%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n025.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 11:55:15 EDT 2023

% Result   : Theorem 0.36s 1.37s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n025.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 19:01:03 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.36/1.37  
% 0.36/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.36/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/1.37  %-----------------------------------------------------
% 0.36/1.37  ncf(matrix, plain, [(714 ^ _102939) ^ [] : [-(subclass(712 ^ [], null_class))], (716 ^ _102939) ^ [] : [712 ^ [] = null_class], (2 ^ _102939) ^ [_103083] : [-(_103083 = _103083)], (4 ^ _102939) ^ [_103190, _103192] : [_103192 = _103190, -(_103190 = _103192)], (10 ^ _102939) ^ [_103394, _103396, _103398] : [-(_103398 = _103394), _103398 = _103396, _103396 = _103394], (20 ^ _102939) ^ [_103707, _103709] : [-(inductive(_103707)), _103709 = _103707, inductive(_103709)], (30 ^ _102939) ^ [_104030, _104032, _104034, _104036] : [-(disjoint(_104034, _104030)), disjoint(_104036, _104032), _104036 = _104034, _104032 = _104030], (44 ^ _102939) ^ [_104446, _104448] : [-(function(_104446)), _104448 = _104446, function(_104448)], (54 ^ _102939) ^ [_104769, _104771, _104773, _104775] : [-(member(_104773, _104769)), member(_104775, _104771), _104775 = _104773, _104771 = _104769], (68 ^ _102939) ^ [_105193, _105195, _105197, _105199] : [-(subclass(_105197, _105193)), subclass(_105199, _105195), _105199 = _105197, _105195 = _105193], (82 ^ _102939) ^ [_105651, _105653, _105655, _105657] : [-(unordered_pair(_105657, _105653) = unordered_pair(_105655, _105651)), _105657 = _105655, _105653 = _105651], (92 ^ _102939) ^ [_105982, _105984] : [_105984 = _105982, -(first(_105984) = first(_105982))], (98 ^ _102939) ^ [_106200, _106202] : [_106202 = _106200, -(second(_106202) = second(_106200))], (104 ^ _102939) ^ [_106418, _106420] : [_106420 = _106418, -(complement(_106420) = complement(_106418))], (110 ^ _102939) ^ [_106664, _106666, _106668, _106670] : [-(intersection(_106670, _106666) = intersection(_106668, _106664)), _106670 = _106668, _106666 = _106664], (120 ^ _102939) ^ [_106995, _106997] : [_106997 = _106995, -(rotate(_106997) = rotate(_106995))], (126 ^ _102939) ^ [_107241, _107243, _107245, _107247] : [-(union(_107247, _107243) = union(_107245, _107241)), _107247 = _107245, _107243 = _107241], (136 ^ _102939) ^ [_107572, _107574] : [_107574 = _107572, -(successor(_107574) = successor(_107572))], (142 ^ _102939) ^ [_107790, _107792] : [_107792 = _107790, -(flip(_107792) = flip(_107790))], (148 ^ _102939) ^ [_108008, _108010] : [_108010 = _108008, -(domain_of(_108010) = domain_of(_108008))], (154 ^ _102939) ^ [_108226, _108228] : [_108228 = _108226, -(range_of(_108228) = range_of(_108226))], (160 ^ _102939) ^ [_108500, _108502, _108504, _108506, _108508, _108510] : [-(restrict(_108510, _108506, _108502) = restrict(_108508, _108504, _108500)), _108510 = _108508, _108506 = _108504, _108502 = _108500], (174 ^ _102939) ^ [_108960, _108962] : [_108962 = _108960, -(power_class(_108962) = power_class(_108960))], (180 ^ _102939) ^ [_109206, _109208, _109210, _109212] : [-(ordered_pair(_109212, _109208) = ordered_pair(_109210, _109206)), _109212 = _109210, _109208 = _109206], (190 ^ _102939) ^ [_109565, _109567, _109569, _109571] : [-(cross_product(_109571, _109567) = cross_product(_109569, _109565)), _109571 = _109569, _109567 = _109565], (200 ^ _102939) ^ [_109924, _109926, _109928, _109930] : [-(compose(_109930, _109926) = compose(_109928, _109924)), _109930 = _109928, _109926 = _109924], (210 ^ _102939) ^ [_110255, _110257] : [_110257 = _110255, -(inverse(_110257) = inverse(_110255))], (216 ^ _102939) ^ [_110473, _110475] : [_110475 = _110473, -(sum_class(_110475) = sum_class(_110473))], (222 ^ _102939) ^ [_110719, _110721, _110723, _110725] : [-(image(_110725, _110721) = image(_110723, _110719)), _110725 = _110723, _110721 = _110719], (232 ^ _102939) ^ [_111050, _111052] : [_111052 = _111050, -(singleton(_111052) = singleton(_111050))], (238 ^ _102939) ^ [_111276, _111278, _111280, _111282] : [-(apply(_111282, _111278) = apply(_111280, _111276)), _111282 = _111280, _111278 = _111276], (258 ^ _102939) ^ [_112038, _112040] : [260 ^ _102939 : [(261 ^ _102939) ^ [] : [-(member(259 ^ [_112038, _112040], _112040))], (263 ^ _102939) ^ [] : [member(259 ^ [_112038, _112040], _112038)]], -(subclass(_112040, _112038))], (248 ^ _102939) ^ [_111724, _111726] : [subclass(_111726, _111724), 251 ^ _102939 : [(252 ^ _102939) ^ [_111861] : [member(_111861, _111726), -(member(_111861, _111724))]]], (267 ^ _102939) ^ [_112366] : [-(subclass(_112366, universal_class))], (269 ^ _102939) ^ [_112502, _112504] : [_112504 = _112502, 272 ^ _102939 : [(273 ^ _102939) ^ [] : [-(subclass(_112504, _112502))], (275 ^ _102939) ^ [] : [-(subclass(_112502, _112504))]]], (277 ^ _102939) ^ [_112739, _112741] : [-(_112741 = _112739), subclass(_112741, _112739), subclass(_112739, _112741)], (287 ^ _102939) ^ [_113083, _113085, _113087] : [member(_113087, unordered_pair(_113085, _113083)), 290 ^ _102939 : [(291 ^ _102939) ^ [] : [-(member(_113087, universal_class))], (293 ^ _102939) ^ [] : [-(_113087 = _113085), -(_113087 = _113083)]]], (299 ^ _102939) ^ [_113428, _113430, _113432] : [-(member(_113432, unordered_pair(_113430, _113428))), member(_113432, universal_class), 304 ^ _102939 : [(305 ^ _102939) ^ [] : [_113432 = _113430], (307 ^ _102939) ^ [] : [_113432 = _113428]]], (311 ^ _102939) ^ [_113806, _113808] : [-(member(unordered_pair(_113808, _113806), universal_class))], (313 ^ _102939) ^ [_113889] : [-(singleton(_113889) = unordered_pair(_113889, _113889))], (315 ^ _102939) ^ [_113986, _113988] : [-(ordered_pair(_113988, _113986) = unordered_pair(singleton(_113988), unordered_pair(_113988, singleton(_113986))))], (317 ^ _102939) ^ [_114165, _114167, _114169, _114171] : [member(ordered_pair(_114171, _114169), cross_product(_114167, _114165)), 320 ^ _102939 : [(321 ^ _102939) ^ [] : [-(member(_114171, _114167))], (323 ^ _102939) ^ [] : [-(member(_114169, _114165))]]], (325 ^ _102939) ^ [_114430, _114432, _114434, _114436] : [-(member(ordered_pair(_114436, _114434), cross_product(_114432, _114430))), member(_114436, _114432), member(_114434, _114430)], (335 ^ _102939) ^ [_114763, _114765] : [342 ^ _102939 : [(343 ^ _102939) ^ [] : [-(first(ordered_pair(_114765, _114763)) = _114765)], (345 ^ _102939) ^ [] : [-(second(ordered_pair(_114765, _114763)) = _114763)]], member(_114765, universal_class), member(_114763, universal_class)], (347 ^ _102939) ^ [_115171, _115173, _115175] : [member(_115171, cross_product(_115175, _115173)), -(_115171 = ordered_pair(first(_115171), second(_115171)))], (353 ^ _102939) ^ [_115436, _115438] : [member(ordered_pair(_115438, _115436), element_relation), 356 ^ _102939 : [(357 ^ _102939) ^ [] : [-(member(_115436, universal_class))], (359 ^ _102939) ^ [] : [-(member(_115438, _115436))]]], (361 ^ _102939) ^ [_115679, _115681] : [-(member(ordered_pair(_115681, _115679), element_relation)), member(_115679, universal_class), member(_115681, _115679)], (371 ^ _102939) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _102939) ^ [_116082, _116084, _116086] : [member(_116082, intersection(_116086, _116084)), 376 ^ _102939 : [(377 ^ _102939) ^ [] : [-(member(_116082, _116086))], (379 ^ _102939) ^ [] : [-(member(_116082, _116084))]]], (381 ^ _102939) ^ [_116333, _116335, _116337] : [-(member(_116333, intersection(_116337, _116335))), member(_116333, _116337), member(_116333, _116335)], (391 ^ _102939) ^ [_116679, _116681] : [member(_116679, complement(_116681)), 394 ^ _102939 : [(395 ^ _102939) ^ [] : [-(member(_116679, universal_class))], (397 ^ _102939) ^ [] : [member(_116679, _116681)]]], (399 ^ _102939) ^ [_116921, _116923] : [-(member(_116921, complement(_116923))), member(_116921, universal_class), -(member(_116921, _116923))], (409 ^ _102939) ^ [_117228, _117230, _117232] : [-(restrict(_117230, _117232, _117228) = intersection(_117230, cross_product(_117232, _117228)))], (411 ^ _102939) ^ [_117319] : [member(_117319, null_class)], (413 ^ _102939) ^ [_117455, _117457] : [member(_117455, domain_of(_117457)), 416 ^ _102939 : [(417 ^ _102939) ^ [] : [-(member(_117455, universal_class))], (419 ^ _102939) ^ [] : [restrict(_117457, singleton(_117455), universal_class) = null_class]]], (421 ^ _102939) ^ [_117709, _117711] : [-(member(_117709, domain_of(_117711))), member(_117709, universal_class), -(restrict(_117711, singleton(_117709), universal_class) = null_class)], (431 ^ _102939) ^ [_118086, _118088, _118090, _118092] : [member(ordered_pair(ordered_pair(_118090, _118088), _118086), rotate(_118092)), 434 ^ _102939 : [(435 ^ _102939) ^ [] : [-(member(ordered_pair(ordered_pair(_118090, _118088), _118086), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _102939) ^ [] : [-(member(ordered_pair(ordered_pair(_118088, _118086), _118090), _118092))]]], (439 ^ _102939) ^ [_118379, _118381, _118383, _118385] : [-(member(ordered_pair(ordered_pair(_118383, _118381), _118379), rotate(_118385))), member(ordered_pair(ordered_pair(_118383, _118381), _118379), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118381, _118379), _118383), _118385)], (449 ^ _102939) ^ [_118711] : [-(subclass(rotate(_118711), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _102939) ^ [_118877, _118879, _118881, _118883] : [member(ordered_pair(ordered_pair(_118883, _118881), _118879), flip(_118877)), 454 ^ _102939 : [(455 ^ _102939) ^ [] : [-(member(ordered_pair(ordered_pair(_118883, _118881), _118879), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _102939) ^ [] : [-(member(ordered_pair(ordered_pair(_118881, _118883), _118879), _118877))]]], (459 ^ _102939) ^ [_119170, _119172, _119174, _119176] : [-(member(ordered_pair(ordered_pair(_119176, _119174), _119172), flip(_119170))), member(ordered_pair(ordered_pair(_119176, _119174), _119172), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_119174, _119176), _119172), _119170)], (469 ^ _102939) ^ [_119502] : [-(subclass(flip(_119502), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _102939) ^ [_119922, _119924, _119926] : [482 ^ _102939 : [(483 ^ _102939) ^ [] : [member(_119922, _119926)], (485 ^ _102939) ^ [] : [member(_119922, _119924)]], -(member(_119922, union(_119926, _119924)))], (471 ^ _102939) ^ [_119654, _119656, _119658] : [member(_119654, union(_119658, _119656)), -(member(_119654, _119658)), -(member(_119654, _119656))], (489 ^ _102939) ^ [_120193] : [-(successor(_120193) = union(_120193, singleton(_120193)))], (491 ^ _102939) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _102939) ^ [_120389, _120391] : [member(ordered_pair(_120391, _120389), successor_relation), 496 ^ _102939 : [(497 ^ _102939) ^ [] : [-(member(_120391, universal_class))], (499 ^ _102939) ^ [] : [-(member(_120389, universal_class))], (501 ^ _102939) ^ [] : [-(successor(_120391) = _120389)]]], (503 ^ _102939) ^ [_120710, _120712] : [-(member(ordered_pair(_120712, _120710), successor_relation)), member(_120712, universal_class), member(_120710, universal_class), successor(_120712) = _120710], (517 ^ _102939) ^ [_121081] : [-(inverse(_121081) = domain_of(flip(cross_product(_121081, universal_class))))], (519 ^ _102939) ^ [_121168] : [-(range_of(_121168) = domain_of(inverse(_121168)))], (521 ^ _102939) ^ [_121266, _121268] : [-(image(_121266, _121268) = range_of(restrict(_121266, _121268, universal_class)))], (523 ^ _102939) ^ [_121399] : [inductive(_121399), 526 ^ _102939 : [(527 ^ _102939) ^ [] : [-(member(null_class, _121399))], (529 ^ _102939) ^ [] : [-(subclass(image(successor_relation, _121399), _121399))]]], (531 ^ _102939) ^ [_121632] : [-(inductive(_121632)), member(null_class, _121632), subclass(image(successor_relation, _121632), _121632)], (542 ^ _102939) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _102939) ^ [] : [-(inductive(540 ^ []))], (546 ^ _102939) ^ [_122077] : [inductive(_122077), -(subclass(540 ^ [], _122077))], (552 ^ _102939) ^ [_122312, _122314] : [member(_122314, sum_class(_122312)), 556 ^ _102939 : [(557 ^ _102939) ^ [] : [-(member(_122314, 555 ^ [_122312, _122314]))], (559 ^ _102939) ^ [] : [-(member(555 ^ [_122312, _122314], _122312))]]], (561 ^ _102939) ^ [_122623, _122625] : [-(member(_122625, sum_class(_122623))), 562 ^ _102939 : [(563 ^ _102939) ^ [_122717] : [member(_122625, _122717), member(_122717, _122623)]]], (571 ^ _102939) ^ [_122977] : [member(_122977, universal_class), -(member(sum_class(_122977), universal_class))], (577 ^ _102939) ^ [_123214, _123216] : [member(_123216, power_class(_123214)), 580 ^ _102939 : [(581 ^ _102939) ^ [] : [-(member(_123216, universal_class))], (583 ^ _102939) ^ [] : [-(subclass(_123216, _123214))]]], (585 ^ _102939) ^ [_123455, _123457] : [-(member(_123457, power_class(_123455))), member(_123457, universal_class), subclass(_123457, _123455)], (595 ^ _102939) ^ [_123746] : [member(_123746, universal_class), -(member(power_class(_123746), universal_class))], (601 ^ _102939) ^ [_123939, _123941] : [-(subclass(compose(_123939, _123941), cross_product(universal_class, universal_class)))], (603 ^ _102939) ^ [_124108, _124110, _124112, _124114] : [member(ordered_pair(_124110, _124108), compose(_124112, _124114)), 606 ^ _102939 : [(607 ^ _102939) ^ [] : [-(member(_124110, universal_class))], (609 ^ _102939) ^ [] : [-(member(_124108, image(_124112, image(_124114, singleton(_124110)))))]]], (611 ^ _102939) ^ [_124389, _124391, _124393, _124395] : [-(member(ordered_pair(_124391, _124389), compose(_124393, _124395))), member(_124391, universal_class), member(_124389, image(_124393, image(_124395, singleton(_124391))))], (621 ^ _102939) ^ [_124753] : [member(_124753, identity_relation), 625 ^ _102939 : [(626 ^ _102939) ^ [] : [-(member(624 ^ [_124753], universal_class))], (628 ^ _102939) ^ [] : [-(_124753 = ordered_pair(624 ^ [_124753], 624 ^ [_124753]))]]], (630 ^ _102939) ^ [_125058] : [-(member(_125058, identity_relation)), 631 ^ _102939 : [(632 ^ _102939) ^ [_125151] : [member(_125151, universal_class), _125058 = ordered_pair(_125151, _125151)]]], (640 ^ _102939) ^ [_125434] : [function(_125434), 643 ^ _102939 : [(644 ^ _102939) ^ [] : [-(subclass(_125434, cross_product(universal_class, universal_class)))], (646 ^ _102939) ^ [] : [-(subclass(compose(_125434, inverse(_125434)), identity_relation))]]], (648 ^ _102939) ^ [_125671] : [-(function(_125671)), subclass(_125671, cross_product(universal_class, universal_class)), subclass(compose(_125671, inverse(_125671)), identity_relation)], (658 ^ _102939) ^ [_125970, _125972] : [-(member(image(_125970, _125972), universal_class)), member(_125972, universal_class), function(_125970)], (678 ^ _102939) ^ [_126617, _126619] : [680 ^ _102939 : [(681 ^ _102939) ^ [] : [-(member(679 ^ [_126617, _126619], _126619))], (683 ^ _102939) ^ [] : [-(member(679 ^ [_126617, _126619], _126617))]], -(disjoint(_126619, _126617))], (668 ^ _102939) ^ [_126302, _126304] : [disjoint(_126304, _126302), 671 ^ _102939 : [(672 ^ _102939) ^ [_126441] : [member(_126441, _126304), member(_126441, _126302)]]], (687 ^ _102939) ^ [_126965] : [-(_126965 = null_class), 691 ^ _102939 : [(692 ^ _102939) ^ [] : [-(member(690 ^ [_126965], universal_class))], (694 ^ _102939) ^ [] : [-(member(690 ^ [_126965], _126965))], (696 ^ _102939) ^ [] : [-(disjoint(690 ^ [_126965], _126965))]]], (698 ^ _102939) ^ [_127375, _127377] : [-(apply(_127377, _127375) = sum_class(image(_127377, singleton(_127375))))], (701 ^ _102939) ^ [] : [-(function(699 ^ []))], (703 ^ _102939) ^ [_127575] : [member(_127575, universal_class), -(_127575 = null_class), -(member(apply(699 ^ [], _127575), _127575))]], input).
% 0.36/1.37  ncf('1',plain,[member(259 ^ [712 ^ [], null_class], null_class)],start(411 ^ 0,bind([[_117319], [259 ^ [712 ^ [], null_class]]]))).
% 0.36/1.37  ncf('1.1',plain,[-(member(259 ^ [712 ^ [], null_class], null_class)), -(subclass(null_class, 712 ^ []))],extension(258 ^ 1,bind([[_112038, _112040], [712 ^ [], null_class]]))).
% 0.36/1.37  ncf('1.1.1',plain,[subclass(null_class, 712 ^ []), -(712 ^ [] = null_class), subclass(712 ^ [], null_class)],extension(277 ^ 2,bind([[_112739, _112741], [null_class, 712 ^ []]]))).
% 0.36/1.37  ncf('1.1.1.1',plain,[712 ^ [] = null_class],extension(716 ^ 3)).
% 0.36/1.37  ncf('1.1.1.2',plain,[-(subclass(712 ^ [], null_class))],extension(714 ^ 3)).
% 0.36/1.37  %-----------------------------------------------------
% 0.36/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------