%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.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 0.77s 1.38s
% Output   : Proof 0.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n028.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 16:20:03 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.77/1.38  
% 0.77/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.77/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/1.38  %-----------------------------------------------------
% 0.77/1.38  ncf(matrix, plain, [(533 ^ _63892) ^ [] : [r3], (20 ^ _63892) ^ [_64640, _64642] : [-(is_a_theorem(_64640)), _64642 = _64640, is_a_theorem(_64642)], (2 ^ _63892) ^ [_64036] : [-(_64036 = _64036)], (4 ^ _63892) ^ [_64143, _64145] : [_64145 = _64143, -(_64143 = _64145)], (10 ^ _63892) ^ [_64347, _64349, _64351] : [-(_64351 = _64347), _64351 = _64349, _64349 = _64347], (30 ^ _63892) ^ [_64965, _64967, _64969, _64971] : [-(or(_64971, _64967) = or(_64969, _64965)), _64971 = _64969, _64967 = _64965], (40 ^ _63892) ^ [_65296, _65298] : [_65298 = _65296, -((not _65298) = (not _65296))], (46 ^ _63892) ^ [_65542, _65544, _65546, _65548] : [-(equiv(_65548, _65544) = equiv(_65546, _65542)), _65548 = _65546, _65544 = _65542], (56 ^ _63892) ^ [_65901, _65903, _65905, _65907] : [-(and(_65907, _65903) = and(_65905, _65901)), _65907 = _65905, _65903 = _65901], (66 ^ _63892) ^ [_66240, _66242, _66244, _66246] : [-(implies(_66246, _66242) = implies(_66244, _66240)), _66246 = _66244, _66242 = _66240], (491 ^ _63892) ^ [] : [-(op_or)], (493 ^ _63892) ^ [] : [-(op_implies_and)], (495 ^ _63892) ^ [] : [-(op_equiv)], (497 ^ _63892) ^ [] : [-(modus_ponens)], (499 ^ _63892) ^ [] : [-(modus_tollens)], (501 ^ _63892) ^ [] : [-(implies_1)], (503 ^ _63892) ^ [] : [-(implies_2)], (505 ^ _63892) ^ [] : [-(implies_3)], (507 ^ _63892) ^ [] : [-(and_1)], (509 ^ _63892) ^ [] : [-(and_2)], (511 ^ _63892) ^ [] : [-(and_3)], (513 ^ _63892) ^ [] : [-(or_1)], (515 ^ _63892) ^ [] : [-(or_2)], (517 ^ _63892) ^ [] : [-(or_3)], (519 ^ _63892) ^ [] : [-(equivalence_1)], (521 ^ _63892) ^ [] : [-(equivalence_2)], (523 ^ _63892) ^ [] : [-(equivalence_3)], (525 ^ _63892) ^ [] : [-(substitution_of_equivalents)], (527 ^ _63892) ^ [] : [-(op_implies_or)], (529 ^ _63892) ^ [] : [-(op_and)], (531 ^ _63892) ^ [] : [-(op_equiv)], (461 ^ _63892) ^ [] : [op_or, 464 ^ _63892 : [(465 ^ _63892) ^ [_77894, _77896] : [-(or(_77896, _77894) = (not and(not _77896, not _77894)))]]], (467 ^ _63892) ^ [] : [op_and, 470 ^ _63892 : [(471 ^ _63892) ^ [_78067, _78069] : [-(and(_78069, _78067) = (not or(not _78069, not _78067)))]]], (473 ^ _63892) ^ [] : [op_implies_and, 476 ^ _63892 : [(477 ^ _63892) ^ [_78240, _78242] : [-(implies(_78242, _78240) = (not and(_78242, not _78240)))]]], (479 ^ _63892) ^ [] : [op_implies_or, 482 ^ _63892 : [(483 ^ _63892) ^ [_78411, _78413] : [-(implies(_78413, _78411) = or(not _78413, _78411))]]], (485 ^ _63892) ^ [] : [op_equiv, 488 ^ _63892 : [(489 ^ _63892) ^ [_78560, _78562] : [-(equiv(_78562, _78560) = and(implies(_78562, _78560), implies(_78560, _78562)))]]], (90 ^ _63892) ^ [] : [93 ^ _63892 : [(94 ^ _63892) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _63892) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _63892) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _63892) ^ [] : [modus_ponens, 79 ^ _63892 : [(80 ^ _63892) ^ [_66698, _66700] : [-(is_a_theorem(_66698)), is_a_theorem(_66700), is_a_theorem(implies(_66700, _66698))]]], (112 ^ _63892) ^ [] : [115 ^ _63892 : [(116 ^ _63892) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _63892) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _63892) ^ [] : [substitution_of_equivalents, 105 ^ _63892 : [(106 ^ _63892) ^ [_67408, _67410] : [is_a_theorem(equiv(_67410, _67408)), -(_67410 = _67408)]]], (122 ^ _63892) ^ [] : [modus_tollens, 