%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL455+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n019.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 0.33s 1.37s
% Output   : Proof 0.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL455+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n019.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 15:51:12 EDT 2023
% 0.12/0.33  % 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 ^ _61998) ^ [] : [r2], (20 ^ _61998) ^ [_62746, _62748] : [-(is_a_theorem(_62746)), _62748 = _62746, is_a_theorem(_62748)], (2 ^ _61998) ^ [_62142] : [-(_62142 = _62142)], (4 ^ _61998) ^ [_62249, _62251] : [_62251 = _62249, -(_62249 = _62251)], (10 ^ _61998) ^ [_62453, _62455, _62457] : [-(_62457 = _62453), _62457 = _62455, _62455 = _62453], (30 ^ _61998) ^ [_63071, _63073, _63075, _63077] : [-(or(_63077, _63073) = or(_63075, _63071)), _63077 = _63075, _63073 = _63071], (40 ^ _61998) ^ [_63402, _63404] : [_63404 = _63402, -((not _63404) = (not _63402))], (46 ^ _61998) ^ [_63648, _63650, _63652, _63654] : [-(equiv(_63654, _63650) = equiv(_63652, _63648)), _63654 = _63652, _63650 = _63648], (56 ^ _61998) ^ [_64007, _64009, _64011, _64013] : [-(and(_64013, _64009) = and(_64011, _64007)), _64013 = _64011, _64009 = _64007], (66 ^ _61998) ^ [_64346, _64348, _64350, _64352] : [-(implies(_64352, _64348) = implies(_64350, _64346)), _64352 = _64350, _64348 = _64346], (491 ^ _61998) ^ [] : [-(op_or)], (493 ^ _61998) ^ [] : [-(op_implies_and)], (495 ^ _61998) ^ [] : [-(op_equiv)], (497 ^ _61998) ^ [] : [-(modus_ponens)], (499 ^ _61998) ^ [] : [-(modus_tollens)], (501 ^ _61998) ^ [] : [-(implies_1)], (503 ^ _61998) ^ [] : [-(implies_2)], (505 ^ _61998) ^ [] : [-(implies_3)], (507 ^ _61998) ^ [] : [-(and_1)], (509 ^ _61998) ^ [] : [-(and_2)], (511 ^ _61998) ^ [] : [-(and_3)], (513 ^ _61998) ^ [] : [-(or_1)], (515 ^ _61998) ^ [] : [-(or_2)], (517 ^ _61998) ^ [] : [-(or_3)], (519 ^ _61998) ^ [] : [-(equivalence_1)], (521 ^ _61998) ^ [] : [-(equivalence_2)], (523 ^ _61998) ^ [] : [-(equivalence_3)], (525 ^ _61998) ^ [] : [-(substitution_of_equivalents)], (527 ^ _61998) ^ [] : [-(op_implies_or)], (529 ^ _61998) ^ [] : [-(op_and)], (531 ^ _61998) ^ [] : [-(op_equiv)], (461 ^ _61998) ^ [] : [op_or, 464 ^ _61998 : [(465 ^ _61998) ^ [_76000, _76002] : [-(or(_76002, _76000) = (not and(not _76002, not _76000)))]]], (467 ^ _61998) ^ [] : [op_and, 470 ^ _61998 : [(471 ^ _61998) ^ [_76173, _76175] : [-(and(_76175, _76173) = (not or(not _76175, not _76173)))]]], (473 ^ _61998) ^ [] : [op_implies_and, 476 ^ _61998 : [(477 ^ _61998) ^ [_76346, _76348] : [-(implies(_76348, _76346) = (not and(_76348, not _76346)))]]], (479 ^ _61998) ^ [] : [op_implies_or, 482 ^ _61998 : [(483 ^ _61998) ^ [_76517, _76519] : [-(implies(_76519, _76517) = or(not _76519, _76517))]]], (485 ^ _61998) ^ [] : [op_equiv, 488 ^ _61998 : [(489 ^ _61998) ^ [_76666, _76668] : [-(equiv(_76668, _76666) = and(implies(_76668, _76666), implies(_76666, _76668)))]]], (90 ^ _61998) ^ [] : [93 ^ _61998 : [(94 ^ _61998) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _61998) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _61998) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _61998) ^ [] : [modus_ponens, 79 ^ _61998 : [(80 ^ _61998) ^ [_64804, _64806] : [-(is_a_theorem(_64804)), is_a_theorem(_64806), is_a_theorem(implies(_64806, _64804))]]], (112 ^ _61998) ^ [] : [115 ^ _61998 : [(116 ^ _61998) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _61998) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _61998) ^ [] : [substitution_of_equivalents, 105 ^ _61998 : [(106 ^ _61998) ^ [_65514, _65516] : [is_a_theorem(equiv(_65516, _65514)), -(_65516 = _65514)]]], (122 ^ _61998) ^ [] : [modus_tollens, 125 ^ _61998 : [(126 ^ _61998) ^ [_66061, _66063] : [-(is_a_theorem(implies(implies(not _66061, not _66063), implies(_66063, _66061))))]]], (128 ^ _61998) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _61998) ^ [] : [implies_1, 139 ^ _61998 : [(140 ^ _61998) ^ [_66465, _66467] : [-(is_a_theorem(implies(_66467, implies(_66465, _66467))))]]], (142 ^ _61998) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _61998) ^ [] : [implies_2, 153 ^ _61998 : [(154 ^ _61998) ^ [_66850, _66852] : [-(is_a_theorem(implies(implies(_66852, implies(_66852, _66850)), implies(_66852, _66850))))]]], (156 ^ _61998) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _61998) ^ [] : [implies_3, 167 ^ _61998 : [(168 ^ _61998) ^ [_67267, _67269, _67271] : [-(is_a_theorem(implies(implies(_67271, _67269), implies(implies(_67269, _67267), implies(_67271, _67267)))))]]], (170 ^ _61998) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _61998) ^ [] : [and_1, 182 ^ _61998 : [(183 ^ _61998) ^ [_67739, _67741] : [-(is_a_theorem(implies(and(_67741, _67739), _67741)))]]], (185 ^ _61998) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _61998) ^ [] : [and_2, 196 ^ _61998 : [(197 ^ _61998) ^ [_68124, _68126] : [-(is_a_theorem(implies(and(_68126, _68124), _68124)))]]], (199 ^ _61998) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _61998) ^ [] : [and_3, 210 ^ _61998 : [(211 ^ _61998) ^ [_68509, _68511] : [-(is_a_theorem(implies(_68511, implies(_68509, and(_68511, _68509)))))]]], (213 ^ _61998) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _61998) ^ [] : [or_1, 224 ^ _61998 : [(225 ^ _61998) ^ [_68903, _68905] : [-(is_a_theorem(implies(_68905, or(_68905, _68903))))]]], (227 ^ _61998) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _61998) ^ [] : [or_2, 238 ^ _61998 : [(239 ^ _61998) ^ [_69288, _69290] : [-(is_a_theorem(implies(_69288, or(_69290, _69288))))]]], (241 ^ _61998) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _61998) ^ [] : [or_3, 252 ^ _61998 : [(253 ^ _61998) ^ [_69687, _69689, _69691] : [-(is_a_theorem(implies(implies(_69691, _69687), implies(implies(_69689, _69687), implies(or(_69691, _69689), _69687)))))]]], (255 ^ _61998) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _61998) ^ [] : [equivalence_1, 267 ^ _61998 : [(268 ^ _61998) ^ [_70171, _70173] : [-(is_a_theorem(implies(equiv(_70173, _70171), implies(_70173, _70171))))]]], (270 ^ _61998) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _61998) ^ [] : [equivalence_2, 281 ^ _61998 : [(282 ^ _61998) ^ [_70565, _70567] : [-(is_a_theorem(implies(equiv(_70567, _70565), implies(_70565, _70567))))]]], (284 ^ _61998) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _61998) ^ [] : [equivalence_3, 295 ^ _61998 : [(296 ^ _61998) ^ [_70959, _70961] : [-(is_a_theorem(implies(implies(_70961, _70959), implies(implies(_70959, _70961), equiv(_70961, _70959)))))]]], (298 ^ _61998) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _61998) ^ [] : [kn1, 309 ^ _61998 : [(310 ^ _61998) ^ [_71357] : [-(is_a_theorem(implies(_71357, and(_71357, _71357))))]]], (312 ^ _61998) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _61998) ^ [] : [kn2, 322 ^ _61998 : [(323 ^ _61998) ^ [_71693, _71695] : [-(is_a_theorem(implies(and(_71695, _71693), _71695)))]]], (325 ^ _61998) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _61998) ^ [] : [kn3, 336 ^ _61998 : [(337 ^ _61998) ^ [_72092, _72094, _72096] : [-(is_a_theorem(implies(implies(_72096, _72094), implies(not and(_72094, _72092), not and(_72092, _72096)))))]]], (339 ^ _61998) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _61998) ^ [] : [cn1, 351 ^ _61998 : [(352 ^ _61998) ^ [_72594, _72596, _72598] : [-(is_a_theorem(implies(implies(_72598, _72596), implies(implies(_72596, _72594), implies(_72598, _72594)))))]]], (354 ^ _61998) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _61998) ^ [] : [cn2, 366 ^ _61998 : [(367 ^ _61998) ^ [_73066, _73068] : [-(is_a_theorem(implies(_73068, implies(not _73068, _73066))))]]], (369 ^ _61998) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _61998) ^ [] : [cn3, 380 ^ _61998 : [(381 ^ _61998) ^ [_73441] : [-(is_a_theorem(implies(implies(not _73441, _73441), _73441)))]]], (383 ^ _61998) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _61998) ^ [] : [r1, 393 ^ _61998 : [(394 ^ _61998) ^ [_73767] : [-(is_a_theorem(implies(or(_73767, _73767), _73767)))]]], (396 ^ _61998) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _61998) ^ [] : [r2, 406 ^ _61998 : [(407 ^ _61998) ^ [_74103, _74105] : [-(is_a_theorem(implies(_74103, or(_74105, _74103))))]]], (409 ^ _61998) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _61998) ^ [] : [r3, 420 ^ _61998 : [(421 ^ _61998) ^ [_74488, _74490] : [-(is_a_theorem(implies(or(_74490, _74488), or(_74488, _74490))))]]], (423 ^ _61998) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _61998) ^ [] : [r4, 434 ^ _61998 : [(435 ^ _61998) ^ [_74896, _74898, _74900] : [-(is_a_theorem(implies(or(_74900, or(_74898, _74896)), or(_74898, or(_74900, _74896)))))]]], (437 ^ _61998) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _61998) ^ [] : [r5, 449 ^ _61998 : [(450 ^ _61998) ^ [_75365, _75367, _75369] : [-(is_a_theorem(implies(implies(_75367, _75365), implies(or(_75369, _75367), or(_75369, _75365)))))]]], (452 ^ _61998) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 0.33/1.37  ncf('1',plain,[r2],start(533 ^ 0)).
% 0.33/1.37  ncf('1.1',plain,[-(r2), is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ [])))],extension(409 ^ 1)).
% 0.33/1.37  ncf('1.1.1',plain,[-(is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ [])))), or_2],extension(235 ^ 2,bind([[_69288, _69290], [411 ^ [], 410 ^ []]]))).
% 0.33/1.37  ncf('1.1.1.1',plain,[-(or_2)],extension(515 ^ 3)).
% 0.33/1.37  %-----------------------------------------------------
% 0.33/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------