%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET079+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n013.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 11:55:19 EDT 2023

% Result   : Theorem 184.18s 178.35s
% Output   : Proof 184.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SET079+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 18:53:20 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 184.18/178.35  
% 184.18/178.35  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 184.18/178.35  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 184.18/178.35  %-----------------------------------------------------
% 184.18/178.35  ncf(matrix, plain, [(714 ^ _137861) ^ [] : [-(member(712 ^ [], universal_class))], (716 ^ _137861) ^ [] : [-(singleton(712 ^ []) = null_class)], !, (277 ^ _112698) ^ [_122478, _122480] : [-(_122480 = _122478), subclass(_122480, _122478), subclass(_122478, _122480)], (469 ^ _112698) ^ [_129241] : [-(subclass(flip(_129241), cross_product(cross_product(universal_class, universal_class), universal_class)))], (687 ^ _112698) ^ [_136704] : [-(_136704 = null_class), 691 ^ _112698 : [(696 ^ _112698) ^ [] : [-(disjoint(690 ^ [_136704], _136704))], (694 ^ _112698) ^ [] : [-(member(690 ^ [_136704], _136704))], (692 ^ _112698) ^ [] : [-(member(690 ^ [_136704], universal_class))]]], (287 ^ _112698) ^ [_122822, _122824, _122826] : [member(_122826, unordered_pair(_122824, _122822)), 290 ^ _112698 : [(291 ^ _112698) ^ [] : [-(member(_122826, universal_class))], (293 ^ _112698) ^ [] : [-(_122826 = _122824), -(_122826 = _122822)]]], (248 ^ _112698) ^ [_121463, _121465] : [subclass(_121465, _121463), 251 ^ _112698 : [(252 ^ _112698) ^ [_121600] : [member(_121600, _121465), -(member(_121600, _121463))]]], (611 ^ _112698) ^ [_134128, _134130, _134132, _134134] : [-(member(ordered_pair(_134130, _134128), compose(_134132, _134134))), member(_134130, universal_class), member(_134128, image(_134132, image(_134134, singleton(_134130))))], (698 ^ _112698) ^ [_137114, _137116] : [-(apply(_137116, _137114) = sum_class(image(_137116, singleton(_137114))))], (503 ^ _112698) ^ [_130449, _130451] : [-(member(ordered_pair(_130451, _130449), successor_relation)), member(_130451, universal_class), member(_130449, universal_class), successor(_130451) = _130449], (439 ^ _112698) ^ [_128118, _128120, _128122, _128124] : [-(member(ordered_pair(ordered_pair(_128122, _128120), _128118), rotate(_128124))), member(ordered_pair(ordered_pair(_128122, _128120), _128118), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_128120, _128118), _128122), _128124)], (459 ^ _112698) ^ [_128909, _128911, _128913, _128915] : [-(member(ordered_pair(ordered_pair(_128915, _128913), _128911), flip(_128909))), member(ordered_pair(ordered_pair(_128915, _128913), _128911), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_128913, _128915), _128911), _128909)], (242 ^ _112698) ^ [_121128, _121130] : [_121130 = _121128, -(singleton(_121130) = singleton(_121128))], (58 ^ _112698) ^ [_114629, _114631] : [-(function(_114629)), _114631 = _114629, function(_114631)], (335 ^ _112698) ^ [_124502, _124504] : [342 ^ _112698 : [(343 ^ _112698) ^ [] : [-(first(ordered_pair(_124504, _124502)) = _124504)], (345 ^ _112698) ^ [] : [-(second(ordered_pair(_124504, _124502)) = _124502)]], member(_124504, universal_class), member(_124502, universal_class)], (20 ^ _112698) ^ [_113446, _113448] : [-(inductive(_113446)), _113448 = _113446, inductive(_113448)], (523 ^ _112698) ^ [_131138] : [inductive(_131138), 526 ^ _112698 : [(527 ^ _112698) ^ [] : [-(member(null_class, _131138))], (529 ^ _112698) ^ [] : [-(subclass(image(successor_relation, _131138), _131138))]]], (210 ^ _112698) ^ [_119994, _119996] : [_119996 = _119994, -(inverse(_119996) = inverse(_119994))], (381 ^ _112698) ^ [_126072, _126074, _126076] : [-(member(_126072, intersection(_126076, _126074))), member(_126072, _126076), member(_126072, _126074)], (311 ^ _112698) ^ [_123545, _123547] : [-(member(unordered_pair(_123547, _123545), universal_class))], (142 ^ _112698) ^ [_117529, _117531] : [_117531 = _117529, -(flip(_117531) = flip(_117529))], (190 ^ _112698) ^ [_119304, _119306, _119308, _119310] : [-(cross_product(_119310, _119306) = cross_product(_119308, _119304)), _119310 = _119308, _119306 = _119304], (361 ^ _112698) ^ [_125418, _125420] : [-(member(ordered_pair(_125420, _125418), element_relation)), member(_125418, universal_class), member(_125420, _125418)], (136 ^ _112698) ^ [_117311, _117313] : [_117313 = _117311, -(successor(_117313) = successor(_117311))], (325 ^ _112698) ^ [_124169, _124171, _124173, _124175] : [-(member(ordered_pair(_124175, _124173), cross_product(_124171, _124169))), member(_124175, _124171), member(_124173, _124169)], (269 ^ _112698) ^ [_122241, _122243] : [_122243 = _122241, 272 ^ _112698 : [(273 ^ _112698) ^ [] : [-(subclass(_122243, _122241))], (275 ^ _112698) ^ [] : [-(subclass(_122241, _122243))]]], (409 ^ _112698) ^ [_126967, _126969, _126971] : [-(restrict(_126969, _126971, _126967) = intersection(_126969, cross_product(_126971, _126967)))], (421 ^ _112698) ^ [_127448, _127450] : [-(member(_127448, domain_of(_127450))), member(_127448, universal_class), -(restrict(_127450, singleton(_127448), universal_class) = null_class)], (621 ^ _112698) ^ [_134492] : [member(_134492, identity_relation), 625 ^ _112698 : [(626 ^ _112698) ^ [] : [-(member(624 ^ [_134492], universal_class))], (628 ^ _112698) ^ [] : [-(_134492 = ordered_pair(624 ^ [_134492], 624 ^ [_134492]))]]], (658 ^ _112698) ^ [_135709, _135711] : [-(member(image(_135709, _135711), universal_class)), member(_135711, universal_class), function(_135709)], (577 ^ _112698) ^ [_132953, _132955] : [member(_132955, power_class(_132953)), 580 ^ _112698 : [(581 ^ _112698) ^ [] : [-(member(_132955, universal_class))], (583 ^ _112698) ^ [] : [-(subclass(_132955, _132953))]]], (120 ^ _112698) ^ [_116734, _116736] : [_116736 = _116734, -(rotate(_116736) = rotate(_116734))], (561 ^ _112698) ^ [_132362, _132364] : [-(member(_132364, sum_class(_132362))), 562 ^ _112698 : [(563 ^ _112698) ^ [_132456] : [member(_132364, _132456), member(_132456, _132362)]]], (353 ^ _112698) ^ [_125175, _125177] : [member(ordered_pair(_125177, _125175), element_relation), 356 ^ _112698 : [(357 ^ _112698) ^ [] : [-(member(_125175, universal_class))], (359 ^ _112698) ^ [] : [-(member(_125177, _125175))]]], (82 ^ _112698) ^ [_115390, _115392, _115394, _115396] : [-(unordered_pair(_115396, _115392) = unordered_pair(_115394, _115390)), _115396 = _115394, _115392 = _115390], (347 ^ _112698) ^ [_124910, _124912, _124914] : [member(_124910, cross_product(_124914, _124912)), -(_124910 = ordered_pair(first(_124910), second(_124910)))], (546 ^ _112698) ^ [_131816] : [inductive(_131816), -(subclass(540 ^ [], _131816))], (678 ^ _112698) ^ [_136356, _136358] : [680 ^ _112698 : [(681 ^ _112698) ^ [] : [-(member(679 ^ [_136356, _136358], _136358))], (683 ^ _112698) ^ [] : [-(member(679 ^ [_136356, _136358], _136356))]], -(disjoint(_136358, _136356))], (313 ^ _112698) ^ [_123628] : [-(singleton(_123628) = unordered_pair(_123628, _123628))], (471 ^ _112698) ^ [_129393, _129395, _129397] : [member(_129393, union(_129397, _129395)), -(member(_129393, _129397)), -(member(_129393, _129395))], (542 ^ _112698) ^ [] : [-(member(540 ^ [], universal_class))], (4 ^ _112698) ^ [_112929, _112931] : [_112931 = _112929, -(_112929 = _112931)], (200 ^ _112698) ^ [_119663, _119665, _119667, _119669] : [-(compose(_119669, _119665) = compose(_119667, _119663)), _119669 = _119667, _119665 = _119663], (481 ^ _112698) ^ [_129661, _129663, _129665] : [482 ^ _112698 : [(483 ^ _112698) ^ [] : [member(_129661, _129665)], (485 ^ _112698) ^ [] : [member(_129661, _129663)]], -(member(_129661, union(_129665, _129663)))], (148 ^ _112698) ^ [_117747, _117749] : [_117749 = _117747, -(domain_of(_117749) = domain_of(_117747))], (703 ^ _112698) ^ [_137314] : [member(_137314, universal_class), -(_137314 = null_class), -(member(apply(699 ^ [], _137314), _137314))], (373 ^ _112698) ^ [_125821, _125823, _125825] : [member(_125821, intersection(_125825, _125823)), 376 ^ _112698 : [(377 ^ _112698) ^ [] : [-(member(_125821, _125825))], (379 ^ _112698) ^ [] : [-(member(_125821, _125823))]]], (595 ^ _112698) ^ [_133485] : [member(_133485, universal_class), -(member(power_class(_133485), universal_class))], (98 ^ _112698) ^ [_115939, _115941] : [_115941 = _115939, -(second(_115941) = second(_115939))], (30 ^ _112698) ^ [_113769, _113771, _113773, _113775] : [-(subclass(_113773, _113769)), subclass(_113775, _113771), _113775 = _113773, _113771 = _113769], (267 ^ _112698) ^ [_122105] : [-(subclass(_122105, universal_class))], (701 ^ _112698) ^ [] : [-(function(699 ^ []))], (519 ^ _112698) ^ [_130907] : [-(range_of(_130907) = domain_of(inverse(_130907)))], (216 ^ _112698) ^ [_120212, _120214] : [_120214 = _120212, -(sum_class(_120214) = sum_class(_120212))], (544 ^ _112698) ^ [] : [-(inductive(540 ^ []))], (44 ^ _112698) ^ [_114213, _114215, _114217, _114219] : [-(disjoint(_114217, _114213)), disjoint(_114219, _114215), _114219 = _114217, _114215 = _114213], (411 ^ _112698) ^ [_127058] : [member(_127058, null_class)], (585 ^ _112698) ^ [_133194, _133196] : [-(member(_133196, power_class(_133194))), member(_133196, universal_class), subclass(_133196, _133194)], (571 ^ _112698) ^ [_132716] : [member(_132716, universal_class), -(member(sum_class(_132716), universal_class))], (154 ^ _112698) ^ [_117965, _117967] : [_117967 = _117965, -(range_of(_117967) = range_of(_117965))], (391 ^ _112698) ^ [_126418, _126420] : [member(_126418, complement(_126420)), 394 ^ _112698 : [(395 ^ _112698) ^ [] : [-(member(_126418, universal_class))], (397 ^ _112698) ^ [] : [member(_126418, _126420)]]], (180 ^ _112698) ^ [_118945, _118947, _118949, _118951] : [-(ordered_pair(_118951, _118947) = ordered_pair(_118949, _118945)), _118951 = _118949, _118947 = _118945], (489 ^ _112698) ^ [_129932] : [-(successor(_129932) = union(_129932, singleton(_129932)))], (630 ^ _112698) ^ [_134797] : [-(member(_134797, identity_relation)), 631 ^ _112698 : [(632 ^ _112698) ^ [_134890] : [member(_134890, universal_class), _134797 = ordered_pair(_134890, _134890)]]], (517 ^ _112698) ^ [_130820] : [-(inverse(_130820) = domain_of(flip(cross_product(_130820, universal_class))))], (552 ^ _112698) ^ [_132051, _132053] : [member(_132053, sum_class(_132051)), 556 ^ _112698 : [(557 ^ _112698) ^ [] : [-(member(_132053, 555 ^ [_132051, _132053]))], (559 ^ _112698) ^ [] : [-(member(555 ^ [_132051, _132053], _132051))]]], (371 ^ _112698) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (160 ^ _112698) ^ [_118239, _118241, _118243, _118245, _118247, _118249] : [-(restrict(_118249, _118245, _118241) = restrict(_118247, _118243, _118239)), _118249 = _118247, _118245 = _118243, _118241 = _118239], (493 ^ _112698) ^ [_130128, _130130] : [member(ordered_pair(_130130, _130128), successor_relation), 496 ^ _112698 : [(501 ^ _112698) ^ [] : [-(successor(_130130) = _130128)], (499 ^ _112698) ^ [] : [-(member(_130128, universal_class))], (497 ^ _112698) ^ [] : [-(member(_130130, universal_class))]]], (413 ^ _112698) ^ [_127194, _127196] : [member(_127194, domain_of(_127196)), 416 ^ _112698 : [(417 ^ _112698) ^ [] : [-(member(_127194, universal_class))], (419 ^ _112698) ^ [] : [restrict(_127196, singleton(_127194), universal_class) = null_class]]], (491 ^ _112698) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (258 ^ _112698) ^ [_121777, _121779] : [260 ^ _112698 : [(261 ^ _112698) ^ [] : [-(member(259 ^ [_121777, _121779], _121779))], (263 ^ _112698) ^ [] : [member(259 ^ [_121777, _121779], _121777)]], -(subclass(_121779, _121777))], (521 ^ _112698) ^ [_131005, _131007] : [-(image(_131005, _131007) = range_of(restrict(_131005, _131007, universal_class)))], (601 ^ _112698) ^ [_133678, _133680] : [-(subclass(compose(_133678, _133680), cross_product(universal_class, universal_class)))], (451 ^ _112698) ^ [_128616, _128618, _128620, _128622] : [member(ordered_pair(ordered_pair(_128622, _128620), _128618), flip(_128616)), 454 ^ _112698 : [(455 ^ _112698) ^ [] : [-(member(ordered_pair(ordered_pair(_128622, _128620), _128618), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _112698) ^ [] : [-(member(ordered_pair(ordered_pair(_128620, _128622), _128618), _128616))]]], (399 ^ _112698) ^ [_126660, _126662] : [-(member(_126660, complement(_126662))), member(_126660, universal_class), -(member(_126660, _126662))], (92 ^ _112698) ^ [_115721, _115723] : [_115723 = _115721, -(first(_115723) = first(_115721))], (174 ^ _112698) ^ [_118699, _118701] : [_118701 = _118699, -(power_class(_118701) = power_class(_118699))], (2 ^ _112698) ^ [_112822] : [-(_112822 = _112822)], (104 ^ _112698) ^ [_116157, _116159] : [_116159 = _116157, -(complement(_116159) = complement(_116157))], (317 ^ _112698) ^ [_123904, _123906, _123908, _123910] : [member(ordered_pair(_123910, _123908), cross_product(_123906, _123904)), 320 ^ _112698 : [(321 ^ _112698) ^ [] : [-(member(_123910, _123906))], (323 ^ _112698) ^ [] : [-(member(_123908, _123904))]]], (531 ^ _112698) ^ [_131371] : [-(inductive(_131371)), member(null_class, _131371), subclass(image(successor_relation, _131371), _131371)], (68 ^ _112698) ^ [_114932, _114934, _114936, _114938] : [-(member(_114936, _114932)), member(_114938, _114934), _114938 = _114936, _114934 = _114932], (315 ^ _112698) ^ [_123725, _123727] : [-(ordered_pair(_123727, _123725) = unordered_pair(singleton(_123727), unordered_pair(_123727, singleton(_123725))))], (431 ^ _112698) ^ [_127825, _127827, _127829, _127831] : [member(ordered_pair(ordered_pair(_127829, _127827), _127825), rotate(_127831)), 434 ^ _112698 : [(435 ^ _112698) ^ [] : [-(member(ordered_pair(ordered_pair(_127829, _127827), _127825), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _112698) ^ [] : [-(member(ordered_pair(ordered_pair(_127827, _127825), _127829), _127831))]]], (110 ^ _112698) ^ [_116403, _116405, _116407, _116409] : [-(intersection(_116409, _116405) = intersection(_116407, _116403)), _116409 = _116407, _116405 = _116403], (640 ^ _112698) ^ [_135173] : [function(_135173), 643 ^ _112698 : [(644 ^ _112698) ^ [] : [-(subclass(_135173, cross_product(universal_class, universal_class)))], (646 ^ _112698) ^ [] : [-(subclass(compose(_135173, inverse(_135173)), identity_relation))]]], (668 ^ _112698) ^ [_136041, _136043] : [disjoint(_136043, _136041), 671 ^ _112698 : [(672 ^ _112698) ^ [_136180] : [member(_136180, _136043), member(_136180, _136041)]]], (449 ^ _112698) ^ [_128450] : [-(subclass(rotate(_128450), cross_product(cross_product(universal_class, universal_class), universal_class)))], (10 ^ _112698) ^ [_113133, _113135, _113137] : [-(_113137 = _113133), _113137 = _113135, _113135 = _113133], (222 ^ _112698) ^ [_120458, _120460, _120462, _120464] : [-(image(_120464, _120460) = image(_120462, _120458)), _120464 = _120462, _120460 = _120458], (648 ^ _112698) ^ [_135410] : [-(function(_135410)), subclass(_135410, cross_product(universal_class, universal_class)), subclass(compose(_135410, inverse(_135410)), identity_relation)], (126 ^ _112698) ^ [_116980, _116982, _116984, _116986] : [-(union(_116986, _116982) = union(_116984, _116980)), _116986 = _116984, _116982 = _116980], (603 ^ _112698) ^ [_133847, _133849, _133851, _133853] : [member(ordered_pair(_133849, _133847), compose(_133851, _133853)), 606 ^ _112698 : [(607 ^ _112698) ^ [] : [-(member(_133849, universal_class))], (609 ^ _112698) ^ [] : [-(member(_133847, image(_133851, image(_133853, singleton(_133849)))))]]], (232 ^ _112698) ^ [_120817, _120819, _120821, _120823] : [-(apply(_120823, _120819) = apply(_120821, _120817)), _120823 = _120821, _120819 = _120817], (299 ^ _112698) ^ [_123167, _123169, _123171] : [-(member(_123171, unordered_pair(_123169, _123167))), member(_123171, universal_class), 304 ^ _112698 : [(305 ^ _112698) ^ [] : [_123171 = _123169], (307 ^ _112698) ^ [] : [_123171 = _123167]]]], input).
