_71257, _71259, _71261] : [-(is_a_theorem(implies(implies(_71261, _71257), implies(implies(_71259, _71257), implies(or(_71261, _71259), _71257)))))]]], (255 ^ _63568) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _63568) ^ [] : [equivalence_1, 267 ^ _63568 : [(268 ^ _63568) ^ [_71741, _71743] : [-(is_a_theorem(implies(equiv(_71743, _71741), implies(_71743, _71741))))]]], (270 ^ _63568) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _63568) ^ [] : [equivalence_2, 281 ^ _63568 : [(282 ^ _63568) ^ [_72135, _72137] : [-(is_a_theorem(implies(equiv(_72137, _72135), implies(_72135, _72137))))]]], (284 ^ _63568) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _63568) ^ [] : [equivalence_3, 295 ^ _63568 : [(296 ^ _63568) ^ [_72529, _72531] : [-(is_a_theorem(implies(implies(_72531, _72529), implies(implies(_72529, _72531), equiv(_72531, _72529)))))]]], (298 ^ _63568) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _63568) ^ [] : [kn1, 309 ^ _63568 : [(310 ^ _63568) ^ [_72927] : [-(is_a_theorem(implies(_72927, and(_72927, _72927))))]]], (312 ^ _63568) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _63568) ^ [] : [kn2, 322 ^ _63568 : [(323 ^ _63568) ^ [_73263, _73265] : [-(is_a_theorem(implies(and(_73265, _73263), _73265)))]]], (325 ^ _63568) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _63568) ^ [] : [kn3, 336 ^ _63568 : [(337 ^ _63568) ^ [_73662, _73664, _73666] : [-(is_a_theorem(implies(implies(_73666, _73664), implies(not and(_73664, _73662), not and(_73662, _73666)))))]]], (339 ^ _63568) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _63568) ^ [] : [cn1, 351 ^ _63568 : [(352 ^ _63568) ^ [_74164, _74166, _74168] : [-(is_a_theorem(implies(implies(_74168, _74166), implies(implies(_74166, _74164), implies(_74168, _74164)))))]]], (354 ^ _63568) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _63568) ^ [] : [cn2, 366 ^ _63568 : [(367 ^ _63568) ^ [_74636, _74638] : [-(is_a_theorem(implies(_74638, implies(not _74638, _74636))))]]], (369 ^ _63568) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _63568) ^ [] : [cn3, 380 ^ _63568 : [(381 ^ _63568) ^ [_75011] : [-(is_a_theorem(implies(implies(not _75011, _75011), _75011)))]]], (383 ^ _63568) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _63568) ^ [] : [r1, 393 ^ _63568 : [(394 ^ _63568) ^ [_75337] : [-(is_a_theorem(implies(or(_75337, _75337), _75337)))]]], (396 ^ _63568) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _63568) ^ [] : [r2, 406 ^ _63568 : [(407 ^ _63568) ^ [_75673, _75675] : [-(is_a_theorem(implies(_75673, or(_75675, _75673))))]]], (409 ^ _63568) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _63568) ^ [] : [r3, 420 ^ _63568 : [(421 ^ _63568) ^ [_76058, _76060] : [-(is_a_theorem(implies(or(_76060, _76058), or(_76058, _76060))))]]], (423 ^ _63568) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _63568) ^ [] : [r4, 434 ^ _63568 : [(435 ^ _63568) ^ [_76466, _76468, _76470] : [-(is_a_theorem(implies(or(_76470, or(_76468, _76466)), or(_76468, or(_76470, _76466)))))]]], (437 ^ _63568) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _63568) ^ [] : [r5, 449 ^ _63568 : [(450 ^ _63568) ^ [_76935, _76937, _76939] : [-(is_a_theorem(implies(implies(_76937, _76935), implies(or(_76939, _76937), or(_76939, _76935)))))]]], (452 ^ _63568) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 1.08/1.36  ncf('1',plain,[cn2],start(533 ^ 0)).
% 1.08/1.36  ncf('1.1',plain,[-(cn2), is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ [])))],extension(369 ^ 1)).
% 1.08/1.36  ncf('1.1.1',plain,[-(is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ [])))), implies(370 ^ [], not and(not 370 ^ [], not 371 ^ [])) = implies(370 ^ [], implies(not 370 ^ [], 371 ^ [])), is_a_theorem(implies(370 ^ [], not and(not 370 ^ [], not 371 ^ [])))],extension(20 ^ 2,bind([[_64316, _64318], [implies(370 ^ [], implies(not 370 ^ [], 371 ^ [])), implies(370 ^ [], not and(not 370 ^ [], not 371 ^ []))]]))).
