%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n016.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 11:55:06 EDT 2023

% Result   : Theorem 101.03s 98.52s
% Output   : Proof 101.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Thu May 18 19:43:26 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 101.03/98.52  
% 101.03/98.52  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 101.03/98.52  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.03/98.52  %-----------------------------------------------------
% 101.03/98.52  ncf(matrix, plain, [(716 ^ _105873) ^ [] : [-(member(712 ^ [], universal_class))], (718 ^ _105873) ^ [] : [-(member(713 ^ [], universal_class))], (720 ^ _105873) ^ [] : [-(714 ^ [] = ordered_pair(712 ^ [], 713 ^ []))], (722 ^ _105873) ^ [] : [first(714 ^ []) = 712 ^ [], second(714 ^ []) = 713 ^ []], (2 ^ _105873) ^ [_106017] : [-(_106017 = _106017)], (4 ^ _105873) ^ [_106124, _106126] : [_106126 = _106124, -(_106124 = _106126)], (10 ^ _105873) ^ [_106328, _106330, _106332] : [-(_106332 = _106328), _106332 = _106330, _106330 = _106328], (20 ^ _105873) ^ [_106641, _106643] : [-(inductive(_106641)), _106643 = _106641, inductive(_106643)], (30 ^ _105873) ^ [_106964, _106966, _106968, _106970] : [-(subclass(_106968, _106964)), subclass(_106970, _106966), _106970 = _106968, _106966 = _106964], (44 ^ _105873) ^ [_107408, _107410, _107412, _107414] : [-(disjoint(_107412, _107408)), disjoint(_107414, _107410), _107414 = _107412, _107410 = _107408], (58 ^ _105873) ^ [_107824, _107826] : [-(function(_107824)), _107826 = _107824, function(_107826)], (68 ^ _105873) ^ [_108127, _108129, _108131, _108133] : [-(member(_108131, _108127)), member(_108133, _108129), _108133 = _108131, _108129 = _108127], (82 ^ _105873) ^ [_108585, _108587, _108589, _108591] : [-(unordered_pair(_108591, _108587) = unordered_pair(_108589, _108585)), _108591 = _108589, _108587 = _108585], (92 ^ _105873) ^ [_108916, _108918] : [_108918 = _108916, -(complement(_108918) = complement(_108916))], (98 ^ _105873) ^ [_109162, _109164, _109166, _109168] : [-(intersection(_109168, _109164) = intersection(_109166, _109162)), _109168 = _109166, _109164 = _109162], (108 ^ _105873) ^ [_109493, _109495] : [_109495 = _109493, -(rotate(_109495) = rotate(_109493))], (114 ^ _105873) ^ [_109739, _109741, _109743, _109745] : [-(union(_109745, _109741) = union(_109743, _109739)), _109745 = _109743, _109741 = _109739], (124 ^ _105873) ^ [_110070, _110072] : [_110072 = _110070, -(successor(_110072) = successor(_110070))], (130 ^ _105873) ^ [_110288, _110290] : [_110290 = _110288, -(flip(_110290) = flip(_110288))], (136 ^ _105873) ^ [_110506, _110508] : [_110508 = _110506, -(domain_of(_110508) = domain_of(_110506))], (142 ^ _105873) ^ [_110724, _110726] : [_110726 = _110724, -(range_of(_110726) = range_of(_110724))], (148 ^ _105873) ^ [_110998, _111000, _111002, _111004, _111006, _111008] : [-(restrict(_111008, _111004, _111000) = restrict(_111006, _111002, _110998)), _111008 = _111006, _111004 = _111002, _111000 = _110998], (162 ^ _105873) ^ [_111458, _111460] : [_111460 = _111458, -(power_class(_111460) = power_class(_111458))], (168 ^ _105873) ^ [_111704, _111706, _111708, _111710] : [-(cross_product(_111710, _111706) = cross_product(_111708, _111704)), _111710 = _111708, _111706 = _111704], (178 ^ _105873) ^ [_112063, _112065, _112067, _112069] : [-(compose(_112069, _112065) = compose(_112067, _112063)), _112069 = _112067, _112065 = _112063], (188 ^ _105873) ^ [_112394, _112396] : [_112396 = _112394, -(inverse(_112396) = inverse(_112394))], (194 ^ _105873) ^ [_112612, _112614] : [_112614 = _112612, -(sum_class(_112614) = sum_class(_112612))], (200 ^ _105873) ^ [_112858, _112860, _112862, _112864] : [-(image(_112864, _112860) = image(_112862, _112858)), _112864 = _112862, _112860 = _112858], (210 ^ _105873) ^ [_113189, _113191] : [_113191 = _113189, -(singleton(_113191) = singleton(_113189))], (216 ^ _105873) ^ [_113435, _113437, _113439, _113441] : [-(apply(_113441, _113437) = apply(_113439, _113435)), _113441 = _113439, _113437 = _113435], (226 ^ _105873) ^ [_113794, _113796, _113798, _113800] : [-(ordered_pair(_113800, _113796) = ordered_pair(_113798, _113794)), _113800 = _113798, _113796 = _113794], (236 ^ _105873) ^ [_114125, _114127] : [_114127 = _114125, -(first(_114127) = first(_114125))], (242 ^ _105873) ^ [_114323, _114325] : [_114325 = _114323, -(second(_114325) = second(_114323))], (258 ^ _105873) ^ [_114972, _114974] : [260 ^ _105873 : [(261 ^ _105873) ^ [] : [-(member(259 ^ [_114972, _114974], _114974))], (263 ^ _105873) ^ [] : [member(259 ^ [_114972, _114974], _114972)]], -(subclass(_114974, _114972))], (248 ^ _105873) ^ [_114658, _114660] : [subclass(_114660, _114658), 251 ^ _105873 : [(252 ^ _105873) ^ [_114795] : [member(_114795, _114660), -(member(_114795, _114658))]]], (267 ^ _105873) ^ [_115300] : [-(subclass(_115300, universal_class))], (269 ^ _105873) ^ [_115436, _115438] : [_115438 = _115436, 272 ^ _105873 : [(273 ^ _105873) ^ [] : [-(subclass(_115438, _115436))], (275 ^ _105873) ^ [] : [-(subclass(_115436, _115438))]]], (277 ^ _105873) ^ [_115673, _115675] : [-(_115675 = _115673), subclass(_115675, _115673), subclass(_115673, _115675)], (287 ^ _105873) ^ [_116017, _116019, _116021] : [member(_116021, unordered_pair(_116019, _116017)), 290 ^ _105873 : [(291 ^ _105873) ^ [] : [-(member(_116021, universal_class))], (293 ^ _105873) ^ [] : [-(_116021 = _116019), -(_116021 = _116017)]]], (299 ^ _105873) ^ [_116362, _116364, _116366] : [-(member(_116366, unordered_pair(_116364, _116362))), member(_116366, universal_class), 304 ^ _105873 : [(305 ^ _105873) ^ [] : [_116366 = _116364], (307 ^ _105873) ^ [] : [_116366 = _116362]]], (311 ^ _105873) ^ [_116740, _116742] : [-(member(unordered_pair(_116742, _116740), universal_class))], (313 ^ _105873) ^ [_116823] : [-(singleton(_116823) = unordered_pair(_116823, _116823))], (315 ^ _105873) ^ [_116920, _116922] : [-(ordered_pair(_116922, _116920) = unordered_pair(singleton(_116922), unordered_pair(_116922, singleton(_116920))))], (317 ^ _105873) ^ [_117099, _117101, _117103, _117105] : [member(ordered_pair(_117105, _117103), cross_product(_117101, _117099)), 320 ^ _105873 : [(321 ^ _105873) ^ [] : [-(member(_117105, _117101))], (323 ^ _105873) ^ [] : [-(member(_117103, _117099))]]], (325 ^ _105873) ^ [_117364, _117366, _117368, _117370] : [-(member(ordered_pair(_117370, _117368), cross_product(_117366, _117364))), member(_117370, _117366), member(_117368, _117364)], (335 ^ _105873) ^ [_117697, _117699] : [342 ^ _105873 : [(343 ^ _105873) ^ [] : [-(first(ordered_pair(_117699, _117697)) = _117699)], (345 ^ _105873) ^ [] : [-(second(ordered_pair(_117699, _117697)) = _117697)]], member(_117699, universal_class), member(_117697, universal_class)], (347 ^ _105873) ^ [_118105, _118107, _118109] : [member(_118105, cross_product(_118109, _118107)), -(_118105 = ordered_pair(first(_118105), second(_118105)))], (353 ^ _105873) ^ [_118370, _118372] : [member(ordered_pair(_118372, _118370), element_relation), 356 ^ _105873 : [(357 ^ _105873) ^ [] : [-(member(_118370, universal_class))], (359 ^ _105873) ^ [] : [-(member(_118372, _118370))]]], (361 ^ _105873) ^ [_118613, _118615] : [-(member(ordered_pair(_118615, _118613), element_relation)), member(_118613, universal_class), member(_118615, _118613)], (371 ^ _105873) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _105873) ^ [_119016, _119018, _119020] : [member(_119016, intersection(_119020, _119018)), 376 ^ _105873 : [(377 ^ _105873) ^ [] : [-(member(_119016, _119020))], (379 ^ _105873) ^ [] : [-(member(_119016, _119018))]]], (381 ^ _105873) ^ [_119267, _119269, _119271] : [-(member(_119267, intersection(_119271, _119269))), member(_119267, _119271), member(_119267, _119269)], (391 ^ _105873) ^ [_119613, _119615] : [member(_119613, complement(_119615)), 394 ^ _105873 : [(395 ^ _105873) ^ [] : [-(member(_119613, universal_class))], (397 ^ _105873) ^ [] : [member(_119613, _119615)]]], (399 ^ _105873) ^ [_119855, _119857] : [-(member(_119855, complement(_119857))), member(_119855, universal_class), -(member(_119855, _119857))], (409 ^ _105873) ^ [_120162, _120164, _120166] : [-(restrict(_120164, _120166, _120162) = intersection(_120164, cross_product(_120166, _120162)))], (411 ^ _105873) ^ [_120253] : [member(_120253, null_class)], (413 ^ _105873) ^ [_120389, _120391] : [member(_120389, domain_of(_120391)), 416 ^ _105873 : [(417 ^ _105873) ^ [] : [-(member(_120389, universal_class))], (419 ^ _105873) ^ [] : [restrict(_120391, singleton(_120389), universal_class) = null_class]]], (421 ^ _105873) ^ [_120643, _120645] : [-(member(_120643, domain_of(_120645))), member(_120643, universal_class), -(restrict(_120645, singleton(_120643), universal_class) = null_class)], (431 ^ _105873) ^ [_121020, _121022, _121024, _121026] : [member(ordered_pair(ordered_pair(_121024, _121022), _121020), rotate(_121026)), 434 ^ _105873 : [(435 ^ _105873) ^ [] : [-(member(ordered_pair(ordered_pair(_121024, _121022), _121020), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _105873) ^ [] : [-(member(ordered_pair(ordered_pair(_121022, _121020), _121024), _121026))]]], (439 ^ _105873) ^ [_121313, _121315, _121317, _121319] : [-(member(ordered_pair(ordered_pair(_121317, _121315), _121313), rotate(_121319))), member(ordered_pair(ordered_pair(_121317, _121315), _121313), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_121315, _121313), _121317), _121319)], (449 ^ _105873) ^ [_121645] : [-(subclass(rotate(_121645), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _105873) ^ [_121811, _121813, _121815, _121817] : [member(ordered_pair(ordered_pair(_121817, _121815), _121813), flip(_121811)), 454 ^ _105873 : [(455 ^ _105873) ^ [] : [-(member(ordered_pair(ordered_pair(_121817, _121815), _121813), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _105873) ^ [] : [-(member(ordered_pair(ordered_pair(_121815, _121817), _121813), _121811))]]], (459 ^ _105873) ^ [_122104, _122106, _122108, _122110] : [-(member(ordered_pair(ordered_pair(_122110, _122108), _122106), flip(_122104))), member(ordered_pair(ordered_pair(_122110, _122108), _122106), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_122108, _122110), _122106), _122104)], (469 ^ _105873) ^ [_122436] : [-(subclass(flip(_122436), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _105873) ^ [_122856, _122858, _122860] : [482 ^ _105873 : [(483 ^ _105873) ^ [] : [member(_122856, _122860)], (485 ^ _105873) ^ [] : [member(_122856, _122858)]], -(member(_122856, union(_122860, _122858)))], (471 ^ _105873) ^ [_122588, _122590, _122592] : [member(_122588, union(_122592, _122590)), -(member(_122588, _122592)), -(member(_122588, _122590))], (489 ^ _105873) ^ [_123127] : [-(successor(_123127) = union(_123127, singleton(_123127)))], (491 ^ _105873) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _105873) ^ [_123323, _123325] : [member(ordered_pair(_123325, _123323), successor_relation), 496 ^ _105873 : [(497 ^ _105873) ^ [] : [-(member(_123325, universal_class))], (499 ^ _105873) ^ [] : [-(member(_123323, universal_class))], (501 ^ _105873) ^ [] : [-(successor(_123325) = _123323)]]], (503 ^ _105873) ^ [_123644, _123646] : [-(member(ordered_pair(_123646, _123644), successor_relation)), member(_123646, universal_class), member(_123644, universal_class), successor(_123646) = _123644], (517 ^ _105873) ^ [_124015] : [-(inverse(_124015) = domain_of(flip(cross_product(_124015, universal_class))))], (519 ^ _105873) ^ [_124102] : [-(range_of(_124102) = domain_of(inverse(_124102)))], (521 ^ _105873) ^ [_124200, _124202] : [-(image(_124200, _124202) = range_of(restrict(_124200, _124202, universal_class)))], (523 ^ _105873) ^ [_124333] : [inductive(_124333), 526 ^ _105873 : [(527 ^ _105873) ^ [] : [-(member(null_class, _124333))], (529 ^ _105873) ^ [] : [-(subclass(image(successor_relation, _124333), _124333))]]], (531 ^ _105873) ^ [_124566] : [-(inductive(_124566)), member(null_class, _124566), subclass(image(successor_relation, _124566), _124566)], (542 ^ _105873) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _105873) ^ [] : [-(inductive(540 ^ []))], (546 ^ _105873) ^ [_125011] : [inductive(_125011), -(subclass(540 ^ [], _125011))], (552 ^ _105873) ^ [_125246, _125248] : [member(_125248, sum_class(_125246)), 556 ^ _105873 : [(557 ^ _105873) ^ [] : [-(member(_125248, 555 ^ [_125246, _125248]))], (559 ^ _105873) ^ [] : [-(member(555 ^ [_125246, _125248], _125246))]]], (561 ^ _105873) ^ [_125557, _125559] : [-(member(_125559, sum_class(_125557))), 562 ^ _105873 : [(563 ^ _105873) ^ [_125651] : [member(_125559, _125651), member(_125651, _125557)]]], (571 ^ _105873) ^ [_125911] : [member(_125911, universal_class), -(member(sum_class(_125911), universal_class))], (577 ^ _105873) ^ [_126148, _126150] : [member(_126150, power_class(_126148)), 580 ^ _105873 : [(581 ^ _105873) ^ [] : [-(member(_126150, universal_class))], (583 ^ _105873) ^ [] : [-(subclass(_126150, _126148))]]], (585 ^ _105873) ^ [_126389, _126391] : [-(member(_126391, power_class(_126389))), member(_126391, universal_class), subclass(_126391, _126389)], (595 ^ _105873) ^ [_126680] : [member(_126680, universal_class), -(member(power_class(_126680), universal_class))], (601 ^ _105873) ^ [_126873, _126875] : [-(subclass(compose(_126873, _126875), cross_product(universal_class, universal_class)))], (603 ^ _105873) ^ [_127042, _127044, _127046, _127048] : [member(ordered_pair(_127044, _127042), compose(_127046, _127048)), 606 ^ _105873 : [(607 ^ _105873) ^ [] : [-(member(_127044, universal_class))], (609 ^ _105873) ^ [] : [-(member(_127042, image(_127046, image(_127048, singleton(_127044)))))]]], (611 ^ _105873) ^ [_127323, _127325, _127327, _127329] : [-(member(ordered_pair(_127325, _127323), compose(_127327, _127329))), member(_127325, universal_class), member(_127323, image(_127327, image(_127329, singleton(_127325))))], (621 ^ _105873) ^ [_127687] : [member(_127687, identity_relation), 625 ^ _105873 : [(626 ^ _105873) ^ [] : [-(member(624 ^ [_127687], universal_class))], (628 ^ _105873) ^ [] : [-(_127687 = ordered_pair(624 ^ [_127687], 624 ^ [_127687]))]]], (630 ^ _105873) ^ [_127992] : [-(member(_127992, identity_relation)), 631 ^ _105873 : [(632 ^ _105873) ^ [_128085] : [member(_128085, universal_class), _127992 = ordered_pair(_128085, _128085)]]], (640 ^ _105873) ^ [_128368] : [function(_128368), 643 ^ _105873 : [(644 ^ _105873) ^ [] : [-(subclass(_128368, cross_product(universal_class, universal_class)))], (646 ^ _105873) ^ [] : [-(subclass(compose(_128368, inverse(_128368)), identity_relation))]]], (648 ^ _105873) ^ [_128605] : [-(function(_128605)), subclass(_128605, cross_product(universal_class, universal_class)), subclass(compose(_128605, inverse(_128605)), identity_relation)], (658 ^ _105873) ^ [_128904, _128906] : [-(member(image(_128904, _128906), universal_class)), member(_128906, universal_class), function(_128904)], (678 ^ _105873) ^ [_129551, _129553] : [680 ^ _105873 : [(681 ^ _105873) ^ [] : [-(member(679 ^ [_129551, _129553], _129553))], (683 ^ _105873) ^ [] : [-(member(679 ^ [_129551, _129553], _129551))]], -(disjoint(_129553, _129551))], (668 ^ _105873) ^ [_129236, _129238] : [disjoint(_129238, _129236), 671 ^ _105873 : [(672 ^ _105873) ^ [_129375] : [member(_129375, _129238), member(_129375, _129236)]]], (687 ^ _105873) ^ [_129899] : [-(_129899 = null_class), 691 ^ _105873 : [(692 ^ _105873) ^ [] : [-(member(690 ^ [_129899], universal_class))], (694 ^ _105873) ^ [] : [-(member(690 ^ [_129899], _129899))], (696 ^ _105873) ^ [] : [-(disjoint(690 ^ [_129899], _129899))]]], (698 ^ _105873) ^ [_130309, _130311] : [-(apply(_130311, _130309) = sum_class(image(_130311, singleton(_130309))))], (701 ^ _105873) ^ [] : [-(function(699 ^ []))], (703 ^ _105873) ^ [_130509] : [member(_130509, universal_class), -(_130509 = null_class), -(member(apply(699 ^ [], _130509), _130509))]], input).
