%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET027+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n005.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 11:55:08 EDT 2023

% Result   : Theorem 43.43s 42.74s
% Output   : Proof 43.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET027+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n005.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 19:08:53 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 43.43/42.74  
% 43.43/42.74  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 43.43/42.74  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.43/42.74  %-----------------------------------------------------
% 43.43/42.74  ncf(matrix, plain, [(720 ^ _137423) ^ [] : [subclass(712 ^ [], 714 ^ [])], (718 ^ _137423) ^ [] : [-(subclass(713 ^ [], 714 ^ []))], (716 ^ _137423) ^ [] : [-(subclass(712 ^ [], 713 ^ []))], !, (409 ^ _112148) ^ [_126417, _126419, _126421] : [-(restrict(_126419, _126421, _126417) = intersection(_126419, cross_product(_126421, _126417)))], (449 ^ _112148) ^ [_127900] : [-(subclass(rotate(_127900), cross_product(cross_product(universal_class, universal_class), universal_class)))], (552 ^ _112148) ^ [_131501, _131503] : [member(_131503, sum_class(_131501)), 556 ^ _112148 : [(559 ^ _112148) ^ [] : [-(member(555 ^ [_131501, _131503], _131501))], (557 ^ _112148) ^ [] : [-(member(_131503, 555 ^ [_131501, _131503]))]]], (431 ^ _112148) ^ [_127275, _127277, _127279, _127281] : [member(ordered_pair(ordered_pair(_127279, _127277), _127275), rotate(_127281)), 434 ^ _112148 : [(437 ^ _112148) ^ [] : [-(member(ordered_pair(ordered_pair(_127277, _127275), _127279), _127281))], (435 ^ _112148) ^ [] : [-(member(ordered_pair(ordered_pair(_127279, _127277), _127275), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (258 ^ _112148) ^ [_121227, _121229] : [260 ^ _112148 : [(263 ^ _112148) ^ [] : [member(259 ^ [_121227, _121229], _121227)], (261 ^ _112148) ^ [] : [-(member(259 ^ [_121227, _121229], _121229))]], -(subclass(_121229, _121227))], (325 ^ _112148) ^ [_123619, _123621, _123623, _123625] : [-(member(ordered_pair(_123625, _123623), cross_product(_123621, _123619))), member(_123625, _123621), member(_123623, _123619)], (585 ^ _112148) ^ [_132644, _132646] : [-(member(_132646, power_class(_132644))), member(_132646, universal_class), subclass(_132646, _132644)], (544 ^ _112148) ^ [] : [-(inductive(540 ^ []))], (335 ^ _112148) ^ [_123952, _123954] : [342 ^ _112148 : [(345 ^ _112148) ^ [] : [-(second(ordered_pair(_123954, _123952)) = _123952)], (343 ^ _112148) ^ [] : [-(first(ordered_pair(_123954, _123952)) = _123954)]], member(_123954, universal_class), member(_123952, universal_class)], (391 ^ _112148) ^ [_125868, _125870] : [member(_125868, complement(_125870)), 394 ^ _112148 : [(397 ^ _112148) ^ [] : [member(_125868, _125870)], (395 ^ _112148) ^ [] : [-(member(_125868, universal_class))]]], (126 ^ _112148) ^ [_116430, _116432, _116434, _116436] : [-(union(_116436, _116432) = union(_116434, _116430)), _116436 = _116434, _116432 = _116430], (222 ^ _112148) ^ [_119908, _119910, _119912, _119914] : [-(image(_119914, _119910) = image(_119912, _119908)), _119914 = _119912, _119910 = _119908], (621 ^ _112148) ^ [_133942] : [member(_133942, identity_relation), 625 ^ _112148 : [(628 ^ _112148) ^ [] : [-(_133942 = ordered_pair(624 ^ [_133942], 624 ^ [_133942]))], (626 ^ _112148) ^ [] : [-(member(624 ^ [_133942], universal_class))]]], (98 ^ _112148) ^ [_115389, _115391] : [_115391 = _115389, -(second(_115391) = second(_115389))], (640 ^ _112148) ^ [_134623] : [function(_134623), 643 ^ _112148 : [(646 ^ _112148) ^ [] : [-(subclass(compose(_134623, inverse(_134623)), identity_relation))], (644 ^ _112148) ^ [] : [-(subclass(_134623, cross_product(universal_class, universal_class)))]]], (20 ^ _112148) ^ [_112896, _112898] : [-(inductive(_112896)), _112898 = _112896, inductive(_112898)], (30 ^ _112148) ^ [_113219, _113221, _113223, _113225] : [-(disjoint(_113223, _113219)), disjoint(_113225, _113221), _113225 = _113223, _113221 = _113219], (489 ^ _112148) ^ [_129382] : [-(successor(_129382) = union(_129382, singleton(_129382)))], (421 ^ _112148) ^ [_126898, _126900] : [-(member(_126898, domain_of(_126900))), member(_126898, universal_class), -(restrict(_126900, singleton(_126898), universal_class) = null_class)], (668 ^ _112148) ^ [_135491, _135493] : [disjoint(_135493, _135491), 671 ^ _112148 : [(672 ^ _112148) ^ [_135630] : [member(_135630, _135493), member(_135630, _135491)]]], (658 ^ _112148) ^ [_135159, _135161] : [-(member(image(_135159, _135161), universal_class)), member(_135161, universal_class), function(_135159)], (411 ^ _112148) ^ [_126508] : [member(_126508, null_class)], (611 ^ _112148) ^ [_133578, _133580, _133582, _133584] : [-(member(ordered_pair(_133580, _133578), compose(_133582, _133584))), member(_133580, universal_class), member(_133578, image(_133582, image(_133584, singleton(_133580))))], (353 ^ _112148) ^ [_124625, _124627] : [member(ordered_pair(_124627, _124625), element_relation), 356 ^ _112148 : [(359 ^ _112148) ^ [] : [-(member(_124627, _124625))], (357 ^ _112148) ^ [] : [-(member(_124625, universal_class))]]], (160 ^ _112148) ^ [_117689, _117691, _117693, _117695, _117697, _117699] : [-(restrict(_117699, _117695, _117691) = restrict(_117697, _117693, _117689)), _117699 = _117697, _117695 = _117693, _117691 = _117689], (277 ^ _112148) ^ [_121928, _121930] : [-(_121930 = _121928), subclass(_121930, _121928), subclass(_121928, _121930)], (373 ^ _112148) ^ [_125271, _125273, _125275] : [member(_125271, intersection(_125275, _125273)), 376 ^ _112148 : [(379 ^ _112148) ^ [] : [-(member(_125271, _125273))], (377 ^ _112148) ^ [] : [-(member(_125271, _125275))]]], (503 ^ _112148) ^ [_129899, _129901] : [-(member(ordered_pair(_129901, _129899), successor_relation)), member(_129901, universal_class), member(_129899, universal_class), successor(_129901) = _129899], (180 ^ _112148) ^ [_118395, _118397, _118399, _118401] : [-(ordered_pair(_118401, _118397) = ordered_pair(_118399, _118395)), _118401 = _118399, _118397 = _118395], (347 ^ _112148) ^ [_124360, _124362, _124364] : [member(_124360, cross_product(_124364, _124362)), -(_124360 = ordered_pair(first(_124360), second(_124360)))], (104 ^ _112148) ^ [_115607, _115609] : [_115609 = _115607, -(complement(_115609) = complement(_115607))], (648 ^ _112148) ^ [_134860] : [-(function(_134860)), subclass(_134860, cross_product(universal_class, universal_class)), subclass(compose(_134860, inverse(_134860)), identity_relation)], (248 ^ _112148) ^ [_120913, _120915] : [subclass(_120915, _120913), 251 ^ _112148 : [(252 ^ _112148) ^ [_121050] : [member(_121050, _120915), -(member(_121050, _120913))]]], (630 ^ _112148) ^ [_134247] : [-(member(_134247, identity_relation)), 631 ^ _112148 : [(632 ^ _112148) ^ [_134340] : [member(_134340, universal_class), _134247 = ordered_pair(_134340, _134340)]]], (54 ^ _112148) ^ [_113958, _113960, _113962, _113964] : [-(member(_113962, _113958)), member(_113964, _113960), _113964 = _113962, _113960 = _113958], (519 ^ _112148) ^ [_130357] : [-(range_of(_130357) = domain_of(inverse(_130357)))], (531 ^ _112148) ^ [_130821] : [-(inductive(_130821)), member(null_class, _130821), subclass(image(successor_relation, _130821), _130821)], (491 ^ _112148) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (4 ^ _112148) ^ [_112379, _112381] : [_112381 = _112379, -(_112379 = _112381)], (10 ^ _112148) ^ [_112583, _112585, _112587] : [-(_112587 = _112583), _112587 = _112585, _112585 = _112583], (687 ^ _112148) ^ [_136154] : [-(_136154 = null_class), 691 ^ _112148 : [(696 ^ _112148) ^ [] : [-(disjoint(690 ^ [_136154], _136154))], (694 ^ _112148) ^ [] : [-(member(690 ^ [_136154], _136154))], (692 ^ _112148) ^ [] : [-(member(690 ^ [_136154], universal_class))]]], (469 ^ _112148) ^ [_128691] : [-(subclass(flip(_128691), cross_product(cross_product(universal_class, universal_class), universal_class)))], (439 ^ _112148) ^ [_127568, _127570, _127572, _127574] : [-(member(ordered_pair(ordered_pair(_127572, _127570), _127568), rotate(_127574))), member(ordered_pair(ordered_pair(_127572, _127570), _127568), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_127570, _127568), _127572), _127574)], (678 ^ _112148) ^ [_135806, _135808] : [680 ^ _112148 : [(683 ^ _112148) ^ [] : [-(member(679 ^ [_135806, _135808], _135806))], (681 ^ _112148) ^ [] : [-(member(679 ^ [_135806, _135808], _135808))]], -(disjoint(_135808, _135806))], (701 ^ _112148) ^ [] : [-(function(699 ^ []))], (216 ^ _112148) ^ [_119662, _119664] : [_119664 = _119662, -(sum_class(_119664) = sum_class(_119662))], (287 ^ _112148) ^ [_122272, _122274, _122276] : [member(_122276, unordered_pair(_122274, _122272)), 290 ^ _112148 : [(293 ^ _112148) ^ [] : [-(_122276 = _122274), -(_122276 = _122272)], (291 ^ _112148) ^ [] : [-(member(_122276, universal_class))]]], (148 ^ _112148) ^ [_117197, _117199] : [_117199 = _117197, -(domain_of(_117199) = domain_of(_117197))], (317 ^ _112148) ^ [_123354, _123356, _123358, _123360] : [member(ordered_pair(_123360, _123358), cross_product(_123356, _123354)), 320 ^ _112148 : [(323 ^ _112148) ^ [] : [-(member(_123358, _123354))], (321 ^ _112148) ^ [] : [-(member(_123360, _123356))]]], (603 ^ _112148) ^ [_133297, _133299, _133301, _133303] : [member(ordered_pair(_133299, _133297), compose(_133301, _133303)), 606 ^ _112148 : [(609 ^ _112148) ^ [] : [-(member(_133297, image(_133301, image(_133303, singleton(_133299)))))], (607 ^ _112148) ^ [] : [-(member(_133299, universal_class))]]], (577 ^ _112148) ^ [_132403, _132405] : [member(_132405, power_class(_132403)), 580 ^ _112148 : [(583 ^ _112148) ^ [] : [-(subclass(_132405, _132403))], (581 ^ _112148) ^ [] : [-(member(_132405, universal_class))]]], (68 ^ _112148) ^ [_114382, _114384, _114386, _114388] : [-(subclass(_114386, _114382)), subclass(_114388, _114384), _114388 = _114386, _114384 = _114382], (44 ^ _112148) ^ [_113635, _113637] : [-(function(_113635)), _113637 = _113635, function(_113637)], (174 ^ _112148) ^ [_118149, _118151] : [_118151 = _118149, -(power_class(_118151) = power_class(_118149))], (210 ^ _112148) ^ [_119444, _119446] : [_119446 = _119444, -(inverse(_119446) = inverse(_119444))], (200 ^ _112148) ^ [_119113, _119115, _119117, _119119] : [-(compose(_119119, _119115) = compose(_119117, _119113)), _119119 = _119117, _119115 = _119113], (142 ^ _112148) ^ [_116979, _116981] : [_116981 = _116979, -(flip(_116981) = flip(_116979))], (451 ^ _112148) ^ [_128066, _128068, _128070, _128072] : [member(ordered_pair(ordered_pair(_128072, _128070), _128068), flip(_128066)), 454 ^ _112148 : [(457 ^ _112148) ^ [] : [-(member(ordered_pair(ordered_pair(_128070, _128072), _128068), _128066))], (455 ^ _112148) ^ [] : [-(member(ordered_pair(ordered_pair(_128072, _128070), _128068), cross_product(cross_product(universal_class, universal_class), universal_class)))]]], (110 ^ _112148) ^ [_115853, _115855, _115857, _115859] : [-(intersection(_115859, _115855) = intersection(_115857, _115853)), _115859 = _115857, _115855 = _115853], (561 ^ _112148) ^ [_131812, _131814] : [-(member(_131814, sum_class(_131812))), 562 ^ _112148 : [(563 ^ _112148) ^ [_131906] : [member(_131814, _131906), member(_131906, _131812)]]], (517 ^ _112148) ^ [_130270] : [-(inverse(_130270) = domain_of(flip(cross_product(_130270, universal_class))))], (399 ^ _112148) ^ [_126110, _126112] : [-(member(_126110, complement(_126112))), member(_126110, universal_class), -(member(_126110, _126112))], (546 ^ _112148) ^ [_131266] : [inductive(_131266), -(subclass(540 ^ [], _131266))], (92 ^ _112148) ^ [_115171, _115173] : [_115173 = _115171, -(first(_115173) = first(_115171))], (698 ^ _112148) ^ [_136564, _136566] : [-(apply(_136566, _136564) = sum_class(image(_136566, singleton(_136564))))], (471 ^ _112148) ^ [_128843, _128845, _128847] : [member(_128843, union(_128847, _128845)), -(member(_128843, _128847)), -(member(_128843, _128845))], (542 ^ _112148) ^ [] : [-(member(540 ^ [], universal_class))], (267 ^ _112148) ^ [_121555] : [-(subclass(_121555, universal_class))], (521 ^ _112148) ^ [_130455, _130457] : [-(image(_130455, _130457) = range_of(restrict(_130455, _130457, universal_class)))], (190 ^ _112148) ^ [_118754, _118756, _118758, _118760] : [-(cross_product(_118760, _118756) = cross_product(_118758, _118754)), _118760 = _118758, _118756 = _118754], (595 ^ _112148) ^ [_132935] : [member(_132935, universal_class), -(member(power_class(_132935), universal_class))], (232 ^ _112148) ^ [_120239, _120241] : [_120241 = _120239, -(singleton(_120241) = singleton(_120239))], (381 ^ _112148) ^ [_125522, _125524, _125526] : [-(member(_125522, intersection(_125526, _125524))), member(_125522, _125526), member(_125522, _125524)], (136 ^ _112148) ^ [_116761, _116763] : [_116763 = _116761, -(successor(_116763) = successor(_116761))], (269 ^ _112148) ^ [_121691, _121693] : [_121693 = _121691, 272 ^ _112148 : [(275 ^ _112148) ^ [] : [-(subclass(_121691, _121693))], (273 ^ _112148) ^ [] : [-(subclass(_121693, _121691))]]], (493 ^ _112148) ^ [_129578, _129580] : [member(ordered_pair(_129580, _129578), successor_relation), 496 ^ _112148 : [(501 ^ _112148) ^ [] : [-(successor(_129580) = _129578)], (499 ^ _112148) ^ [] : [-(member(_129578, universal_class))], (497 ^ _112148) ^ [] : [-(member(_129580, universal_class))]]], (2 ^ _112148) ^ [_112272] : [-(_112272 = _112272)], (313 ^ _112148) ^ [_123078] : [-(singleton(_123078) = unordered_pair(_123078, _123078))], (601 ^ _112148) ^ [_133128, _133130] : [-(subclass(compose(_133128, _133130), cross_product(universal_class, universal_class)))], (703 ^ _112148) ^ [_136764] : [member(_136764, universal_class), -(_136764 = null_class), -(member(apply(699 ^ [], _136764), _136764))], (238 ^ _112148) ^ [_120465, _120467, _120469, _120471] : [-(apply(_120471, _120467) = apply(_120469, _120465)), _120471 = _120469, _120467 = _120465], (571 ^ _112148) ^ [_132166] : [member(_132166, universal_class), -(member(sum_class(_132166), universal_class))], (311 ^ _112148) ^ [_122995, _122997] : [-(member(unordered_pair(_122997, _122995), universal_class))], (315 ^ _112148) ^ [_123175, _123177] : [-(ordered_pair(_123177, _123175) = unordered_pair(singleton(_123177), unordered_pair(_123177, singleton(_123175))))], (413 ^ _112148) ^ [_126644, _126646] : [member(_126644, domain_of(_126646)), 416 ^ _112148 : [(419 ^ _112148) ^ [] : [restrict(_126646, singleton(_126644), universal_class) = null_class], (417 ^ _112148) ^ [] : [-(member(_126644, universal_class))]]], (523 ^ _112148) ^ [_130588] : [inductive(_130588), 526 ^ _112148 : [(529 ^ _112148) ^ [] : [-(subclass(image(successor_relation, _130588), _130588))], (527 ^ _112148) ^ [] : [-(member(null_class, _130588))]]], (361 ^ _112148) ^ [_124868, _124870] : [-(member(ordered_pair(_124870, _124868), element_relation)), member(_124868, universal_class), member(_124870, _124868)], (82 ^ _112148) ^ [_114840, _114842, _114844, _114846] : [-(unordered_pair(_114846, _114842) = unordered_pair(_114844, _114840)), _114846 = _114844, _114842 = _114840], (120 ^ _112148) ^ [_116184, _116186] : [_116186 = _116184, -(rotate(_116186) = rotate(_116184))], (459 ^ _112148) ^ [_128359, _128361, _128363, _128365] : [-(member(ordered_pair(ordered_pair(_128365, _128363), _128361), flip(_128359))), member(ordered_pair(ordered_pair(_128365, _128363), _128361), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_128363, _128365), _128361), _128359)], (371 ^ _112148) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (299 ^ _112148) ^ [_122617, _122619, _122621] : [-(member(_122621, unordered_pair(_122619, _122617))), member(_122621, universal_class), 304 ^ _112148 : [(307 ^ _112148) ^ [] : [_122621 = _122617], (305 ^ _112148) ^ [] : [_122621 = _122619]]], (154 ^ _112148) ^ [_117415, _117417] : [_117417 = _117415, -(range_of(_117417) = range_of(_117415))], (481 ^ _112148) ^ [_129111, _129113, _129115] : [482 ^ _112148 : [(485 ^ _112148) ^ [] : [member(_129111, _129113)], (483 ^ _112148) ^ [] : [member(_129111, _129115)]], -(member(_129111, union(_129115, _129113)))]], input).
% 43.43/42.74  ncf('1',plain,[-(subclass(713 ^ [], 714 ^ []))],start(718 ^ 0)).
% 43.43/42.74  ncf('1.1',plain,[subclass(713 ^ [], 714 ^ []), 252 : member(259 ^ [714 ^ [], 712 ^ []], 713 ^ []), 252 : -(member(259 ^ [714 ^ [], 712 ^ []], 714 ^ []))],extension(248 ^ 1,bind([[_120913, _120915, _121050], [714 ^ [], 713 ^ [], 259 ^ [714 ^ [], 712 ^ []]]]))).
% 43.43/42.74  ncf('1.1.1',plain,[-(member(259 ^ [714 ^ [], 712 ^ []], 713 ^ [])), 252 : member(259 ^ [714 ^ [], 712 ^ []], 712 ^ []), 252 : subclass(712 ^ [], 713 ^ [])],extension(248 ^ 4,bind([[_120913, _120915, _121050], [713 ^ [], 712 ^ [], 259 ^ [714 ^ [], 712 ^ []]]]))).
% 43.43/42.74  ncf('1.1.1.1',plain,[-(member(259 ^ [714 ^ [], 712 ^ []], 712 ^ [])), -(subclass(712 ^ [], 714 ^ []))],extension(258 ^ 7,bind([[_121227, _121229], [714 ^ [], 712 ^ []]]))).
% 43.43/42.74  ncf('1.1.1.1.1',plain,[subclass(712 ^ [], 714 ^ [])],extension(720 ^ 8)).
% 43.43/42.74  ncf('1.1.1.2',plain,[-(subclass(712 ^ [], 713 ^ []))],extension(716 ^ 5)).
% 43.43/42.74  ncf('1.1.2',plain,[member(259 ^ [714 ^ [], 712 ^ []], 714 ^ []), -(subclass(712 ^ [], 714 ^ []))],extension(258 ^ 4,bind([[_121227, _121229], [714 ^ [], 712 ^ []]]))).
% 43.43/42.74  ncf('1.1.2.1',plain,[subclass(712 ^ [], 714 ^ [])],extension(720 ^ 5)).
% 43.43/42.74  %-----------------------------------------------------
% 43.43/42.74  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------