%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL490+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n026.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 11:33:22 EDT 2023

% Result   : Theorem 0.64s 1.39s
% Output   : Proof 0.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : LCL490+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.13  % Command  : nanocop.sh %s %d
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May 18 16:30:05 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.64/1.39  
% 0.64/1.39  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.64/1.39  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/1.39  %-----------------------------------------------------
% 0.64/1.39  ncf(matrix, plain, [(517 ^ _63663) ^ [] : [or_1], (20 ^ _63663) ^ [_64411, _64413] : [-(is_a_theorem(_64411)), _64413 = _64411, is_a_theorem(_64413)], (2 ^ _63663) ^ [_63807] : [-(_63807 = _63807)], (4 ^ _63663) ^ [_63914, _63916] : [_63916 = _63914, -(_63914 = _63916)], (10 ^ _63663) ^ [_64118, _64120, _64122] : [-(_64122 = _64118), _64122 = _64120, _64120 = _64118], (30 ^ _63663) ^ [_64736, _64738, _64740, _64742] : [-(or(_64742, _64738) = or(_64740, _64736)), _64742 = _64740, _64738 = _64736], (40 ^ _63663) ^ [_65067, _65069] : [_65069 = _65067, -((not _65069) = (not _65067))], (46 ^ _63663) ^ [_65313, _65315, _65317, _65319] : [-(equiv(_65319, _65315) = equiv(_65317, _65313)), _65319 = _65317, _65315 = _65313], (56 ^ _63663) ^ [_65672, _65674, _65676, _65678] : [-(and(_65678, _65674) = and(_65676, _65672)), _65678 = _65676, _65674 = _65672], (66 ^ _63663) ^ [_66011, _66013, _66015, _66017] : [-(implies(_66017, _66013) = implies(_66015, _66011)), _66017 = _66015, _66013 = _66011], (491 ^ _63663) ^ [] : [-(op_implies_or)], (493 ^ _63663) ^ [] : [-(op_and)], (495 ^ _63663) ^ [] : [-(op_equiv)], (497 ^ _63663) ^ [] : [-(modus_ponens)], (499 ^ _63663) ^ [] : [-(r1)], (501 ^ _63663) ^ [] : [-(r2)], (503 ^ _63663) ^ [] : [-(r3)], (505 ^ _63663) ^ [] : [-(r4)], (507 ^ _63663) ^ [] : [-(r5)], (509 ^ _63663) ^ [] : [-(substitution_of_equivalents)], (511 ^ _63663) ^ [] : [-(op_or)], (513 ^ _63663) ^ [] : [-(op_implies_and)], (515 ^ _63663) ^ [] : [-(op_equiv)], (461 ^ _63663) ^ [] : [op_or, 464 ^ _63663 : [(465 ^ _63663) ^ [_77665, _77667] : [-(or(_77667, _77665) = (not and(not _77667, not _77665)))]]], (467 ^ _63663) ^ [] : [op_and, 470 ^ _63663 : [(471 ^ _63663) ^ [_77838, _77840] : [-(and(_77840, _77838) = (not or(not _77840, not _77838)))]]], (473 ^ _63663) ^ [] : [op_implies_and, 476 ^ _63663 : [(477 ^ _63663) ^ [_78011, _78013] : [-(implies(_78013, _78011) = (not and(_78013, not _78011)))]]], (479 ^ _63663) ^ [] : [op_implies_or, 482 ^ _63663 : [(483 ^ _63663) ^ [_78182, _78184] : [-(implies(_78184, _78182) = or(not _78184, _78182))]]], (485 ^ _63663) ^ [] : [op_equiv, 488 ^ _63663 : [(489 ^ _63663) ^ [_78331, _78333] : [-(equiv(_78333, _78331) = and(implies(_78333, _78331), implies(_78331, _78333)))]]], (90 ^ _63663) ^ [] : [93 ^ _63663 : [(94 ^ _63663) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _63663) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _63663) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _63663) ^ [] : [modus_ponens, 79 ^ _63663 : [(80 ^ _63663) ^ [_66469, _66471] : [-(is_a_theorem(_66469)), is_a_theorem(_66471), is_a_theorem(implies(_66471, _66469))]]], (112 ^ _63663) ^ [] : [115 ^ _63663 : [(116 ^ _63663) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _63663) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _63663) ^ [] : [substitution_of_equivalents, 105 ^ _63663 : [(106 ^ _63663) ^ [_67179, _67181] : [is_a_theorem(equiv(_67181, _67179)), -(_67181 = _67179)]]], (122 ^ _63663) ^ [] : [modus_tollens, 125 ^ _63663 : [(126 ^ _63663) ^ [_67726, _67728] : [-(is_a_theorem(implies(implies(not _67726, not _67728), implies(_67728, _67726))))]]], (128 ^ _63663) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _63663) ^ [] : [implies_1, 139 ^ _63663 : [(140 ^ _63663) ^ [_68130, _68132] : [-(is_a_theorem(implies(_68132, implies(_68130, _68132))))]]], (142 ^ _63663) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _63663) ^ [] : [implies_2, 153 ^ _63663 : [(154 ^ _63663) ^ [_68515, _68517] : [-(is_a_theorem(implies(implies(_68517, implies(_68517, _68515)), implies(_68517, _68515))))]]], (156 ^ _63663) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _63663) ^ [] : [implies_3, 167 ^ _63663 : [(168 ^ _63663) ^ [_68932, _68934, _68936] : [-(is_a_theorem(implies(implies(_68936, _68934), implies(implies(_68934, _68932), implies(_68936, _68932)))))]]], (170 ^ _63663) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _63663) ^ [] : [and_1, 182 ^ _63663 : [(183 ^ _63663) ^ [_69404, _69406] : [-(is_a_theorem(implies(and(_69406, _69404), _69406)))]]], (185 ^ _63663) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _63663) ^ [] : [and_2, 196 ^ _63663 : [(197 ^ _63663) ^ [_69789, _69791] : [-(is_a_theorem(implies(and(_69791, _69789), _69789)))]]], (199 ^ _63663) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _63663) ^ [] : [and_3, 210 ^ _63663 : [(211 ^ _63663) ^ [_70174, _70176] : [-(is_a_theorem(implies(_70176, implies(_70174, and(_70176, _70174)))))]]], (213 ^ _63663) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _63663) ^ [] : [or_1, 224 ^ _63663 : [(225 ^ _63663) ^ [_70568, _70570] : [-(is_a_theorem(implies(_70570, or(_70570, _70568))))]]], (227 ^ _63663) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _63663) ^ [] : [or_2, 238 ^ _63663 : [(239 ^ _63663) ^ [_70953, _70955] : [-(is_a_theorem(implies(_70953, or(_70955, _70953))))]]], (241 ^ _63663) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _63663) ^ [] : [or_3, 252 ^ _63663 : [(253 ^ _63663) ^ [_71352, _71354, _71356] : [-(is_a_theorem(implies(implies(_71356, _71352), implies(implies(_71354, _71352), implies(or(_71356, _71354), _71352)))))]]], (255 ^ _63663) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _63663) ^ [] : [equivalence_1, 267 ^ _63663 : [(268 ^ _63663) ^ [_71836, _71838] : [-(is_a_theorem(implies(equiv(_71838, _71836), implies(_71838, _71836))))]]], (270 ^ _63663) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _63663) ^ [] : [equivalence_2, 281 ^ _63663 : [(282 ^ _63663) ^ [_72230, _72232] : [-(is_a_theorem(implies(equiv(_72232, _72230), implies(_72230, _72232))))]]], (284 ^ _63663) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _63663) ^ [] : [equivalence_3, 295 ^ _63663 : [(296 ^ _63663) ^ [_72624, _72626] : [-(is_a_theorem(implies(implies(_72626, _72624), implies(implies(_72624, _72626), equiv(_72626, _72624)))))]]], (298 ^ _63663) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _63663) ^ [] : [kn1, 309 ^ _63663 : [(310 ^ _63663) ^ [_73022] : [-(is_a_theorem(implies(_73022, and(_73022, _73022))))]]], (312 ^ _63663) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _63663) ^ [] : [kn2, 322 ^ _63663 : [(323 ^ _63663) ^ [_73358, _73360] : [-(is_a_theorem(implies(and(_73360, _73358), _73360)))]]], (325 ^ _63663) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _63663) ^ [] : [kn3, 336 ^ _63663 : [(337 ^ _63663) ^ [_73757, _73759, _73761] : [-(is_a_theorem(implies(implies(_73761, _73759), implies(not