% 184.18/178.35  ncf('1',plain,[-(member(712 ^ [], universal_class))],start(714 ^ 0)).
% 184.18/178.35  ncf('1.1',plain,[member(712 ^ [], universal_class), -(member(712 ^ [], unordered_pair(712 ^ [], 712 ^ []))), 305 : 712 ^ [] = 712 ^ []],extension(299 ^ 1,bind([[_123167, _123169, _123171], [712 ^ [], 712 ^ [], 712 ^ []]]))).
% 184.18/178.35  ncf('1.1.1',plain,[member(712 ^ [], unordered_pair(712 ^ [], 712 ^ [])), 252 : -(member(712 ^ [], singleton(712 ^ []))), 252 : subclass(unordered_pair(712 ^ [], 712 ^ []), singleton(712 ^ []))],extension(248 ^ 2,bind([[_121463, _121465, _121600], [singleton(712 ^ []), unordered_pair(712 ^ [], 712 ^ []), 712 ^ []]]))).
% 184.18/178.35  ncf('1.1.1.1',plain,[member(712 ^ [], singleton(712 ^ [])), 252 : -(member(712 ^ [], null_class)), 252 : subclass(singleton(712 ^ []), null_class)],extension(248 ^ 5,bind([[_121463, _121465, _121600], [null_class, singleton(712 ^ []), 712 ^ []]]))).
% 184.18/178.35  ncf('1.1.1.1.1',plain,[member(712 ^ [], null_class)],extension(411 ^ 8,bind([[_127058], [712 ^ []]]))).
% 184.18/178.35  ncf('1.1.1.1.2',plain,[-(subclass(singleton(712 ^ []), null_class)), singleton(712 ^ []) = null_class],extension(269 ^ 6,bind([[_122241, _122243], [null_class, singleton(712 ^ [])]]))).
% 184.18/178.35  ncf('1.1.1.1.2.1',plain,[-(singleton(712 ^ []) = null_class)],extension(716 ^ 7)).
% 184.18/178.35  ncf('1.1.1.2',plain,[-(subclass(unordered_pair(712 ^ [], 712 ^ []), singleton(712 ^ []))), singleton(712 ^ []) = unordered_pair(712 ^ [], 712 ^ [])],extension(269 ^ 3,bind([[_122241, _122243], [unordered_pair(712 ^ [], 712 ^ []), singleton(712 ^ [])]]))).
% 184.18/178.35  ncf('1.1.1.2.1',plain,[-(singleton(712 ^ []) = unordered_pair(712 ^ [], 712 ^ []))],extension(313 ^ 4,bind([[_123628], [712 ^ []]]))).
% 184.18/178.35  ncf('1.1.2',plain,[-(712 ^ [] = 712 ^ []), subclass(712 ^ [], 712 ^ []), subclass(712 ^ [], 712 ^ [])],extension(277 ^ 4,bind([[_122478, _122480], [712 ^ [], 712 ^ []]]))).
% 184.18/178.35  ncf('1.1.2.1',plain,[-(subclass(712 ^ [], 712 ^ [])), 261 : -(member(259 ^ [712 ^ [], 712 ^ []], 712 ^ []))],extension(258 ^ 5,bind([[_121777, _121779], [712 ^ [], 712 ^ []]]))).
% 184.18/178.35  ncf('1.1.2.1.1',plain,[member(259 ^ [712 ^ [], 712 ^ []], 712 ^ [])],extension(263 ^ 8)).
% 184.18/178.35  ncf('1.1.2.2',plain,[-(subclass(712 ^ [], 712 ^ []))],lemmata('[1, 1].x')).
% 184.18/178.35  %-----------------------------------------------------
% 184.18/178.35  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------