%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET074+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 11:55:18 EDT 2023

% Result   : Theorem 44.17s 43.76s
% Output   : Proof 44.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET074+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n016.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May 18 19:18:26 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 44.17/43.76  
% 44.17/43.76  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 44.17/43.76  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.17/43.76  %-----------------------------------------------------
% 44.17/43.76  ncf(matrix, plain, [(717 ^ _137858) ^ [] : [-(unordered_pair(712 ^ [], 713 ^ []) = null_class)], (715 ^ _137858) ^ [] : [-(member(713 ^ [], universal_class))], !, (409 ^ _112641) ^ [_126910, _126912, _126914] : [-(restrict(_126912, _126914, _126910) = intersection(_126912, cross_product(_126914, _126910)))], (449 ^ _112641) ^ [_128393] : [-(subclass(rotate(_128393), cross_product(cross_product(universal_class, universal_class), universal_class)))], (552 ^ _112641) ^ [_131994, _131996] : [member(_131996, sum_class(_131994)), 556 ^ _112641 : [(559 ^ _112641) ^ [] : [-(member(555 ^ [_131994, _131996], _131994))], (557 ^ _112641) ^ [] : [-(member(_131996, 555 ^ [_131994, _131996]))]]], (431 ^ _112641) ^ [_127768, _127770, _127772, _127774] : [member(ordered_pair(ordered_pair(_127772, _127770), _127768), rotate(_127774)), 434 ^ _112641 : [(437 ^ _112641) ^ [] : [-(member(ordered_pair(ordered_pair(_127770, _127768), _127772), _127774))], (435 ^ _112641) ^ [] : [-(member(ordered_pair(ordered_pair(_127772, _127770), _127768), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (258 ^ _112641) ^ [_121720, _121722] : [260 ^ _112641 : [(263 ^ _112641) ^ [] : [member(259 ^ [_121720, _121722], _121720)], (261 ^ _112641) ^ [] : [-(member(259 ^ [_121720, _121722], _121722))]], -(subclass(_121722, _121720))], (325 ^ _112641) ^ [_124112, _124114, _124116, _124118] : [-(member(ordered_pair(_124118, _124116), cross_product(_124114, _124112))), member(_124118, _124114), member(_124116, _124112)], (585 ^ _112641) ^ [_133137, _133139] : [-(member(_133139, power_class(_133137))), member(_133139, universal_class), subclass(_133139, _133137)], (544 ^ _112641) ^ [] : [-(inductive(540 ^ []))], (335 ^ _112641) ^ [_124445, _124447] : [342 ^ _112641 : [(345 ^ _112641) ^ [] : [-(second(ordered_pair(_124447, _124445)) = _124445)], (343 ^ _112641) ^ [] : [-(first(ordered_pair(_124447, _124445)) = _124447)]], member(_124447, universal_class), member(_124445, universal_class)], (391 ^ _112641) ^ [_126361, _126363] : [member(_126361, complement(_126363)), 394 ^ _112641 : [(397 ^ _112641) ^ [] : [member(_126361, _126363)], (395 ^ _112641) ^ [] : [-(member(_126361, universal_class))]]], (126 ^ _112641) ^ [_116895, _116897] : [_116897 = _116895, -(successor(_116897) = successor(_116895))], (222 ^ _112641) ^ [_120373, _120375] : [_120375 = _120373, -(singleton(_120375) = singleton(_120373))], (621 ^ _112641) ^ [_134435] : [member(_134435, identity_relation), 625 ^ _112641 : [(628 ^ _112641) ^ [] : [-(_134435 = ordered_pair(624 ^ [_134435], 624 ^ [_134435]))], (626 ^ _112641) ^ [] : [-(member(624 ^ [_134435], universal_class))]]], (94 ^ _112641) ^ [_115741, _115743] : [_115743 = _115741, -(complement(_115743) = complement(_115741))], (640 ^ _112641) ^ [_135116] : [function(_135116), 643 ^ _112641 : [(646 ^ _112641) ^ [] : [-(subclass(compose(_135116, inverse(_135116)), identity_relation))], (644 ^ _112641) ^ [] : [-(subclass(_135116, cross_product(universal_class, universal_class)))]]], (20 ^ _112641) ^ [_113389, _113391] : [-(inductive(_113389)), _113391 = _113389, inductive(_113391)], (30 ^ _112641) ^ [_113712, _113714, _113716, _113718] : [-(subclass(_113716, _113712)), subclass(_113718, _113714), _113718 = _113716, _113714 = _113712], (489 ^ _112641) ^ [_129875] : [-(successor(_129875) = union(_129875, singleton(_129875)))], (421 ^ _112641) ^ [_127391, _127393] : [-(member(_127391, domain_of(_127393))), member(_127391, universal_class), -(restrict(_127393, singleton(_127391), universal_class) = null_class)], (668 ^ _112641) ^ [_135984, _135986] : [disjoint(_135986, _135984), 671 ^ _112641 : [(672 ^ _112641) ^ [_136123] : [member(_136123, _135986), member(_136123, _135984)]]], (658 ^ _112641) ^ [_135652, _135654] : [-(member(image(_135652, _135654), universal_class)), member(_135654, universal_class), function(_135652)], (411 ^ _112641) ^ [_127001] : [member(_127001, null_class)], (611 ^ _112641) ^ [_134071, _134073, _134075, _134077] : [-(member(ordered_pair(_134073, _134071), compose(_134075, _134077))), member(_134073, universal_class), member(_134071, image(_134075, image(_134077, singleton(_134073))))], (353 ^ _112641) ^ [_125118, _125120] : [member(ordered_pair(_125120, _125118), element_relation), 356 ^ _112641 : [(359 ^ _112641) ^ [] : [-(member(_125120, _125118))], (357 ^ _112641) ^ [] : [-(member(_125118, universal_class))]]], (164 ^ _112641) ^ [_118283, _118285] : [_118285 = _118283, -(power_class(_118285) = power_class(_118283))], (277 ^ _112641) ^ [_122421, _122423] : [-(_122423 = _122421), subclass(_122423, _122421), subclass(_122421, _122423)], (373 ^ _112641) ^ [_125764, _125766, _125768] : [member(_125764, intersection(_125768, _125766)), 376 ^ _112641 : [(379 ^ _112641) ^ [] : [-(member(_125764, _125766))], (377 ^ _112641) ^ [] : [-(member(_125764, _125768))]]], (503 ^ _112641) ^ [_130392, _130394] : [-(member(ordered_pair(_130394, _130392), successor_relation)), member(_130394, universal_class), member(_130392, universal_class), successor(_130394) = _130392], (180 ^ _112641) ^ [_118888, _118890, _118892, _118894] : [-(cross_product(_118894, _118890) = cross_product(_118892, _118888)), _118894 = _118892, _118890 = _118888], (347 ^ _112641) ^ [_124853, _124855, _124857] : [member(_124853, cross_product(_124857, _124855)), -(_124853 = ordered_pair(first(_124853), second(_124853)))], (100 ^ _112641) ^ [_115987, _115989, _115991, _115993] : [-(intersection(_115993, _115989) = intersection(_115991, _115987)), _115993 = _115991, _115989 = _115987], (648 ^ _112641) ^ [_135353] : [-(function(_135353)), subclass(_135353, cross_product(universal_class, universal_class)), subclass(compose(_135353, inverse(_135353)), identity_relation)], (248 ^ _112641) ^ [_121406, _121408] : [subclass(_121408, _121406), 251 ^ _112641 : [(252 ^ _112641) ^ [_121543] : [member(_121543, _121408), -(member(_121543, _121406))]]], (630 ^ _112641) ^ [_134740] : [-(member(_134740, identity_relation)), 631 ^ _112641 : [(632 ^ _112641) ^ [_134833] : [member(_134833, universal_class), _134740 = ordered_pair(_134833, _134833)]]], (58 ^ _112641) ^ [_114572, _114574] : [-(function(_114572)), _114574 = _114572, function(_114574)], (519 ^ _112641) ^ [_130850] : [-(range_of(_130850) = domain_of(inverse(_130850)))], (531 ^ _112641) ^ [_131314] : [-(inductive(_131314)), member(null_class, _131314), subclass(image(successor_relation, _131314), _131314)], (491 ^ _112641) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (4 ^ _112641) ^ [_112872, _112874] : [_112874 = _112872, -(_112872 = _112874)], (10 ^ _112641) ^ [_113076, _113078, _113080] : [-(_113080 = _113076), _113080 = _113078, _113078 = _113076], (687 ^ _112641) ^ [_136647] : [-(_136647 = null_class), 691 ^ _112641 : [(696 ^ _112641) ^ [] : [-(disjoint(690 ^ [_136647], _136647))], (694 ^ _112641) ^ [] : [-(member(690 ^ [_136647], _136647))], (692 ^ _112641) ^ [] : [-(member(690 ^ [_136647], universal_class))]]], (469 ^ _112641) ^ [_129184] : [-(subclass(flip(_129184), cross_product(cross_product(universal_class, universal_class), universal_class)))], (439 ^ _112641) ^ [_128061, _128063, _128065, _128067] : [-(member(ordered_pair(ordered_pair(_128065, _128063), _128061), rotate(_128067))), member(ordered_pair(ordered_pair(_128065, _128063), _128061), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_128063, _128061), _128065), _128067)], (678 ^ _112641) ^ [_136299, _136301] : [680 ^ _112641 : [(683 ^ _112641) ^ [] : [-(member(679 ^ [_136299, _136301], _136299))], (681 ^ _112641) ^ [] : [-(member(679 ^ [_136299, _136301], _136301))]], -(disjoint(_136301, _136299))], (701 ^ _112641) ^ [] : [-(function(699 ^ []))], (212 ^ _112641) ^ [_120042, _120044, _120046, _120048] : [-(image(_120048, _120044) = image(_120046, _120042)), _120048 = _120046, _120044 = _120042], (287 ^ _112641) ^ [_122765, _122767, _122769] : [member(_122769, unordered_pair(_122767, _122765)), 290 ^ _112641 : [(293 ^ _112641) ^ [] : [-(_122769 = _122767), -(_122769 = _122765)], (291 ^ _112641) ^ [] : [-(member(_122769, universal_class))]]], (144 ^ _112641) ^ [_117549, _117551] : [_117551 = _117549, -(range_of(_117551) = range_of(_117549))], (317 ^ _112641) ^ [_123847, _123849, _123851, _123853] : [member(ordered_pair(_123853, _123851), cross_product(_123849, _123847)), 320 ^ _112641 : [(323 ^ _112641) ^ [] : [-(member(_123851, _123847))], (321 ^ _112641) ^ [] : [-(member(_123853, _123849))]]], (603 ^ _112641) ^ [_133790, _133792, _133794, _133796] : [member(ordered_pair(_133792, _133790), compose(_133794, _133796)), 606 ^ _112641 : [(609 ^ _112641) ^ [] : [-(member(_133790, image(_133794, image(_133796, singleton(_133792)))))], (607 ^ _112641) ^ [] : [-(member(_133792, universal_class))]]], (577 ^ _112641) ^ [_132896, _132898] : [member(_132898, power_class(_132896)), 580 ^ _112641 : [(583 ^ _112641) ^ [] : [-(subclass(_132898, _132896))], (581 ^ _112641) ^ [] : [-(member(_132898, universal_class))]]], (68 ^ _112641) ^ [_114875, _114877, _114879, _114881] : [-(member(_114879, _114875)), member(_114881, _114877), _114881 = _114879, _114877 = _114875], (44 ^ _112641) ^ [_114156, _114158, _114160, _114162] : [-(disjoint(_114160, _114156)), disjoint(_114162, _114158), _114162 = _114160, _114158 = _114156], (170 ^ _112641) ^ [_118529, _118531, _118533, _118535] : [-(ordered_pair(_118535, _118531) = ordered_pair(_118533, _118529)), _118535 = _118533, _118531 = _118529], (206 ^ _112641) ^ [_119796, _119798] : [_119798 = _119796, -(sum_class(_119798) = sum_class(_119796))], (200 ^ _112641) ^ [_119578, _119580] : [_119580 = _119578, -(inverse(_119580) = inverse(_119578))], (138 ^ _112641) ^ [_117331, _117333] : [_117333 = _117331, -(domain_of(_117333) = domain_of(_117331))], (451 ^ _112641) ^ [_128559, _128561, _128563, _128565] : [member(ordered_pair(ordered_pair(_128565, _128563), _128561), flip(_128559)), 454 ^ _112641 : [(457 ^ _112641) ^ [] : [-(member(ordered_pair(ordered_pair(_128563, _128565), _128561), _128559))], (455 ^ _112641) ^ [] : [-(member(ordered_pair(ordered_pair(_128565, _128563), _128561), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (110 ^ _112641) ^ [_116318, _116320] : [_116320 = _116318, -(rotate(_116320) = rotate(_116318))], (561 ^ _112641) ^ [_132305, _132307] : [-(member(_132307, sum_class(_132305))), 562 ^ _112641 : [(563 ^ _112641) ^ [_132399] : [member(_132307, _132399), member(_132399, _132305)]]], (517 ^ _112641) ^ [_130763] : [-(inverse(_130763) = domain_of(flip(cross_product(_130763, universal_class))))], (399 ^ _112641) ^ [_126603, _126605] : [-(member(_126603, complement(_126605))), member(_126603, universal_class), -(member(_126603, _126605))], (546 ^ _112641) ^ [_131759] : [inductive(_131759), -(subclass(540 ^ [], _131759))], (88 ^ _112641) ^ [_115523, _115525] : [_115525 = _115523, -(second(_115525) = second(_115523))], (698 ^ _112641) ^ [_137057, _137059] : [-(apply(_137059, _137057) = sum_class(image(_137059, singleton(_137057))))], (471 ^ _112641) ^ [_129336, _129338, _129340] : [member(_129336, union(_129340, _129338)), -(member(_129336, _129340)), -(member(_129336, _129338))], (542 ^ _112641) ^ [] : [-(member(540 ^ [], universal_class))], (267 ^ _112641) ^ [_122048] : [-(subclass(_122048, universal_class))], (521 ^ _112641) ^ [_130948, _130950] : [-(image(_130948, _130950) = range_of(restrict(_130948, _130950, universal_class)))], (190 ^ _112641) ^ [_119247, _119249, _119251, _119253] : [-(compose(_119253, _119249) = compose(_119251, _119247)), _119253 = _119251, _119249 = _119247], (595 ^ _112641) ^ [_133428] : [member(_133428, universal_class), -(member(power_class(_133428), universal_class))], (228 ^ _112641) ^ [_120619, _120621, _120623, _120625] : [-(apply(_120625, _120621) = apply(_120623, _120619)), _120625 = _120623, _120621 = _120619], (381 ^ _112641) ^ [_126015, _126017, _126019] : [-(member(_126015, intersection(_126019, _126017))), member(_126015, _126019), member(_126015, _126017)], (132 ^ _112641) ^ [_117113, _117115] : [_117115 = _117113, -(flip(_117115) = flip(_117113))], (269 ^ _112641) ^ [_122184, _122186] : [_122186 = _122184, 272 ^ _112641 : [(275 ^ _112641) ^ [] : [-(subclass(_122184, _122186))], (273 ^ _112641) ^ [] : [-(subclass(_122186, _122184))]]], (493 ^ _112641) ^ [_130071, _130073] : [member(ordered_pair(_130073, _130071), successor_relation), 496 ^ _112641 : [(501 ^ _112641) ^ [] : [-(successor(_130073) = _130071)], (499 ^ _112641) ^ [] : [-(member(_130071, universal_class))], (497 ^ _112641) ^ [] : [-(member(_130073, universal_class))]]], (2 ^ _112641) ^ [_112765] : [-(_112765 = _112765)], (313 ^ _112641) ^ [_123571] : [-(singleton(_123571) = unordered_pair(_123571, _123571))], (601 ^ _112641) ^ [_133621, _133623] : [-(subclass(compose(_133621, _133623), cross_product(universal_class, universal_class)))], (703 ^ _112641) ^ [_137257] : [member(_137257, universal_class), -(_137257 = null_class), -(member(apply(699 ^ [], _137257), _137257))], (238 ^ _112641) ^ [_120958, _120960, _120962, _120964] : [-(unordered_pair(_120964, _120960) = unordered_pair(_120962, _120958)), _120964 = _120962, _120960 = _120958], (571 ^ _112641) ^ [_132659] : [member(_132659, universal_class), -(member(sum_class(_132659), universal_class))], (311 ^ _112641) ^ [_123488, _123490] : [-(member(unordered_pair(_123490, _123488), universal_class))], (315 ^ _112641) ^ [_123668, _123670] : [-(ordered_pair(_123670, _123668) = unordered_pair(singleton(_123670), unordered_pair(_123670, singleton(_123668))))], (413 ^ _112641) ^ [_127137, _127139] : [member(_127137, domain_of(_127139)), 416 ^ _112641 : [(419 ^ _112641) ^ [] : [restrict(_127139, singleton(_127137), universal_class) = null_class], (417 ^ _112641) ^ [] : [-(member(_127137, universal_class))]]], (523 ^ _112641) ^ [_131081] : [inductive(_131081), 526 ^ _112641 : [(529 ^ _112641) ^ [] : [-(subclass(image(successor_relation, _131081), _131081))], (527 ^ _112641) ^ [] : [-(member(null_class, _131081))]]], (361 ^ _112641) ^ [_125361, _125363] : [-(member(ordered_pair(_125363, _125361), element_relation)), member(_125361, universal_class), member(_125363, _125361)], (82 ^ _112641) ^ [_115305, _115307] : [_115307 = _115305, -(first(_115307) = first(_115305))], (116 ^ _112641) ^ [_116564, _116566, _116568, _116570] : [-(union(_116570, _116566) = union(_116568, _116564)), _116570 = _116568, _116566 = _116564], (459 ^ _112641) ^ [_128852, _128854, _128856, _128858] : [-(member(ordered_pair(ordered_pair(_128858, _128856), _128854), flip(_128852))), member(ordered_pair(ordered_pair(_128858, _128856), _128854), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_128856, _128858), _128854), _128852)], (371 ^ _112641) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (299 ^ _112641) ^ [_123110, _123112, _123114] : [-(member(_123114, unordered_pair(_123112, _123110))), member(_123114, universal_class), 304 ^ _112641 : [(307 ^ _112641) ^ [] : [_123114 = _123110], (305 ^ _112641) ^ [] : [_123114 = _123112]]], (150 ^ _112641) ^ [_117823, _117825, _117827, _117829, _117831, _117833] : [-(restrict(_117833, _117829, _117825) = restrict(_117831, _117827, _117823)), _117833 = _117831, _117829 = _117827, _117825 = _117823], (481 ^ _112641) ^ [_129604, _129606, _129608] : [482 ^ _112641 : [(485 ^ _112641) ^ [] : [member(_129604, _129606)], (483 ^ _112641) ^ [] : [member(_129604, _129608)]], -(member(_129604, union(_129608, _129606)))]], input).
% 44.17/43.76  ncf('1',plain,[-(unordered_pair(712 ^ [], 713 ^ []) = null_class)],start(717 ^ 0)).
% 44.17/43.76  ncf('1.1',plain,[unordered_pair(712 ^ [], 713 ^ []) = null_class, -(member(second(ordered_pair(713 ^ [], 713 ^ [])), null_class)), member(713 ^ [], unordered_pair(712 ^ [], 713 ^ [])), 713 ^ [] = second(ordered_pair(713 ^ [], 713 ^ []))],extension(68 ^ 1,bind([[_114875, _114877, _114879, _114881], [null_class, unordered_pair(712 ^ [], 713 ^ []), second(ordered_pair(713 ^ [], 713 ^ [])), 713 ^ []]]))).
% 44.17/43.76  ncf('1.1.1',plain,[member(second(ordered_pair(713 ^ [], 713 ^ [])), null_class)],extension(411 ^ 2,bind([[_127001], [second(ordered_pair(713 ^ [], 713 ^ []))]]))).
% 44.17/43.76  ncf('1.1.2',plain,[-(member(713 ^ [], unordered_pair(712 ^ [], 713 ^ []))), member(713 ^ [], universal_class), 307 : 713 ^ [] = 713 ^ []],extension(299 ^ 2,bind([[_123110, _123112, _123114], [713 ^ [], 712 ^ [], 713 ^ []]]))).
% 44.17/43.76  ncf('1.1.2.1',plain,[-(member(713 ^ [], universal_class))],extension(715 ^ 3)).
% 44.17/43.76  ncf('1.1.2.2',plain,[-(713 ^ [] = 713 ^ [])],extension(2 ^ 5,bind([[_112765], [713 ^ []]]))).
% 44.17/43.76  ncf('1.1.3',plain,[-(713 ^ [] = second(ordered_pair(713 ^ [], 713 ^ []))), second(ordered_pair(713 ^ [], 713 ^ [])) = 713 ^ []],extension(4 ^ 2,bind([[_112872, _112874], [713 ^ [], second(ordered_pair(713 ^ [], 713 ^ []))]]))).
% 44.17/43.76  ncf('1.1.3.1',plain,[-(second(ordered_pair(713 ^ [], 713 ^ [])) = 713 ^ []), member(713 ^ [], universal_class), member(713 ^ [], universal_class)],extension(335 ^ 3,bind([[_124445, _124447], [713 ^ [], 713 ^ []]]))).
% 44.17/43.76  ncf('1.1.3.1.1',plain,[-(member(713 ^ [], universal_class))],extension(715 ^ 4)).
% 44.17/43.76  ncf('1.1.3.1.2',plain,[-(member(713 ^ [], universal_class))],lemmata('[3, 1, 1].x')).
% 44.17/43.76  %-----------------------------------------------------
% 44.17/43.76  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------