%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET073+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n031.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 11:55:18 EDT 2023

% Result   : Theorem 44.06s 43.72s
% Output   : Proof 44.06s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SET073+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.02/0.12  % Command  : nanocop.sh %s %d
% 0.10/0.31  % Computer : n031.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May 18 19:45:10 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 44.06/43.72  
% 44.06/43.72  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 44.06/43.72  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.06/43.72  %-----------------------------------------------------
% 44.06/43.72  ncf(matrix, plain, [(717 ^ _137851) ^ [] : [-(unordered_pair(712 ^ [], 713 ^ []) = null_class)], (715 ^ _137851) ^ [] : [-(member(712 ^ [], universal_class))], !, (409 ^ _112637) ^ [_126906, _126908, _126910] : [-(restrict(_126908, _126910, _126906) = intersection(_126908, cross_product(_126910, _126906)))], (449 ^ _112637) ^ [_128389] : [-(subclass(rotate(_128389), cross_product(cross_product(universal_class, universal_class), universal_class)))], (552 ^ _112637) ^ [_131990, _131992] : [member(_131992, sum_class(_131990)), 556 ^ _112637 : [(559 ^ _112637) ^ [] : [-(member(555 ^ [_131990, _131992], _131990))], (557 ^ _112637) ^ [] : [-(member(_131992, 555 ^ [_131990, _131992]))]]], (431 ^ _112637) ^ [_127764, _127766, _127768, _127770] : [member(ordered_pair(ordered_pair(_127768, _127766), _127764), rotate(_127770)), 434 ^ _112637 : [(437 ^ _112637) ^ [] : [-(member(ordered_pair(ordered_pair(_127766, _127764), _127768), _127770))], (435 ^ _112637) ^ [] : [-(member(ordered_pair(ordered_pair(_127768, _127766), _127764), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (258 ^ _112637) ^ [_121716, _121718] : [260 ^ _112637 : [(263 ^ _112637) ^ [] : [member(259 ^ [_121716, _121718], _121716)], (261 ^ _112637) ^ [] : [-(member(259 ^ [_121716, _121718], _121718))]], -(subclass(_121718, _121716))], (325 ^ _112637) ^ [_124108, _124110, _124112, _124114] : [-(member(ordered_pair(_124114, _124112), cross_product(_124110, _124108))), member(_124114, _124110), member(_124112, _124108)], (585 ^ _112637) ^ [_133133, _133135] : [-(member(_133135, power_class(_133133))), member(_133135, universal_class), subclass(_133135, _133133)], (544 ^ _112637) ^ [] : [-(inductive(540 ^ []))], (335 ^ _112637) ^ [_124441, _124443] : [342 ^ _112637 : [(345 ^ _112637) ^ [] : [-(second(ordered_pair(_124443, _124441)) = _124441)], (343 ^ _112637) ^ [] : [-(first(ordered_pair(_124443, _124441)) = _124443)]], member(_124443, universal_class), member(_124441, universal_class)], (391 ^ _112637) ^ [_126357, _126359] : [member(_126357, complement(_126359)), 394 ^ _112637 : [(397 ^ _112637) ^ [] : [member(_126357, _126359)], (395 ^ _112637) ^ [] : [-(member(_126357, universal_class))]]], (126 ^ _112637) ^ [_116891, _116893] : [_116893 = _116891, -(successor(_116893) = successor(_116891))], (222 ^ _112637) ^ [_120369, _120371] : [_120371 = _120369, -(singleton(_120371) = singleton(_120369))], (621 ^ _112637) ^ [_134431] : [member(_134431, identity_relation), 625 ^ _112637 : [(628 ^ _112637) ^ [] : [-(_134431 = ordered_pair(624 ^ [_134431], 624 ^ [_134431]))], (626 ^ _112637) ^ [] : [-(member(624 ^ [_134431], universal_class))]]], (94 ^ _112637) ^ [_115737, _115739] : [_115739 = _115737, -(complement(_115739) = complement(_115737))], (640 ^ _112637) ^ [_135112] : [function(_135112), 643 ^ _112637 : [(646 ^ _112637) ^ [] : [-(subclass(compose(_135112, inverse(_135112)), identity_relation))], (644 ^ _112637) ^ [] : [-(subclass(_135112, cross_product(universal_class, universal_class)))]]], (20 ^ _112637) ^ [_113385, _113387] : [-(inductive(_113385)), _113387 = _113385, inductive(_113387)], (30 ^ _112637) ^ [_113708, _113710, _113712, _113714] : [-(subclass(_113712, _113708)), subclass(_113714, _113710), _113714 = _113712, _113710 = _113708], (489 ^ _112637) ^ [_129871] : [-(successor(_129871) = union(_129871, singleton(_129871)))], (421 ^ _112637) ^ [_127387, _127389] : [-(member(_127387, domain_of(_127389))), member(_127387, universal_class), -(restrict(_127389, singleton(_127387), universal_class) = null_class)], (668 ^ _112637) ^ [_135980, _135982] : [disjoint(_135982, _135980), 671 ^ _112637 : [(672 ^ _112637) ^ [_136119] : [member(_136119, _135982), member(_136119, _135980)]]], (658 ^ _112637) ^ [_135648, _135650] : [-(member(image(_135648, _135650), universal_class)), member(_135650, universal_class), function(_135648)], (411 ^ _112637) ^ [_126997] : [member(_126997, null_class)], (611 ^ _112637) ^ [_134067, _134069, _134071, _134073] : [-(member(ordered_pair(_134069, _134067), compose(_134071, _134073))), member(_134069, universal_class), member(_134067, image(_134071, image(_134073, singleton(_134069))))], (353 ^ _112637) ^ [_125114, _125116] : [member(ordered_pair(_125116, _125114), element_relation), 356 ^ _112637 : [(359 ^ _112637) ^ [] : [-(member(_125116, _125114))], (357 ^ _112637) ^ [] : [-(member(_125114, universal_class))]]], (164 ^ _112637) ^ [_118279, _118281] : [_118281 = _118279, -(power_class(_118281) = power_class(_118279))], (277 ^ _112637) ^ [_122417, _122419] : [-(_122419 = _122417), subclass(_122419, _122417), subclass(_122417, _122419)], (373 ^ _112637) ^ [_125760, _125762, _125764] : [member(_125760, intersection(_125764, _125762)), 376 ^ _112637 : [(379 ^ _112637) ^ [] : [-(member(_125760, _125762))], (377 ^ _112637) ^ [] : [-(member(_125760, _125764))]]], (503 ^ _112637) ^ [_130388, _130390] : [-(member(ordered_pair(_130390, _130388), successor_relation)), member(_130390, universal_class), member(_130388, universal_class), successor(_130390) = _130388], (180 ^ _112637) ^ [_118884, _118886, _118888, _118890] : [-(cross_product(_118890, _118886) = cross_product(_118888, _118884)), _118890 = _118888, _118886 = _118884], (347 ^ _112637) ^ [_124849, _124851, _124853] : [member(_124849, cross_product(_124853, _124851)), -(_124849 = ordered_pair(first(_124849), second(_124849)))], (100 ^ _112637) ^ [_115983, _115985, _115987, _115989] : [-(intersection(_115989, _115985) = intersection(_115987, _115983)), _115989 = _115987, _115985 = _115983], (648 ^ _112637) ^ [_135349] : [-(function(_135349)), subclass(_135349, cross_product(universal_class, universal_class)), subclass(compose(_135349, inverse(_135349)), identity_relation)], (248 ^ _112637) ^ [_121402, _121404] : [subclass(_121404, _121402), 251 ^ _112637 : [(252 ^ _112637) ^ [_121539] : [member(_121539, _121404), -(member(_121539, _121402))]]], (630 ^ _112637) ^ [_134736] : [-(member(_134736, identity_relation)), 631 ^ _112637 : [(632 ^ _112637) ^ [_134829] : [member(_134829, universal_class), _134736 = ordered_pair(_134829, _134829)]]], (58 ^ _112637) ^ [_114568, _114570] : [-(function(_114568)), _114570 = _114568, function(_114570)], (519 ^ _112637) ^ [_130846] : [-(range_of(_130846) = domain_of(inverse(_130846)))], (531 ^ _112637) ^ [_131310] : [-(inductive(_131310)), member(null_class, _131310), subclass(image(successor_relation, _131310), _131310)], (491 ^ _112637) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (4 ^ _112637) ^ [_112868, _112870] : [_112870 = _112868, -(_112868 = _112870)], (10 ^ _112637) ^ [_113072, _113074, _113076] : [-(_113076 = _113072), _113076 = _113074, _113074 = _113072], (687 ^ _112637) ^ [_136643] : [-(_136643 = null_class), 691 ^ _112637 : [(696 ^ _112637) ^ [] : [-(disjoint(690 ^ [_136643], _136643))], (694 ^ _112637) ^ [] : [-(member(690 ^ [_136643], _136643))], (692 ^ _112637) ^ [] : [-(member(690 ^ [_136643], universal_class))]]], (469 ^ _112637) ^ [_129180] : [-(subclass(flip(_129180), cross_product(cross_product(universal_class, universal_class), universal_class)))], (439 ^ _112637) ^ [_128057, _128059, _128061, _128063] : [-(member(ordered_pair(ordered_pair(_128061, _128059), _128057), rotate(_128063))), member(ordered_pair(ordered_pair(_128061, _128059), _128057), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_128059, _128057), _128061), _128063)], (678 ^ _112637) ^ [_136295, _136297] : [680 ^ _112637 : [(683 ^ _112637) ^ [] : [-(member(679 ^ [_136295, _136297], _136295))], (681 ^ _112637) ^ [] : [-(member(679 ^ [_136295, _136297], _136297))]], -(disjoint(_136297, _136295))], (701 ^ _112637) ^ [] : [-(function(699 ^ []))], (212 ^ _112637) ^ [_120038, _120040, _120042, _120044] : [-(image(_120044, _120040) = image(_120042, _120038)), _120044 = _120042, _120040 = _120038], (287 ^ _112637) ^ [_122761, _122763, _122765] : [member(_122765, unordered_pair(_122763, _122761)), 290 ^ _112637 : [(293 ^ _112637) ^ [] : [-(_122765 = _122763), -(_122765 = _122761)], (291 ^ _112637) ^ [] : [-(member(_122765, universal_class))]]], (144 ^ _112637) ^ [_117545, _117547] : [_117547 = _117545, -(range_of(_117547) = range_of(_117545))], (317 ^ _112637) ^ [_123843, _123845, _123847, _123849] : [member(ordered_pair(_123849, _123847), cross_product(_123845, _123843)), 320 ^ _112637 : [(323 ^ _112637) ^ [] : [-(member(_123847, _123843))], (321 ^ _112637) ^ [] : [-(member(_123849, _123845))]]], (603 ^ _112637) ^ [_133786, _133788, _133790, _133792] : [member(ordered_pair(_133788, _133786), compose(_133790, _133792)), 606 ^ _112637 : [(609 ^ _112637) ^ [] : [-(member(_133786, image(_133790, image(_133792, singleton(_133788)))))], (607 ^ _112637) ^ [] : [-(member(_133788, universal_class))]]], (577 ^ _112637) ^ [_132892, _132894] : [member(_132894, power_class(_132892)), 580 ^ _112637 : [(583 ^ _112637) ^ [] : [-(subclass(_132894, _132892))], (581 ^ _112637) ^ [] : [-(member(_132894, universal_class))]]], (68 ^ _112637) ^ [_114871, _114873, _114875, _114877] : [-(member(_114875, _114871)), member(_114877, _114873), _114877 = _114875, _114873 = _114871], (44 ^ _112637) ^ [_114152, _114154, _114156, _114158] : [-(disjoint(_114156, _114152)), disjoint(_114158, _114154), _114158 = _114156, _114154 = _114152], (170 ^ _112637) ^ [_118525, _118527, _118529, _118531] : [-(ordered_pair(_118531, _118527) = ordered_pair(_118529, _118525)), _118531 = _118529, _118527 = _118525], (206 ^ _112637) ^ [_119792, _119794] : [_119794 = _119792, -(sum_class(_119794) = sum_class(_119792))], (200 ^ _112637) ^ [_119574, _119576] : [_119576 = _119574, -(inverse(_119576) = inverse(_119574))], (138 ^ _112637) ^ [_117327, _117329] : [_117329 = _117327, -(domain_of(_117329) = domain_of(_117327))], (451 ^ _112637) ^ [_128555, _128557, _128559, _128561] : [member(ordered_pair(ordered_pair(_128561, _128559), _128557), flip(_128555)), 454 ^ _112637 : [(457 ^ _112637) ^ [] : [-(member(ordered_pair(ordered_pair(_128559, _128561), _128557), _128555))], (455 ^ _112637) ^ [] : [-(member(ordered_pair(ordered_pair(_128561, _128559), _128557), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (110 ^ _112637) ^ [_116314, _116316] : [_116316 = _116314, -(rotate(_116316) = rotate(_116314))], (561 ^ _112637) ^ [_132301, _132303] : [-(member(_132303, sum_class(_132301))), 562 ^ _112637 : [(563 ^ _112637) ^ [_132395] : [member(_132303, _132395), member(_132395, _132301)]]], (517 ^ _112637) ^ [_130759] : [-(inverse(_130759) = domain_of(flip(cross_product(_130759, universal_class))))], (399 ^ _112637) ^ [_126599, _126601] : [-(member(_126599, complement(_126601))), member(_126599, universal_class), -(member(_126599, _126601))], (546 ^ _112637) ^ [_131755] : [inductive(_131755), -(subclass(540 ^ [], _131755))], (88 ^ _112637) ^ [_115519, _115521] : [_115521 = _115519, -(second(_115521) = second(_115519))], (698 ^ _112637) ^ [_137053, _137055] : [-(apply(_137055, _137053) = sum_class(image(_137055, singleton(_137053))))], (471 ^ _112637) ^ [_129332, _129334, _129336] : [member(_129332, union(_129336, _129334)), -(member(_129332, _129336)), -(member(_129332, _129334))], (542 ^ _112637) ^ [] : [-(member(540 ^ [], universal_class))], (267 ^ _112637) ^ [_122044] : [-(subclass(_122044, universal_class))], (521 ^ _112637) ^ [_130944, _130946] : [-(image(_130944, _130946) = range_of(restrict(_130944, _130946, universal_class)))], (190 ^ _112637) ^ [_119243, _119245, _119247, _119249] : [-(compose(_119249, _119245) = compose(_119247, _119243)), _119249 = _119247, _119245 = _119243], (595 ^ _112637) ^ [_133424] : [member(_133424, universal_class), -(member(power_class(_133424), universal_class))], (228 ^ _112637) ^ [_120615, _120617, _120619, _120621] : [-(apply(_120621, _120617) = apply(_120619, _120615)), _120621 = _120619, _120617 = _120615], (381 ^ _112637) ^ [_126011, _126013, _126015] : [-(member(_126011, intersection(_126015, _126013))), member(_126011, _126015), member(_126011, _126013)], (132 ^ _112637) ^ [_117109, _117111] : [_117111 = _117109, -(flip(_117111) = flip(_117109))], (269 ^ _112637) ^ [_122180, _122182] : [_122182 = _122180, 272 ^ _112637 : [(275 ^ _112637) ^ [] : [-(subclass(_122180, _122182))], (273 ^ _112637) ^ [] : [-(subclass(_122182, _122180))]]], (493 ^ _112637) ^ [_130067, _130069] : [member(ordered_pair(_130069, _130067), successor_relation), 496 ^ _112637 : [(501 ^ _112637) ^ [] : [-(successor(_130069) = _130067)], (499 ^ _112637) ^ [] : [-(member(_130067, universal_class))], (497 ^ _112637) ^ [] : [-(member(_130069, universal_class))]]], (2 ^ _112637) ^ [_112761] : [-(_112761 = _112761)], (313 ^ _112637) ^ [_123567] : [-(singleton(_123567) = unordered_pair(_123567, _123567))], (601 ^ _112637) ^ [_133617, _133619] : [-(subclass(compose(_133617, _133619), cross_product(universal_class, universal_class)))], (703 ^ _112637) ^ [_137253] : [member(_137253, universal_class), -(_137253 = null_class), -(member(apply(699 ^ [], _137253), _137253))], (238 ^ _112637) ^ [_120954, _120956, _120958, _120960] : [-(unordered_pair(_120960, _120956) = unordered_pair(_120958, _120954)), _120960 = _120958, _120956 = _120954], (571 ^ _112637) ^ [_132655] : [member(_132655, universal_class), -(member(sum_class(_132655), universal_class))], (311 ^ _112637) ^ [_123484, _123486] : [-(member(unordered_pair(_123486, _123484), universal_class))], (315 ^ _112637) ^ [_123664, _123666] : [-(ordered_pair(_123666, _123664) = unordered_pair(singleton(_123666), unordered_pair(_123666, singleton(_123664))))], (413 ^ _112637) ^ [_127133, _127135] : [member(_127133, domain_of(_127135)), 416 ^ _112637 : [(419 ^ _112637) ^ [] : [restrict(_127135, singleton(_127133), universal_class) = null_class], (417 ^ _112637) ^ [] : [-(member(_127133, universal_class))]]], (523 ^ _112637) ^ [_131077] : [inductive(_131077), 526 ^ _112637 : [(529 ^ _112637) ^ [] : [-(subclass(image(successor_relation, _131077), _131077))], (527 ^ _112637) ^ [] : [-(member(null_class, _131077))]]], (361 ^ _112637) ^ [_125357, _125359] : [-(member(ordered_pair(_125359, _125357), element_relation)), member(_125357, universal_class), member(_125359, _125357)], (82 ^ _112637) ^ [_115301, _115303] : [_115303 = _115301, -(first(_115303) = first(_115301))], (116 ^ _112637) ^ [_116560, _116562, _116564, _116566] : [-(union(_116566, _116562) = union(_116564, _116560)), _116566 = _116564, _116562 = _116560], (459 ^ _112637) ^ [_128848, _128850, _128852, _128854] : [-(member(ordered_pair(ordered_pair(_128854, _128852), _128850), flip(_128848))), member(ordered_pair(ordered_pair(_128854, _128852), _128850), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_128852, _128854), _128850), _128848)], (371 ^ _112637) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (299 ^ _112637) ^ [_123106, _123108, _123110] : [-(member(_123110, unordered_pair(_123108, _123106))), member(_123110, universal_class), 304 ^ _112637 : [(307 ^ _112637) ^ [] : [_123110 = _123106], (305 ^ _112637) ^ [] : [_123110 = _123108]]], (150 ^ _112637) ^ [_117819, _117821, _117823, _117825, _117827, _117829] : [-(restrict(_117829, _117825, _117821) = restrict(_117827, _117823, _117819)), _117829 = _117827, _117825 = _117823, _117821 = _117819], (481 ^ _112637) ^ [_129600, _129602, _129604] : [482 ^ _112637 : [(485 ^ _112637) ^ [] : [member(_129600, _129602)], (483 ^ _112637) ^ [] : [member(_129600, _129604)]], -(member(_129600, union(_129604, _129602)))]], input).
% 44.06/43.72  ncf('1',plain,[-(unordered_pair(712 ^ [], 713 ^ []) = null_class)],start(717 ^ 0)).
% 44.06/43.72  ncf('1.1',plain,[unordered_pair(712 ^ [], 713 ^ []) = null_class, -(member(second(ordered_pair(712 ^ [], 712 ^ [])), null_class)), member(712 ^ [], unordered_pair(712 ^ [], 713 ^ [])), 712 ^ [] = second(ordered_pair(712 ^ [], 712 ^ []))],extension(68 ^ 1,bind([[_114871, _114873, _114875, _114877], [null_class, unordered_pair(712 ^ [], 713 ^ []), second(ordered_pair(712 ^ [], 712 ^ [])), 712 ^ []]]))).
% 44.06/43.72  ncf('1.1.1',plain,[member(second(ordered_pair(712 ^ [], 712 ^ [])), null_class)],extension(411 ^ 2,bind([[_126997], [second(ordered_pair(712 ^ [], 712 ^ []))]]))).
% 44.06/43.72  ncf('1.1.2',plain,[-(member(712 ^ [], unordered_pair(712 ^ [], 713 ^ []))), member(712 ^ [], universal_class), 305 : 712 ^ [] = 712 ^ []],extension(299 ^ 2,bind([[_123106, _123108, _123110], [713 ^ [], 712 ^ [], 712 ^ []]]))).
% 44.06/43.72  ncf('1.1.2.1',plain,[-(member(712 ^ [], universal_class))],extension(715 ^ 3)).
% 44.06/43.72  ncf('1.1.2.2',plain,[-(712 ^ [] = 712 ^ [])],extension(2 ^ 5,bind([[_112761], [712 ^ []]]))).
% 44.06/43.72  ncf('1.1.3',plain,[-(712 ^ [] = second(ordered_pair(712 ^ [], 712 ^ []))), second(ordered_pair(712 ^ [], 712 ^ [])) = 712 ^ []],extension(4 ^ 2,bind([[_112868, _112870], [712 ^ [], second(ordered_pair(712 ^ [], 712 ^ []))]]))).
% 44.06/43.72  ncf('1.1.3.1',plain,[-(second(ordered_pair(712 ^ [], 712 ^ [])) = 712 ^ []), member(712 ^ [], universal_class), member(712 ^ [], universal_class)],extension(335 ^ 3,bind([[_124441, _124443], [712 ^ [], 712 ^ []]]))).
% 44.06/43.72  ncf('1.1.3.1.1',plain,[-(member(712 ^ [], universal_class))],extension(715 ^ 4)).
% 44.06/43.72  ncf('1.1.3.1.2',plain,[-(member(712 ^ [], universal_class))],lemmata('[3, 1, 1].x')).
% 44.06/43.72  %-----------------------------------------------------
% 44.06/43.72  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------