%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET062+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n003.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 0.33s 1.37s
% Output   : Proof 0.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET062+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n003.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 19:06:30 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.33/1.37  
% 0.33/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.33/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/1.37  %-----------------------------------------------------
% 0.33/1.37  ncf(matrix, plain, [(714 ^ _102308) ^ [] : [subclass(null_class, 712 ^ [])], (2 ^ _102308) ^ [_102452] : [-(_102452 = _102452)], (4 ^ _102308) ^ [_102559, _102561] : [_102561 = _102559, -(_102559 = _102561)], (10 ^ _102308) ^ [_102763, _102765, _102767] : [-(_102767 = _102763), _102767 = _102765, _102765 = _102763], (20 ^ _102308) ^ [_103076, _103078] : [-(inductive(_103076)), _103078 = _103076, inductive(_103078)], (30 ^ _102308) ^ [_103399, _103401, _103403, _103405] : [-(disjoint(_103403, _103399)), disjoint(_103405, _103401), _103405 = _103403, _103401 = _103399], (44 ^ _102308) ^ [_103815, _103817] : [-(function(_103815)), _103817 = _103815, function(_103817)], (54 ^ _102308) ^ [_104138, _104140, _104142, _104144] : [-(member(_104142, _104138)), member(_104144, _104140), _104144 = _104142, _104140 = _104138], (68 ^ _102308) ^ [_104562, _104564, _104566, _104568] : [-(subclass(_104566, _104562)), subclass(_104568, _104564), _104568 = _104566, _104564 = _104562], (82 ^ _102308) ^ [_105020, _105022, _105024, _105026] : [-(unordered_pair(_105026, _105022) = unordered_pair(_105024, _105020)), _105026 = _105024, _105022 = _105020], (92 ^ _102308) ^ [_105351, _105353] : [_105353 = _105351, -(first(_105353) = first(_105351))], (98 ^ _102308) ^ [_105569, _105571] : [_105571 = _105569, -(second(_105571) = second(_105569))], (104 ^ _102308) ^ [_105787, _105789] : [_105789 = _105787, -(complement(_105789) = complement(_105787))], (110 ^ _102308) ^ [_106033, _106035, _106037, _106039] : [-(intersection(_106039, _106035) = intersection(_106037, _106033)), _106039 = _106037, _106035 = _106033], (120 ^ _102308) ^ [_106364, _106366] : [_106366 = _106364, -(rotate(_106366) = rotate(_106364))], (126 ^ _102308) ^ [_106610, _106612, _106614, _106616] : [-(union(_106616, _106612) = union(_106614, _106610)), _106616 = _106614, _106612 = _106610], (136 ^ _102308) ^ [_106941, _106943] : [_106943 = _106941, -(successor(_106943) = successor(_106941))], (142 ^ _102308) ^ [_107159, _107161] : [_107161 = _107159, -(flip(_107161) = flip(_107159))], (148 ^ _102308) ^ [_107377, _107379] : [_107379 = _107377, -(domain_of(_107379) = domain_of(_107377))], (154 ^ _102308) ^ [_107595, _107597] : [_107597 = _107595, -(range_of(_107597) = range_of(_107595))], (160 ^ _102308) ^ [_107869, _107871, _107873, _107875, _107877, _107879] : [-(restrict(_107879, _107875, _107871) = restrict(_107877, _107873, _107869)), _107879 = _107877, _107875 = _107873, _107871 = _107869], (174 ^ _102308) ^ [_108329, _108331] : [_108331 = _108329, -(power_class(_108331) = power_class(_108329))], (180 ^ _102308) ^ [_108575, _108577, _108579, _108581] : [-(ordered_pair(_108581, _108577) = ordered_pair(_108579, _108575)), _108581 = _108579, _108577 = _108575], (190 ^ _102308) ^ [_108934, _108936, _108938, _108940] : [-(cross_product(_108940, _108936) = cross_product(_108938, _108934)), _108940 = _108938, _108936 = _108934], (200 ^ _102308) ^ [_109293, _109295, _109297, _109299] : [-(compose(_109299, _109295) = compose(_109297, _109293)), _109299 = _109297, _109295 = _109293], (210 ^ _102308) ^ [_109624, _109626] : [_109626 = _109624, -(inverse(_109626) = inverse(_109624))], (216 ^ _102308) ^ [_109842, _109844] : [_109844 = _109842, -(sum_class(_109844) = sum_class(_109842))], (222 ^ _102308) ^ [_110088, _110090, _110092, _110094] : [-(image(_110094, _110090) = image(_110092, _110088)), _110094 = _110092, _110090 = _110088], (232 ^ _102308) ^ [_110419, _110421] : [_110421 = _110419, -(singleton(_110421) = singleton(_110419))], (238 ^ _102308) ^ [_110645, _110647, _110649, _110651] : [-(apply(_110651, _110647) = apply(_110649, _110645)), _110651 = _110649, _110647 = _110645], (258 ^ _102308) ^ [_111407, _111409] : [260 ^ _102308 : [(261 ^ _102308) ^ [] : [-(member(259 ^ [_111407, _111409], _111409))], (263 ^ _102308) ^ [] : [member(259 ^ [_111407, _111409], _111407)]], -(subclass(_111409, _111407))], (248 ^ _102308) ^ [_111093, _111095] : [subclass(_111095, _111093), 251 ^ _102308 : [(252 ^ _102308) ^ [_111230] : [member(_111230, _111095), -(member(_111230, _111093))]]], (267 ^ _102308) ^ [_111735] : [-(subclass(_111735, universal_class))], (269 ^ _102308) ^ [_111871, _111873] : [_111873 = _111871, 272 ^ _102308 : [(273 ^ _102308) ^ [] : [-(subclass(_111873, _111871))], (275 ^ _102308) ^ [] : [-(subclass(_111871, _111873))]]], (277 ^ _102308) ^ [_112108, _112110] : [-(_112110 = _112108), subclass(_112110, _112108), subclass(_112108, _112110)], (287 ^ _102308) ^ [_112452, _112454, _112456] : [member(_112456, unordered_pair(_112454, _112452)), 290 ^ _102308 : [(291 ^ _102308) ^ [] : [-(member(_112456, universal_class))], (293 ^ _102308) ^ [] : [-(_112456 = _112454), -(_112456 = _112452)]]], (299 ^ _102308) ^ [_112797, _112799, _112801] : [-(member(_112801, unordered_pair(_112799, _112797))), member(_112801, universal_class), 304 ^ _102308 : [(305 ^ _102308) ^ [] : [_112801 = _112799], (307 ^ _102308) ^ [] : [_112801 = _112797]]], (311 ^ _102308) ^ [_113175, _113177] : [-(member(unordered_pair(_113177, _113175), universal_class))], (313 ^ _102308) ^ [_113258] : [-(singleton(_113258) = unordered_pair(_113258, _113258))], (315 ^ _102308) ^ [_113355, _113357] : [-(ordered_pair(_113357, _113355) = unordered_pair(singleton(_113357), unordered_pair(_113357, singleton(_113355))))], (317 ^ _102308) ^ [_113534, _113536, _113538, _113540] : [member(ordered_pair(_113540, _113538), cross_product(_113536, _113534)), 320 ^ _102308 : [(321 ^ _102308) ^ [] : [-(member(_113540, _113536))], (323 ^ _102308) ^ [] : [-(member(_113538, _113534))]]], (325 ^ _102308) ^ [_113799, _113801, _113803, _113805] : [-(member(ordered_pair(_113805, _113803), cross_product(_113801, _113799))), member(_113805, _113801), member(_113803, _113799)], (335 ^ _102308) ^ [_114132, _114134] : [342 ^ _102308 : [(343 ^ _102308) ^ [] : [-(first(ordered_pair(_114134, _114132)) = _114134)], (345 ^ _102308) ^ [] : [-(second(ordered_pair(_114134, _114132)) = _114132)]], member(_114134, universal_class), member(_114132, universal_class)], (347 ^ _102308) ^ [_114540, _114542, _114544] : [member(_114540, cross_product(_114544, _114542)), -(_114540 = ordered_pair(first(_114540), second(_114540)))], (353 ^ _102308) ^ [_114805, _114807] : [member(ordered_pair(_114807, _114805), element_relation), 356 ^ _102308 : [(357 ^ _102308) ^ [] : [-(member(_114805, universal_class))], (359 ^ _102308) ^ [] : [-(member(_114807, _114805))]]], (361 ^ _102308) ^ [_115048, _115050] : [-(member(ordered_pair(_115050, _115048), element_relation)), member(_115048, universal_class), member(_115050, _115048)], (371 ^ _102308) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _102308) ^ [_115451, _115453, _115455] : [member(_115451, intersection(_115455, _115453)), 376 ^ _102308 : [(377 ^ _102308) ^ [] : [-(member(_115451, _115455))], (379 ^ _102308) ^ [] : [-(member(_115451, _115453))]]], (381 ^ _102308) ^ [_115702, _115704, _115706] : [-(member(_115702, intersection(_115706, _115704))), member(_115702, _115706), member(_115702, _115704)], (391 ^ _102308) ^ [_116048, _116050] : [member(_116048, complement(_116050)), 394 ^ _102308 : [(395 ^ _102308) ^ [] : [-(member(_116048, universal_class))], (397 ^ _102308) ^ [] : [member(_116048, _116050)]]], (399 ^ _102308) ^ [_116290, _116292] : [-(member(_116290, complement(_116292))), member(_116290, universal_class), -(member(_116290, _116292))], (409 ^ _102308) ^ [_116597, _116599, _116601] : [-(restrict(_116599, _116601, _116597) = intersection(_116599, cross_product(_116601, _116597)))], (411 ^ _102308) ^ [_116688] : [member(_116688, null_class)], (413 ^ _102308) ^ [_116824, _116826] : [member(_116824, domain_of(_116826)), 416 ^ _102308 : [(417 ^ _102308) ^ [] : [-(member(_116824, universal_class))], (419 ^ _102308) ^ [] : [restrict(_116826, singleton(_116824), universal_class) = null_class]]], (421 ^ _102308) ^ [_117078, _117080] : [-(member(_117078, domain_of(_117080))), member(_117078, universal_class), -(restrict(_117080, singleton(_117078), universal_class) = null_class)], (431 ^ _102308) ^ [_117455, _117457, _117459, _117461] : [member(ordered_pair(ordered_pair(_117459, _117457), _117455), rotate(_117461)), 434 ^ _102308 : [(435 ^ _102308) ^ [] : [-(member(ordered_pair(ordered_pair(_117459, _117457), _117455), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _102308) ^ [] : [-(member(ordered_pair(ordered_pair(_117457, _117455), _117459), _117461))]]], (439 ^ _102308) ^ [_117748, _117750, _117752, _117754] : [-(member(ordered_pair(ordered_pair(_117752, _117750), _117748), rotate(_117754))), member(ordered_pair(ordered_pair(_117752, _117750), _117748), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_117750, _117748), _117752), _117754)], (449 ^ _102308) ^ [_118080] : [-(subclass(rotate(_118080), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _102308) ^ [_118246, _118248, _118250, _118252] : [member(ordered_pair(ordered_pair(_118252, _118250), _118248), flip(_118246)), 454 ^ _102308 : [(455 ^ _102308) ^ [] : [-(member(ordered_pair(ordered_pair(_118252, _118250), _118248), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _102308) ^ [] : [-(member(ordered_pair(ordered_pair(_118250, _118252), _118248), _118246))]]], (459 ^ _102308) ^ [_118539, _118541, _118543, _118545] : [-(member(ordered_pair(ordered_pair(_118545, _118543), _118541), flip(_118539))), member(ordered_pair(ordered_pair(_118545, _118543), _118541), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118543, _118545), _118541), _118539)], (469 ^ _102308) ^ [_118871] : [-(subclass(flip(_118871), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _102308) ^ [_119291, _119293, _119295] : [482 ^ _102308 : [(483 ^ _102308) ^ [] : [member(_119291, _119295)], (485 ^ _102308) ^ [] : [member(_119291, _119293)]], -(member(_119291, union(_119295, _119293)))], (471 ^ _102308) ^ [_119023, _119025, _119027] : [member(_119023, union(_119027, _119025)), -(member(_119023, _119027)), -(member(_119023, _119025))], (489 ^ _102308) ^ [_119562] : [-(successor(_119562) = union(_119562, singleton(_119562)))], (491 ^ _102308) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _102308) ^ [_119758, _119760] : [member(ordered_pair(_119760, _119758), successor_relation), 496 ^ _102308 : [(497 ^ _102308) ^ [] : [-(member(_119760, universal_class))], (499 ^ _102308) ^ [] : [-(member(_119758, universal_class))], (501 ^ _102308) ^ [] : [-(successor(_119760) = _119758)]]], (503 ^ _102308) ^ [_120079, _120081] : [-(member(ordered_pair(_120081, _120079), successor_relation)), member(_120081, universal_class), member(_120079, universal_class), successor(_120081) = _120079], (517 ^ _102308) ^ [_120450] : [-(inverse(_120450) = domain_of(flip(cross_product(_120450, universal_class))))], (519 ^ _102308) ^ [_120537] : [-(range_of(_120537) = domain_of(inverse(_120537)))], (521 ^ _102308) ^ [_120635, _120637] : [-(image(_120635, _120637) = range_of(restrict(_120635, _120637, universal_class)))], (523 ^ _102308) ^ [_120768] : [inductive(_120768), 526 ^ _102308 : [(527 ^ _102308) ^ [] : [-(member(null_class, _120768))], (529 ^ _102308) ^ [] : [-(subclass(image(successor_relation, _120768), _120768))]]], (531 ^ _102308) ^ [_121001] : [-(inductive(_121001)), member(null_class, _121001), subclass(image(successor_relation, _121001), _121001)], (542 ^ _102308) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _102308) ^ [] : [-(inductive(540 ^ []))], (546 ^ _102308) ^ [_121446] : [inductive(_121446), -(subclass(540 ^ [], _121446))], (552 ^ _102308) ^ [_121681, _121683] : [member(_121683, sum_class(_121681)), 556 ^ _102308 : [(557 ^ _102308) ^ [] : [-(member(_121683, 555 ^ [_121681, _121683]))], (559 ^ _102308) ^ [] : [-(member(555 ^ [_121681, _121683], _121681))]]], (561 ^ _102308) ^ [_121992, _121994] : [-(member(_121994, sum_class(_121992))), 562 ^ _102308 : [(563 ^ _102308) ^ [_122086] : [member(_121994, _122086), member(_122086, _121992)]]], (571 ^ _102308) ^ [_122346] : [member(_122346, universal_class), -(member(sum_class(_122346), universal_class))], (577 ^ _102308) ^ [_122583, _122585] : [member(_122585, power_class(_122583)), 580 ^ _102308 : [(581 ^ _102308) ^ [] : [-(member(_122585, universal_class))], (583 ^ _102308) ^ [] : [-(subclass(_122585, _122583))]]], (585 ^ _102308) ^ [_122824, _122826] : [-(member(_122826, power_class(_122824))), member(_122826, universal_class), subclass(_122826, _122824)], (595 ^ _102308) ^ [_123115] : [member(_123115, universal_class), -(member(power_class(_123115), universal_class))], (601 ^ _102308) ^ [_123308, _123310] : [-(subclass(compose(_123308, _123310), cross_product(universal_class, universal_class)))], (603 ^ _102308) ^ [_123477, _123479, _123481, _123483] : [member(ordered_pair(_123479, _123477), compose(_123481, _123483)), 606 ^ _102308 : [(607 ^ _102308) ^ [] : [-(member(_123479, universal_class))], (609 ^ _102308) ^ [] : [-(member(_123477, image(_123481, image(_123483, singleton(_123479)))))]]], (611 ^ _102308) ^ [_123758, _123760, _123762, _123764] : [-(member(ordered_pair(_123760, _123758), compose(_123762, _123764))), member(_123760, universal_class), member(_123758, image(_123762, image(_123764, singleton(_123760))))], (621 ^ _102308) ^ [_124122] : [member(_124122, identity_relation), 625 ^ _102308 : [(626 ^ _102308) ^ [] : [-(member(624 ^ [_124122], universal_class))], (628 ^ _102308) ^ [] : [-(_124122 = ordered_pair(624 ^ [_124122], 624 ^ [_124122]))]]], (630 ^ _102308) ^ [_124427] : [-(member(_124427, identity_relation)), 631 ^ _102308 : [(632 ^ _102308) ^ [_124520] : [member(_124520, universal_class), _124427 = ordered_pair(_124520, _124520)]]], (640 ^ _102308) ^ [_124803] : [function(_124803), 643 ^ _102308 : [(644 ^ _102308) ^ [] : [-(subclass(_124803, cross_product(universal_class, universal_class)))], (646 ^ _102308) ^ [] : [-(subclass(compose(_124803, inverse(_124803)), identity_relation))]]], (648 ^ _102308) ^ [_125040] : [-(function(_125040)), subclass(_125040, cross_product(universal_class, universal_class)), subclass(compose(_125040, inverse(_125040)), identity_relation)], (658 ^ _102308) ^ [_125339, _125341] : [-(member(image(_125339, _125341), universal_class)), member(_125341, universal_class), function(_125339)], (678 ^ _102308) ^ [_125986, _125988] : [680 ^ _102308 : [(681 ^ _102308) ^ [] : [-(member(679 ^ [_125986, _125988], _125988))], (683 ^ _102308) ^ [] : [-(member(679 ^ [_125986, _125988], _125986))]], -(disjoint(_125988, _125986))], (668 ^ _102308) ^ [_125671, _125673] : [disjoint(_125673, _125671), 671 ^ _102308 : [(672 ^ _102308) ^ [_125810] : [member(_125810, _125673), member(_125810, _125671)]]], (687 ^ _102308) ^ [_126334] : [-(_126334 = null_class), 691 ^ _102308 : [(692 ^ _102308) ^ [] : [-(member(690 ^ [_126334], universal_class))], (694 ^ _102308) ^ [] : [-(member(690 ^ [_126334], _126334))], (696 ^ _102308) ^ [] : [-(disjoint(690 ^ [_126334], _126334))]]], (698 ^ _102308) ^ [_126744, _126746] : [-(apply(_126746, _126744) = sum_class(image(_126746, singleton(_126744))))], (701 ^ _102308) ^ [] : [-(function(699 ^ []))], (703 ^ _102308) ^ [_126944] : [member(_126944, universal_class), -(_126944 = null_class), -(member(apply(699 ^ [], _126944), _126944))]], input).
% 0.33/1.37  ncf('1',plain,[member(259 ^ [712 ^ [], null_class], null_class)],start(411 ^ 0,bind([[_116688], [259 ^ [712 ^ [], null_class]]]))).
% 0.33/1.37  ncf('1.1',plain,[-(member(259 ^ [712 ^ [], null_class], null_class)), -(subclass(null_class, 712 ^ []))],extension(258 ^ 1,bind([[_111407, _111409], [712 ^ [], null_class]]))).
% 0.33/1.37  ncf('1.1.1',plain,[subclass(null_class, 712 ^ [])],extension(714 ^ 2)).
% 0.33/1.37  %-----------------------------------------------------
% 0.33/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------