%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET081+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n013.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 0.38s 1.37s
% Output   : Proof 0.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET081+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n013.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 19:14:05 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.38/1.37  
% 0.38/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.38/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/1.37  %-----------------------------------------------------
% 0.38/1.37  ncf(matrix, plain, [(715 ^ _103388) ^ [] : [-(member(713 ^ [], singleton(712 ^ [])))], (717 ^ _103388) ^ [] : [713 ^ [] = 712 ^ []], (2 ^ _103388) ^ [_103532] : [-(_103532 = _103532)], (4 ^ _103388) ^ [_103639, _103641] : [_103641 = _103639, -(_103639 = _103641)], (10 ^ _103388) ^ [_103843, _103845, _103847] : [-(_103847 = _103843), _103847 = _103845, _103845 = _103843], (20 ^ _103388) ^ [_104156, _104158] : [-(inductive(_104156)), _104158 = _104156, inductive(_104158)], (30 ^ _103388) ^ [_104479, _104481, _104483, _104485] : [-(subclass(_104483, _104479)), subclass(_104485, _104481), _104485 = _104483, _104481 = _104479], (44 ^ _103388) ^ [_104923, _104925, _104927, _104929] : [-(disjoint(_104927, _104923)), disjoint(_104929, _104925), _104929 = _104927, _104925 = _104923], (58 ^ _103388) ^ [_105339, _105341] : [-(function(_105339)), _105341 = _105339, function(_105341)], (68 ^ _103388) ^ [_105642, _105644, _105646, _105648] : [-(member(_105646, _105642)), member(_105648, _105644), _105648 = _105646, _105644 = _105642], (82 ^ _103388) ^ [_106100, _106102, _106104, _106106] : [-(unordered_pair(_106106, _106102) = unordered_pair(_106104, _106100)), _106106 = _106104, _106102 = _106100], (92 ^ _103388) ^ [_106431, _106433] : [_106433 = _106431, -(first(_106433) = first(_106431))], (98 ^ _103388) ^ [_106649, _106651] : [_106651 = _106649, -(second(_106651) = second(_106649))], (104 ^ _103388) ^ [_106867, _106869] : [_106869 = _106867, -(complement(_106869) = complement(_106867))], (110 ^ _103388) ^ [_107113, _107115, _107117, _107119] : [-(intersection(_107119, _107115) = intersection(_107117, _107113)), _107119 = _107117, _107115 = _107113], (120 ^ _103388) ^ [_107444, _107446] : [_107446 = _107444, -(rotate(_107446) = rotate(_107444))], (126 ^ _103388) ^ [_107690, _107692, _107694, _107696] : [-(union(_107696, _107692) = union(_107694, _107690)), _107696 = _107694, _107692 = _107690], (136 ^ _103388) ^ [_108021, _108023] : [_108023 = _108021, -(successor(_108023) = successor(_108021))], (142 ^ _103388) ^ [_108239, _108241] : [_108241 = _108239, -(flip(_108241) = flip(_108239))], (148 ^ _103388) ^ [_108457, _108459] : [_108459 = _108457, -(domain_of(_108459) = domain_of(_108457))], (154 ^ _103388) ^ [_108675, _108677] : [_108677 = _108675, -(range_of(_108677) = range_of(_108675))], (160 ^ _103388) ^ [_108949, _108951, _108953, _108955, _108957, _108959] : [-(restrict(_108959, _108955, _108951) = restrict(_108957, _108953, _108949)), _108959 = _108957, _108955 = _108953, _108951 = _108949], (174 ^ _103388) ^ [_109409, _109411] : [_109411 = _109409, -(power_class(_109411) = power_class(_109409))], (180 ^ _103388) ^ [_109655, _109657, _109659, _109661] : [-(ordered_pair(_109661, _109657) = ordered_pair(_109659, _109655)), _109661 = _109659, _109657 = _109655], (190 ^ _103388) ^ [_110014, _110016, _110018, _110020] : [-(cross_product(_110020, _110016) = cross_product(_110018, _110014)), _110020 = _110018, _110016 = _110014], (200 ^ _103388) ^ [_110373, _110375, _110377, _110379] : [-(compose(_110379, _110375) = compose(_110377, _110373)), _110379 = _110377, _110375 = _110373], (210 ^ _103388) ^ [_110704, _110706] : [_110706 = _110704, -(inverse(_110706) = inverse(_110704))], (216 ^ _103388) ^ [_110922, _110924] : [_110924 = _110922, -(sum_class(_110924) = sum_class(_110922))], (222 ^ _103388) ^ [_111168, _111170, _111172, _111174] : [-(image(_111174, _111170) = image(_111172, _111168)), _111174 = _111172, _111170 = _111168], (242 ^ _103388) ^ [_111838, _111840] : [_111840 = _111838, -(singleton(_111840) = singleton(_111838))], (232 ^ _103388) ^ [_111527, _111529, _111531, _111533] : [-(apply(_111533, _111529) = apply(_111531, _111527)), _111533 = _111531, _111529 = _111527], (258 ^ _103388) ^ [_112487, _112489] : [260 ^ _103388 : [(261 ^ _103388) ^ [] : [-(member(259 ^ [_112487, _112489], _112489))], (263 ^ _103388) ^ [] : [member(259 ^ [_112487, _112489], _112487)]], -(subclass(_112489, _112487))], (248 ^ _103388) ^ [_112173, _112175] : [subclass(_112175, _112173), 251 ^ _103388 : [(252 ^ _103388) ^ [_112310] : [member(_112310, _112175), -(member(_112310, _112173))]]], (267 ^ _103388) ^ [_112815] : [-(subclass(_112815, universal_class))], (269 ^ _103388) ^ [_112951, _112953] : [_112953 = _112951, 272 ^ _103388 : [(273 ^ _103388) ^ [] : [-(subclass(_112953, _112951))], (275 ^ _103388) ^ [] : [-(subclass(_112951, _112953))]]], (277 ^ _103388) ^ [_113188, _113190] : [-(_113190 = _113188), subclass(_113190, _113188), subclass(_113188, _113190)], (287 ^ _103388) ^ [_113532, _113534, _113536] : [member(_113536, unordered_pair(_113534, _113532)), 290 ^ _103388 : [(291 ^ _103388) ^ [] : [-(member(_113536, universal_class))], (293 ^ _103388) ^ [] : [-(_113536 = _113534), -(_113536 = _113532)]]], (299 ^ _103388) ^ [_113877, _113879, _113881] : [-(member(_113881, unordered_pair(_113879, _113877))), member(_113881, universal_class), 304 ^ _103388 : [(305 ^ _103388) ^ [] : [_113881 = _113879], (307 ^ _103388) ^ [] : [_113881 = _113877]]], (311 ^ _103388) ^ [_114255, _114257] : [-(member(unordered_pair(_114257, _114255), universal_class))], (313 ^ _103388) ^ [_114338] : [-(singleton(_114338) = unordered_pair(_114338, _114338))], (315 ^ _103388) ^ [_114435, _114437] : [-(ordered_pair(_114437, _114435) = unordered_pair(singleton(_114437), unordered_pair(_114437, singleton(_114435))))], (317 ^ _103388) ^ [_114614, _114616, _114618, _114620] : [member(ordered_pair(_114620, _114618), cross_product(_114616, _114614)), 320 ^ _103388 : [(321 ^ _103388) ^ [] : [-(member(_114620, _114616))], (323 ^ _103388) ^ [] : [-(member(_114618, _114614))]]], (325 ^ _103388) ^ [_114879, _114881, _114883, _114885] : [-(member(ordered_pair(_114885, _114883), cross_product(_114881, _114879))), member(_114885, _114881), member(_114883, _114879)], (335 ^ _103388) ^ [_115212, _115214] : [342 ^ _103388 : [(343 ^ _103388) ^ [] : [-(first(ordered_pair(_115214, _115212)) = _115214)], (345 ^ _103388) ^ [] : [-(second(ordered_pair(_115214, _115212)) = _115212)]], member(_115214, universal_class), member(_115212, universal_class)], (347 ^ _103388) ^ [_115620, _115622, _115624] : [member(_115620, cross_product(_115624, _115622)), -(_115620 = ordered_pair(first(_115620), second(_115620)))], (353 ^ _103388) ^ [_115885, _115887] : [member(ordered_pair(_115887, _115885), element_relation), 356 ^ _103388 : [(357 ^ _103388) ^ [] : [-(member(_115885, universal_class))], (359 ^ _103388) ^ [] : [-(member(_115887, _115885))]]], (361 ^ _103388) ^ [_116128, _116130] : [-(member(ordered_pair(_116130, _116128), element_relation)), member(_116128, universal_class), member(_116130, _116128)], (371 ^ _103388) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _103388) ^ [_116531, _116533, _116535] : [member(_116531, intersection(_116535, _116533)), 376 ^ _103388 : [(377 ^ _103388) ^ [] : [-(member(_116531, _116535))], (379 ^ _103388) ^ [] : [-(member(_116531, _116533))]]], (381 ^ _103388) ^ [_116782, _116784, _116786] : [-(member(_116782, intersection(_116786, _116784))), member(_116782, _116786), member(_116782, _116784)], (391 ^ _103388) ^ [_117128, _117130] : [member(_117128, complement(_117130)), 394 ^ _103388 : [(395 ^ _103388) ^ [] : [-(member(_117128, universal_class))], (397 ^ _103388) ^ [] : [member(_117128, _117130)]]], (399 ^ _103388) ^ [_117370, _117372] : [-(member(_117370, complement(_117372))), member(_117370, universal_class), -(member(_117370, _117372))], (409 ^ _103388) ^ [_117677, _117679, _117681] : [-(restrict(_117679, _117681, _117677) = intersection(_117679, cross_product(_117681, _117677)))], (411 ^ _103388) ^ [_117768] : [member(_117768, null_class)], (413 ^ _103388) ^ [_117904, _117906] : [member(_117904, domain_of(_117906)), 416 ^ _103388 : [(417 ^ _103388) ^ [] : [-(member(_117904, universal_class))], (419 ^ _103388) ^ [] : [restrict(_117906, singleton(_117904), universal_class) = null_class]]], (421 ^ _103388) ^ [_118158, _118160] : [-(member(_118158, domain_of(_118160))), member(_118158, universal_class), -(restrict(_118160, singleton(_118158), universal_class) = null_class)], (431 ^ _103388) ^ [_118535, _118537, _118539, _118541] : [member(ordered_pair(ordered_pair(_118539, _118537), _118535), rotate(_118541)), 434 ^ _103388 : [(435 ^ _103388) ^ [] : [-(member(ordered_pair(ordered_pair(_118539, _118537), _118535), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _103388) ^ [] : [-(member(ordered_pair(ordered_pair(_118537, _118535), _118539), _118541))]]], (439 ^ _103388) ^ [_118828, _118830, _118832, _118834] : [-(member(ordered_pair(ordered_pair(_118832, _118830), _118828), rotate(_118834))), member(ordered_pair(ordered_pair(_118832, _118830), _118828), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118830, _118828), _118832), _118834)], (449 ^ _103388) ^ [_119160] : [-(subclass(rotate(_119160), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _103388) ^ [_119326, _119328, _119330, _119332] : [member(ordered_pair(ordered_pair(_119332, _119330), _119328), flip(_119326)), 454 ^ _103388 : [(455 ^ _103388) ^ [] : [-(member(ordered_pair(ordered_pair(_119332, _119330), _119328), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _103388) ^ [] : [-(member(ordered_pair(ordered_pair(_119330, _119332), _119328), _119326))]]], (459 ^ _103388) ^ [_119619, _119621, _119623, _119625] : [-(member(ordered_pair(ordered_pair(_119625, _119623), _119621), flip(_119619))), member(ordered_pair(ordered_pair(_119625, _119623), _119621), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_119623, _119625), _119621), _119619)], (469 ^ _103388) ^ [_119951] : [-(subclass(flip(_119951), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _103388) ^ [_120371, _120373, _120375] : [482 ^ _103388 : [(483 ^ _103388) ^ [] : [member(_120371, _120375)], (485 ^ _103388) ^ [] : [member(_120371, _120373)]], -(member(_120371, union(_120375, _120373)))], (471 ^ _103388) ^ [_120103, _120105, _120107] : [member(_120103, union(_120107, _120105)), -(member(_120103, _120107)), -(member(_120103, _120105))], (489 ^ _103388) ^ [_120642] : [-(successor(_120642) = union(_120642, singleton(_120642)))], (491 ^ _103388) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _103388) ^ [_120838, _120840] : [member(ordered_pair(_120840, _120838), successor_relation), 496 ^ _103388 : [(497 ^ _103388) ^ [] : [-(member(_120840, universal_class))], (499 ^ _103388) ^ [] : [-(member(_120838, universal_class))], (501 ^ _103388) ^ [] : [-(successor(_120840) = _120838)]]], (503 ^ _103388) ^ [_121159, _121161] : [-(member(ordered_pair(_121161, _121159), successor_relation)), member(_121161, universal_class), member(_121159, universal_class), successor(_121161) = _121159], (517 ^ _103388) ^ [_121530] : [-(inverse(_121530) = domain_of(flip(cross_product(_121530, universal_class))))], (519 ^ _103388) ^ [_121617] : [-(range_of(_121617) = domain_of(inverse(_121617)))], (521 ^ _103388) ^ [_121715, _121717] : [-(image(_121715, _121717) = range_of(restrict(_121715, _121717, universal_class)))], (523 ^ _103388) ^ [_121848] : [inductive(_121848), 526 ^ _103388 : [(527 ^ _103388) ^ [] : [-(member(null_class, _121848))], (529 ^ _103388) ^ [] : [-(subclass(image(successor_relation, _121848), _121848))]]], (531 ^ _103388) ^ [_122081] : [-(inductive(_122081)), member(null_class, _122081), subclass(image(successor_relation, _122081), _122081)], (542 ^ _103388) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _103388) ^ [] : [-(inductive(540 ^ []))], (546 ^ _103388) ^ [_122526] : [inductive(_122526), -(subclass(540 ^ [], _122526))], (552 ^ _103388) ^ [_122761, _122763] : [member(_122763, sum_class(_122761)), 556 ^ _103388 : [(557 ^ _103388) ^ [] : [-(member(_122763, 555 ^ [_122761, _122763]))], (559 ^ _103388) ^ [] : [-(member(555 ^ [_122761, _122763], _122761))]]], (561 ^ _103388) ^ [_123072, _123074] : [-(member(_123074, sum_class(_123072))), 562 ^ _103388 : [(563 ^ _103388) ^ [_123166] : [member(_123074, _123166), member(_123166, _123072)]]], (571 ^ _103388) ^ [_123426] : [member(_123426, universal_class), -(member(sum_class(_123426), universal_class))], (577 ^ _103388) ^ [_123663, _123665] : [member(_123665, power_class(_123663)), 580 ^ _103388 : [(581 ^ _103388) ^ [] : [-(member(_123665, universal_class))], (583 ^ _103388) ^ [] : [-(subclass(_123665, _123663))]]], (585 ^ _103388) ^ [_123904, _123906] : [-(member(_123906, power_class(_123904))), member(_123906, universal_class), subclass(_123906, _123904)], (595 ^ _103388) ^ [_124195] : [member(_124195, universal_class), -(member(power_class(_124195), universal_class))], (601 ^ _103388) ^ [_124388, _124390] : [-(subclass(compose(_124388, _124390), cross_product(universal_class, universal_class)))], (603 ^ _103388) ^ [_124557, _124559, _124561, _124563] : [member(ordered_pair(_124559, _124557), compose(_124561, _124563)), 606 ^ _103388 : [(607 ^ _103388) ^ [] : [-(member(_124559, universal_class))], (609 ^ _103388) ^ [] : [-(member(_124557, image(_124561, image(_124563, singleton(_124559)))))]]], (611 ^ _103388) ^ [_124838, _124840, _124842, _124844] : [-(member(ordered_pair(_124840, _124838), compose(_124842, _124844))), member(_124840, universal_class), member(_124838, image(_124842, image(_124844, singleton(_124840))))], (621 ^ _103388) ^ [_125202] : [member(_125202, identity_relation), 625 ^ _103388 : [(626 ^ _103388) ^ [] : [-(member(624 ^ [_125202], universal_class))], (628 ^ _103388) ^ [] : [-(_125202 = ordered_pair(624 ^ [_125202], 624 ^ [_125202]))]]], (630 ^ _103388) ^ [_125507] : [-(member(_125507, identity_relation)), 631 ^ _103388 : [(632 ^ _103388) ^ [_125600] : [member(_125600, universal_class), _125507 = ordered_pair(_125600, _125600)]]], (640 ^ _103388) ^ [_125883] : [function(_125883), 643 ^ _103388 : [(644 ^ _103388) ^ [] : [-(subclass(_125883, cross_product(universal_class, universal_class)))], (646 ^ _103388) ^ [] : [-(subclass(compose(_125883, inverse(_125883)), identity_relation))]]], (648 ^ _103388) ^ [_126120] : [-(function(_126120)), subclass(_126120, cross_product(universal_class, universal_class)), subclass(compose(_126120, inverse(_126120)), identity_relation)], (658 ^ _103388) ^ [_126419, _126421] : [-(member(image(_126419, _126421), universal_class)), member(_126421, universal_class), function(_126419)], (678 ^ _103388) ^ [_127066, _127068] : [680 ^ _103388 : [(681 ^ _103388) ^ [] : [-(member(679 ^ [_127066, _127068], _127068))], (683 ^ _103388) ^ [] : [-(member(679 ^ [_127066, _127068], _127066))]], -(disjoint(_127068, _127066))], (668 ^ _103388) ^ [_126751, _126753] : [disjoint(_126753, _126751), 671 ^ _103388 : [(672 ^ _103388) ^ [_126890] : [member(_126890, _126753), member(_126890, _126751)]]], (687 ^ _103388) ^ [_127414] : [-(_127414 = null_class), 691 ^ _103388 : [(692 ^ _103388) ^ [] : [-(member(690 ^ [_127414], universal_class))], (694 ^ _103388) ^ [] : [-(member(690 ^ [_127414], _127414))], (696 ^ _103388) ^ [] : [-(disjoint(690 ^ [_127414], _127414))]]], (698 ^ _103388) ^ [_127824, _127826] : [-(apply(_127826, _127824) = sum_class(image(_127826, singleton(_127824))))], (701 ^ _103388) ^ [] : [-(function(699 ^ []))], (703 ^ _103388) ^ [_128024] : [member(_128024, universal_class), -(_128024 = null_class), -(member(apply(699 ^ [], _128024), _128024))]], input).
% 0.38/1.37  ncf('1',plain,[713 ^ [] = 712 ^ []],start(717 ^ 0)).
% 0.38/1.37  ncf('1.1',plain,[-(713 ^ [] = 712 ^ []), 293 : -(713 ^ [] = 712 ^ []), 293 : member(713 ^ [], unordered_pair(712 ^ [], 712 ^ []))],extension(287 ^ 1,bind([[_113532, _113534, _113536], [712 ^ [], 712 ^ [], 713 ^ []]]))).
% 0.38/1.37  ncf('1.1.1',plain,[713 ^ [] = 712 ^ []],reduction('1')).
% 0.38/1.37  ncf('1.1.2',plain,[-(member(713 ^ [], unordered_pair(712 ^ [], 712 ^ []))), member(713 ^ [], singleton(712 ^ [])), 713 ^ [] = 713 ^ [], singleton(712 ^ []) = unordered_pair(712 ^ [], 712 ^ [])],extension(68 ^ 2,bind([[_105642, _105644, _105646, _105648], [unordered_pair(712 ^ [], 712 ^ []), singleton(712 ^ []), 713 ^ [], 713 ^ []]]))).
% 0.38/1.37  ncf('1.1.2.1',plain,[-(member(713 ^ [], singleton(712 ^ [])))],extension(715 ^ 3)).
% 0.38/1.37  ncf('1.1.2.2',plain,[-(713 ^ [] = 713 ^ [])],extension(2 ^ 3,bind([[_103532], [713 ^ []]]))).
% 0.38/1.37  ncf('1.1.2.3',plain,[-(singleton(712 ^ []) = unordered_pair(712 ^ [], 712 ^ []))],extension(313 ^ 3,bind([[_114338], [712 ^ []]]))).
% 0.38/1.37  %-----------------------------------------------------
% 0.38/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------