%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL459+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n003.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 11:33:20 EDT 2023

% Result   : Theorem 0.33s 1.37s
% Output   : Proof 0.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : LCL459+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n003.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 15:46:45 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.33/1.37  
% 0.33/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.33/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/1.37  %-----------------------------------------------------
% 0.33/1.37  ncf(matrix, plain, [(533 ^ _62839) ^ [] : [kn1], (20 ^ _62839) ^ [_63587, _63589] : [-(is_a_theorem(_63587)), _63589 = _63587, is_a_theorem(_63589)], (2 ^ _62839) ^ [_62983] : [-(_62983 = _62983)], (4 ^ _62839) ^ [_63090, _63092] : [_63092 = _63090, -(_63090 = _63092)], (10 ^ _62839) ^ [_63294, _63296, _63298] : [-(_63298 = _63294), _63298 = _63296, _63296 = _63294], (30 ^ _62839) ^ [_63912, _63914, _63916, _63918] : [-(or(_63918, _63914) = or(_63916, _63912)), _63918 = _63916, _63914 = _63912], (40 ^ _62839) ^ [_64243, _64245] : [_64245 = _64243, -((not _64245) = (not _64243))], (46 ^ _62839) ^ [_64489, _64491, _64493, _64495] : [-(equiv(_64495, _64491) = equiv(_64493, _64489)), _64495 = _64493, _64491 = _64489], (56 ^ _62839) ^ [_64848, _64850, _64852, _64854] : [-(and(_64854, _64850) = and(_64852, _64848)), _64854 = _64852, _64850 = _64848], (66 ^ _62839) ^ [_65187, _65189, _65191, _65193] : [-(implies(_65193, _65189) = implies(_65191, _65187)), _65193 = _65191, _65189 = _65187], (491 ^ _62839) ^ [] : [-(op_or)], (493 ^ _62839) ^ [] : [-(op_implies_and)], (495 ^ _62839) ^ [] : [-(op_equiv)], (497 ^ _62839) ^ [] : [-(modus_ponens)], (499 ^ _62839) ^ [] : [-(modus_tollens)], (501 ^ _62839) ^ [] : [-(implies_1)], (503 ^ _62839) ^ [] : [-(implies_2)], (505 ^ _62839) ^ [] : [-(implies_3)], (507 ^ _62839) ^ [] : [-(and_1)], (509 ^ _62839) ^ [] : [-(and_2)], (511 ^ _62839) ^ [] : [-(and_3)], (513 ^ _62839) ^ [] : [-(or_1)], (515 ^ _62839) ^ [] : [-(or_2)], (517 ^ _62839) ^ [] : [-(or_3)], (519 ^ _62839) ^ [] : [-(equivalence_1)], (521 ^ _62839) ^ [] : [-(equivalence_2)], (523 ^ _62839) ^ [] : [-(equivalence_3)], (525 ^ _62839) ^ [] : [-(substitution_of_equivalents)], (527 ^ _62839) ^ [] : [-(op_or)], (529 ^ _62839) ^ [] : [-(op_implies_and)], (531 ^ _62839) ^ [] : [-(op_equiv)], (461 ^ _62839) ^ [] : [op_or, 464 ^ _62839 : [(465 ^ _62839) ^ [_76841, _76843] : [-(or(_76843, _76841) = (not and(not _76843, not _76841)))]]], (467 ^ _62839) ^ [] : [op_and, 470 ^ _62839 : [(471 ^ _62839) ^ [_77014, _77016] : [-(and(_77016, _77014) = (not or(not _77016, not _77014)))]]], (473 ^ _62839) ^ [] : [op_implies_and, 476 ^ _62839 : [(477 ^ _62839) ^ [_77187, _77189] : [-(implies(_77189, _77187) = (not and(_77189, not _77187)))]]], (479 ^ _62839) ^ [] : [op_implies_or, 482 ^ _62839 : [(483 ^ _62839) ^ [_77358, _77360] : [-(implies(_77360, _77358) = or(not _77360, _77358))]]], (485 ^ _62839) ^ [] : [op_equiv, 488 ^ _62839 : [(489 ^ _62839) ^ [_77507, _77509] : [-(equiv(_77509, _77507) = and(implies(_77509, _77507), implies(_77507, _77509)))]]], (90 ^ _62839) ^ [] : [93 ^ _62839 : [(94 ^ _62839) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _62839) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _62839) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _62839) ^ [] : [modus_ponens, 79 ^ _62839 : [(80 ^ _62839) ^ [_65645, _65647] : [-(is_a_theorem(_65645)), is_a_theorem(_65647), is_a_theorem(implies(_65647, _65645))]]], (112 ^ _62839) ^ [] : [115 ^ _62839 : [(116 ^ _62839) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _62839) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _62839) ^ [] : [substitution_of_equivalents, 105 ^ _62839 : [(106 ^ _62839) ^ [_66355, _66357] : [is_a_theorem(equiv(_66357, _66355)), -(_66357 = _66355)]]], (122 ^ _62839) ^ [] : [modus_tollens, 125 ^ _62839 : [(126 ^ _62839) ^ [_66902, _66904] : [-(is_a_theorem(implies(implies(not _66902, not _66904), implies(_66904, _66902))))]]], (128 ^ _62839) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _62839) ^ [] : [implies_1, 139 ^ _62839 : [(140 ^ _62839) ^ [_67306, _67308] : [-(is_a_theorem(implies(_67308, implies(_67306, _67308))))]]], (142 ^ _62839) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _62839) ^ [] : [implies_2, 153 ^ _62839 : [(154 ^ _62839) ^ [_67691, _67693] : [-(is_a_theorem(implies(implies(_67693, implies(_67693, _67691)), implies(_67693, _67691))))]]], (156 ^ _62839) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _62839) ^ [] : [implies_3, 167 ^ _62839 : [(168 ^ _62839) ^ [_68108, _68110, _68112] : [-(is_a_theorem(implies(implies(_68112, _68110), implies(implies(_68110, _68108), implies(_68112, _68108)))))]]], (170 ^ _62839) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _62839) ^ [] : [and_1, 182 ^ _62839 : [(183 ^ _62839) ^ [_68580, _68582] : [-(is_a_theorem(implies(and(_68582, _68580), _68582)))]]], (185 ^ _62839) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _62839) ^ [] : [and_2, 196 ^ _62839 : [(197 ^ _62839) ^ [_68965, _68967] : [-(is_a_theorem(implies(and(_68967, _68965), _68965)))]]], (199 ^ _62839) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _62839) ^ [] : [and_3, 210 ^ _62839 : [(211 ^ _62839) ^ [_69350, _69352] : [-(is_a_theorem(implies(_69352, implies(_69350, and(_69352, _69350)))))]]], (213 ^ _62839) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _62839) ^ [] : [or_1, 224 ^ _62839 : [(225 ^ _62839) ^ [_69744, _69746] : [-(is_a_theorem(implies(_69746, or(_69746, _69744))))]]], (227 ^ _62839) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _62839) ^ [] : [or_2, 238 ^ _62839 : [(239 ^ _62839) ^ [_70129, _70131] : [-(is_a_theorem(implies(_70129, or(_70131, _70129))))]]], (241 ^ _62839) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _62839) ^ [] : [or_3, 252 ^ _62839 : [(253 ^ _62839) ^ [_70528, _70530, _70532] : [-(is_a_theorem(implies(implies(_70532, _70528), implies(implies(_70530, _70528), implies(or(_70532, _70530), _70528)))))]]], (255 ^ _62839) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _62839) ^ [] : [equivalence_1, 267 ^ _62839 : [(268 ^ _62839) ^ [_71012, _71014] : [-(is_a_theorem(implies(equiv(_71014, _71012), implies(_71014, _71012))))]]], (270 ^ _62839) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _62839) ^ [] : [equivalence_2, 281 ^ _62839 : [(282 ^ _62839) ^ [_71406, _71408] : [-(is_a_theorem(implies(equiv(_71408, _71406), implies(_71406, _71408))))]]], (284 ^ _62839) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _62839) ^ [] : [equivalence_3, 295 ^ _62839 : [(296 ^ _62839) ^ [_71800, _71802] : [-(is_a_theorem(implies(implies(_71802, _71800), implies(implies(_71800, _71802), equiv(_71802, _71800)))))]]], (298 ^ _62839) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _62839) ^ [] : [kn1, 309 ^ _62839 : [(310 ^ _62839) ^ [_72198] : [-(is_a_theorem(implies(_72198, and(_72198, _72198))))]]], (312 ^ _62839) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _62839) ^ [] : [kn2, 322 ^ _62839 : [(323 ^ _62839) ^ [_72534, _72536] : [-(is_a_theorem(implies(and(_72536, _72534), _72536)))]]], (325 ^ _62839) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _62839) ^ [] : [kn3, 336 ^ _62839 : [(337 ^ _62839) ^ [_72933, _72935, _72937] : [-(is_a_theorem(implies(implies(_72937, _72935), implies(not and(_72935, _72933), not and(_72933, _72937)))))]]], (339 ^ _62839) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _62839) ^ [] : [cn1, 351 ^ _62839 : [(352 ^ _62839) ^ [_73435, _73437, _73439] : [-(is_a_theorem(implies(implies(_73439, _73437), implies(implies(_73437, _73435), implies(_73439, _73435)))))]]], (354 ^ _62839) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _62839) ^ [] : [cn2, 366 ^ _62839 : [(367 ^ _62839) ^ [_73907, _73909] : [-(is_a_theorem(implies(_73909, implies(not _73909, _73907))))]]], (369 ^ _62839) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _62839) ^ [] : [cn3, 380 ^ _62839 : [(381 ^ _62839) ^ [_74282] : [-(is_a_theorem(implies(implies(not _74282, _74282), _74282)))]]], (383 ^ _62839) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _62839) ^ [] : [r1, 393 ^ _62839 : [(394 ^ _62839) ^ [_74608] : [-(is_a_theorem(implies(or(_74608, _74608), _74608)))]]], (396 ^ _62839) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _62839) ^ [] : [r2, 406 ^ _62839 : [(407 ^ _62839) ^ [_74944, _74946] : [-(is_a_theorem(implies(_74944, or(_74946, _74944))))]]], (409 ^ _62839) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _62839) ^ [] : [r3, 420 ^ _62839 : [(421 ^ _62839) ^ [_75329, _75331] : [-(is_a_theorem(implies(or(_75331, _75329), or(_75329, _75331))))]]], (423 ^ _62839) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _62839) ^ [] : [r4, 434 ^ _62839 : [(435 ^ _62839) ^ [_75737, _75739, _75741] : [-(is_a_theorem(implies(or(_75741, or(_75739, _75737)), or(_75739, or(_75741, _75737)))))]]], (437 ^ _62839) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _62839) ^ [] : [r5, 449 ^ _62839 : [(450 ^ _62839) ^ [_76206, _76208, _76210] : [-(is_a_theorem(implies(implies(_76208, _76206), implies(or(_76210, _76208), or(_76210, _76206)))))]]], (452 ^ _62839) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 0.33/1.37  ncf('1',plain,[kn1],start(533 ^ 0)).
% 0.33/1.37  ncf('1.1',plain,[-(kn1), is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ [])))],extension(312 ^ 1)).
% 0.33/1.37  ncf('1.1.1',plain,[-(is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ [])))), 80 : is_a_theorem(implies(313 ^ [], implies(313 ^ [], and(313 ^ [], 313 ^ [])))), 80 : is_a_theorem(implies(implies(313 ^ [], implies(313 ^ [], and(313 ^ [], 313 ^ []))), implies(313 ^ [], and(313 ^ [], 313 ^ [])))), 80 : modus_ponens],extension(76 ^ 2,bind([[_65645, _65647], [implies(313 ^ [], and(313 ^ [], 313 ^ [])), implies(313 ^ [], implies(313 ^ [], and(313 ^ [], 313 ^ [])))]]))).
% 0.33/1.37  ncf('1.1.1.1',plain,[-(is_a_theorem(implies(313 ^ [], implies(313 ^ [], and(313 ^ [], 313 ^ []))))), and_3],extension(207 ^ 5,bind([[_69350, _69352], [313 ^ [], 313 ^ []]]))).
% 0.33/1.37  ncf('1.1.1.1.1',plain,[-(and_3)],extension(511 ^ 6)).
% 0.33/1.37  ncf('1.1.1.2',plain,[-(is_a_theorem(implies(implies(313 ^ [], implies(313 ^ [], and(313 ^ [], 313 ^ []))), implies(313 ^ [], and(313 ^ [], 313 ^ []))))), implies_2],extension(150 ^ 5,bind([[_67691, _67693], [and(313 ^ [], 313 ^ []), 313 ^ []]]))).
% 0.33/1.37  ncf('1.1.1.2.1',plain,[-(implies_2)],extension(503 ^ 6)).
% 0.33/1.37  ncf('1.1.1.3',plain,[-(modus_ponens)],extension(497 ^ 3)).
% 0.33/1.37  %-----------------------------------------------------
% 0.33/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------