125 ^ _63892 : [(126 ^ _63892) ^ [_67955, _67957] : [-(is_a_theorem(implies(implies(not _67955, not _67957), implies(_67957, _67955))))]]], (128 ^ _63892) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _63892) ^ [] : [implies_1, 139 ^ _63892 : [(140 ^ _63892) ^ [_68359, _68361] : [-(is_a_theorem(implies(_68361, implies(_68359, _68361))))]]], (142 ^ _63892) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _63892) ^ [] : [implies_2, 153 ^ _63892 : [(154 ^ _63892) ^ [_68744, _68746] : [-(is_a_theorem(implies(implies(_68746, implies(_68746, _68744)), implies(_68746, _68744))))]]], (156 ^ _63892) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _63892) ^ [] : [implies_3, 167 ^ _63892 : [(168 ^ _63892) ^ [_69161, _69163, _69165] : [-(is_a_theorem(implies(implies(_69165, _69163), implies(implies(_69163, _69161), implies(_69165, _69161)))))]]], (170 ^ _63892) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _63892) ^ [] : [and_1, 182 ^ _63892 : [(183 ^ _63892) ^ [_69633, _69635] : [-(is_a_theorem(implies(and(_69635, _69633), _69635)))]]], (185 ^ _63892) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _63892) ^ [] : [and_2, 196 ^ _63892 : [(197 ^ _63892) ^ [_70018, _70020] : [-(is_a_theorem(implies(and(_70020, _70018), _70018)))]]], (199 ^ _63892) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _63892) ^ [] : [and_3, 210 ^ _63892 : [(211 ^ _63892) ^ [_70403, _70405] : [-(is_a_theorem(implies(_70405, implies(_70403, and(_70405, _70403)))))]]], (213 ^ _63892) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _63892) ^ [] : [or_1, 224 ^ _63892 : [(225 ^ _63892) ^ [_70797, _70799] : [-(is_a_theorem(implies(_70799, or(_70799, _70797))))]]], (227 ^ _63892) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _63892) ^ [] : [or_2, 238 ^ _63892 : [(239 ^ _63892) ^ [_71182, _71184] : [-(is_a_theorem(implies(_71182, or(_71184, _71182))))]]], (241 ^ _63892) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _63892) ^ [] : [or_3, 252 ^ _63892 : [(253 ^ _63892) ^ [_71581, _71583, _71585] : [-(is_a_theorem(implies(implies(_71585, _71581), implies(implies(_71583, _71581), implies(or(_71585, _71583), _71581)))))]]], (255 ^ _63892) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _63892) ^ [] : [equivalence_1, 267 ^ _63892 : [(268 ^ _63892) ^ [_72065, _72067] : [-(is_a_theorem(implies(equiv(_72067, _72065), implies(_72067, _72065))))]]], (270 ^ _63892) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _63892) ^ [] : [equivalence_2, 281 ^ _63892 : [(282 ^ _63892) ^ [_72459, _72461] : [-(is_a_theorem(implies(equiv(_72461, _72459), implies(_72459, _72461))))]]], (284 ^ _63892) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _63892) ^ [] : [equivalence_3, 295 ^ _63892 : [(296 ^ _63892) ^ [_72853, _72855] : [-(is_a_theorem(implies(implies(_72855, _72853), implies(implies(_72853, _72855), equiv(_72855, _72853)))))]]], (298 ^ _63892) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _63892) ^ [] : [kn1, 309 ^ _63892 : [(310 ^ _63892) ^ [_73251] : [-(is_a_theorem(implies(_73251, and(_73251, _73251))))]]], (312 ^ _63892) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _63892) ^ [] : [kn2, 322 ^ _63892 : [(323 ^ _63892) ^ [_73587, _73589] : [-(is_a_theorem(implies(and(_73589, _73587), _73589)))]]], (325 ^ _63892) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _63892) ^ [] : [kn3, 336 ^ _63892 : [(337 ^ _63892) ^ [_73986, _73988, _73990] : [-(is_a_theorem(implies(implies(_73990, _73988), implies(not and(_73988, _73986), not and(_73986, _73990)))))]]], (339 ^ _63892) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _63892) ^ [] : [cn1, 351 ^ _63892 : [(352 ^ _63892) ^ [_74488, _74490, _74492] : [-(is_a_theorem(implies(implies(_74492, _74490), implies(implies(_74490, _74488), implies(_74492, _74488)))))]]], (354 ^ _63892) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _63892) ^ [] : [cn2, 366 ^ _63892 : [(367 ^ _63892) ^ [_74960, _74962] : [-(is_a_theorem(implies(_74962, implies(not _74962, _74960))))]]], (369 ^ _63892) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _63892) ^ [] : [cn3, 380 ^ _63892 : [(381 ^ _63892) ^ [_75335] : [-(is_a_theorem(implies(implies(not _75335, _75335), _75335)))]]], (383 ^ _63892) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _63892) ^ [] : [r1, 393 ^ _63892 : [(394 ^ _63892) ^ [_75661] : [-(is_a_theorem(implies(or(_75661, _75661), _75661)))]]], (396 ^ _63892) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _63892) ^ [] : [r2, 406 ^ _63892 : [(407 ^ _63892) ^ [_75997, _75999] : [-(is_a_theorem(implies(_75997, or(_75999, _75997))))]]], (409 ^ _63892) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _63892) ^ [] : [r3, 420 ^ _63892 : [(421 ^ _63892) ^ [_76382, _76384] : [-(is_a_theorem(implies(or(_76384, _76382), or(_76382, _76384))))]]], (423 ^ _63892) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _63892) ^ [] : [r4, 434 ^ _63892 : [(435 ^ _63892) ^ [_76790, _76792, _76794] : [-(is_a_theorem(implies(or(_76794, or(_76792, _76790)), or(_76792, or(_76794, _76790)))))]]], (437 ^ _63892) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _63892) ^ [] : [r5, 449 ^ _63892 : [(450 ^ _63892) ^ [_77259, _77261, _77263] : [-(is_a_theorem(implies(implies(_77261, _77259), implies(or(_77263, _77261), or(_77263, _77259)))))]]], (452 ^ _63892) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 0.77/1.38  ncf('1',plain,[r3],start(533 ^ 0)).
% 0.77/1.38  ncf('1.1',plain,[-(r3), is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ [])))],extension(423 ^ 1)).
% 0.77/1.38  ncf('1.1.1',plain,[-(is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ [])))), 80 : is_a_theorem(implies(425 ^ [], or(425 ^ [], 424 ^ []))), 80 : is_a_theorem(implies(implies(425 ^ [], or(425 ^ [], 424 ^ [])), implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ [])))), 80 : modus_ponens],extension(76 ^ 2,bind([[_66698, _66700], [implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ [])), implies(425 ^ [], or(425 ^ [], 424 ^ []))]]))).
% 0.77/1.38  ncf('1.1.1.1',plain,[-(is_a_theorem(implies(425 ^ [], or(425 ^ [], 424 ^ [])))), or_1],extension(221 ^ 5,bind([[_70797, _70799], [424 ^ [], 425 ^ []]]))).
% 0.77/1.38  ncf('1.1.1.1.1',plain,[-(or_1)],extension(513 ^ 6)).
% 0.77/1.38  ncf('1.1.1.2',plain,[-(is_a_theorem(implies(implies(425 ^ [], or(425 ^ [], 424 ^ [])), implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))))), is_a_theorem(implies(424 ^ [], or(425 ^ [], 424 ^ []))), is_a_theorem(implies(implies(424 ^ [], or(425 ^ [], 424 ^ [])), implies(implies(425 ^ [], or(425 ^ [], 424 ^ [])), implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ [])))))],extension(80 ^ 5,bind([[_66698, _66700], [implies(implies(425 ^ [], or(425 ^ [], 424 ^ [])), implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), implies(424 ^ [], or(425 ^ [], 424 ^ []))]]))).
% 0.77/1.38  ncf('1.1.1.2.1',plain,[-(is_a_theorem(implies(424 ^ [], or(425 ^ [], 424 ^ [])))), or_2],extension(235 ^ 6,bind([[_71182, _71184], [424 ^ [], 425 ^ []]]))).
% 0.77/1.38  ncf('1.1.1.2.1.1',plain,[-(or_2)],extension(515 ^ 7)).
% 0.77/1.38  ncf('1.1.1.2.2',plain,[-(is_a_theorem(implies(implies(424 ^ [], or(425 ^ [], 424 ^ [])), implies(implies(425 ^ [], or(425 ^ [], 424 ^ [])), implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ [])))))), or_3],extension(249 ^ 6,bind([[_71581, _71583, _71585], [or(425 ^ [], 424 ^ []), 425 ^ [], 424 ^ []]]))).
% 0.77/1.38  ncf('1.1.1.2.2.1',plain,[-(or_3)],extension(517 ^ 7)).
% 0.77/1.38  ncf('1.1.1.3',plain,[-(modus_ponens)],extension(497 ^ 3)).
% 0.77/1.38  %-----------------------------------------------------
% 0.77/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------