%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL469+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n017.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 11:33:21 EDT 2023

% Result   : Theorem 0.42s 1.37s
% Output   : Proof 0.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : LCL469+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n017.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 15:38:00 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.42/1.37  
% 0.42/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.42/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/1.37  %-----------------------------------------------------
% 0.42/1.37  ncf(matrix, plain, [(513 ^ _61666) ^ [] : [or_1], (20 ^ _61666) ^ [_62414, _62416] : [-(is_a_theorem(_62414)), _62416 = _62414, is_a_theorem(_62416)], (2 ^ _61666) ^ [_61810] : [-(_61810 = _61810)], (4 ^ _61666) ^ [_61917, _61919] : [_61919 = _61917, -(_61917 = _61919)], (10 ^ _61666) ^ [_62121, _62123, _62125] : [-(_62125 = _62121), _62125 = _62123, _62123 = _62121], (30 ^ _61666) ^ [_62739, _62741, _62743, _62745] : [-(or(_62745, _62741) = or(_62743, _62739)), _62745 = _62743, _62741 = _62739], (40 ^ _61666) ^ [_63070, _63072] : [_63072 = _63070, -((not _63072) = (not _63070))], (46 ^ _61666) ^ [_63316, _63318, _63320, _63322] : [-(equiv(_63322, _63318) = equiv(_63320, _63316)), _63322 = _63320, _63318 = _63316], (56 ^ _61666) ^ [_63675, _63677, _63679, _63681] : [-(and(_63681, _63677) = and(_63679, _63675)), _63681 = _63679, _63677 = _63675], (66 ^ _61666) ^ [_64014, _64016, _64018, _64020] : [-(implies(_64020, _64016) = implies(_64018, _64014)), _64020 = _64018, _64016 = _64014], (491 ^ _61666) ^ [] : [-(op_or)], (493 ^ _61666) ^ [] : [-(op_implies)], (495 ^ _61666) ^ [] : [-(op_equiv)], (497 ^ _61666) ^ [] : [-(modus_ponens)], (499 ^ _61666) ^ [] : [-(cn1)], (501 ^ _61666) ^ [] : [-(cn2)], (503 ^ _61666) ^ [] : [-(cn3)], (505 ^ _61666) ^ [] : [-(substitution_of_equivalents)], (507 ^ _61666) ^ [] : [-(op_or)], (509 ^ _61666) ^ [] : [-(op_implies_and)], (511 ^ _61666) ^ [] : [-(op_equiv)], (461 ^ _61666) ^ [] : [op_or, 464 ^ _61666 : [(465 ^ _61666) ^ [_75668, _75670] : [-(or(_75670, _75668) = (not and(not _75670, not _75668)))]]], (467 ^ _61666) ^ [] : [op_and, 470 ^ _61666 : [(471 ^ _61666) ^ [_75841, _75843] : [-(and(_75843, _75841) = (not or(not _75843, not _75841)))]]], (473 ^ _61666) ^ [] : [op_implies_and, 476 ^ _61666 : [(477 ^ _61666) ^ [_76014, _76016] : [-(implies(_76016, _76014) = (not and(_76016, not _76014)))]]], (479 ^ _61666) ^ [] : [op_implies_or, 482 ^ _61666 : [(483 ^ _61666) ^ [_76185, _76187] : [-(implies(_76187, _76185) = or(not _76187, _76185))]]], (485 ^ _61666) ^ [] : [op_equiv, 488 ^ _61666 : [(489 ^ _61666) ^ [_76334, _76336] : [-(equiv(_76336, _76334) = and(implies(_76336, _76334), implies(_76334, _76336)))]]], (90 ^ _61666) ^ [] : [93 ^ _61666 : [(94 ^ _61666) ^ [] : [-(is_a_theorem(91 ^ []))], (96 ^ _61666) ^ [] : [-(is_a_theorem(implies(91 ^ [], 92 ^ [])))], (98 ^ _61666) ^ [] : [is_a_theorem(92 ^ [])]], -(modus_ponens)], (76 ^ _61666) ^ [] : [modus_ponens, 79 ^ _61666 : [(80 ^ _61666) ^ [_64472, _64474] : [-(is_a_theorem(_64472)), is_a_theorem(_64474), is_a_theorem(implies(_64474, _64472))]]], (112 ^ _61666) ^ [] : [115 ^ _61666 : [(116 ^ _61666) ^ [] : [-(is_a_theorem(equiv(113 ^ [], 114 ^ [])))], (118 ^ _61666) ^ [] : [113 ^ [] = 114 ^ []]], -(substitution_of_equivalents)], (102 ^ _61666) ^ [] : [substitution_of_equivalents, 105 ^ _61666 : [(106 ^ _61666) ^ [_65182, _65184] : [is_a_theorem(equiv(_65184, _65182)), -(_65184 = _65182)]]], (122 ^ _61666) ^ [] : [modus_tollens, 125 ^ _61666 : [(126 ^ _61666) ^ [_65729, _65731] : [-(is_a_theorem(implies(implies(not _65729, not _65731), implies(_65731, _65729))))]]], (128 ^ _61666) ^ [] : [is_a_theorem(implies(implies(not 130 ^ [], not 129 ^ []), implies(129 ^ [], 130 ^ []))), -(modus_tollens)], (136 ^ _61666) ^ [] : [implies_1, 139 ^ _61666 : [(140 ^ _61666) ^ [_66133, _66135] : [-(is_a_theorem(implies(_66135, implies(_66133, _66135))))]]], (142 ^ _61666) ^ [] : [is_a_theorem(implies(143 ^ [], implies(144 ^ [], 143 ^ []))), -(implies_1)], (150 ^ _61666) ^ [] : [implies_2, 153 ^ _61666 : [(154 ^ _61666) ^ [_66518, _66520] : [-(is_a_theorem(implies(implies(_66520, implies(_66520, _66518)), implies(_66520, _66518))))]]], (156 ^ _61666) ^ [] : [is_a_theorem(implies(implies(157 ^ [], implies(157 ^ [], 158 ^ [])), implies(157 ^ [], 158 ^ []))), -(implies_2)], (164 ^ _61666) ^ [] : [implies_3, 167 ^ _61666 : [(168 ^ _61666) ^ [_66935, _66937, _66939] : [-(is_a_theorem(implies(implies(_66939, _66937), implies(implies(_66937, _66935), implies(_66939, _66935)))))]]], (170 ^ _61666) ^ [] : [is_a_theorem(implies(implies(171 ^ [], 172 ^ []), implies(implies(172 ^ [], 173 ^ []), implies(171 ^ [], 173 ^ [])))), -(implies_3)], (179 ^ _61666) ^ [] : [and_1, 182 ^ _61666 : [(183 ^ _61666) ^ [_67407, _67409] : [-(is_a_theorem(implies(and(_67409, _67407), _67409)))]]], (185 ^ _61666) ^ [] : [is_a_theorem(implies(and(186 ^ [], 187 ^ []), 186 ^ [])), -(and_1)], (193 ^ _61666) ^ [] : [and_2, 196 ^ _61666 : [(197 ^ _61666) ^ [_67792, _67794] : [-(is_a_theorem(implies(and(_67794, _67792), _67792)))]]], (199 ^ _61666) ^ [] : [is_a_theorem(implies(and(200 ^ [], 201 ^ []), 201 ^ [])), -(and_2)], (207 ^ _61666) ^ [] : [and_3, 210 ^ _61666 : [(211 ^ _61666) ^ [_68177, _68179] : [-(is_a_theorem(implies(_68179, implies(_68177, and(_68179, _68177)))))]]], (213 ^ _61666) ^ [] : [is_a_theorem(implies(214 ^ [], implies(215 ^ [], and(214 ^ [], 215 ^ [])))), -(and_3)], (221 ^ _61666) ^ [] : [or_1, 224 ^ _61666 : [(225 ^ _61666) ^ [_68571, _68573] : [-(is_a_theorem(implies(_68573, or(_68573, _68571))))]]], (227 ^ _61666) ^ [] : [is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ []))), -(or_1)], (235 ^ _61666) ^ [] : [or_2, 238 ^ _61666 : [(239 ^ _61666) ^ [_68956, _68958] : [-(is_a_theorem(implies(_68956, or(_68958, _68956))))]]], (241 ^ _61666) ^ [] : [is_a_theorem(implies(243 ^ [], or(242 ^ [], 243 ^ []))), -(or_2)], (249 ^ _61666) ^ [] : [or_3, 252 ^ _61666 : [(253 ^ _61666) ^ [_69355, _69357, _69359] : [-(is_a_theorem(implies(implies(_69359, _69355), implies(implies(_69357, _69355), implies(or(_69359, _69357), _69355)))))]]], (255 ^ _61666) ^ [] : [is_a_theorem(implies(implies(256 ^ [], 258 ^ []), implies(implies(257 ^ [], 258 ^ []), implies(or(256 ^ [], 257 ^ []), 258 ^ [])))), -(or_3)], (264 ^ _61666) ^ [] : [equivalence_1, 267 ^ _61666 : [(268 ^ _61666) ^ [_69839, _69841] : [-(is_a_theorem(implies(equiv(_69841, _69839), implies(_69841, _69839))))]]], (270 ^ _61666) ^ [] : [is_a_theorem(implies(equiv(271 ^ [], 272 ^ []), implies(271 ^ [], 272 ^ []))), -(equivalence_1)], (278 ^ _61666) ^ [] : [equivalence_2, 281 ^ _61666 : [(282 ^ _61666) ^ [_70233, _70235] : [-(is_a_theorem(implies(equiv(_70235, _70233), implies(_70233, _70235))))]]], (284 ^ _61666) ^ [] : [is_a_theorem(implies(equiv(285 ^ [], 286 ^ []), implies(286 ^ [], 285 ^ []))), -(equivalence_2)], (292 ^ _61666) ^ [] : [equivalence_3, 295 ^ _61666 : [(296 ^ _61666) ^ [_70627, _70629] : [-(is_a_theorem(implies(implies(_70629, _70627), implies(implies(_70627, _70629), equiv(_70629, _70627)))))]]], (298 ^ _61666) ^ [] : [is_a_theorem(implies(implies(299 ^ [], 300 ^ []), implies(implies(300 ^ [], 299 ^ []), equiv(299 ^ [], 300 ^ [])))), -(equivalence_3)], (306 ^ _61666) ^ [] : [kn1, 309 ^ _61666 : [(310 ^ _61666) ^ [_71025] : [-(is_a_theorem(implies(_71025, and(_71025, _71025))))]]], (312 ^ _61666) ^ [] : [is_a_theorem(implies(313 ^ [], and(313 ^ [], 313 ^ []))), -(kn1)], (319 ^ _61666) ^ [] : [kn2, 322 ^ _61666 : [(323 ^ _61666) ^ [_71361, _71363] : [-(is_a_theorem(implies(and(_71363, _71361), _71363)))]]], (325 ^ _61666) ^ [] : [is_a_theorem(implies(and(326 ^ [], 327 ^ []), 326 ^ [])), -(kn2)], (333 ^ _61666) ^ [] : [kn3, 336 ^ _61666 : [(337 ^ _61666) ^ [_71760, _71762, _71764] : [-(is_a_theorem(implies(implies(_71764, _71762), implies(not and(_71762, _71760), not and(_71760, _71764)))))]]], (339 ^ _61666) ^ [] : [is_a_theorem(implies(implies(340 ^ [], 341 ^ []), implies(not and(341 ^ [], 342 ^ []), not and(342 ^ [], 340 ^ [])))), -(kn3)], (348 ^ _61666) ^ [] : [cn1, 