%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET054+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n010.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 0.35s 1.38s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET054+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 19:05:27 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.35/1.38  
% 0.35/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.35/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  ncf(matrix, plain, [(714 ^ _102557) ^ [] : [subclass(712 ^ [], 712 ^ [])], (2 ^ _102557) ^ [_102701] : [-(_102701 = _102701)], (4 ^ _102557) ^ [_102808, _102810] : [_102810 = _102808, -(_102808 = _102810)], (10 ^ _102557) ^ [_103012, _103014, _103016] : [-(_103016 = _103012), _103016 = _103014, _103014 = _103012], (20 ^ _102557) ^ [_103325, _103327] : [-(inductive(_103325)), _103327 = _103325, inductive(_103327)], (30 ^ _102557) ^ [_103648, _103650, _103652, _103654] : [-(disjoint(_103652, _103648)), disjoint(_103654, _103650), _103654 = _103652, _103650 = _103648], (44 ^ _102557) ^ [_104064, _104066] : [-(function(_104064)), _104066 = _104064, function(_104066)], (54 ^ _102557) ^ [_104387, _104389, _104391, _104393] : [-(member(_104391, _104387)), member(_104393, _104389), _104393 = _104391, _104389 = _104387], (68 ^ _102557) ^ [_104811, _104813, _104815, _104817] : [-(subclass(_104815, _104811)), subclass(_104817, _104813), _104817 = _104815, _104813 = _104811], (82 ^ _102557) ^ [_105269, _105271, _105273, _105275] : [-(unordered_pair(_105275, _105271) = unordered_pair(_105273, _105269)), _105275 = _105273, _105271 = _105269], (92 ^ _102557) ^ [_105600, _105602] : [_105602 = _105600, -(first(_105602) = first(_105600))], (98 ^ _102557) ^ [_105818, _105820] : [_105820 = _105818, -(second(_105820) = second(_105818))], (104 ^ _102557) ^ [_106036, _106038] : [_106038 = _106036, -(complement(_106038) = complement(_106036))], (110 ^ _102557) ^ [_106282, _106284, _106286, _106288] : [-(intersection(_106288, _106284) = intersection(_106286, _106282)), _106288 = _106286, _106284 = _106282], (120 ^ _102557) ^ [_106613, _106615] : [_106615 = _106613, -(rotate(_106615) = rotate(_106613))], (126 ^ _102557) ^ [_106859, _106861, _106863, _106865] : [-(union(_106865, _106861) = union(_106863, _106859)), _106865 = _106863, _106861 = _106859], (136 ^ _102557) ^ [_107190, _107192] : [_107192 = _107190, -(successor(_107192) = successor(_107190))], (142 ^ _102557) ^ [_107408, _107410] : [_107410 = _107408, -(flip(_107410) = flip(_107408))], (148 ^ _102557) ^ [_107626, _107628] : [_107628 = _107626, -(domain_of(_107628) = domain_of(_107626))], (154 ^ _102557) ^ [_107844, _107846] : [_107846 = _107844, -(range_of(_107846) = range_of(_107844))], (160 ^ _102557) ^ [_108118, _108120, _108122, _108124, _108126, _108128] : [-(restrict(_108128, _108124, _108120) = restrict(_108126, _108122, _108118)), _108128 = _108126, _108124 = _108122, _108120 = _108118], (174 ^ _102557) ^ [_108578, _108580] : [_108580 = _108578, -(power_class(_108580) = power_class(_108578))], (180 ^ _102557) ^ [_108824, _108826, _108828, _108830] : [-(ordered_pair(_108830, _108826) = ordered_pair(_108828, _108824)), _108830 = _108828, _108826 = _108824], (190 ^ _102557) ^ [_109183, _109185, _109187, _109189] : [-(cross_product(_109189, _109185) = cross_product(_109187, _109183)), _109189 = _109187, _109185 = _109183], (200 ^ _102557) ^ [_109542, _109544, _109546, _109548] : [-(compose(_109548, _109544) = compose(_109546, _109542)), _109548 = _109546, _109544 = _109542], (210 ^ _102557) ^ [_109873, _109875] : [_109875 = _109873, -(inverse(_109875) = inverse(_109873))], (216 ^ _102557) ^ [_110091, _110093] : [_110093 = _110091, -(sum_class(_110093) = sum_class(_110091))], (222 ^ _102557) ^ [_110337, _110339, _110341, _110343] : [-(image(_110343, _110339) = image(_110341, _110337)), _110343 = _110341, _110339 = _110337], (232 ^ _102557) ^ [_110668, _110670] : [_110670 = _110668, -(singleton(_110670) = singleton(_110668))], (238 ^ _102557) ^ [_110894, _110896, _110898, _110900] : [-(apply(_110900, _110896) = apply(_110898, _110894)), _110900 = _110898, _110896 = _110894], (258 ^ _102557) ^ [_111656, _111658] : [260 ^ _102557 : [(261 ^ _102557) ^ [] : [-(member(259 ^ [_111656, _111658], _111658))], (263 ^ _102557) ^ [] : [member(259 ^ [_111656, _111658], _111656)]], -(subclass(_111658, _111656))], (248 ^ _102557) ^ [_111342, _111344] : [subclass(_111344, _111342), 251 ^ _102557 : [(252 ^ _102557) ^ [_111479] : [member(_111479, _111344), -(member(_111479, _111342))]]], (267 ^ _102557) ^ [_111984] : [-(subclass(_111984, universal_class))], (269 ^ _102557) ^ [_112120, _112122] : [_112122 = _112120, 272 ^ _102557 : [(273 ^ _102557) ^ [] : [-(subclass(_112122, _112120))], (275 ^ _102557) ^ [] : [-(subclass(_112120, _112122))]]], (277 ^ _102557) ^ [_112357, _112359] : [-(_112359 = _112357), subclass(_112359, _112357), subclass(_112357, _112359)], (287 ^ _102557) ^ [_112701, _112703, _112705] : [member(_112705, unordered_pair(_112703, _112701)), 290 ^ _102557 : [(291 ^ _102557) ^ [] : [-(member(_112705, universal_class))], (293 ^ _102557) ^ [] : [-(_112705 = _112703), -(_112705 = _112701)]]], (299 ^ _102557) ^ [_113046, _113048, _113050] : [-(member(_113050, unordered_pair(_113048, _113046))), member(_113050, universal_class), 304 ^ _102557 : [(305 ^ _102557) ^ [] : [_113050 = _113048], (307 ^ _102557) ^ [] : [_113050 = _113046]]], (311 ^ _102557) ^ [_113424, _113426] : [-(member(unordered_pair(_113426, _113424), universal_class))], (313 ^ _102557) ^ [_113507] : [-(singleton(_113507) = unordered_pair(_113507, _113507))], (315 ^ _102557) ^ [_113604, _113606] : [-(ordered_pair(_113606, _113604) = unordered_pair(singleton(_113606), unordered_pair(_113606, singleton(_113604))))], (317 ^ _102557) ^ [_113783, _113785, _113787, _113789] : [member(ordered_pair(_113789, _113787), cross_product(_113785, _113783)), 320 ^ _102557 : [(321 ^ _102557) ^ [] : [-(member(_113789, _113785))], (323 ^ _102557) ^ [] : [-(member(_113787, _113783))]]], (325 ^ _102557) ^ [_114048, _114050, _114052, _114054] : [-(member(ordered_pair(_114054, _114052), cross_product(_114050, _114048))), member(_114054, _114050), member(_114052, _114048)], (335 ^ _102557) ^ [_114381, _114383] : [342 ^ _102557 : [(343 ^ _102557) ^ [] : [-(first(ordered_pair(_114383, _114381)) = _114383)], (345 ^ _102557) ^ [] : [-(second(ordered_pair(_114383, _114381)) = _114381)]], member(_114383, universal_class), member(_114381, universal_class)], (347 ^ _102557) ^ [_114789, _114791, _114793] : [member(_114789, cross_product(_114793, _114791)), -(_114789 = ordered_pair(first(_114789), second(_114789)))], (353 ^ _102557) ^ [_115054, _115056] : [member(ordered_pair(_115056, _115054), element_relation), 356 ^ _102557 : [(357 ^ _102557) ^ [] : [-(member(_115054, universal_class))], (359 ^ _102557) ^ [] : [-(member(_115056, _115054))]]], (361 ^ _102557) ^ [_115297, _115299] : [-(member(ordered_pair(_115299, _115297), element_relation)), member(_115297, universal_class), member(_115299, _115297)], (371 ^ _102557) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _102557) ^ [_115700, _115702, _115704] : [member(_115700, intersection(_115704, _115702)), 376 ^ _102557 : [(377 ^ _102557) ^ [] : [-(member(_115700, _115704))], (379 ^ _102557) ^ [] : [-(member(_115700, _115702))]]], (381 ^ _102557) ^ [_115951, _115953, _115955] : [-(member(_115951, intersection(_115955, _115953))), member(_115951, _115955), member(_115951, _115953)], (391 ^ _102557) ^ [_116297, _116299] : [member(_116297, complement(_116299)), 394 ^ _102557 : [(395 ^ _102557) ^ [] : [-(member(_116297, universal_class))], (397 ^ _102557) ^ [] : [member(_116297, _116299)]]], (399 ^ _102557) ^ [_116539, _116541] : [-(member(_116539, complement(_116541))), member(_116539, universal_class), -(member(_116539, _116541))], (409 ^ _102557) ^ [_116846, _116848, _116850] : [-(restrict(_116848, _116850, _116846) = intersection(_116848, cross_product(_116850, _116846)))], (411 ^ _102557) ^ [_116937] : [member(_116937, null_class)], (413 ^ _102557) ^ [_117073, _117075] : [member(_117073, domain_of(_117075)), 416 ^ _102557 : [(417 ^ _102557) ^ [] : [-(member(_117073, universal_class))], (419 ^ _102557) ^ [] : [restrict(_117075, singleton(_117073), universal_class) = null_class]]], (421 ^ _102557) ^ [_117327, _117329] : [-(member(_117327, domain_of(_117329))), member(_117327, universal_class), -(restrict(_117329, singleton(_117327), universal_class) = null_class)], (431 ^ _102557) ^ [_117704, _117706, _117708, _117710] : [member(ordered_pair(ordered_pair(_117708, _117706), _117704), rotate(_117710)), 434 ^ _102557 : [(435 ^ _102557) ^ [] : [-(member(ordered_pair(ordered_pair(_117708, _117706), _117704), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _102557) ^ [] : [-(member(ordered_pair(ordered_pair(_117706, _117704), _117708), _117710))]]], (439 ^ _102557) ^ [_117997, _117999, _118001, _118003] : [-(member(ordered_pair(ordered_pair(_118001, _117999), _117997), rotate(_118003))), member(ordered_pair(ordered_pair(_118001, _117999), _117997), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_117999, _117997), _118001), _118003)], (449 ^ _102557) ^ [_118329] : [-(subclass(rotate(_118329), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _102557) ^ [_118495, _118497, _118499, _118501] : [member(ordered_pair(ordered_pair(_118501, _118499), _118497), flip(_118495)), 454 ^ _102557 : [(455 ^ _102557) ^ [] : [-(member(ordered_pair(ordered_pair(_118501, _118499), _118497), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _102557) ^ [] : [-(member(ordered_pair(ordered_pair(_118499, _118501), _118497), _118495))]]], (459 ^ _102557) ^ [_118788, _118790, _118792, _118794] : [-(member(ordered_pair(ordered_pair(_118794, _118792), _118790), flip(_118788))), member(ordered_pair(ordered_pair(_118794, _118792), _118790), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118792, _118794), _118790), _118788)], (469 ^ _102557) ^ [_119120] : [-(subclass(flip(_119120), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _102557) ^ [_119540, _119542, _119544] : [482 ^ _102557 : [(483 ^ _102557) ^ [] : [member(_119540, _119544)], (485 ^ _102557) ^ [] : [member(_119540, _119542)]], -(member(_119540, union(_119544, _119542)))], (471 ^ _102557) ^ [_119272, _119274, _119276] : [member(_119272, union(_119276, _119274)), -(member(_119272, _119276)), -(member(_119272, _119274))], (489 ^ _102557) ^ [_119811] : [-(successor(_119811) = union(_119811, singleton(_119811)))], (491 ^ _102557) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _102557) ^ [_120007, _120009] : [member(ordered_pair(_120009, _120007), successor_relation), 496 ^ _102557 : [(497 ^ _102557) ^ [] : [-(member(_120009, universal_class))], (499 ^ _102557) ^ [] : [-(member(_120007, universal_class))], (501 ^ _102557) ^ [] : [-(successor(_120009) = _120007)]]], (503 ^ _102557) ^ [_120328, _120330] : [-(member(ordered_pair(_120330, _120328), successor_relation)), member(_120330, universal_class), member(_120328, universal_class), successor(_120330) = _120328], (517 ^ _102557) ^ [_120699] : [-(inverse(_120699) = domain_of(flip(cross_product(_120699, universal_class))))], (519 ^ _102557) ^ [_120786] : [-(range_of(_120786) = domain_of(inverse(_120786)))], (521 ^ _102557) ^ [_120884, _120886] : [-(image(_120884, _120886) = range_of(restrict(_120884, _120886, universal_class)))], (523 ^ _102557) ^ [_121017] : [inductive(_121017), 526 ^ _102557 : [(527 ^ _102557) ^ [] : [-(member(null_class, _121017))], (529 ^ _102557) ^ [] : [-(subclass(image(successor_relation, _121017), _121017))]]], (531 ^ _102557) ^ [_121250] : [-(inductive(_121250)), member(null_class, _121250), subclass(image(successor_relation, _121250), _121250)], (542 ^ _102557) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _102557) ^ [] : [-(inductive(540 ^ []))], (546 ^ _102557) ^ [_121695] : [inductive(_121695), -(subclass(540 ^ [], _121695))], (552 ^ _102557) ^ [_121930, _121932] : [member(_121932, sum_class(_121930)), 556 ^ _102557 : [(557 ^ _102557) ^ [] : [-(member(_121932, 555 ^ [_121930, _121932]))], (559 ^ _102557) ^ [] : [-(member(555 ^ [_121930, _121932], _121930))]]], (561 ^ _102557) ^ [_122241, _122243] : [-(member(_122243, sum_class(_122241))), 562 ^ _102557 : [(563 ^ _102557) ^ [_122335] : [member(_122243, _122335), member(_122335, _122241)]]], (571 ^ _102557) ^ [_122595] : [member(_122595, universal_class), -(member(sum_class(_122595), universal_class))], (577 ^ _102557) ^ [_122832, _122834] : [member(_122834, power_class(_122832)), 580 ^ _102557 : [(581 ^ _102557) ^ [] : [-(member(_122834, universal_class))], (583 ^ _102557) ^ [] : [-(subclass(_122834, _122832))]]], (585 ^ _102557) ^ [_123073, _123075] : [-(member(_123075, power_class(_123073))), member(_123075, universal_class), subclass(_123075, _123073)], (595 ^ _102557) ^ [_123364] : [member(_123364, universal_class), -(member(power_class(_123364), universal_class))], (601 ^ _102557) ^ [_123557, _123559] : [-(subclass(compose(_123557, _123559), cross_product(universal_class, universal_class)))], (603 ^ _102557) ^ [_123726, _123728, _123730, _123732] : [member(ordered_pair(_123728, _123726), compose(_123730, _123732)), 606 ^ _102557 : [(607 ^ _102557) ^ [] : [-(member(_123728, universal_class))], (609 ^ _102557) ^ [] : [-(member(_123726, image(_123730, image(_123732, singleton(_123728)))))]]], (611 ^ _102557) ^ [_124007, _124009, _124011, _124013] : [-(member(ordered_pair(_124009, _124007), compose(_124011, _124013))), member(_124009, universal_class), member(_124007, image(_124011, image(_124013, singleton(_124009))))], (621 ^ _102557) ^ [_124371] : [member(_124371, identity_relation), 625 ^ _102557 : [(626 ^ _102557) ^ [] : [-(member(624 ^ [_124371], universal_class))], (628 ^ _102557) ^ [] : [-(_124371 = ordered_pair(624 ^ [_124371], 624 ^ [_124371]))]]], (630 ^ _102557) ^ [_124676] : [-(member(_124676, identity_relation)), 631 ^ _102557 : [(632 ^ _102557) ^ [_124769] : [member(_124769, universal_class), _124676 = ordered_pair(_124769, _124769)]]], (640 ^ _102557) ^ [_125052] : [function(_125052), 643 ^ _102557 : [(644 ^ _102557) ^ [] : [-(subclass(_125052, cross_product(universal_class, universal_class)))], (646 ^ _102557) ^ [] : [-(subclass(compose(_125052, inverse(_125052)), identity_relation))]]], (648 ^ _102557) ^ [_125289] : [-(function(_125289)), subclass(_125289, cross_product(universal_class, universal_class)), subclass(compose(_125289, inverse(_125289)), identity_relation)], (658 ^ _102557) ^ [_125588, _125590] : [-(member(image(_125588, _125590), universal_class)), member(_125590, universal_class), function(_125588)], (678 ^ _102557) ^ [_126235, _126237] : [680 ^ _102557 : [(681 ^ _102557) ^ [] : [-(member(679 ^ [_126235, _126237], _126237))], (683 ^ _102557) ^ [] : [-(member(679 ^ [_126235, _126237], _126235))]], -(disjoint(_126237, _126235))], (668 ^ _102557) ^ [_125920, _125922] : [disjoint(_125922, _125920), 671 ^ _102557 : [(672 ^ _102557) ^ [_126059] : [member(_126059, _125922), member(_126059, _125920)]]], (687 ^ _102557) ^ [_126583] : [-(_126583 = null_class), 691 ^ _102557 : [(692 ^ _102557) ^ [] : [-(member(690 ^ [_126583], universal_class))], (694 ^ _102557) ^ [] : [-(member(690 ^ [_126583], _126583))], (696 ^ _102557) ^ [] : [-(disjoint(690 ^ [_126583], _126583))]]], (698 ^ _102557) ^ [_126993, _126995] : [-(apply(_126995, _126993) = sum_class(image(_126995, singleton(_126993))))], (701 ^ _102557) ^ [] : [-(function(699 ^ []))], (703 ^ _102557) ^ [_127193] : [member(_127193, universal_class), -(_127193 = null_class), -(member(apply(699 ^ [], _127193), _127193))]], input).
% 0.35/1.38  ncf('1',plain,[subclass(712 ^ [], 712 ^ [])],start(714 ^ 0)).
% 0.35/1.38  ncf('1.1',plain,[-(subclass(712 ^ [], 712 ^ [])), 261 : -(member(259 ^ [712 ^ [], 712 ^ []], 712 ^ []))],extension(258 ^ 1,bind([[_111656, _111658], [712 ^ [], 712 ^ []]]))).
% 0.35/1.38  ncf('1.1.1',plain,[member(259 ^ [712 ^ [], 712 ^ []], 712 ^ [])],extension(263 ^ 4)).
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------