%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET077+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.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 11:55:19 EDT 2023

% Result   : Theorem 0.40s 1.38s
% Output   : Proof 0.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET077+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 19:28:33 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.40/1.38  
% 0.40/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.40/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/1.38  %-----------------------------------------------------
% 0.40/1.38  ncf(matrix, plain, [(714 ^ _103091) ^ [] : [member(singleton(712 ^ []), universal_class)], (2 ^ _103091) ^ [_103235] : [-(_103235 = _103235)], (4 ^ _103091) ^ [_103342, _103344] : [_103344 = _103342, -(_103342 = _103344)], (10 ^ _103091) ^ [_103546, _103548, _103550] : [-(_103550 = _103546), _103550 = _103548, _103548 = _103546], (20 ^ _103091) ^ [_103859, _103861] : [-(inductive(_103859)), _103861 = _103859, inductive(_103861)], (30 ^ _103091) ^ [_104182, _104184, _104186, _104188] : [-(subclass(_104186, _104182)), subclass(_104188, _104184), _104188 = _104186, _104184 = _104182], (44 ^ _103091) ^ [_104626, _104628, _104630, _104632] : [-(disjoint(_104630, _104626)), disjoint(_104632, _104628), _104632 = _104630, _104628 = _104626], (58 ^ _103091) ^ [_105042, _105044] : [-(function(_105042)), _105044 = _105042, function(_105044)], (68 ^ _103091) ^ [_105345, _105347, _105349, _105351] : [-(member(_105349, _105345)), member(_105351, _105347), _105351 = _105349, _105347 = _105345], (82 ^ _103091) ^ [_105803, _105805, _105807, _105809] : [-(unordered_pair(_105809, _105805) = unordered_pair(_105807, _105803)), _105809 = _105807, _105805 = _105803], (92 ^ _103091) ^ [_106134, _106136] : [_106136 = _106134, -(first(_106136) = first(_106134))], (98 ^ _103091) ^ [_106352, _106354] : [_106354 = _106352, -(second(_106354) = second(_106352))], (104 ^ _103091) ^ [_106570, _106572] : [_106572 = _106570, -(complement(_106572) = complement(_106570))], (110 ^ _103091) ^ [_106816, _106818, _106820, _106822] : [-(intersection(_106822, _106818) = intersection(_106820, _106816)), _106822 = _106820, _106818 = _106816], (120 ^ _103091) ^ [_107147, _107149] : [_107149 = _107147, -(rotate(_107149) = rotate(_107147))], (126 ^ _103091) ^ [_107393, _107395, _107397, _107399] : [-(union(_107399, _107395) = union(_107397, _107393)), _107399 = _107397, _107395 = _107393], (136 ^ _103091) ^ [_107724, _107726] : [_107726 = _107724, -(successor(_107726) = successor(_107724))], (142 ^ _103091) ^ [_107942, _107944] : [_107944 = _107942, -(flip(_107944) = flip(_107942))], (148 ^ _103091) ^ [_108160, _108162] : [_108162 = _108160, -(domain_of(_108162) = domain_of(_108160))], (154 ^ _103091) ^ [_108378, _108380] : [_108380 = _108378, -(range_of(_108380) = range_of(_108378))], (160 ^ _103091) ^ [_108652, _108654, _108656, _108658, _108660, _108662] : [-(restrict(_108662, _108658, _108654) = restrict(_108660, _108656, _108652)), _108662 = _108660, _108658 = _108656, _108654 = _108652], (174 ^ _103091) ^ [_109112, _109114] : [_109114 = _109112, -(power_class(_109114) = power_class(_109112))], (180 ^ _103091) ^ [_109358, _109360, _109362, _109364] : [-(ordered_pair(_109364, _109360) = ordered_pair(_109362, _109358)), _109364 = _109362, _109360 = _109358], (190 ^ _103091) ^ [_109717, _109719, _109721, _109723] : [-(cross_product(_109723, _109719) = cross_product(_109721, _109717)), _109723 = _109721, _109719 = _109717], (200 ^ _103091) ^ [_110076, _110078, _110080, _110082] : [-(compose(_110082, _110078) = compose(_110080, _110076)), _110082 = _110080, _110078 = _110076], (210 ^ _103091) ^ [_110407, _110409] : [_110409 = _110407, -(inverse(_110409) = inverse(_110407))], (216 ^ _103091) ^ [_110625, _110627] : [_110627 = _110625, -(sum_class(_110627) = sum_class(_110625))], (222 ^ _103091) ^ [_110871, _110873, _110875, _110877] : [-(image(_110877, _110873) = image(_110875, _110871)), _110877 = _110875, _110873 = _110871], (242 ^ _103091) ^ [_111541, _111543] : [_111543 = _111541, -(singleton(_111543) = singleton(_111541))], (232 ^ _103091) ^ [_111230, _111232, _111234, _111236] : [-(apply(_111236, _111232) = apply(_111234, _111230)), _111236 = _111234, _111232 = _111230], (258 ^ _103091) ^ [_112190, _112192] : [260 ^ _103091 : [(261 ^ _103091) ^ [] : [-(member(259 ^ [_112190, _112192], _112192))], (263 ^ _103091) ^ [] : [member(259 ^ [_112190, _112192], _112190)]], -(subclass(_112192, _112190))], (248 ^ _103091) ^ [_111876, _111878] : [subclass(_111878, _111876), 251 ^ _103091 : [(252 ^ _103091) ^ [_112013] : [member(_112013, _111878), -(member(_112013, _111876))]]], (267 ^ _103091) ^ [_112518] : [-(subclass(_112518, universal_class))], (269 ^ _103091) ^ [_112654, _112656] : [_112656 = _112654, 272 ^ _103091 : [(273 ^ _103091) ^ [] : [-(subclass(_112656, _112654))], (275 ^ _103091) ^ [] : [-(subclass(_112654, _112656))]]], (277 ^ _103091) ^ [_112891, _112893] : [-(_112893 = _112891), subclass(_112893, _112891), subclass(_112891, _112893)], (287 ^ _103091) ^ [_113235, _113237, _113239] : [member(_113239, unordered_pair(_113237, _113235)), 290 ^ _103091 : [(291 ^ _103091) ^ [] : [-(member(_113239, universal_class))], (293 ^ _103091) ^ [] : [-(_113239 = _113237), -(_113239 = _113235)]]], (299 ^ _103091) ^ [_113580, _113582, _113584] : [-(member(_113584, unordered_pair(_113582, _113580))), member(_113584, universal_class), 304 ^ _103091 : [(305 ^ _103091) ^ [] : [_113584 = _113582], (307 ^ _103091) ^ [] : [_113584 = _113580]]], (311 ^ _103091) ^ [_113958, _113960] : [-(member(unordered_pair(_113960, _113958), universal_class))], (313 ^ _103091) ^ [_114041] : [-(singleton(_114041) = unordered_pair(_114041, _114041))], (315 ^ _103091) ^ [_114138, _114140] : [-(ordered_pair(_114140, _114138) = unordered_pair(singleton(_114140), unordered_pair(_114140, singleton(_114138))))], (317 ^ _103091) ^ [_114317, _114319, _114321, _114323] : [member(ordered_pair(_114323, _114321), cross_product(_114319, _114317)), 320 ^ _103091 : [(321 ^ _103091) ^ [] : [-(member(_114323, _114319))], (323 ^ _103091) ^ [] : [-(member(_114321, _114317))]]], (325 ^ _103091) ^ [_114582, _114584, _114586, _114588] : [-(member(ordered_pair(_114588, _114586), cross_product(_114584, _114582))), member(_114588, _114584), member(_114586, _114582)], (335 ^ _103091) ^ [_114915, _114917] : [342 ^ _103091 : [(343 ^ _103091) ^ [] : [-(first(ordered_pair(_114917, _114915)) = _114917)], (345 ^ _103091) ^ [] : [-(second(ordered_pair(_114917, _114915)) = _114915)]], member(_114917, universal_class), member(_114915, universal_class)], (347 ^ _103091) ^ [_115323, _115325, _115327] : [member(_115323, cross_product(_115327, _115325)), -(_115323 = ordered_pair(first(_115323), second(_115323)))], (353 ^ _103091) ^ [_115588, _115590] : [member(ordered_pair(_115590, _115588), element_relation), 356 ^ _103091 : [(357 ^ _103091) ^ [] : [-(member(_115588, universal_class))], (359 ^ _103091) ^ [] : [-(member(_115590, _115588))]]], (361 ^ _103091) ^ [_115831, _115833] : [-(member(ordered_pair(_115833, _115831), element_relation)), member(_115831, universal_class), member(_115833, _115831)], (371 ^ _103091) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _103091) ^ [_116234, _116236, _116238] : [member(_116234, intersection(_116238, _116236)), 376 ^ _103091 : [(377 ^ _103091) ^ [] : [-(member(_116234, _116238))], (379 ^ _103091) ^ [] : [-(member(_116234, _116236))]]], (381 ^ _103091) ^ [_116485, _116487, _116489] : [-(member(_116485, intersection(_116489, _116487))), member(_116485, _116489), member(_116485, _116487)], (391 ^ _103091) ^ [_116831, _116833] : [member(_116831, complement(_116833)), 394 ^ _103091 : [(395 ^ _103091) ^ [] : [-(member(_116831, universal_class))], (397 ^ _103091) ^ [] : [member(_116831, _116833)]]], (399 ^ _103091) ^ [_117073, _117075] : [-(member(_117073, complement(_117075))), member(_117073, universal_class), -(member(_117073, _117075))], (409 ^ _103091) ^ [_117380, _117382, _117384] : [-(restrict(_117382, _117384, _117380) = intersection(_117382, cross_product(_117384, _117380)))], (411 ^ _103091) ^ [_117471] : [member(_117471, null_class)], (413 ^ _103091) ^ [_117607, _117609] : [member(_117607, domain_of(_117609)), 416 ^ _103091 : [(417 ^ _103091) ^ [] : [-(member(_117607, universal_class))], (419 ^ _103091) ^ [] : [restrict(_117609, singleton(_117607), universal_class) = null_class]]], (421 ^ _103091) ^ [_117861, _117863] : [-(member(_117861, domain_of(_117863))), member(_117861, universal_class), -(restrict(_117863, singleton(_117861), universal_class) = null_class)], (431 ^ _103091) ^ [_118238, _118240, _118242, _118244] : [member(ordered_pair(ordered_pair(_118242, _118240), _118238), rotate(_118244)), 434 ^ _103091 : [(435 ^ _103091) ^ [] : [-(member(ordered_pair(ordered_pair(_118242, _118240), _118238), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _103091) ^ [] : [-(member(ordered_pair(ordered_pair(_118240, _118238), _118242), _118244))]]], (439 ^ _103091) ^ [_118531, _118533, _118535, _118537] : [-(member(ordered_pair(ordered_pair(_118535, _118533), _118531), rotate(_118537))), member(ordered_pair(ordered_pair(_118535, _118533), _118531), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118533, _118531), _118535), _118537)], (449 ^ _103091) ^ [_118863] : [-(subclass(rotate(_118863), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _103091) ^ [_119029, _119031, _119033, _119035] : [member(ordered_pair(ordered_pair(_119035, _119033), _119031), flip(_119029)), 454 ^ _103091 : [(455 ^ _103091) ^ [] : [-(member(ordered_pair(ordered_pair(_119035, _119033), _119031), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _103091) ^ [] : [-(member(ordered_pair(ordered_pair(_119033, _119035), _119031), _119029))]]], (459 ^ _103091) ^ [_119322, _119324, _119326, _119328] : [-(member(ordered_pair(ordered_pair(_119328, _119326), _119324), flip(_119322))), member(ordered_pair(ordered_pair(_119328, _119326), _119324), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_119326, _119328), _119324), _119322)], (469 ^ _103091) ^ [_119654] : [-(subclass(flip(_119654), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _103091) ^ [_120074, _120076, _120078] : [482 ^ _103091 : [(483 ^ _103091) ^ [] : [member(_120074, _120078)], (485 ^ _103091) ^ [] : [member(_120074, _120076)]], -(member(_120074, union(_120078, _120076)))], (471 ^ _103091) ^ [_119806, _119808, _119810] : [member(_119806, union(_119810, _119808)), -(member(_119806, _119810)), -(member(_119806, _119808))], (489 ^ _103091) ^ [_120345] : [-(successor(_120345) = union(_120345, singleton(_120345)))], (491 ^ _103091) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _103091) ^ [_120541, _120543] : [member(ordered_pair(_120543, _120541), successor_relation), 496 ^ _103091 : [(497 ^ _103091) ^ [] : [-(member(_120543, universal_class))], (499 ^ _103091) ^ [] : [-(member(_120541, universal_class))], (501 ^ _103091) ^ [] : [-(successor(_120543) = _120541)]]], (503 ^ _103091) ^ [_120862, _120864] : [-(member(ordered_pair(_120864, _120862), successor_relation)), member(_120864, universal_class), member(_120862, universal_class), successor(_120864) = _120862], (517 ^ _103091) ^ [_121233] : [-(inverse(_121233) = domain_of(flip(cross_product(_121233, universal_class))))], (519 ^ _103091) ^ [_121320] : [-(range_of(_121320) = domain_of(inverse(_121320)))], (521 ^ _103091) ^ [_121418, _121420] : [-(image(_121418, _121420) = range_of(restrict(_121418, _121420, universal_class)))], (523 ^ _103091) ^ [_121551] : [inductive(_121551), 526 ^ _103091 : [(527 ^ _103091) ^ [] : [-(member(null_class, _121551))], (529 ^ _103091) ^ [] : [-(subclass(image(successor_relation, _121551), _121551))]]], (531 ^ _103091) ^ [_121784] : [-(inductive(_121784)), member(null_class, _121784), subclass(image(successor_relation, _121784), _121784)], (542 ^ _103091) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _103091) ^ [] : [-(inductive(540 ^ []))], (546 ^ _103091) ^ [_122229] : [inductive(_122229), -(subclass(540 ^ [], _122229))], (552 ^ _103091) ^ [_122464, _122466] : [member(_122466, sum_class(_122464)), 556 ^ _103091 : [(557 ^ _103091) ^ [] : [-(member(_122466, 555 ^ [_122464, _122466]))], (559 ^ _103091) ^ [] : [-(member(555 ^ [_122464, _122466], _122464))]]], (561 ^ _103091) ^ [_122775, _122777] : [-(member(_122777, sum_class(_122775))), 562 ^ _103091 : [(563 ^ _103091) ^ [_122869] : [member(_122777, _122869), member(_122869, _122775)]]], (571 ^ _103091) ^ [_123129] : [member(_123129, universal_class), -(member(sum_class(_123129), universal_class))], (577 ^ _103091) ^ [_123366, _123368] : [member(_123368, power_class(_123366)), 580 ^ _103091 : [(581 ^ _103091) ^ [] : [-(member(_123368, universal_class))], (583 ^ _103091) ^ [] : [-(subclass(_123368, _123366))]]], (585 ^ _103091) ^ [_123607, _123609] : [-(member(_123609, power_class(_123607))), member(_123609, universal_class), subclass(_123609, _123607)], (595 ^ _103091) ^ [_123898] : [member(_123898, universal_class), -(member(power_class(_123898), universal_class))], (601 ^ _103091) ^ [_124091, _124093] : [-(subclass(compose(_124091, _124093), cross_product(universal_class, universal_class)))], (603 ^ _103091) ^ [_124260, _124262, _124264, _124266] : [member(ordered_pair(_124262, _124260), compose(_124264, _124266)), 606 ^ _103091 : [(607 ^ _103091) ^ [] : [-(member(_124262, universal_class))], (609 ^ _103091) ^ [] : [-(member(_124260, image(_124264, image(_124266, singleton(_124262)))))]]], (611 ^ _103091) ^ [_124541, _124543, _124545, _124547] : [-(member(ordered_pair(_124543, _124541), compose(_124545, _124547))), member(_124543, universal_class), member(_124541, image(_124545, image(_124547, singleton(_124543))))], (621 ^ _103091) ^ [_124905] : [member(_124905, identity_relation), 625 ^ _103091 : [(626 ^ _103091) ^ [] : [-(member(624 ^ [_124905], universal_class))], (628 ^ _103091) ^ [] : [-(_124905 = ordered_pair(624 ^ [_124905], 624 ^ [_124905]))]]], (630 ^ _103091) ^ [_125210] : [-(member(_125210, identity_relation)), 631 ^ _103091 : [(632 ^ _103091) ^ [_125303] : [member(_125303, universal_class), _125210 = ordered_pair(_125303, _125303)]]], (640 ^ _103091) ^ [_125586] : [function(_125586), 643 ^ _103091 : [(644 ^ _103091) ^ [] : [-(subclass(_125586, cross_product(universal_class, universal_class)))], (646 ^ _103091) ^ [] : [-(subclass(compose(_125586, inverse(_125586)), identity_relation))]]], (648 ^ _103091) ^ [_125823] : [-(function(_125823)), subclass(_125823, cross_product(universal_class, universal_class)), subclass(compose(_125823, inverse(_125823)), identity_relation)], (658 ^ _103091) ^ [_126122, _126124] : [-(member(image(_126122, _126124), universal_class)), member(_126124, universal_class), function(_126122)], (678 ^ _103091) ^ [_126769, _126771] : [680 ^ _103091 : [(681 ^ _103091) ^ [] : [-(member(679 ^ [_126769, _126771], _126771))], (683 ^ _103091) ^ [] : [-(member(679 ^ [_126769, _126771], _126769))]], -(disjoint(_126771, _126769))], (668 ^ _103091) ^ [_126454, _126456] : [disjoint(_126456, _126454), 671 ^ _103091 : [(672 ^ _103091) ^ [_126593] : [member(_126593, _126456), member(_126593, _126454)]]], (687 ^ _103091) ^ [_127117] : [-(_127117 = null_class), 691 ^ _103091 : [(692 ^ _103091) ^ [] : [-(member(690 ^ [_127117], universal_class))], (694 ^ _103091) ^ [] : [-(member(690 ^ [_127117], _127117))], (696 ^ _103091) ^ [] : [-(disjoint(690 ^ [_127117], _127117))]]], (698 ^ _103091) ^ [_127527, _127529] : [-(apply(_127529, _127527) = sum_class(image(_127529, singleton(_127527))))], (701 ^ _103091) ^ [] : [-(function(699 ^ []))], (703 ^ _103091) ^ [_127727] : [member(_127727, universal_class), -(_127727 = null_class), -(member(apply(699 ^ [], _127727), _127727))]], input).
% 0.40/1.38  ncf('1',plain,[member(singleton(712 ^ []), universal_class)],start(714 ^ 0)).
% 0.40/1.38  ncf('1.1',plain,[-(member(singleton(712 ^ []), universal_class)), member(unordered_pair(712 ^ [], 712 ^ []), universal_class), unordered_pair(712 ^ [], 712 ^ []) = singleton(712 ^ []), universal_class = universal_class],extension(68 ^ 1,bind([[_105345, _105347, _105349, _105351], [universal_class, universal_class, singleton(712 ^ []), unordered_pair(712 ^ [], 712 ^ [])]]))).
% 0.40/1.38  ncf('1.1.1',plain,[-(member(unordered_pair(712 ^ [], 712 ^ []), universal_class)), member(unordered_pair(712 ^ [], 712 ^ []), universal_class), unordered_pair(712 ^ [], 712 ^ []) = unordered_pair(712 ^ [], 712 ^ []), universal_class = universal_class],extension(68 ^ 2,bind([[_105345, _105347, _105349, _105351], [universal_class, universal_class, unordered_pair(712 ^ [], 712 ^ []), unordered_pair(712 ^ [], 712 ^ [])]]))).
% 0.40/1.38  ncf('1.1.1.1',plain,[-(member(unordered_pair(712 ^ [], 712 ^ []), universal_class))],extension(311 ^ 3,bind([[_113958, _113960], [712 ^ [], 712 ^ []]]))).
% 0.40/1.38  ncf('1.1.1.2',plain,[-(unordered_pair(712 ^ [], 712 ^ []) = unordered_pair(712 ^ [], 712 ^ []))],extension(2 ^ 3,bind([[_103235], [unordered_pair(712 ^ [], 712 ^ [])]]))).
% 0.40/1.38  ncf('1.1.1.3',plain,[-(universal_class = universal_class)],extension(2 ^ 3,bind([[_103235], [universal_class]]))).
% 0.40/1.38  ncf('1.1.2',plain,[-(unordered_pair(712 ^ [], 712 ^ []) = singleton(712 ^ [])), singleton(712 ^ []) = unordered_pair(712 ^ [], 712 ^ [])],extension(4 ^ 2,bind([[_103342, _103344], [unordered_pair(712 ^ [], 712 ^ []), singleton(712 ^ [])]]))).
% 0.40/1.38  ncf('1.1.2.1',plain,[-(singleton(712 ^ []) = unordered_pair(712 ^ [], 712 ^ []))],extension(313 ^ 3,bind([[_114041], [712 ^ []]]))).
% 0.40/1.38  ncf('1.1.3',plain,[-(universal_class = universal_class)],extension(2 ^ 2,bind([[_103235], [universal_class]]))).
% 0.40/1.38  %-----------------------------------------------------
% 0.40/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------