351 ^ _61666 : [(352 ^ _61666) ^ [_72262, _72264, _72266] : [-(is_a_theorem(implies(implies(_72266, _72264), implies(implies(_72264, _72262), implies(_72266, _72262)))))]]], (354 ^ _61666) ^ [] : [is_a_theorem(implies(implies(355 ^ [], 356 ^ []), implies(implies(356 ^ [], 357 ^ []), implies(355 ^ [], 357 ^ [])))), -(cn1)], (363 ^ _61666) ^ [] : [cn2, 366 ^ _61666 : [(367 ^ _61666) ^ [_72734, _72736] : [-(is_a_theorem(implies(_72736, implies(not _72736, _72734))))]]], (369 ^ _61666) ^ [] : [is_a_theorem(implies(370 ^ [], implies(not 370 ^ [], 371 ^ []))), -(cn2)], (377 ^ _61666) ^ [] : [cn3, 380 ^ _61666 : [(381 ^ _61666) ^ [_73109] : [-(is_a_theorem(implies(implies(not _73109, _73109), _73109)))]]], (383 ^ _61666) ^ [] : [is_a_theorem(implies(implies(not 384 ^ [], 384 ^ []), 384 ^ [])), -(cn3)], (390 ^ _61666) ^ [] : [r1, 393 ^ _61666 : [(394 ^ _61666) ^ [_73435] : [-(is_a_theorem(implies(or(_73435, _73435), _73435)))]]], (396 ^ _61666) ^ [] : [is_a_theorem(implies(or(397 ^ [], 397 ^ []), 397 ^ [])), -(r1)], (403 ^ _61666) ^ [] : [r2, 406 ^ _61666 : [(407 ^ _61666) ^ [_73771, _73773] : [-(is_a_theorem(implies(_73771, or(_73773, _73771))))]]], (409 ^ _61666) ^ [] : [is_a_theorem(implies(411 ^ [], or(410 ^ [], 411 ^ []))), -(r2)], (417 ^ _61666) ^ [] : [r3, 420 ^ _61666 : [(421 ^ _61666) ^ [_74156, _74158] : [-(is_a_theorem(implies(or(_74158, _74156), or(_74156, _74158))))]]], (423 ^ _61666) ^ [] : [is_a_theorem(implies(or(424 ^ [], 425 ^ []), or(425 ^ [], 424 ^ []))), -(r3)], (431 ^ _61666) ^ [] : [r4, 434 ^ _61666 : [(435 ^ _61666) ^ [_74564, _74566, _74568] : [-(is_a_theorem(implies(or(_74568, or(_74566, _74564)), or(_74566, or(_74568, _74564)))))]]], (437 ^ _61666) ^ [] : [is_a_theorem(implies(or(438 ^ [], or(439 ^ [], 440 ^ [])), or(439 ^ [], or(438 ^ [], 440 ^ [])))), -(r4)], (446 ^ _61666) ^ [] : [r5, 449 ^ _61666 : [(450 ^ _61666) ^ [_75033, _75035, _75037] : [-(is_a_theorem(implies(implies(_75035, _75033), implies(or(_75037, _75035), or(_75037, _75033)))))]]], (452 ^ _61666) ^ [] : [is_a_theorem(implies(implies(454 ^ [], 455 ^ []), implies(or(453 ^ [], 454 ^ []), or(453 ^ [], 455 ^ [])))), -(r5)]], input).
% 0.42/1.37  ncf('1',plain,[or_1],start(513 ^ 0)).
% 0.42/1.37  ncf('1.1',plain,[-(or_1), is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ [])))],extension(227 ^ 1)).
% 0.42/1.37  ncf('1.1.1',plain,[-(is_a_theorem(implies(228 ^ [], or(228 ^ [], 229 ^ [])))), implies(228 ^ [], not and(not 228 ^ [], not 229 ^ [])) = implies(228 ^ [], or(228 ^ [], 229 ^ [])), is_a_theorem(implies(228 ^ [], not and(not 228 ^ [], not 229 ^ [])))],extension(20 ^ 2,bind([[_62414, _62416], [implies(228 ^ [], or(228 ^ [], 229 ^ [])), implies(228 ^ [], not and(not 228 ^ [], not 229 ^ []))]]))).