and(_73759, _73757), not and(_73757, _73761)))))]]], (339 ^ _63663) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _63663) ^ [] : [cn1, 351 ^ _63663 : [(352 ^ _63663) ^ [_74259, _74261, _74263] : [-(is_a_theorem(implies(implies(_74263, _74261), implies(implies(_74261, _74259), implies(_74263, _74259)))))]]], (354 ^ _63663) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _63663) ^ [] : [cn2, 366 ^ _63663 : [(367 ^ _63663) ^ [_74731, _74733] : [-(is_a_theorem(implies(_74733, implies(not _74733, _74731))))]]], (369 ^ _63663) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _63663) ^ [] : [cn3, 380 ^ _63663 : [(381 ^ _63663) ^ [_75106] : [-(is_a_theorem(implies(implies(not _75106, _75106), _75106)))]]], (383 ^ _63663) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _63663) ^ [] : [r1, 393 ^ _63663 : [(394 ^ _63663) ^ [_75432] : [-(is_a_theorem(implies(or(_75432, _75432), _75432)))]]], (396 ^ _63663) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _63663) ^ [] : [r2, 406 ^ _63663 : [(407 ^ _63663) ^ [_75768, _75770] : [-(is_a_theorem(implies(_75768, or(_75770, _75768))))]]], (409 ^ _63663) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _63663) ^ [] : [r3, 420 ^ _63663 : [(421 ^ _63663) ^ [_76153, _76155] : [-(is_a_theorem(implies(or(_76155, _76153), or(_76153, _76155))))]]], (423 ^ _63663) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _63663) ^ [] : [r4, 434 ^ _63663 : [(435 ^ _63663) ^ [_76561, _76563, _76565] : [-(is_a_theorem(implies(or(_76565, or(_76563, _76561)), or(_76563, or(_76565, _76561)))))]]], (437 ^ _63663) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _63663) ^ [] : [r5, 449 ^ _63663 : [(450 ^ _63663) ^ [_77030, _77032, _77034] : [-(is_a_theorem(implies(implies(_77032, _77030), implies(or(_77034, _77032), or(_77034, _77030)))))]]], (452 ^ _63663) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 0.64/1.39  ncf('1',plain,[or_1],start(517 ^ 0)).
% 0.64/1.39  ncf('1.1',plain,[-(or_1), is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ [])))],extension(227 ^ 1)).
% 0.64/1.39  ncf('1.1.1',plain,[-(is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ [])))), or(not 228 ^ [], or(228 ^ [], 229 ^ [])) = implies(228 ^ [], or(228 ^ [], 229 ^ [])), is_a_theorem(or(not 228 ^ [], or(228 ^ [], 229 ^ [])))],extension(20 ^ 2,bind([[_64411, _64413], [implies(228 ^ [], or(228 ^ [], 229 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ []))]]))).
% 0.64/1.39  ncf('1.1.1.1',plain,[-(or(not 228 ^ [], or(228 ^ [], 229 ^ [])) = implies(228 ^ [], or(228 ^ [], 229 ^ []))), implies(228 ^ [], or(228 ^ [], 229 ^ [])) = or(not 228 ^ [], or(228 ^ [], 229 ^ []))],extension(4 ^ 3,bind([[_63914, _63916], [or(not 228 ^ [], or(228 ^ [], 229 ^ [])), implies(228 ^ [], or(228 ^ [], 229 ^ []))]]))).
% 0.64/1.39  ncf('1.1.1.1.1',plain,[-(implies(228 ^ [], or(228 ^ [], 229 ^ [])) = or(not 228 ^ [], or(228 ^ [], 229 ^ []))), implies(228 ^ [], or(228 ^ [], 229 ^ [])) = or(not 228 ^ [], or(228 ^ [], 229 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ [])) = or(not 228 ^ [], or(228 ^ [], 229 ^ []))],extension(10 ^ 4,bind([[_64118, _64120, _64122], [or(not 228 ^ [], or(228 ^ [], 229 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ [])), implies(228 ^ [], or(228 ^ [], 229 ^ []))]]))).
% 0.64/1.39  ncf('1.1.1.1.1.1',plain,[-(implies(228 ^ [], or(228 ^ [], 229 ^ [])) = or(not 228 ^ [], or(228 ^ [], 229 ^ []))), op_implies_or],extension(479 ^ 5,bind([[_78182, _78184], [or(228 ^ [], 229 ^ []), 228 ^ []]]))).
% 0.64/1.39  ncf('1.1.1.1.1.1.1',plain,[-(op_implies_or)],extension(491 ^ 6)).
