%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL483+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n002.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 0.87s 1.37s
% Output   : Proof 0.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL483+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n002.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 16:05:04 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.87/1.37  
% 0.87/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.87/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.87/1.37  %-----------------------------------------------------
% 0.87/1.37  ncf(matrix, plain, [(517 ^ _62350) ^ [] : [modus_tollens], (20 ^ _62350) ^ [_63098, _63100] : [-(is_a_theorem(_63098)), _63100 = _63098, is_a_theorem(_63100)], (2 ^ _62350) ^ [_62494] : [-(_62494 = _62494)], (4 ^ _62350) ^ [_62601, _62603] : [_62603 = _62601, -(_62601 = _62603)], (10 ^ _62350) ^ [_62805, _62807, _62809] : [-(_62809 = _62805), _62809 = _62807, _62807 = _62805], (30 ^ _62350) ^ [_63423, _63425, _63427, _63429] : [-(or(_63429, _63425) = or(_63427, _63423)), _63429 = _63427, _63425 = _63423], (40 ^ _62350) ^ [_63754, _63756] : [_63756 = _63754, -((not _63756) = (not _63754))], (46 ^ _62350) ^ [_64000, _64002, _64004, _64006] : [-(equiv(_64006, _64002) = equiv(_64004, _64000)), _64006 = _64004, _64002 = _64000], (56 ^ _62350) ^ [_64359, _64361, _64363, _64365] : [-(and(_64365, _64361) = and(_64363, _64359)), _64365 = _64363, _64361 = _64359], (66 ^ _62350) ^ [_64698, _64700, _64702, _64704] : [-(implies(_64704, _64700) = implies(_64702, _64698)), _64704 = _64702, _64700 = _64698], (491 ^ _62350) ^ [] : [-(op_implies_or)], (493 ^ _62350) ^ [] : [-(op_and)], (495 ^ _62350) ^ [] : [-(op_equiv)], (497 ^ _62350) ^ [] : [-(modus_ponens)], (499 ^ _62350) ^ [] : [-(r1)], (501 ^ _62350) ^ [] : [-(r2)], (503 ^ _62350) ^ [] : [-(r3)], (505 ^ _62350) ^ [] : [-(r4)], (507 ^ _62350) ^ [] : [-(r5)], (509 ^ _62350) ^ [] : [-(substitution_of_equivalents)], (511 ^ _62350) ^ [] : [-(op_or)], (513 ^ _62350) ^ [] : [-(op_implies_and)], (515 ^ _62350) ^ [] : [-(op_equiv)], (461 ^ _62350) ^ [] : [op_or, 464 ^ _62350 : [(465 ^ _62350) ^ [_76352, _76354] : [-(or(_76354, _76352) = (not and(not _76354, not _76352)))]]], (467 ^ _62350) ^ [] : [op_and, 470 ^ _62350 : [(471 ^ _62350) ^ [_76525, _76527] : [-(and(_76527, _76525) = (not or(not _76527, not _76525)))]]], (473 ^ _62350) ^ [] : [op_implies_and, 476 ^ _62350 : [(477 ^ _62350) ^ [_76698, _76700] : [-(implies(_76700, _76698) = (not and(_76700, not _76698)))]]], (479 ^ _62350) ^ [] : [op_implies_or, 482 ^ _62350 : [(483 ^ _62350) ^ [_76869, _76871] : [-(implies(_76871, _76869) = or(not _76871, _76869))]]], (485 ^ _62350) ^ [] : [op_equiv, 488 ^ _62350 : [(489 ^ _62350) ^ [_77018, _77020] : [-(equiv(_77020, _77018) = and(implies(_77020, _77018), implies(_77018, _77020)))]]], (90 ^ _62350) ^ [] : [93 ^ _62350 : [(94 ^ _62350) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _62350) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _62350) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _62350) ^ [] : [modus_ponens, 79 ^ _62350 : [(80 ^ _62350) ^ [_65156, _65158] : [-(is_a_theorem(_65156)), is_a_theorem(_65158), is_a_theorem(implies(_65158, _65156))]]], (112 ^ _62350) ^ [] : [115 ^ _62350 : [(116 ^ _62350) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _62350) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _62350) ^ [] : [substitution_of_equivalents, 105 ^ _62350 : [(106 ^ _62350) ^ [_65866, _65868] : [is_a_theorem(equiv(_65868, _65866)), -(_65868 = _65866)]]], (122 ^ _62350) ^ [] : [modus_tollens, 125 ^ _62350 : [(126 ^ _62350) ^ [_66413, _66415] : [-(is_a_theorem(implies(implies(not _66413, not _66415), implies(_66415, _66413))))]]], (128 ^ _62350) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _62350) ^ [] : [implies_1, 139 ^ _62350 : [(140 ^ _62350) ^ [_66817, _66819] : [-(is_a_theorem(implies(_66819, implies(_66817, _66819))))]]], (142 ^ _62350) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _62350) ^ [] : [implies_2, 153 ^ _62350 : [(154 ^ _62350) ^ [_67202, _67204] : [-(is_a_theorem(implies(implies(_67204, implies(_67204, _67202)), implies(_67204, _67202))))]]], (156 ^ _62350) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _62350) ^ [] : [implies_3, 167 ^ _62350 : [(168 ^ _62350) ^ [_67619, _67621, _67623] : [-(is_a_theorem(implies(implies(_67623, _67621), implies(implies(_67621, _67619), implies(_67623, _67619)))))]]], (170 ^ _62350) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _62350) ^ [] : [and_1, 182 ^ _62350 : [(183 ^ _62350) ^ [_68091, _68093] : [-(is_a_theorem(implies(and(_68093, _68091), _68093)))]]], (185 ^ _62350) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _62350) ^ [] : [and_2, 196 ^ _62350 : [(197 ^ _62350) ^ [_68476, _68478] : [-(is_a_theorem(implies(and(_68478, _68476), _68476)))]]], (199 ^ _62350) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _62350) ^ [] : [and_3, 210 ^ _62350 : [(211 ^ _62350) ^ [_68861, _68863] : [-(is_a_theorem(implies(_68863, implies(_68861, and(_68863, _68861)))))]]], (213 ^ _62350) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _62350) ^ [] : [or_1, 224 ^ _62350 : [(225 ^ _62350) ^ [_69255, _69257] : [-(is_a_theorem(implies(_69257, or(_69257, _69255))))]]], (227 ^ _62350) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _62350) ^ [] : [or_2, 238 ^ _62350 : [(239 ^ _62350) ^ [_69640, _69642] : [-(is_a_theorem(implies(_69640, or(_69642, _69640))))]]], (241 ^ _62350) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _62350) ^ [] : [or_3, 252 ^ _62350 : [(253 ^ _62350) ^ [_70039, _70041, _70043] : [-(is_a_theorem(implies(implies(_70043, _70039), implies(implies(_70041, _70039), implies(or(_70043, _70041), _70039)))))]]], (255 ^ _62350) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _62350) ^ [] : [equivalence_1, 267 ^ _62350 : [(268 ^ _62350) ^ [_70523, _70525] : [-(is_a_theorem(implies(equiv(_70525, _70523), implies(_70525, _70523))))]]], (270 ^ _62350) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _62350) ^ [] : [equivalence_2, 281 ^ _62350 : [(282 ^ _62350) ^ [_70917, _70919] : [-(is_a_theorem(implies(equiv(_70919, _70917), implies(_70917, _70919))))]]], (284 ^ _62350) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _62350) ^ [] : [equivalence_3, 295 ^ _62350 : [(296 ^ _62350) ^ [_71311, _71313] : [-(is_a_theorem(implies(implies(_71313, _71311), implies(implies(_71311, _71313), equiv(_71313, _71311)))))]]], (298 ^ _62350) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _62350) ^ [] : [kn1, 309 ^ _62350 : [(310 ^ _62350) ^ [_71709] : [-(is_a_theorem(implies(_71709, and(_71709, _71709))))]]], (312 ^ _62350) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _62350) ^ [] : [kn2, 322 ^ _62350 : [(323 ^ _62350) ^ [_72045, _72047] : [-(is_a_theorem(implies(and(_72047, _72045), _72047)))]]], (325 ^ _62350) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _62350) ^ [] : [kn3, 336 ^ _62350 : [(337 ^ _62350) ^ [_72444, _72446, _72448] : [-(is_a_theorem(implies(implies(_72448, _72446), implies(not and(_72446, _72444), not and(_72444, _72448)))))]]], (339 ^ _62350) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _62350) ^ [] : [cn1, 351 ^ _62350 : [(352 ^ _62350) ^ [_72946, _72948, _72950] : [-(is_a_theorem(implies(implies(_72950, _72948), implies(implies(_72948, _72946), implies(_72950, _72946)))))]]], (354 ^ _62350) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _62350) ^ [] : [cn2, 366 ^ _62350 : [(367 ^ _62350) ^ [_73418, _73420] : [-(is_a_theorem(implies(_73420, implies(not _73420, _73418))))]]], (369 ^ _62350) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _62350) ^ [] : [cn3, 380 ^ _62350 : [(381 ^ _62350) ^ [_73793] : [-(is_a_theorem(implies(implies(not _73793, _73793), _73793)))]]], (383 ^ _62350) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _62350) ^ [] : [r1, 393 ^ _62350 : [(394 ^ _62350) ^ [_74119] : [-(is_a_theorem(implies(or(_74119, _74119), _74119)))]]], (396 ^ _62350) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _62350) ^ [] : [r2, 406 ^ _62350 : [(407 ^ _62350) ^ [_74455, _74457] : [-(is_a_theorem(implies(_74455, or(_74457, _74455))))]]], (409 ^ _62350) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _62350) ^ [] : [r3, 420 ^ _62350 : [(421 ^ _62350) ^ [_74840, _74842] : [-(is_a_theorem(implies(or(_74842, _74840), or(_74840, _74842))))]]], (423 ^ _62350) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _62350) ^ [] : [r4, 434 ^ _62350 : [(435 ^ _62350) ^ [_75248, _75250, _75252] : [-(is_a_theorem(implies(or(_75252, or(_75250, _75248)), or(_75250, or(_75252, _75248)))))]]], (437 ^ _62350) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _62350) ^ [] : [r5, 449 ^ _62350 : [(450 ^ _62350) ^ [_75717, _75719, _75721] : [-(is_a_theorem(implies(implies(_75719, _75717), implies(or(_75721, _75719), or(_75721, _75717)))))]]], (452 ^ _62350) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 0.87/1.37  ncf('1',plain,[modus_tollens],start(517 ^ 0)).
% 0.87/1.37  ncf('1.1',plain,[-(modus_tollens), is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ [])))],extension(128 ^ 1)).
% 0.87/1.37  ncf('1.1.1',plain,[-(is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ [])))), implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ [])) = implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ [])), is_a_theorem(implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ [])))],extension(20 ^ 2,bind([[_63098, _63100], [implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ [])), implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ []))]]))).
% 0.87/1.37  ncf('1.1.1.1',plain,[-(implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ [])) = implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ [])) = implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ []))],extension(4 ^ 3,bind([[_62601, _62603], [implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ [])), implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))]]))).