% 0.42/1.37  ncf('1.1.1.1',plain,[-(implies(228 ^ [], not and(not 228 ^ [], not 229 ^ [])) = implies(228 ^ [], or(228 ^ [], 229 ^ []))), implies(228 ^ [], or(228 ^ [], 229 ^ [])) = implies(228 ^ [], not and(not 228 ^ [], not 229 ^ []))],extension(4 ^ 3,bind([[_61917, _61919], [implies(228 ^ [], not and(not 228 ^ [], not 229 ^ [])), implies(228 ^ [], or(228 ^ [], 229 ^ []))]]))).
% 0.42/1.37  ncf('1.1.1.1.1',plain,[-(implies(228 ^ [], or(228 ^ [], 229 ^ [])) = implies(228 ^ [], not and(not 228 ^ [], not 229 ^ []))), 228 ^ [] = 228 ^ [], or(228 ^ [], 229 ^ []) = (not and(not 228 ^ [], not 229 ^ []))],extension(66 ^ 4,bind([[_64014, _64016, _64018, _64020], [not and(not 228 ^ [], not 229 ^ []), or(228 ^ [], 229 ^ []), 228 ^ [], 228 ^ []]]))).
% 0.42/1.37  ncf('1.1.1.1.1.1',plain,[-(228 ^ [] = 228 ^ [])],extension(2 ^ 5,bind([[_61810], [228 ^ []]]))).
% 0.42/1.37  ncf('1.1.1.1.1.2',plain,[-(or(228 ^ [], 229 ^ []) = (not and(not 228 ^ [], not 229 ^ []))), op_or],extension(461 ^ 5,bind([[_75668, _75670], [229 ^ [], 228 ^ []]]))).
% 0.42/1.37  ncf('1.1.1.1.1.2.1',plain,[-(op_or)],extension(491 ^ 6)).
% 0.42/1.37  ncf('1.1.1.2',plain,[-(is_a_theorem(implies(228 ^ [], not and(not 228 ^ [], not 229 ^ [])))), implies(228 ^ [], implies(not 228 ^ [], 229 ^ [])) = implies(228 ^ [], not and(not 228 ^ [], not 229 ^ [])), is_a_theorem(implies(228 ^ [], implies(not 228 ^ [], 229 ^ [])))],extension(20 ^ 3,bind([[_62414, _62416], [implies(228 ^ [], not and(not 228 ^ [], not 229 ^ [])), implies(228 ^ [], implies(not 228 ^ [], 229 ^ []))]]))).
% 0.42/1.37  ncf('1.1.1.2.1',plain,[-(implies(228 ^ [], implies(not 228 ^ [], 229 ^ [])) = implies(228 ^ [], not and(not 228 ^ [], not 229 ^ []))), 228 ^ [] = 228 ^ [], implies(not 228 ^ [], 229 ^ []) = (not and(not 228 ^ [], not 229 ^ []))],extension(66 ^ 4,bind([[_64014, _64016, _64018, _64020], [not and(not 228 ^ [], not 229 ^ []), implies(not 228 ^ [], 229 ^ []), 228 ^ [], 228 ^ []]]))).
% 0.42/1.37  ncf('1.1.1.2.1.1',plain,[-(228 ^ [] = 228 ^ [])],extension(2 ^ 5,bind([[_61810], [228 ^ []]]))).
% 0.42/1.37  ncf('1.1.1.2.1.2',plain,[-(implies(not 228 ^ [], 229 ^ []) = (not and(not 228 ^ [], not 229 ^ []))), op_implies_and],extension(473 ^ 5,bind([[_76014, _76016], [229 ^ [], not 228 ^ []]]))).
% 0.42/1.37  ncf('1.1.1.2.1.2.1',plain,[-(op_implies_and)],extension(509 ^ 6)).
% 0.42/1.37  ncf('1.1.1.2.2',plain,[-(is_a_theorem(implies(228 ^ [], implies(not 228 ^ [], 229 ^ [])))), cn2],extension(363 ^ 4,bind([[_72734, _72736], [229 ^ [], 228 ^ []]]))).
% 0.42/1.37  ncf('1.1.1.2.2.1',plain,[-(cn2)],extension(501 ^ 5)).
% 0.42/1.37  %-----------------------------------------------------
% 0.42/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------