% 0.64/1.39  ncf('1.1.1.1.1.2',plain,[-(or(not 228 ^ [], or(228 ^ [], 229 ^ [])) = or(not 228 ^ [], or(228 ^ [], 229 ^ [])))],extension(2 ^ 5,bind([[_63807], [or(not 228 ^ [], or(228 ^ [], 229 ^ []))]]))).
% 0.64/1.39  ncf('1.1.1.2',plain,[-(is_a_theorem(or(not 228 ^ [], or(228 ^ [], 229 ^ [])))), 80 : is_a_theorem(or(not 228 ^ [], or(229 ^ [], 228 ^ []))), 80 : is_a_theorem(implies(or(not 228 ^ [], or(229 ^ [], 228 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ [])))), 80 : modus_ponens],extension(76 ^ 3,bind([[_66469, _66471], [or(not 228 ^ [], or(228 ^ [], 229 ^ [])), or(not 228 ^ [], or(229 ^ [], 228 ^ []))]]))).
% 0.64/1.39  ncf('1.1.1.2.1',plain,[-(is_a_theorem(or(not 228 ^ [], or(229 ^ [], 228 ^ [])))), implies(228 ^ [], or(229 ^ [], 228 ^ [])) = or(not 228 ^ [], or(229 ^ [], 228 ^ [])), is_a_theorem(implies(228 ^ [], or(229 ^ [], 228 ^ [])))],extension(20 ^ 6,bind([[_64411, _64413], [or(not 228 ^ [], or(229 ^ [], 228 ^ [])), implies(228 ^ [], or(229 ^ [], 228 ^ []))]]))).
% 0.64/1.39  ncf('1.1.1.2.1.1',plain,[-(implies(228 ^ [], or(229 ^ [], 228 ^ [])) = or(not 228 ^ [], or(229 ^ [], 228 ^ []))), op_implies_or],extension(479 ^ 7,bind([[_78182, _78184], [or(229 ^ [], 228 ^ []), 228 ^ []]]))).
% 0.64/1.39  ncf('1.1.1.2.1.1.1',plain,[-(op_implies_or)],extension(491 ^ 8)).
% 0.64/1.39  ncf('1.1.1.2.1.2',plain,[-(is_a_theorem(implies(228 ^ [], or(229 ^ [], 228 ^ [])))), r2],extension(403 ^ 7,bind([[_75768, _75770], [228 ^ [], 229 ^ []]]))).
% 0.64/1.39  ncf('1.1.1.2.1.2.1',plain,[-(r2)],extension(501 ^ 8)).
% 0.64/1.39  ncf('1.1.1.2.2',plain,[-(is_a_theorem(implies(or(not 228 ^ [], or(229 ^ [], 228 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ []))))), is_a_theorem(implies(or(229 ^ [], 228 ^ []), or(228 ^ [], 229 ^ []))), is_a_theorem(implies(implies(or(229 ^ [], 228 ^ []), or(228 ^ [], 229 ^ [])), implies(or(not 228 ^ [], or(229 ^ [], 228 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ [])))))],extension(80 ^ 6,bind([[_66469, _66471], [implies(or(not 228 ^ [], or(229 ^ [], 228 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ []))), implies(or(229 ^ [], 228 ^ []), or(228 ^ [], 229 ^ []))]]))).
% 0.64/1.39  ncf('1.1.1.2.2.1',plain,[-(is_a_theorem(implies(or(229 ^ [], 228 ^ []), or(228 ^ [], 229 ^ [])))), r3],extension(417 ^ 7,bind([[_76153, _76155], [228 ^ [], 229 ^ []]]))).
% 0.64/1.39  ncf('1.1.1.2.2.1.1',plain,[-(r3)],extension(503 ^ 8)).
% 0.64/1.39  ncf('1.1.1.2.2.2',plain,[-(is_a_theorem(implies(implies(or(229 ^ [], 228 ^ []), or(228 ^ [], 229 ^ [])), implies(or(not 228 ^ [], or(229 ^ [], 228 ^ [])), or(not 228 ^ [], or(228 ^ [], 229 ^ [])))))), r5],extension(446 ^ 7,bind([[_77030, _77032, _77034], [or(228 ^ [], 229 ^ []), or(229 ^ [], 228 ^ []), not 228 ^ []]]))).
% 0.64/1.39  ncf('1.1.1.2.2.2.1',plain,[-(r5)],extension(507 ^ 8)).
% 0.64/1.39  ncf('1.1.1.2.3',plain,[-(modus_ponens)],extension(497 ^ 4)).
% 0.64/1.39  %-----------------------------------------------------
% 0.64/1.39  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------