%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET060+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 11:55:14 EDT 2023

% Result   : Theorem 0.37s 1.40s
% Output   : Proof 0.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET060+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May 18 19:04:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.37/1.40  
% 0.37/1.40  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.37/1.40  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/1.40  %-----------------------------------------------------
% 0.37/1.40  ncf(matrix, plain, [(715 ^ _103339) ^ [] : [-(member(713 ^ [], intersection(complement(712 ^ []), 712 ^ [])))], (2 ^ _103339) ^ [_103483] : [-(_103483 = _103483)], (4 ^ _103339) ^ [_103590, _103592] : [_103592 = _103590, -(_103590 = _103592)], (10 ^ _103339) ^ [_103794, _103796, _103798] : [-(_103798 = _103794), _103798 = _103796, _103796 = _103794], (20 ^ _103339) ^ [_104107, _104109] : [-(inductive(_104107)), _104109 = _104107, inductive(_104109)], (30 ^ _103339) ^ [_104430, _104432, _104434, _104436] : [-(subclass(_104434, _104430)), subclass(_104436, _104432), _104436 = _104434, _104432 = _104430], (44 ^ _103339) ^ [_104874, _104876, _104878, _104880] : [-(disjoint(_104878, _104874)), disjoint(_104880, _104876), _104880 = _104878, _104876 = _104874], (58 ^ _103339) ^ [_105290, _105292] : [-(function(_105290)), _105292 = _105290, function(_105292)], (68 ^ _103339) ^ [_105593, _105595, _105597, _105599] : [-(member(_105597, _105593)), member(_105599, _105595), _105599 = _105597, _105595 = _105593], (82 ^ _103339) ^ [_106051, _106053, _106055, _106057] : [-(unordered_pair(_106057, _106053) = unordered_pair(_106055, _106051)), _106057 = _106055, _106053 = _106051], (92 ^ _103339) ^ [_106382, _106384] : [_106384 = _106382, -(first(_106384) = first(_106382))], (98 ^ _103339) ^ [_106600, _106602] : [_106602 = _106600, -(second(_106602) = second(_106600))], (104 ^ _103339) ^ [_106818, _106820] : [_106820 = _106818, -(rotate(_106820) = rotate(_106818))], (110 ^ _103339) ^ [_107064, _107066, _107068, _107070] : [-(union(_107070, _107066) = union(_107068, _107064)), _107070 = _107068, _107066 = _107064], (120 ^ _103339) ^ [_107395, _107397] : [_107397 = _107395, -(successor(_107397) = successor(_107395))], (126 ^ _103339) ^ [_107613, _107615] : [_107615 = _107613, -(flip(_107615) = flip(_107613))], (132 ^ _103339) ^ [_107831, _107833] : [_107833 = _107831, -(domain_of(_107833) = domain_of(_107831))], (138 ^ _103339) ^ [_108049, _108051] : [_108051 = _108049, -(range_of(_108051) = range_of(_108049))], (144 ^ _103339) ^ [_108323, _108325, _108327, _108329, _108331, _108333] : [-(restrict(_108333, _108329, _108325) = restrict(_108331, _108327, _108323)), _108333 = _108331, _108329 = _108327, _108325 = _108323], (158 ^ _103339) ^ [_108783, _108785] : [_108785 = _108783, -(power_class(_108785) = power_class(_108783))], (164 ^ _103339) ^ [_109029, _109031, _109033, _109035] : [-(ordered_pair(_109035, _109031) = ordered_pair(_109033, _109029)), _109035 = _109033, _109031 = _109029], (174 ^ _103339) ^ [_109388, _109390, _109392, _109394] : [-(cross_product(_109394, _109390) = cross_product(_109392, _109388)), _109394 = _109392, _109390 = _109388], (184 ^ _103339) ^ [_109747, _109749, _109751, _109753] : [-(compose(_109753, _109749) = compose(_109751, _109747)), _109753 = _109751, _109749 = _109747], (194 ^ _103339) ^ [_110078, _110080] : [_110080 = _110078, -(inverse(_110080) = inverse(_110078))], (200 ^ _103339) ^ [_110296, _110298] : [_110298 = _110296, -(sum_class(_110298) = sum_class(_110296))], (206 ^ _103339) ^ [_110542, _110544, _110546, _110548] : [-(image(_110548, _110544) = image(_110546, _110542)), _110548 = _110546, _110544 = _110542], (216 ^ _103339) ^ [_110873, _110875] : [_110875 = _110873, -(singleton(_110875) = singleton(_110873))], (222 ^ _103339) ^ [_111119, _111121, _111123, _111125] : [-(apply(_111125, _111121) = apply(_111123, _111119)), _111125 = _111123, _111121 = _111119], (242 ^ _103339) ^ [_111789, _111791] : [_111791 = _111789, -(complement(_111791) = complement(_111789))], (232 ^ _103339) ^ [_111478, _111480, _111482, _111484] : [-(intersection(_111484, _111480) = intersection(_111482, _111478)), _111484 = _111482, _111480 = _111478], (258 ^ _103339) ^ [_112438, _112440] : [260 ^ _103339 : [(261 ^ _103339) ^ [] : [-(member(259 ^ [_112438, _112440], _112440))], (263 ^ _103339) ^ [] : [member(259 ^ [_112438, _112440], _112438)]], -(subclass(_112440, _112438))], (248 ^ _103339) ^ [_112124, _112126] : [subclass(_112126, _112124), 251 ^ _103339 : [(252 ^ _103339) ^ [_112261] : [member(_112261, _112126), -(member(_112261, _112124))]]], (267 ^ _103339) ^ [_112766] : [-(subclass(_112766, universal_class))], (269 ^ _103339) ^ [_112902, _112904] : [_112904 = _112902, 272 ^ _103339 : [(273 ^ _103339) ^ [] : [-(subclass(_112904, _112902))], (275 ^ _103339) ^ [] : [-(subclass(_112902, _112904))]]], (277 ^ _103339) ^ [_113139, _113141] : [-(_113141 = _113139), subclass(_113141, _113139), subclass(_113139, _113141)], (287 ^ _103339) ^ [_113483, _113485, _113487] : [member(_113487, unordered_pair(_113485, _113483)), 290 ^ _103339 : [(291 ^ _103339) ^ [] : [-(member(_113487, universal_class))], (293 ^ _103339) ^ [] : [-(_113487 = _113485), -(_113487 = _113483)]]], (299 ^ _103339) ^ [_113828, _113830, _113832] : [-(member(_113832, unordered_pair(_113830, _113828))), member(_113832, universal_class), 304 ^ _103339 : [(305 ^ _103339) ^ [] : [_113832 = _113830], (307 ^ _103339) ^ [] : [_113832 = _113828]]], (311 ^ _103339) ^ [_114206, _114208] : [-(member(unordered_pair(_114208, _114206), universal_class))], (313 ^ _103339) ^ [_114289] : [-(singleton(_114289) = unordered_pair(_114289, _114289))], (315 ^ _103339) ^ [_114386, _114388] : [-(ordered_pair(_114388, _114386) = unordered_pair(singleton(_114388), unordered_pair(_114388, singleton(_114386))))], (317 ^ _103339) ^ [_114565, _114567, _114569, _114571] : [member(ordered_pair(_114571, _114569), cross_product(_114567, _114565)), 320 ^ _103339 : [(321 ^ _103339) ^ [] : [-(member(_114571, _114567))], (323 ^ _103339) ^ [] : [-(member(_114569, _114565))]]], (325 ^ _103339) ^ [_114830, _114832, _114834, _114836] : [-(member(ordered_pair(_114836, _114834), cross_product(_114832, _114830))), member(_114836, _114832), member(_114834, _114830)], (335 ^ _103339) ^ [_115163, _115165] : [342 ^ _103339 : [(343 ^ _103339) ^ [] : [-(first(ordered_pair(_115165, _115163)) = _115165)], (345 ^ _103339) ^ [] : [-(second(ordered_pair(_115165, _115163)) = _115163)]], member(_115165, universal_class), member(_115163, universal_class)], (347 ^ _103339) ^ [_115571, _115573, _115575] : [member(_115571, cross_product(_115575, _115573)), -(_115571 = ordered_pair(first(_115571), second(_115571)))], (353 ^ _103339) ^ [_115836, _115838] : [member(ordered_pair(_115838, _115836), element_relation), 356 ^ _103339 : [(357 ^ _103339) ^ [] : [-(member(_115836, universal_class))], (359 ^ _103339) ^ [] : [-(member(_115838, _115836))]]], (361 ^ _103339) ^ [_116079, _116081] : [-(member(ordered_pair(_116081, _116079), element_relation)), member(_116079, universal_class), member(_116081, _116079)], (371 ^ _103339) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _103339) ^ [_116482, _116484, _116486] : [member(_116482, intersection(_116486, _116484)), 376 ^ _103339 : [(377 ^ _103339) ^ [] : [-(member(_116482, _116486))], (379 ^ _103339) ^ [] : [-(member(_116482, _116484))]]], (381 ^ _103339) ^ [_116733, _116735, _116737] : [-(member(_116733, intersection(_116737, _116735))), member(_116733, _116737), member(_116733, _116735)], (391 ^ _103339) ^ [_117079, _117081] : [member(_117079, complement(_117081)), 394 ^ _103339 : [(395 ^ _103339) ^ [] : [-(member(_117079, universal_class))], (397 ^ _103339) ^ [] : [member(_117079, _117081)]]], (399 ^ _103339) ^ [_117321, _117323] : [-(member(_117321, complement(_117323))), member(_117321, universal_class), -(member(_117321, _117323))], (409 ^ _103339) ^ [_117628, _117630, _117632] : [-(restrict(_117630, _117632, _117628) = intersection(_117630, cross_product(_117632, _117628)))], (411 ^ _103339) ^ [_117719] : [member(_117719, null_class)], (413 ^ _103339) ^ [_117855, _117857] : [member(_117855, domain_of(_117857)), 416 ^ _103339 : [(417 ^ _103339) ^ [] : [-(member(_117855, universal_class))], (419 ^ _103339) ^ [] : [restrict(_117857, singleton(_117855), universal_class) = null_class]]], (421 ^ _103339) ^ [_118109, _118111] : [-(member(_118109, domain_of(_118111))), member(_118109, universal_class), -(restrict(_118111, singleton(_118109), universal_class) = null_class)], (431 ^ _103339) ^ [_118486, _118488, _118490, _118492] : [member(ordered_pair(ordered_pair(_118490, _118488), _118486), rotate(_118492)), 434 ^ _103339 : [(435 ^ _103339) ^ [] : [-(member(ordered_pair(ordered_pair(_118490, _118488), _118486), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _103339) ^ [] : [-(member(ordered_pair(ordered_pair(_118488, _118486), _118490), _118492))]]], (439 ^ _103339) ^ [_118779, _118781, _118783, _118785] : [-(member(ordered_pair(ordered_pair(_118783, _118781), _118779), rotate(_118785))), member(ordered_pair(ordered_pair(_118783, _118781), _118779), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118781, _118779), _118783), _118785)], (449 ^ _103339) ^ [_119111] : [-(subclass(rotate(_119111), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _103339) ^ [_119277, _119279, _119281, _119283] : [member(ordered_pair(ordered_pair(_119283, _119281), _119279), flip(_119277)), 454 ^ _103339 : [(455 ^ _103339) ^ [] : [-(member(ordered_pair(ordered_pair(_119283, _119281), _119279), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _103339) ^ [] : [-(member(ordered_pair(ordered_pair(_119281, _119283), _119279), _119277))]]], (459 ^ _103339) ^ [_119570, _119572, _119574, _119576] : [-(member(ordered_pair(ordered_pair(_119576, _119574), _119572), flip(_119570))), member(ordered_pair(ordered_pair(_119576, _119574), _119572), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_119574, _119576), _119572), _119570)], (469 ^ _103339) ^ [_119902] : [-(subclass(flip(_119902), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _103339) ^ [_120322, _120324, _120326] : [482 ^ _103339 : [(483 ^ _103339) ^ [] : [member(_120322, _120326)], (485 ^ _103339) ^ [] : [member(_120322, _120324)]], -(member(_120322, union(_120326, _120324)))], (471 ^ _103339) ^ [_120054, _120056, _120058] : [member(_120054, union(_120058, _120056)), -(member(_120054, _120058)), -(member(_120054, _120056))], (489 ^ _103339) ^ [_120593] : [-(successor(_120593) = union(_120593, singleton(_120593)))], (491 ^ _103339) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _103339) ^ [_120789, _120791] : [member(ordered_pair(_120791, _120789), successor_relation), 496 ^ _103339 : [(497 ^ _103339) ^ [] : [-(member(_120791, universal_class))], (499 ^ _103339) ^ [] : [-(member(_120789, universal_class))], (501 ^ _103339) ^ [] : [-(successor(_120791) = _120789)]]], (503 ^ _103339) ^ [_121110, _121112] : [-(member(ordered_pair(_121112, _121110), successor_relation)), member(_121112, universal_class), member(_121110, universal_class), successor(_121112) = _121110], (517 ^ _103339) ^ [_121481] : [-(inverse(_121481) = domain_of(flip(cross_product(_121481, universal_class))))], (519 ^ _103339) ^ [_121568] : [-(range_of(_121568) = domain_of(inverse(_121568)))], (521 ^ _103339) ^ [_121666, _121668] : [-(image(_121666, _121668) = range_of(restrict(_121666, _121668, universal_class)))], (523 ^ _103339) ^ [_121799] : [inductive(_121799), 526 ^ _103339 : [(527 ^ _103339) ^ [] : [-(member(null_class, _121799))], (529 ^ _103339) ^ [] : [-(subclass(image(successor_relation, _121799), _121799))]]], (531 ^ _103339) ^ [_122032] : [-(inductive(_122032)), member(null_class, _122032), subclass(image(successor_relation, _122032), _122032)], (542 ^ _103339) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _103339) ^ [] : [-(inductive(540 ^ []))], (546 ^ _103339) ^ [_122477] : [inductive(_122477), -(subclass(540 ^ [], _122477))], (552 ^ _103339) ^ [_122712, _122714] : [member(_122714, sum_class(_122712)), 556 ^ _103339 : [(557 ^ _103339) ^ [] : [-(member(_122714, 555 ^ [_122712, _122714]))], (559 ^ _103339) ^ [] : [-(member(555 ^ [_122712, _122714], _122712))]]], (561 ^ _103339) ^ [_123023, _123025] : [-(member(_123025, sum_class(_123023))), 562 ^ _103339 : [(563 ^ _103339) ^ [_123117] : [member(_123025, _123117), member(_123117, _123023)]]], (571 ^ _103339) ^ [_123377] : [member(_123377, universal_class), -(member(sum_class(_123377), universal_class))], (577 ^ _103339) ^ [_123614, _123616] : [member(_123616, power_class(_123614)), 580 ^ _103339 : [(581 ^ _103339) ^ [] : [-(member(_123616, universal_class))], (583 ^ _103339) ^ [] : [-(subclass(_123616, _123614))]]], (585 ^ _103339) ^ [_123855, _123857] : [-(member(_123857, power_class(_123855))), member(_123857, universal_class), subclass(_123857, _123855)], (595 ^ _103339) ^ [_124146] : [member(_124146, universal_class), -(member(power_class(_124146), universal_class))], (601 ^ _103339) ^ [_124339, _124341] : [-(subclass(compose(_124339, _124341), cross_product(universal_class, universal_class)))], (603 ^ _103339) ^ [_124508, _124510, _124512, _124514] : [member(ordered_pair(_124510, _124508), compose(_124512, _124514)), 606 ^ _103339 : [(607 ^ _103339) ^ [] : [-(member(_124510, universal_class))], (609 ^ _103339) ^ [] : [-(member(_124508, image(_124512, image(_124514, singleton(_124510)))))]]], (611 ^ _103339) ^ [_124789, _124791, _124793, _124795] : [-(member(ordered_pair(_124791, _124789), compose(_124793, _124795))), member(_124791, universal_class), member(_124789, image(_124793, image(_124795, singleton(_124791))))], (621 ^ _103339) ^ [_125153] : [member(_125153, identity_relation), 625 ^ _103339 : [(626 ^ _103339) ^ [] : [-(member(624 ^ [_125153], universal_class))], (628 ^ _103339) ^ [] : [-(_125153 = ordered_pair(624 ^ [_125153], 624 ^ [_125153]))]]], (630 ^ _103339) ^ [_125458] : [-(member(_125458, identity_relation)), 631 ^ _103339 : [(632 ^ _103339) ^ [_125551] : [member(_125551, universal_class), _125458 = ordered_pair(_125551, _125551)]]], (640 ^ _103339) ^ [_125834] : [function(_125834), 643 ^ _103339 : [(644 ^ _103339) ^ [] : [-(subclass(_125834, cross_product(universal_class, universal_class)))], (646 ^ _103339) ^ [] : [-(subclass(compose(_125834, inverse(_125834)), identity_relation))]]], (648 ^ _103339) ^ [_126071] : [-(function(_126071)), subclass(_126071, cross_product(universal_class, universal_class)), subclass(compose(_126071, inverse(_126071)), identity_relation)], (658 ^ _103339) ^ [_126370, _126372] : [-(member(image(_126370, _126372), universal_class)), member(_126372, universal_class), function(_126370)], (678 ^ _103339) ^ [_127017, _127019] : [680 ^ _103339 : [(681 ^ _103339) ^ [] : [-(member(679 ^ [_127017, _127019], _127019))], (683 ^ _103339) ^ [] : [-(member(679 ^ [_127017, _127019], _127017))]], -(disjoint(_127019, _127017))], (668 ^ _103339) ^ [_126702, _126704] : [disjoint(_126704, _126702), 671 ^ _103339 : [(672 ^ _103339) ^ [_126841] : [member(_126841, _126704), member(_126841, _126702)]]], (687 ^ _103339) ^ [_127365] : [-(_127365 = null_class), 691 ^ _103339 : [(692 ^ _103339) ^ [] : [-(member(690 ^ [_127365], universal_class))], (694 ^ _103339) ^ [] : [-(member(690 ^ [_127365], _127365))], (696 ^ _103339) ^ [] : [-(disjoint(690 ^ [_127365], _127365))]]], (698 ^ _103339) ^ [_127775, _127777] : [-(apply(_127777, _127775) = sum_class(image(_127777, singleton(_127775))))], (701 ^ _103339) ^ [] : [-(function(699 ^ []))], (703 ^ _103339) ^ [_127975] : [member(_127975, universal_class), -(_127975 = null_class), -(member(apply(699 ^ [], _127975), _127975))]], input).
% 0.37/1.40  ncf('1',plain,[member(713 ^ [], complement(712 ^ [])), 397 : member(713 ^ [], 712 ^ [])],start(391 ^ 0,bind([[_117079, _117081], [713 ^ [], 712 ^ []]]))).
% 0.37/1.40  ncf('1.1',plain,[-(member(713 ^ [], complement(712 ^ []))), member(713 ^ [], intersection(complement(712 ^ []), 712 ^ []))],extension(373 ^ 1,bind([[_116482, _116484, _116486], [713 ^ [], 712 ^ [], complement(712 ^ [])]]))).
% 0.37/1.40  ncf('1.1.1',plain,[-(member(713 ^ [], intersection(complement(712 ^ []), 712 ^ [])))],extension(715 ^ 2)).
% 0.37/1.40  ncf('1.2',plain,[-(member(713 ^ [], 712 ^ [])), member(713 ^ [], intersection(complement(712 ^ []), 712 ^ []))],extension(373 ^ 3,bind([[_116482, _116484, _116486], [713 ^ [], 712 ^ [], complement(712 ^ [])]]))).
% 0.37/1.40  ncf('1.2.1',plain,[-(member(713 ^ [], intersection(complement(712 ^ []), 712 ^ [])))],extension(715 ^ 4)).
% 0.37/1.40  %-----------------------------------------------------
% 0.37/1.40  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------