% 1.08/1.36  ncf('1.1.1.1',plain,[-(implies(370 ^ [], not and(not 370 ^ [], not 371 ^ [])) = implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), implies(370 ^ [], implies(not 370 ^ [], 371 ^ [])) = implies(370 ^ [], not and(not 370 ^ [], not 371 ^ []))],extension(4 ^ 3,bind([[_63819, _63821], [implies(370 ^ [], not and(not 370 ^ [], not 371 ^ [])), implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))]]))).
% 1.08/1.36  ncf('1.1.1.1.1',plain,[-(implies(370 ^ [], implies(not 370 ^ [], 371 ^ [])) = implies(370 ^ [], not and(not 370 ^ [], not 371 ^ []))), 370 ^ [] = 370 ^ [], implies(not 370 ^ [], 371 ^ []) = (not and(not 370 ^ [], not 371 ^ []))],extension(66 ^ 4,bind([[_65916, _65918, _65920, _65922], [not and(not 370 ^ [], not 371 ^ []), implies(not 370 ^ [], 371 ^ []), 370 ^ [], 370 ^ []]]))).
% 1.08/1.36  ncf('1.1.1.1.1.1',plain,[-(370 ^ [] = 370 ^ [])],extension(2 ^ 5,bind([[_63712], [370 ^ []]]))).
% 1.08/1.36  ncf('1.1.1.1.1.2',plain,[-(implies(not 370 ^ [], 371 ^ []) = (not and(not 370 ^ [], not 371 ^ []))), op_implies_and],extension(473 ^ 5,bind([[_77916, _77918], [371 ^ [], not 370 ^ []]]))).
% 1.08/1.36  ncf('1.1.1.1.1.2.1',plain,[-(op_implies_and)],extension(493 ^ 6)).
% 1.08/1.36  ncf('1.1.1.2',plain,[-(is_a_theorem(implies(370 ^ [], not and(not 370 ^ [], not 371 ^ [])))), implies(370 ^ [], or(370 ^ [], 371 ^ [])) = implies(370 ^ [], not and(not 370 ^ [], not 371 ^ [])), is_a_theorem(implies(370 ^ [], or(370 ^ [], 371 ^ [])))],extension(20 ^ 3,bind([[_64316, _64318], [implies(370 ^ [], not and(not 370 ^ [], not 371 ^ [])), implies(370 ^ [], or(370 ^ [], 371 ^ []))]]))).
% 1.08/1.36  ncf('1.1.1.2.1',plain,[-(implies(370 ^ [], or(370 ^ [], 371 ^ [])) = implies(370 ^ [], not and(not 370 ^ [], not 371 ^ []))), 370 ^ [] = 370 ^ [], or(370 ^ [], 371 ^ []) = (not and(not 370 ^ [], not 371 ^ []))],extension(66 ^ 4,bind([[_65916, _65918, _65920, _65922], [not and(not 370 ^ [], not 371 ^ []), or(370 ^ [], 371 ^ []), 370 ^ [], 370 ^ []]]))).
% 1.08/1.36  ncf('1.1.1.2.1.1',plain,[-(370 ^ [] = 370 ^ [])],extension(2 ^ 5,bind([[_63712], [370 ^ []]]))).
% 1.08/1.36  ncf('1.1.1.2.1.2',plain,[-(or(370 ^ [], 371 ^ []) = (not and(not 370 ^ [], not 371 ^ []))), op_or],extension(461 ^ 5,bind([[_77570, _77572], [371 ^ [], 370 ^ []]]))).
% 1.08/1.36  ncf('1.1.1.2.1.2.1',plain,[-(op_or)],extension(491 ^ 6)).
% 1.08/1.36  ncf('1.1.1.2.2',plain,[-(is_a_theorem(implies(370 ^ [], or(370 ^ [], 371 ^ [])))), or_1],extension(221 ^ 4,bind([[_70473, _70475], [371 ^ [], 370 ^ []]]))).
% 1.08/1.36  ncf('1.1.1.2.2.1',plain,[-(or_1)],extension(513 ^ 5)).
% 1.08/1.36  %-----------------------------------------------------
% 1.08/1.36  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------