% 0.87/1.37  ncf('1.1.1.1.1',plain,[-(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ [])) = implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ []))), implies(not 130 ^ [], not 129 ^ []) = (not and(not 130 ^ [], not not 129 ^ [])), implies(129 ^ [], 130 ^ []) = or(not 129 ^ [], 130 ^ [])],extension(66 ^ 4,bind([[_64698, _64700, _64702, _64704], [or(not 129 ^ [], 130 ^ []), implies(129 ^ [], 130 ^ []), not and(not 130 ^ [], not not 129 ^ []), implies(not 130 ^ [], not 129 ^ [])]]))).
% 0.87/1.37  ncf('1.1.1.1.1.1',plain,[-(implies(not 130 ^ [], not 129 ^ []) = (not and(not 130 ^ [], not not 129 ^ []))), op_implies_and],extension(473 ^ 5,bind([[_76698, _76700], [not 129 ^ [], not 130 ^ []]]))).
% 0.87/1.37  ncf('1.1.1.1.1.1.1',plain,[-(op_implies_and)],extension(513 ^ 6)).
% 0.87/1.37  ncf('1.1.1.1.1.2',plain,[-(implies(129 ^ [], 130 ^ []) = or(not 129 ^ [], 130 ^ [])), op_implies_or],extension(479 ^ 5,bind([[_76869, _76871], [130 ^ [], 129 ^ []]]))).
% 0.87/1.37  ncf('1.1.1.1.1.2.1',plain,[-(op_implies_or)],extension(491 ^ 6)).
% 0.87/1.37  ncf('1.1.1.2',plain,[-(is_a_theorem(implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ [])))), implies(or(130 ^ [], not 129 ^ []), or(not 129 ^ [], 130 ^ [])) = implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ [])), is_a_theorem(implies(or(130 ^ [], not 129 ^ []), or(not 129 ^ [], 130 ^ [])))],extension(20 ^ 3,bind([[_63098, _63100], [implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ [])), implies(or(130 ^ [], not 129 ^ []), or(not 129 ^ [], 130 ^ []))]]))).
% 0.87/1.37  ncf('1.1.1.2.1',plain,[-(implies(or(130 ^ [], not 129 ^ []), or(not 129 ^ [], 130 ^ [])) = implies(not and(not 130 ^ [], not not 129 ^ []), or(not 129 ^ [], 130 ^ []))), or(130 ^ [], not 129 ^ []) = (not and(not 130 ^ [], not not 129 ^ [])), or(not 129 ^ [], 130 ^ []) = or(not 129 ^ [], 130 ^ [])],extension(66 ^ 4,bind([[_64698, _64700, _64702, _64704], [or(not 129 ^ [], 130 ^ []), or(not 129 ^ [], 130 ^ []), not and(not 130 ^ [], not not 129 ^ []), or(130 ^ [], not 129 ^ [])]]))).
% 0.87/1.37  ncf('1.1.1.2.1.1',plain,[-(or(130 ^ [], not 129 ^ []) = (not and(not 130 ^ [], not not 129 ^ []))), op_or],extension(461 ^ 5,bind([[_76352, _76354], [not 129 ^ [], 130 ^ []]]))).
% 0.87/1.37  ncf('1.1.1.2.1.1.1',plain,[-(op_or)],extension(511 ^ 6)).
% 0.87/1.37  ncf('1.1.1.2.1.2',plain,[-(or(not 129 ^ [], 130 ^ []) = or(not 129 ^ [], 130 ^ []))],extension(2 ^ 5,bind([[_62494], [or(not 129 ^ [], 130 ^ [])]]))).
% 0.87/1.37  ncf('1.1.1.2.2',plain,[-(is_a_theorem(implies(or(130 ^ [], not 129 ^ []), or(not 129 ^ [], 130 ^ [])))), r3],extension(417 ^ 4,bind([[_74840, _74842], [not 129 ^ [], 130 ^ []]]))).
% 0.87/1.37  ncf('1.1.1.2.2.1',plain,[-(r3)],extension(503 ^ 5)).
% 0.87/1.37  %-----------------------------------------------------
% 0.87/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------