% 101.03/98.52  ncf('1',plain,[first(714 ^ []) = 712 ^ [], second(714 ^ []) = 713 ^ []],start(722 ^ 0)).
% 101.03/98.52  ncf('1.1',plain,[-(first(714 ^ []) = 712 ^ []), first(714 ^ []) = first(ordered_pair(712 ^ [], 713 ^ [])), first(ordered_pair(712 ^ [], 713 ^ [])) = 712 ^ []],extension(10 ^ 1,bind([[_106328, _106330, _106332], [712 ^ [], first(ordered_pair(712 ^ [], 713 ^ [])), first(714 ^ [])]]))).
% 101.03/98.52  ncf('1.1.1',plain,[-(first(714 ^ []) = first(ordered_pair(712 ^ [], 713 ^ []))), 714 ^ [] = ordered_pair(712 ^ [], 713 ^ [])],extension(236 ^ 2,bind([[_114125, _114127], [ordered_pair(712 ^ [], 713 ^ []), 714 ^ []]]))).
% 101.03/98.52  ncf('1.1.1.1',plain,[-(714 ^ [] = ordered_pair(712 ^ [], 713 ^ []))],extension(720 ^ 3)).
% 101.03/98.52  ncf('1.1.2',plain,[-(first(ordered_pair(712 ^ [], 713 ^ [])) = 712 ^ []), member(712 ^ [], universal_class), member(713 ^ [], universal_class)],extension(335 ^ 2,bind([[_117697, _117699], [713 ^ [], 712 ^ []]]))).
% 101.03/98.52  ncf('1.1.2.1',plain,[-(member(712 ^ [], universal_class))],extension(716 ^ 3)).
% 101.03/98.52  ncf('1.1.2.2',plain,[-(member(713 ^ [], universal_class))],extension(718 ^ 3)).
% 101.03/98.52  ncf('1.2',plain,[-(second(714 ^ []) = 713 ^ []), second(714 ^ []) = second(ordered_pair(712 ^ [], 713 ^ [])), second(ordered_pair(712 ^ [], 713 ^ [])) = 713 ^ []],extension(10 ^ 1,bind([[_106328, _106330, _106332], [713 ^ [], second(ordered_pair(712 ^ [], 713 ^ [])), second(714 ^ [])]]))).
% 101.03/98.52  ncf('1.2.1',plain,[-(second(714 ^ []) = second(ordered_pair(712 ^ [], 713 ^ []))), 714 ^ [] = ordered_pair(712 ^ [], 713 ^ [])],extension(242 ^ 2,bind([[_114323, _114325], [ordered_pair(712 ^ [], 713 ^ []), 714 ^ []]]))).
% 101.03/98.52  ncf('1.2.1.1',plain,[-(714 ^ [] = ordered_pair(712 ^ [], 713 ^ []))],extension(720 ^ 3)).
% 101.03/98.52  ncf('1.2.2',plain,[-(second(ordered_pair(712 ^ [], 713 ^ [])) = 713 ^ []), member(712 ^ [], universal_class), member(713 ^ [], universal_class)],extension(335 ^ 2,bind([[_117697, _117699], [713 ^ [], 712 ^ []]]))).
% 101.03/98.52  ncf('1.2.2.1',plain,[-(member(712 ^ [], universal_class))],extension(716 ^ 3)).
% 101.03/98.52  ncf('1.2.2.2',plain,[-(member(713 ^ [], universal_class))],extension(718 ^ 3)).
% 101.03/98.52  %-----------------------------------------------------
% 101.03/98.52  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------