%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n021.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 11:55:13 EDT 2023

% Result   : Theorem 1.42s 2.42s
% Output   : Proof 1.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n021.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 19:11:57 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 1.42/2.42  
% 1.42/2.42  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.42/2.42  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.42/2.42  %-----------------------------------------------------
% 1.42/2.42  ncf(matrix, plain, [(715 ^ _105819) ^ [] : [712 ^ [] = 713 ^ []], (717 ^ _105819) ^ [_131241] : [member(_131241, 712 ^ []), -(member(_131241, 713 ^ []))], (723 ^ _105819) ^ [_131413] : [member(_131413, 713 ^ []), -(member(_131413, 712 ^ []))], (2 ^ _105819) ^ [_105963] : [-(_105963 = _105963)], (4 ^ _105819) ^ [_106070, _106072] : [_106072 = _106070, -(_106070 = _106072)], (10 ^ _105819) ^ [_106274, _106276, _106278] : [-(_106278 = _106274), _106278 = _106276, _106276 = _106274], (20 ^ _105819) ^ [_106587, _106589] : [-(inductive(_106587)), _106589 = _106587, inductive(_106589)], (30 ^ _105819) ^ [_106910, _106912, _106914, _106916] : [-(subclass(_106914, _106910)), subclass(_106916, _106912), _106916 = _106914, _106912 = _106910], (44 ^ _105819) ^ [_107354, _107356, _107358, _107360] : [-(disjoint(_107358, _107354)), disjoint(_107360, _107356), _107360 = _107358, _107356 = _107354], (58 ^ _105819) ^ [_107770, _107772] : [-(function(_107770)), _107772 = _107770, function(_107772)], (68 ^ _105819) ^ [_108073, _108075, _108077, _108079] : [-(member(_108077, _108073)), member(_108079, _108075), _108079 = _108077, _108075 = _108073], (82 ^ _105819) ^ [_108531, _108533, _108535, _108537] : [-(unordered_pair(_108537, _108533) = unordered_pair(_108535, _108531)), _108537 = _108535, _108533 = _108531], (92 ^ _105819) ^ [_108862, _108864] : [_108864 = _108862, -(first(_108864) = first(_108862))], (98 ^ _105819) ^ [_109080, _109082] : [_109082 = _109080, -(second(_109082) = second(_109080))], (104 ^ _105819) ^ [_109298, _109300] : [_109300 = _109298, -(complement(_109300) = complement(_109298))], (110 ^ _105819) ^ [_109544, _109546, _109548, _109550] : [-(intersection(_109550, _109546) = intersection(_109548, _109544)), _109550 = _109548, _109546 = _109544], (120 ^ _105819) ^ [_109875, _109877] : [_109877 = _109875, -(rotate(_109877) = rotate(_109875))], (126 ^ _105819) ^ [_110121, _110123, _110125, _110127] : [-(union(_110127, _110123) = union(_110125, _110121)), _110127 = _110125, _110123 = _110121], (136 ^ _105819) ^ [_110452, _110454] : [_110454 = _110452, -(successor(_110454) = successor(_110452))], (142 ^ _105819) ^ [_110670, _110672] : [_110672 = _110670, -(flip(_110672) = flip(_110670))], (148 ^ _105819) ^ [_110888, _110890] : [_110890 = _110888, -(domain_of(_110890) = domain_of(_110888))], (154 ^ _105819) ^ [_111106, _111108] : [_111108 = _111106, -(range_of(_111108) = range_of(_111106))], (160 ^ _105819) ^ [_111380, _111382, _111384, _111386, _111388, _111390] : [-(restrict(_111390, _111386, _111382) = restrict(_111388, _111384, _111380)), _111390 = _111388, _111386 = _111384, _111382 = _111380], (174 ^ _105819) ^ [_111840, _111842] : [_111842 = _111840, -(power_class(_111842) = power_class(_111840))], (180 ^ _105819) ^ [_112086, _112088, _112090, _112092] : [-(ordered_pair(_112092, _112088) = ordered_pair(_112090, _112086)), _112092 = _112090, _112088 = _112086], (190 ^ _105819) ^ [_112445, _112447, _112449, _112451] : [-(cross_product(_112451, _112447) = cross_product(_112449, _112445)), _112451 = _112449, _112447 = _112445], (200 ^ _105819) ^ [_112804, _112806, _112808, _112810] : [-(compose(_112810, _112806) = compose(_112808, _112804)), _112810 = _112808, _112806 = _112804], (210 ^ _105819) ^ [_113135, _113137] : [_113137 = _113135, -(inverse(_113137) = inverse(_113135))], (216 ^ _105819) ^ [_113353, _113355] : [_113355 = _113353, -(sum_class(_113355) = sum_class(_113353))], (222 ^ _105819) ^ [_113599, _113601, _113603, _113605] : [-(image(_113605, _113601) = image(_113603, _113599)), _113605 = _113603, _113601 = _113599], (232 ^ _105819) ^ [_113930, _113932] : [_113932 = _113930, -(singleton(_113932) = singleton(_113930))], (238 ^ _105819) ^ [_114156, _114158, _114160, _114162] : [-(apply(_114162, _114158) = apply(_114160, _114156)), _114162 = _114160, _114158 = _114156], (258 ^ _105819) ^ [_114918, _114920] : [260 ^ _105819 : [(261 ^ _105819) ^ [] : [-(member(259 ^ [_114918, _114920], _114920))], (263 ^ _105819) ^ [] : [member(259 ^ [_114918, _114920], _114918)]], -(subclass(_114920, _114918))], (248 ^ _105819) ^ [_114604, _114606] : [subclass(_114606, _114604), 251 ^ _105819 : [(252 ^ _105819) ^ [_114741] : [member(_114741, _114606), -(member(_114741, _114604))]]], (267 ^ _105819) ^ [_115246] : [-(subclass(_115246, universal_class))], (269 ^ _105819) ^ [_115382, _115384] : [_115384 = _115382, 272 ^ _105819 : [(273 ^ _105819) ^ [] : [-(subclass(_115384, _115382))], (275 ^ _105819) ^ [] : [-(subclass(_115382, _115384))]]], (277 ^ _105819) ^ [_115619, _115621] : [-(_115621 = _115619), subclass(_115621, _115619), subclass(_115619, _115621)], (287 ^ _105819) ^ [_115963, _115965, _115967] : [member(_115967, unordered_pair(_115965, _115963)), 290 ^ _105819 : [(291 ^ _105819) ^ [] : [-(member(_115967, universal_class))], (293 ^ _105819) ^ [] : [-(_115967 = _115965), -(_115967 = _115963)]]], (299 ^ _105819) ^ [_116308, _116310, _116312] : [-(member(_116312, unordered_pair(_116310, _116308))), member(_116312, universal_class), 304 ^ _105819 : [(305 ^ _105819) ^ [] : [_116312 = _116310], (307 ^ _105819) ^ [] : [_116312 = _116308]]], (311 ^ _105819) ^ [_116686, _116688] : [-(member(unordered_pair(_116688, _116686), universal_class))], (313 ^ _105819) ^ [_116769] : [-(singleton(_116769) = unordered_pair(_116769, _116769))], (315 ^ _105819) ^ [_116866, _116868] : [-(ordered_pair(_116868, _116866) = unordered_pair(singleton(_116868), unordered_pair(_116868, singleton(_116866))))], (317 ^ _105819) ^ [_117045, _117047, _117049, _117051] : [member(ordered_pair(_117051, _117049), cross_product(_117047, _117045)), 320 ^ _105819 : [(321 ^ _105819) ^ [] : [-(member(_117051, _117047))], (323 ^ _105819) ^ [] : [-(member(_117049, _117045))]]], (325 ^ _105819) ^ [_117310, _117312, _117314, _117316] : [-(member(ordered_pair(_117316, _117314), cross_product(_117312, _117310))), member(_117316, _117312), member(_117314, _117310)], (335 ^ _105819) ^ [_117643, _117645] : [342 ^ _105819 : [(343 ^ _105819) ^ [] : [-(first(ordered_pair(_117645, _117643)) = _117645)], (345 ^ _105819) ^ [] : [-(second(ordered_pair(_117645, _117643)) = _117643)]], member(_117645, universal_class), member(_117643, universal_class)], (347 ^ _105819) ^ [_118051, _118053, _118055] : [member(_118051, cross_product(_118055, _118053)), -(_118051 = ordered_pair(first(_118051), second(_118051)))], (353 ^ _105819) ^ [_118316, _118318] : [member(ordered_pair(_118318, _118316), element_relation), 356 ^ _105819 : [(357 ^ _105819) ^ [] : [-(member(_118316, universal_class))], (359 ^ _105819) ^ [] : [-(member(_118318, _118316))]]], (361 ^ _105819) ^ [_118559, _118561] : [-(member(ordered_pair(_118561, _118559), element_relation)), member(_118559, universal_class), member(_118561, _118559)], (371 ^ _105819) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _105819) ^ [_118962, _118964, _118966] : [member(_118962, intersection(_118966, _118964)), 376 ^ _105819 : [(377 ^ _105819) ^ [] : [-(member(_118962, _118966))], (379 ^ _105819) ^ [] : [-(member(_118962, _118964))]]], (381 ^ _105819) ^ [_119213, _119215, _119217] : [-(member(_119213, intersection(_119217, _119215))), member(_119213, _119217), member(_119213, _119215)], (391 ^ _105819) ^ [_119559, _119561] : [member(_119559, complement(_119561)), 394 ^ _105819 : [(395 ^ _105819) ^ [] : [-(member(_119559, universal_class))], (397 ^ _105819) ^ [] : [member(_119559, _119561)]]], (399 ^ _105819) ^ [_119801, _119803] : [-(member(_119801, complement(_119803))), member(_119801, universal_class), -(member(_119801, _119803))], (409 ^ _105819) ^ [_120108, _120110, _120112] : [-(restrict(_120110, _120112, _120108) = intersection(_120110, cross_product(_120112, _120108)))], (411 ^ _105819) ^ [_120199] : [member(_120199, null_class)], (413 ^ _105819) ^ [_120335, _120337] : [member(_120335, domain_of(_120337)), 416 ^ _105819 : [(417 ^ _105819) ^ [] : [-(member(_120335, universal_class))], (419 ^ _105819) ^ [] : [restrict(_120337, singleton(_120335), universal_class) = null_class]]], (421 ^ _105819) ^ [_120589, _120591] : [-(member(_120589, domain_of(_120591))), member(_120589, universal_class), -(restrict(_120591, singleton(_120589), universal_class) = null_class)], (431 ^ _105819) ^ [_120966, _120968, _120970, _120972] : [member(ordered_pair(ordered_pair(_120970, _120968), _120966), rotate(_120972)), 434 ^ _105819 : [(435 ^ _105819) ^ [] : [-(member(ordered_pair(ordered_pair(_120970, _120968), _120966), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _105819) ^ [] : [-(member(ordered_pair(ordered_pair(_120968, _120966), _120970), _120972))]]], (439 ^ _105819) ^ [_121259, _121261, _121263, _121265] : [-(member(ordered_pair(ordered_pair(_121263, _121261), _121259), rotate(_121265))), member(ordered_pair(ordered_pair(_121263, _121261), _121259), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_121261, _121259), _121263), _121265)], (449 ^ _105819) ^ [_121591] : [-(subclass(rotate(_121591), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _105819) ^ [_121757, _121759, _121761, _121763] : [member(ordered_pair(ordered_pair(_121763, _121761), _121759), flip(_121757)), 454 ^ _105819 : [(455 ^ _105819) ^ [] : [-(member(ordered_pair(ordered_pair(_121763, _121761), _121759), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _105819) ^ [] : [-(member(ordered_pair(ordered_pair(_121761, _121763), _121759), _121757))]]], (459 ^ _105819) ^ [_122050, _122052, _122054, _122056] : [-(member(ordered_pair(ordered_pair(_122056, _122054), _122052), flip(_122050))), member(ordered_pair(ordered_pair(_122056, _122054), _122052), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_122054, _122056), _122052), _122050)], (469 ^ _105819) ^ [_122382] : [-(subclass(flip(_122382), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _105819) ^ [_122802, _122804, _122806] : [482 ^ _105819 : [(483 ^ _105819) ^ [] : [member(_122802, _122806)], (485 ^ _105819) ^ [] : [member(_122802, _122804)]], -(member(_122802, union(_122806, _122804)))], (471 ^ _105819) ^ [_122534, _122536, _122538] : [member(_122534, union(_122538, _122536)), -(member(_122534, _122538)), -(member(_122534, _122536))], (489 ^ _105819) ^ [_123073] : [-(successor(_123073) = union(_123073, singleton(_123073)))], (491 ^ _105819) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _105819) ^ [_123269, _123271] : [member(ordered_pair(_123271, _123269), successor_relation), 496 ^ _105819 : [(497 ^ _105819) ^ [] : [-(member(_123271, universal_class))], (499 ^ _105819) ^ [] : [-(member(_123269, universal_class))], (501 ^ _105819) ^ [] : [-(successor(_123271) = _123269)]]], (503 ^ _105819) ^ [_123590, _123592] : [-(member(ordered_pair(_123592, _123590), successor_relation)), member(_123592, universal_class), member(_123590, universal_class), successor(_123592) = _123590], (517 ^ _105819) ^ [_123961] : [-(inverse(_123961) = domain_of(flip(cross_product(_123961, universal_class))))], (519 ^ _105819) ^ [_124048] : [-(range_of(_124048) = domain_of(inverse(_124048)))], (521 ^ _105819) ^ [_124146, _124148] : [-(image(_124146, _124148) = range_of(restrict(_124146, _124148, universal_class)))], (523 ^ _105819) ^ [_124279] : [inductive(_124279), 526 ^ _105819 : [(527 ^ _105819) ^ [] : [-(member(null_class, _124279))], (529 ^ _105819) ^ [] : [-(subclass(image(successor_relation, _124279), _124279))]]], (531 ^ _105819) ^ [_124512] : [-(inductive(_124512)), member(null_class, _124512), subclass(image(successor_relation, _124512), _124512)], (542 ^ _105819) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _105819) ^ [] : [-(inductive(540 ^ []))], (546 ^ _105819) ^ [_124957] : [inductive(_124957), -(subclass(540 ^ [], _124957))], (552 ^ _105819) ^ [_125192, _125194] : [member(_125194, sum_class(_125192)), 556 ^ _105819 : [(557 ^ _105819) ^ [] : [-(member(_125194, 555 ^ [_125192, _125194]))], (559 ^ _105819) ^ [] : [-(member(555 ^ [_125192, _125194], _125192))]]], (561 ^ _105819) ^ [_125503, _125505] : [-(member(_125505, sum_class(_125503))), 562 ^ _105819 : [(563 ^ _105819) ^ [_125597] : [member(_125505, _125597), member(_125597, _125503)]]], (571 ^ _105819) ^ [_125857] : [member(_125857, universal_class), -(member(sum_class(_125857), universal_class))], (577 ^ _105819) ^ [_126094, _126096] : [member(_126096, power_class(_126094)), 580 ^ _105819 : [(581 ^ _105819) ^ [] : [-(member(_126096, universal_class))], (583 ^ _105819) ^ [] : [-(subclass(_126096, _126094))]]], (585 ^ _105819) ^ [_126335, _126337] : [-(member(_126337, power_class(_126335))), member(_126337, universal_class), subclass(_126337, _126335)], (595 ^ _105819) ^ [_126626] : [member(_126626, universal_class), -(member(power_class(_126626), universal_class))], (601 ^ _105819) ^ [_126819, _126821] : [-(subclass(compose(_126819, _126821), cross_product(universal_class, universal_class)))], (603 ^ _105819) ^ [_126988, _126990, _126992, _126994] : [member(ordered_pair(_126990, _126988), compose(_126992, _126994)), 606 ^ _105819 : [(607 ^ _105819) ^ [] : [-(member(_126990, universal_class))], (609 ^ _105819) ^ [] : [-(member(_126988, image(_126992, image(_126994, singleton(_126990)))))]]], (611 ^ _105819) ^ [_127269, _127271, _127273, _127275] : [-(member(ordered_pair(_127271, _127269), compose(_127273, _127275))), member(_127271, universal_class), member(_127269, image(_127273, image(_127275, singleton(_127271))))], (621 ^ _105819) ^ [_127633] : [member(_127633, identity_relation), 625 ^ _105819 : [(626 ^ _105819) ^ [] : [-(member(624 ^ [_127633], universal_class))], (628 ^ _105819) ^ [] : [-(_127633 = ordered_pair(624 ^ [_127633], 624 ^ [_127633]))]]], (630 ^ _105819) ^ [_127938] : [-(member(_127938, identity_relation)), 631 ^ _105819 : [(632 ^ _105819) ^ [_128031] : [member(_128031, universal_class), _127938 = ordered_pair(_128031, _128031)]]], (640 ^ _105819) ^ [_128314] : [function(_128314), 643 ^ _105819 : [(644 ^ _105819) ^ [] : [-(subclass(_128314, cross_product(universal_class, universal_class)))], (646 ^ _105819) ^ [] : [-(subclass(compose(_128314, inverse(_128314)), identity_relation))]]], (648 ^ _105819) ^ [_128551] : [-(function(_128551)), subclass(_128551, cross_product(universal_class, universal_class)), subclass(compose(_128551, inverse(_128551)), identity_relation)], (658 ^ _105819) ^ [_128850, _128852] : [-(member(image(_128850, _128852), universal_class)), member(_128852, universal_class), function(_128850)], (678 ^ _105819) ^ [_129497, _129499] : [680 ^ _105819 : [(681 ^ _105819) ^ [] : [-(member(679 ^ [_129497, _129499], _129499))], (683 ^ _105819) ^ [] : [-(member(679 ^ [_129497, _129499], _129497))]], -(disjoint(_129499, _129497))], (668 ^ _105819) ^ [_129182, _129184] : [disjoint(_129184, _129182), 671 ^ _105819 : [(672 ^ _105819) ^ [_129321] : [member(_129321, _129184), member(_129321, _129182)]]], (687 ^ _105819) ^ [_129845] : [-(_129845 = null_class), 691 ^ _105819 : [(692 ^ _105819) ^ [] : [-(member(690 ^ [_129845], universal_class))], (694 ^ _105819) ^ [] : [-(member(690 ^ [_129845], _129845))], (696 ^ _105819) ^ [] : [-(disjoint(690 ^ [_129845], _129845))]]], (698 ^ _105819) ^ [_130255, _130257] : [-(apply(_130257, _130255) = sum_class(image(_130257, singleton(_130255))))], (701 ^ _105819) ^ [] : [-(function(699 ^ []))], (703 ^ _105819) ^ [_130455] : [member(_130455, universal_class), -(_130455 = null_class), -(member(apply(699 ^ [], _130455), _130455))]], input).
% 1.42/2.42  ncf('1',plain,[712 ^ [] = 713 ^ []],start(715 ^ 0)).
% 1.42/2.42  ncf('1.1',plain,[-(712 ^ [] = 713 ^ []), subclass(712 ^ [], 713 ^ []), subclass(713 ^ [], 712 ^ [])],extension(277 ^ 1,bind([[_115619, _115621], [713 ^ [], 712 ^ []]]))).
% 1.42/2.42  ncf('1.1.1',plain,[-(subclass(712 ^ [], 713 ^ [])), 261 : -(member(259 ^ [713 ^ [], 712 ^ []], 712 ^ []))],extension(258 ^ 2,bind([[_114918, _114920], [713 ^ [], 712 ^ []]]))).
% 1.42/2.42  ncf('1.1.1.1',plain,[member(259 ^ [713 ^ [], 712 ^ []], 712 ^ []), -(member(259 ^ [713 ^ [], 712 ^ []], 713 ^ []))],extension(717 ^ 5,bind([[_131241], [259 ^ [713 ^ [], 712 ^ []]]]))).
% 1.42/2.42  ncf('1.1.1.1.1',plain,[member(259 ^ [713 ^ [], 712 ^ []], 713 ^ [])],extension(263 ^ 6)).
% 1.42/2.42  ncf('1.1.2',plain,[-(subclass(713 ^ [], 712 ^ [])), 261 : -(member(259 ^ [712 ^ [], 713 ^ []], 713 ^ []))],extension(258 ^ 2,bind([[_114918, _114920], [712 ^ [], 713 ^ []]]))).
% 1.42/2.42  ncf('1.1.2.1',plain,[member(259 ^ [712 ^ [], 713 ^ []], 713 ^ []), -(member(259 ^ [712 ^ [], 713 ^ []], 712 ^ []))],extension(723 ^ 5,bind([[_131413], [259 ^ [712 ^ [], 713 ^ []]]]))).
% 1.42/2.42  ncf('1.1.2.1.1',plain,[member(259 ^ [712 ^ [], 713 ^ []], 712 ^ [])],extension(263 ^ 6)).
% 1.42/2.42  %-----------------------------------------------------
% 1.42/2.42  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------