%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET061+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.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 0.35s 1.39s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET061+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.13  % Command  : nanocop.sh %s %d
% 0.15/0.35  % Computer : n020.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 19:07:17 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.35/1.39  
% 0.35/1.39  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.35/1.39  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/1.39  %-----------------------------------------------------
% 0.35/1.39  ncf(matrix, plain, [(714 ^ _102658) ^ [_127879] : [-(member(712 ^ [_127879], _127879))], (2 ^ _102658) ^ [_102802] : [-(_102802 = _102802)], (4 ^ _102658) ^ [_102909, _102911] : [_102911 = _102909, -(_102909 = _102911)], (10 ^ _102658) ^ [_103113, _103115, _103117] : [-(_103117 = _103113), _103117 = _103115, _103115 = _103113], (20 ^ _102658) ^ [_103426, _103428] : [-(inductive(_103426)), _103428 = _103426, inductive(_103428)], (30 ^ _102658) ^ [_103749, _103751, _103753, _103755] : [-(subclass(_103753, _103749)), subclass(_103755, _103751), _103755 = _103753, _103751 = _103749], (44 ^ _102658) ^ [_104193, _104195, _104197, _104199] : [-(disjoint(_104197, _104193)), disjoint(_104199, _104195), _104199 = _104197, _104195 = _104193], (58 ^ _102658) ^ [_104609, _104611] : [-(function(_104609)), _104611 = _104609, function(_104611)], (68 ^ _102658) ^ [_104912, _104914, _104916, _104918] : [-(member(_104916, _104912)), member(_104918, _104914), _104918 = _104916, _104914 = _104912], (82 ^ _102658) ^ [_105370, _105372, _105374, _105376] : [-(unordered_pair(_105376, _105372) = unordered_pair(_105374, _105370)), _105376 = _105374, _105372 = _105370], (92 ^ _102658) ^ [_105701, _105703] : [_105703 = _105701, -(first(_105703) = first(_105701))], (98 ^ _102658) ^ [_105919, _105921] : [_105921 = _105919, -(second(_105921) = second(_105919))], (104 ^ _102658) ^ [_106137, _106139] : [_106139 = _106137, -(complement(_106139) = complement(_106137))], (110 ^ _102658) ^ [_106383, _106385, _106387, _106389] : [-(intersection(_106389, _106385) = intersection(_106387, _106383)), _106389 = _106387, _106385 = _106383], (120 ^ _102658) ^ [_106714, _106716] : [_106716 = _106714, -(rotate(_106716) = rotate(_106714))], (126 ^ _102658) ^ [_106960, _106962, _106964, _106966] : [-(union(_106966, _106962) = union(_106964, _106960)), _106966 = _106964, _106962 = _106960], (136 ^ _102658) ^ [_107291, _107293] : [_107293 = _107291, -(successor(_107293) = successor(_107291))], (142 ^ _102658) ^ [_107509, _107511] : [_107511 = _107509, -(flip(_107511) = flip(_107509))], (148 ^ _102658) ^ [_107727, _107729] : [_107729 = _107727, -(domain_of(_107729) = domain_of(_107727))], (154 ^ _102658) ^ [_107945, _107947] : [_107947 = _107945, -(range_of(_107947) = range_of(_107945))], (160 ^ _102658) ^ [_108219, _108221, _108223, _108225, _108227, _108229] : [-(restrict(_108229, _108225, _108221) = restrict(_108227, _108223, _108219)), _108229 = _108227, _108225 = _108223, _108221 = _108219], (174 ^ _102658) ^ [_108679, _108681] : [_108681 = _108679, -(power_class(_108681) = power_class(_108679))], (180 ^ _102658) ^ [_108925, _108927, _108929, _108931] : [-(ordered_pair(_108931, _108927) = ordered_pair(_108929, _108925)), _108931 = _108929, _108927 = _108925], (190 ^ _102658) ^ [_109284, _109286, _109288, _109290] : [-(cross_product(_109290, _109286) = cross_product(_109288, _109284)), _109290 = _109288, _109286 = _109284], (200 ^ _102658) ^ [_109643, _109645, _109647, _109649] : [-(compose(_109649, _109645) = compose(_109647, _109643)), _109649 = _109647, _109645 = _109643], (210 ^ _102658) ^ [_109974, _109976] : [_109976 = _109974, -(inverse(_109976) = inverse(_109974))], (216 ^ _102658) ^ [_110192, _110194] : [_110194 = _110192, -(sum_class(_110194) = sum_class(_110192))], (222 ^ _102658) ^ [_110438, _110440, _110442, _110444] : [-(image(_110444, _110440) = image(_110442, _110438)), _110444 = _110442, _110440 = _110438], (232 ^ _102658) ^ [_110769, _110771] : [_110771 = _110769, -(singleton(_110771) = singleton(_110769))], (238 ^ _102658) ^ [_110995, _110997, _110999, _111001] : [-(apply(_111001, _110997) = apply(_110999, _110995)), _111001 = _110999, _110997 = _110995], (258 ^ _102658) ^ [_111757, _111759] : [260 ^ _102658 : [(261 ^ _102658) ^ [] : [-(member(259 ^ [_111757, _111759], _111759))], (263 ^ _102658) ^ [] : [member(259 ^ [_111757, _111759], _111757)]], -(subclass(_111759, _111757))], (248 ^ _102658) ^ [_111443, _111445] : [subclass(_111445, _111443), 251 ^ _102658 : [(252 ^ _102658) ^ [_111580] : [member(_111580, _111445), -(member(_111580, _111443))]]], (267 ^ _102658) ^ [_112085] : [-(subclass(_112085, universal_class))], (269 ^ _102658) ^ [_112221, _112223] : [_112223 = _112221, 272 ^ _102658 : [(273 ^ _102658) ^ [] : [-(subclass(_112223, _112221))], (275 ^ _102658) ^ [] : [-(subclass(_112221, _112223))]]], (277 ^ _102658) ^ [_112458, _112460] : [-(_112460 = _112458), subclass(_112460, _112458), subclass(_112458, _112460)], (287 ^ _102658) ^ [_112802, _112804, _112806] : [member(_112806, unordered_pair(_112804, _112802)), 290 ^ _102658 : [(291 ^ _102658) ^ [] : [-(member(_112806, universal_class))], (293 ^ _102658) ^ [] : [-(_112806 = _112804), -(_112806 = _112802)]]], (299 ^ _102658) ^ [_113147, _113149, _113151] : [-(member(_113151, unordered_pair(_113149, _113147))), member(_113151, universal_class), 304 ^ _102658 : [(305 ^ _102658) ^ [] : [_113151 = _113149], (307 ^ _102658) ^ [] : [_113151 = _113147]]], (311 ^ _102658) ^ [_113525, _113527] : [-(member(unordered_pair(_113527, _113525), universal_class))], (313 ^ _102658) ^ [_113608] : [-(singleton(_113608) = unordered_pair(_113608, _113608))], (315 ^ _102658) ^ [_113705, _113707] : [-(ordered_pair(_113707, _113705) = unordered_pair(singleton(_113707), unordered_pair(_113707, singleton(_113705))))], (317 ^ _102658) ^ [_113884, _113886, _113888, _113890] : [member(ordered_pair(_113890, _113888), cross_product(_113886, _113884)), 320 ^ _102658 : [(321 ^ _102658) ^ [] : [-(member(_113890, _113886))], (323 ^ _102658) ^ [] : [-(member(_113888, _113884))]]], (325 ^ _102658) ^ [_114149, _114151, _114153, _114155] : [-(member(ordered_pair(_114155, _114153), cross_product(_114151, _114149))), member(_114155, _114151), member(_114153, _114149)], (335 ^ _102658) ^ [_114482, _114484] : [342 ^ _102658 : [(343 ^ _102658) ^ [] : [-(first(ordered_pair(_114484, _114482)) = _114484)], (345 ^ _102658) ^ [] : [-(second(ordered_pair(_114484, _114482)) = _114482)]], member(_114484, universal_class), member(_114482, universal_class)], (347 ^ _102658) ^ [_114890, _114892, _114894] : [member(_114890, cross_product(_114894, _114892)), -(_114890 = ordered_pair(first(_114890), second(_114890)))], (353 ^ _102658) ^ [_115155, _115157] : [member(ordered_pair(_115157, _115155), element_relation), 356 ^ _102658 : [(357 ^ _102658) ^ [] : [-(member(_115155, universal_class))], (359 ^ _102658) ^ [] : [-(member(_115157, _115155))]]], (361 ^ _102658) ^ [_115398, _115400] : [-(member(ordered_pair(_115400, _115398), element_relation)), member(_115398, universal_class), member(_115400, _115398)], (371 ^ _102658) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _102658) ^ [_115801, _115803, _115805] : [member(_115801, intersection(_115805, _115803)), 376 ^ _102658 : [(377 ^ _102658) ^ [] : [-(member(_115801, _115805))], (379 ^ _102658) ^ [] : [-(member(_115801, _115803))]]], (381 ^ _102658) ^ [_116052, _116054, _116056] : [-(member(_116052, intersection(_116056, _116054))), member(_116052, _116056), member(_116052, _116054)], (391 ^ _102658) ^ [_116398, _116400] : [member(_116398, complement(_116400)), 394 ^ _102658 : [(395 ^ _102658) ^ [] : [-(member(_116398, universal_class))], (397 ^ _102658) ^ [] : [member(_116398, _116400)]]], (399 ^ _102658) ^ [_116640, _116642] : [-(member(_116640, complement(_116642))), member(_116640, universal_class), -(member(_116640, _116642))], (409 ^ _102658) ^ [_116947, _116949, _116951] : [-(restrict(_116949, _116951, _116947) = intersection(_116949, cross_product(_116951, _116947)))], (411 ^ _102658) ^ [_117038] : [member(_117038, null_class)], (413 ^ _102658) ^ [_117174, _117176] : [member(_117174, domain_of(_117176)), 416 ^ _102658 : [(417 ^ _102658) ^ [] : [-(member(_117174, universal_class))], (419 ^ _102658) ^ [] : [restrict(_117176, singleton(_117174), universal_class) = null_class]]], (421 ^ _102658) ^ [_117428, _117430] : [-(member(_117428, domain_of(_117430))), member(_117428, universal_class), -(restrict(_117430, singleton(_117428), universal_class) = null_class)], (431 ^ _102658) ^ [_117805, _117807, _117809, _117811] : [member(ordered_pair(ordered_pair(_117809, _117807), _117805), rotate(_117811)), 434 ^ _102658 : [(435 ^ _102658) ^ [] : [-(member(ordered_pair(ordered_pair(_117809, _117807), _117805), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _102658) ^ [] : [-(member(ordered_pair(ordered_pair(_117807, _117805), _117809), _117811))]]], (439 ^ _102658) ^ [_118098, _118100, _118102, _118104] : [-(member(ordered_pair(ordered_pair(_118102, _118100), _118098), rotate(_118104))), member(ordered_pair(ordered_pair(_118102, _118100), _118098), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118100, _118098), _118102), _118104)], (449 ^ _102658) ^ [_118430] : [-(subclass(rotate(_118430), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _102658) ^ [_118596, _118598, _118600, _118602] : [member(ordered_pair(ordered_pair(_118602, _118600), _118598), flip(_118596)), 454 ^ _102658 : [(455 ^ _102658) ^ [] : [-(member(ordered_pair(ordered_pair(_118602, _118600), _118598), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _102658) ^ [] : [-(member(ordered_pair(ordered_pair(_118600, _118602), _118598), _118596))]]], (459 ^ _102658) ^ [_118889, _118891, _118893, _118895] : [-(member(ordered_pair(ordered_pair(_118895, _118893), _118891), flip(_118889))), member(ordered_pair(ordered_pair(_118895, _118893), _118891), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118893, _118895), _118891), _118889)], (469 ^ _102658) ^ [_119221] : [-(subclass(flip(_119221), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _102658) ^ [_119641, _119643, _119645] : [482 ^ _102658 : [(483 ^ _102658) ^ [] : [member(_119641, _119645)], (485 ^ _102658) ^ [] : [member(_119641, _119643)]], -(member(_119641, union(_119645, _119643)))], (471 ^ _102658) ^ [_119373, _119375, _119377] : [member(_119373, union(_119377, _119375)), -(member(_119373, _119377)), -(member(_119373, _119375))], (489 ^ _102658) ^ [_119912] : [-(successor(_119912) = union(_119912, singleton(_119912)))], (491 ^ _102658) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _102658) ^ [_120108, _120110] : [member(ordered_pair(_120110, _120108), successor_relation), 496 ^ _102658 : [(497 ^ _102658) ^ [] : [-(member(_120110, universal_class))], (499 ^ _102658) ^ [] : [-(member(_120108, universal_class))], (501 ^ _102658) ^ [] : [-(successor(_120110) = _120108)]]], (503 ^ _102658) ^ [_120429, _120431] : [-(member(ordered_pair(_120431, _120429), successor_relation)), member(_120431, universal_class), member(_120429, universal_class), successor(_120431) = _120429], (517 ^ _102658) ^ [_120800] : [-(inverse(_120800) = domain_of(flip(cross_product(_120800, universal_class))))], (519 ^ _102658) ^ [_120887] : [-(range_of(_120887) = domain_of(inverse(_120887)))], (521 ^ _102658) ^ [_120985, _120987] : [-(image(_120985, _120987) = range_of(restrict(_120985, _120987, universal_class)))], (523 ^ _102658) ^ [_121118] : [inductive(_121118), 526 ^ _102658 : [(527 ^ _102658) ^ [] : [-(member(null_class, _121118))], (529 ^ _102658) ^ [] : [-(subclass(image(successor_relation, _121118), _121118))]]], (531 ^ _102658) ^ [_121351] : [-(inductive(_121351)), member(null_class, _121351), subclass(image(successor_relation, _121351), _121351)], (542 ^ _102658) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _102658) ^ [] : [-(inductive(540 ^ []))], (546 ^ _102658) ^ [_121796] : [inductive(_121796), -(subclass(540 ^ [], _121796))], (552 ^ _102658) ^ [_122031, _122033] : [member(_122033, sum_class(_122031)), 556 ^ _102658 : [(557 ^ _102658) ^ [] : [-(member(_122033, 555 ^ [_122031, _122033]))], (559 ^ _102658) ^ [] : [-(member(555 ^ [_122031, _122033], _122031))]]], (561 ^ _102658) ^ [_122342, _122344] : [-(member(_122344, sum_class(_122342))), 562 ^ _102658 : [(563 ^ _102658) ^ [_122436] : [member(_122344, _122436), member(_122436, _122342)]]], (571 ^ _102658) ^ [_122696] : [member(_122696, universal_class), -(member(sum_class(_122696), universal_class))], (577 ^ _102658) ^ [_122933, _122935] : [member(_122935, power_class(_122933)), 580 ^ _102658 : [(581 ^ _102658) ^ [] : [-(member(_122935, universal_class))], (583 ^ _102658) ^ [] : [-(subclass(_122935, _122933))]]], (585 ^ _102658) ^ [_123174, _123176] : [-(member(_123176, power_class(_123174))), member(_123176, universal_class), subclass(_123176, _123174)], (595 ^ _102658) ^ [_123465] : [member(_123465, universal_class), -(member(power_class(_123465), universal_class))], (601 ^ _102658) ^ [_123658, _123660] : [-(subclass(compose(_123658, _123660), cross_product(universal_class, universal_class)))], (603 ^ _102658) ^ [_123827, _123829, _123831, _123833] : [member(ordered_pair(_123829, _123827), compose(_123831, _123833)), 606 ^ _102658 : [(607 ^ _102658) ^ [] : [-(member(_123829, universal_class))], (609 ^ _102658) ^ [] : [-(member(_123827, image(_123831, image(_123833, singleton(_123829)))))]]], (611 ^ _102658) ^ [_124108, _124110, _124112, _124114] : [-(member(ordered_pair(_124110, _124108), compose(_124112, _124114))), member(_124110, universal_class), member(_124108, image(_124112, image(_124114, singleton(_124110))))], (621 ^ _102658) ^ [_124472] : [member(_124472, identity_relation), 625 ^ _102658 : [(626 ^ _102658) ^ [] : [-(member(624 ^ [_124472], universal_class))], (628 ^ _102658) ^ [] : [-(_124472 = ordered_pair(624 ^ [_124472], 624 ^ [_124472]))]]], (630 ^ _102658) ^ [_124777] : [-(member(_124777, identity_relation)), 631 ^ _102658 : [(632 ^ _102658) ^ [_124870] : [member(_124870, universal_class), _124777 = ordered_pair(_124870, _124870)]]], (640 ^ _102658) ^ [_125153] : [function(_125153), 643 ^ _102658 : [(644 ^ _102658) ^ [] : [-(subclass(_125153, cross_product(universal_class, universal_class)))], (646 ^ _102658) ^ [] : [-(subclass(compose(_125153, inverse(_125153)), identity_relation))]]], (648 ^ _102658) ^ [_125390] : [-(function(_125390)), subclass(_125390, cross_product(universal_class, universal_class)), subclass(compose(_125390, inverse(_125390)), identity_relation)], (658 ^ _102658) ^ [_125689, _125691] : [-(member(image(_125689, _125691), universal_class)), member(_125691, universal_class), function(_125689)], (678 ^ _102658) ^ [_126336, _126338] : [680 ^ _102658 : [(681 ^ _102658) ^ [] : [-(member(679 ^ [_126336, _126338], _126338))], (683 ^ _102658) ^ [] : [-(member(679 ^ [_126336, _126338], _126336))]], -(disjoint(_126338, _126336))], (668 ^ _102658) ^ [_126021, _126023] : [disjoint(_126023, _126021), 671 ^ _102658 : [(672 ^ _102658) ^ [_126160] : [member(_126160, _126023), member(_126160, _126021)]]], (687 ^ _102658) ^ [_126684] : [-(_126684 = null_class), 691 ^ _102658 : [(692 ^ _102658) ^ [] : [-(member(690 ^ [_126684], universal_class))], (694 ^ _102658) ^ [] : [-(member(690 ^ [_126684], _126684))], (696 ^ _102658) ^ [] : [-(disjoint(690 ^ [_126684], _126684))]]], (698 ^ _102658) ^ [_127094, _127096] : [-(apply(_127096, _127094) = sum_class(image(_127096, singleton(_127094))))], (701 ^ _102658) ^ [] : [-(function(699 ^ []))], (703 ^ _102658) ^ [_127294] : [member(_127294, universal_class), -(_127294 = null_class), -(member(apply(699 ^ [], _127294), _127294))]], input).
% 0.35/1.39  ncf('1',plain,[member(712 ^ [complement(universal_class)], complement(universal_class)), 397 : member(712 ^ [complement(universal_class)], universal_class)],start(391 ^ 0,bind([[_116398, _116400], [712 ^ [complement(universal_class)], universal_class]]))).
% 0.35/1.39  ncf('1.1',plain,[-(member(712 ^ [complement(universal_class)], complement(universal_class)))],extension(714 ^ 1,bind([[_127879], [complement(universal_class)]]))).
% 0.35/1.39  ncf('1.2',plain,[-(member(712 ^ [complement(universal_class)], universal_class))],extension(395 ^ 3)).
% 0.35/1.39  %-----------------------------------------------------
% 0.35/1.39  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------