%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n015.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 11:55:20 EDT 2023

% Result   : Theorem 0.34s 1.38s
% Output   : Proof 0.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n015.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May 18 19:17:52 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.34/1.38  
% 0.34/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.34/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.34/1.38  %-----------------------------------------------------
% 0.34/1.38  ncf(matrix, plain, [(714 ^ _104469) ^ [_129761] : [member(_129761, universal_class), 712 ^ [] = singleton(_129761)], (720 ^ _104469) ^ [_129920] : [722 ^ _104469 : [(723 ^ _104469) ^ [] : [-(member(721 ^ [_129920], universal_class))], (725 ^ _104469) ^ [] : [-(712 ^ [] = singleton(721 ^ [_129920]))]], _129920 = 712 ^ []], (2 ^ _104469) ^ [_104613] : [-(_104613 = _104613)], (4 ^ _104469) ^ [_104720, _104722] : [_104722 = _104720, -(_104720 = _104722)], (10 ^ _104469) ^ [_104924, _104926, _104928] : [-(_104928 = _104924), _104928 = _104926, _104926 = _104924], (20 ^ _104469) ^ [_105237, _105239] : [-(inductive(_105237)), _105239 = _105237, inductive(_105239)], (30 ^ _104469) ^ [_105560, _105562, _105564, _105566] : [-(subclass(_105564, _105560)), subclass(_105566, _105562), _105566 = _105564, _105562 = _105560], (44 ^ _104469) ^ [_106004, _106006, _106008, _106010] : [-(disjoint(_106008, _106004)), disjoint(_106010, _106006), _106010 = _106008, _106006 = _106004], (58 ^ _104469) ^ [_106420, _106422] : [-(function(_106420)), _106422 = _106420, function(_106422)], (68 ^ _104469) ^ [_106723, _106725, _106727, _106729] : [-(member(_106727, _106723)), member(_106729, _106725), _106729 = _106727, _106725 = _106723], (82 ^ _104469) ^ [_107181, _107183, _107185, _107187] : [-(unordered_pair(_107187, _107183) = unordered_pair(_107185, _107181)), _107187 = _107185, _107183 = _107181], (92 ^ _104469) ^ [_107512, _107514] : [_107514 = _107512, -(first(_107514) = first(_107512))], (98 ^ _104469) ^ [_107730, _107732] : [_107732 = _107730, -(second(_107732) = second(_107730))], (104 ^ _104469) ^ [_107948, _107950] : [_107950 = _107948, -(complement(_107950) = complement(_107948))], (110 ^ _104469) ^ [_108194, _108196, _108198, _108200] : [-(intersection(_108200, _108196) = intersection(_108198, _108194)), _108200 = _108198, _108196 = _108194], (120 ^ _104469) ^ [_108525, _108527] : [_108527 = _108525, -(rotate(_108527) = rotate(_108525))], (126 ^ _104469) ^ [_108771, _108773, _108775, _108777] : [-(union(_108777, _108773) = union(_108775, _108771)), _108777 = _108775, _108773 = _108771], (136 ^ _104469) ^ [_109102, _109104] : [_109104 = _109102, -(successor(_109104) = successor(_109102))], (142 ^ _104469) ^ [_109320, _109322] : [_109322 = _109320, -(flip(_109322) = flip(_109320))], (148 ^ _104469) ^ [_109538, _109540] : [_109540 = _109538, -(domain_of(_109540) = domain_of(_109538))], (154 ^ _104469) ^ [_109756, _109758] : [_109758 = _109756, -(range_of(_109758) = range_of(_109756))], (160 ^ _104469) ^ [_110030, _110032, _110034, _110036, _110038, _110040] : [-(restrict(_110040, _110036, _110032) = restrict(_110038, _110034, _110030)), _110040 = _110038, _110036 = _110034, _110032 = _110030], (174 ^ _104469) ^ [_110490, _110492] : [_110492 = _110490, -(power_class(_110492) = power_class(_110490))], (180 ^ _104469) ^ [_110736, _110738, _110740, _110742] : [-(ordered_pair(_110742, _110738) = ordered_pair(_110740, _110736)), _110742 = _110740, _110738 = _110736], (190 ^ _104469) ^ [_111095, _111097, _111099, _111101] : [-(cross_product(_111101, _111097) = cross_product(_111099, _111095)), _111101 = _111099, _111097 = _111095], (200 ^ _104469) ^ [_111454, _111456, _111458, _111460] : [-(compose(_111460, _111456) = compose(_111458, _111454)), _111460 = _111458, _111456 = _111454], (210 ^ _104469) ^ [_111785, _111787] : [_111787 = _111785, -(inverse(_111787) = inverse(_111785))], (216 ^ _104469) ^ [_112003, _112005] : [_112005 = _112003, -(sum_class(_112005) = sum_class(_112003))], (222 ^ _104469) ^ [_112249, _112251, _112253, _112255] : [-(image(_112255, _112251) = image(_112253, _112249)), _112255 = _112253, _112251 = _112249], (242 ^ _104469) ^ [_112919, _112921] : [_112921 = _112919, -(singleton(_112921) = singleton(_112919))], (232 ^ _104469) ^ [_112608, _112610, _112612, _112614] : [-(apply(_112614, _112610) = apply(_112612, _112608)), _112614 = _112612, _112610 = _112608], (258 ^ _104469) ^ [_113568, _113570] : [260 ^ _104469 : [(261 ^ _104469) ^ [] : [-(member(259 ^ [_113568, _113570], _113570))], (263 ^ _104469) ^ [] : [member(259 ^ [_113568, _113570], _113568)]], -(subclass(_113570, _113568))], (248 ^ _104469) ^ [_113254, _113256] : [subclass(_113256, _113254), 251 ^ _104469 : [(252 ^ _104469) ^ [_113391] : [member(_113391, _113256), -(member(_113391, _113254))]]], (267 ^ _104469) ^ [_113896] : [-(subclass(_113896, universal_class))], (269 ^ _104469) ^ [_114032, _114034] : [_114034 = _114032, 272 ^ _104469 : [(273 ^ _104469) ^ [] : [-(subclass(_114034, _114032))], (275 ^ _104469) ^ [] : [-(subclass(_114032, _114034))]]], (277 ^ _104469) ^ [_114269, _114271] : [-(_114271 = _114269), subclass(_114271, _114269), subclass(_114269, _114271)], (287 ^ _104469) ^ [_114613, _114615, _114617] : [member(_114617, unordered_pair(_114615, _114613)), 290 ^ _104469 : [(291 ^ _104469) ^ [] : [-(member(_114617, universal_class))], (293 ^ _104469) ^ [] : [-(_114617 = _114615), -(_114617 = _114613)]]], (299 ^ _104469) ^ [_114958, _114960, _114962] : [-(member(_114962, unordered_pair(_114960, _114958))), member(_114962, universal_class), 304 ^ _104469 : [(305 ^ _104469) ^ [] : [_114962 = _114960], (307 ^ _104469) ^ [] : [_114962 = _114958]]], (311 ^ _104469) ^ [_115336, _115338] : [-(member(unordered_pair(_115338, _115336), universal_class))], (313 ^ _104469) ^ [_115419] : [-(singleton(_115419) = unordered_pair(_115419, _115419))], (315 ^ _104469) ^ [_115516, _115518] : [-(ordered_pair(_115518, _115516) = unordered_pair(singleton(_115518), unordered_pair(_115518, singleton(_115516))))], (317 ^ _104469) ^ [_115695, _115697, _115699, _115701] : [member(ordered_pair(_115701, _115699), cross_product(_115697, _115695)), 320 ^ _104469 : [(321 ^ _104469) ^ [] : [-(member(_115701, _115697))], (323 ^ _104469) ^ [] : [-(member(_115699, _115695))]]], (325 ^ _104469) ^ [_115960, _115962, _115964, _115966] : [-(member(ordered_pair(_115966, _115964), cross_product(_115962, _115960))), member(_115966, _115962), member(_115964, _115960)], (335 ^ _104469) ^ [_116293, _116295] : [342 ^ _104469 : [(343 ^ _104469) ^ [] : [-(first(ordered_pair(_116295, _116293)) = _116295)], (345 ^ _104469) ^ [] : [-(second(ordered_pair(_116295, _116293)) = _116293)]], member(_116295, universal_class), member(_116293, universal_class)], (347 ^ _104469) ^ [_116701, _116703, _116705] : [member(_116701, cross_product(_116705, _116703)), -(_116701 = ordered_pair(first(_116701), second(_116701)))], (353 ^ _104469) ^ [_116966, _116968] : [member(ordered_pair(_116968, _116966), element_relation), 356 ^ _104469 : [(357 ^ _104469) ^ [] : [-(member(_116966, universal_class))], (359 ^ _104469) ^ [] : [-(member(_116968, _116966))]]], (361 ^ _104469) ^ [_117209, _117211] : [-(member(ordered_pair(_117211, _117209), element_relation)), member(_117209, universal_class), member(_117211, _117209)], (371 ^ _104469) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _104469) ^ [_117612, _117614, _117616] : [member(_117612, intersection(_117616, _117614)), 376 ^ _104469 : [(377 ^ _104469) ^ [] : [-(member(_117612, _117616))], (379 ^ _104469) ^ [] : [-(member(_117612, _117614))]]], (381 ^ _104469) ^ [_117863, _117865, _117867] : [-(member(_117863, intersection(_117867, _117865))), member(_117863, _117867), member(_117863, _117865)], (391 ^ _104469) ^ [_118209, _118211] : [member(_118209, complement(_118211)), 394 ^ _104469 : [(395 ^ _104469) ^ [] : [-(member(_118209, universal_class))], (397 ^ _104469) ^ [] : [member(_118209, _118211)]]], (399 ^ _104469) ^ [_118451, _118453] : [-(member(_118451, complement(_118453))), member(_118451, universal_class), -(member(_118451, _118453))], (409 ^ _104469) ^ [_118758, _118760, _118762] : [-(restrict(_118760, _118762, _118758) = intersection(_118760, cross_product(_118762, _118758)))], (411 ^ _104469) ^ [_118849] : [member(_118849, null_class)], (413 ^ _104469) ^ [_118985, _118987] : [member(_118985, domain_of(_118987)), 416 ^ _104469 : [(417 ^ _104469) ^ [] : [-(member(_118985, universal_class))], (419 ^ _104469) ^ [] : [restrict(_118987, singleton(_118985), universal_class) = null_class]]], (421 ^ _104469) ^ [_119239, _119241] : [-(member(_119239, domain_of(_119241))), member(_119239, universal_class), -(restrict(_119241, singleton(_119239), universal_class) = null_class)], (431 ^ _104469) ^ [_119616, _119618, _119620, _119622] : [member(ordered_pair(ordered_pair(_119620, _119618), _119616), rotate(_119622)), 434 ^ _104469 : [(435 ^ _104469) ^ [] : [-(member(ordered_pair(ordered_pair(_119620, _119618), _119616), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _104469) ^ [] : [-(member(ordered_pair(ordered_pair(_119618, _119616), _119620), _119622))]]], (439 ^ _104469) ^ [_119909, _119911, _119913, _119915] : [-(member(ordered_pair(ordered_pair(_119913, _119911), _119909), rotate(_119915))), member(ordered_pair(ordered_pair(_119913, _119911), _119909), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_119911, _119909), _119913), _119915)], (449 ^ _104469) ^ [_120241] : [-(subclass(rotate(_120241), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _104469) ^ [_120407, _120409, _120411, _120413] : [member(ordered_pair(ordered_pair(_120413, _120411), _120409), flip(_120407)), 454 ^ _104469 : [(455 ^ _104469) ^ [] : [-(member(ordered_pair(ordered_pair(_120413, _120411), _120409), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _104469) ^ [] : [-(member(ordered_pair(ordered_pair(_120411, _120413), _120409), _120407))]]], (459 ^ _104469) ^ [_120700, _120702, _120704, _120706] : [-(member(ordered_pair(ordered_pair(_120706, _120704), _120702), flip(_120700))), member(ordered_pair(ordered_pair(_120706, _120704), _120702), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_120704, _120706), _120702), _120700)], (469 ^ _104469) ^ [_121032] : [-(subclass(flip(_121032), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _104469) ^ [_121452, _121454, _121456] : [482 ^ _104469 : [(483 ^ _104469) ^ [] : [member(_121452, _121456)], (485 ^ _104469) ^ [] : [member(_121452, _121454)]], -(member(_121452, union(_121456, _121454)))], (471 ^ _104469) ^ [_121184, _121186, _121188] : [member(_121184, union(_121188, _121186)), -(member(_121184, _121188)), -(member(_121184, _121186))], (489 ^ _104469) ^ [_121723] : [-(successor(_121723) = union(_121723, singleton(_121723)))], (491 ^ _104469) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _104469) ^ [_121919, _121921] : [member(ordered_pair(_121921, _121919), successor_relation), 496 ^ _104469 : [(497 ^ _104469) ^ [] : [-(member(_121921, universal_class))], (499 ^ _104469) ^ [] : [-(member(_121919, universal_class))], (501 ^ _104469) ^ [] : [-(successor(_121921) = _121919)]]], (503 ^ _104469) ^ [_122240, _122242] : [-(member(ordered_pair(_122242, _122240), successor_relation)), member(_122242, universal_class), member(_122240, universal_class), successor(_122242) = _122240], (517 ^ _104469) ^ [_122611] : [-(inverse(_122611) = domain_of(flip(cross_product(_122611, universal_class))))], (519 ^ _104469) ^ [_122698] : [-(range_of(_122698) = domain_of(inverse(_122698)))], (521 ^ _104469) ^ [_122796, _122798] : [-(image(_122796, _122798) = range_of(restrict(_122796, _122798, universal_class)))], (523 ^ _104469) ^ [_122929] : [inductive(_122929), 526 ^ _104469 : [(527 ^ _104469) ^ [] : [-(member(null_class, _122929))], (529 ^ _104469) ^ [] : [-(subclass(image(successor_relation, _122929), _122929))]]], (531 ^ _104469) ^ [_123162] : [-(inductive(_123162)), member(null_class, _123162), subclass(image(successor_relation, _123162), _123162)], (542 ^ _104469) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _104469) ^ [] : [-(inductive(540 ^ []))], (546 ^ _104469) ^ [_123607] : [inductive(_123607), -(subclass(540 ^ [], _123607))], (552 ^ _104469) ^ [_123842, _123844] : [member(_123844, sum_class(_123842)), 556 ^ _104469 : [(557 ^ _104469) ^ [] : [-(member(_123844, 555 ^ [_123842, _123844]))], (559 ^ _104469) ^ [] : [-(member(555 ^ [_123842, _123844], _123842))]]], (561 ^ _104469) ^ [_124153, _124155] : [-(member(_124155, sum_class(_124153))), 562 ^ _104469 : [(563 ^ _104469) ^ [_124247] : [member(_124155, _124247), member(_124247, _124153)]]], (571 ^ _104469) ^ [_124507] : [member(_124507, universal_class), -(member(sum_class(_124507), universal_class))], (577 ^ _104469) ^ [_124744, _124746] : [member(_124746, power_class(_124744)), 580 ^ _104469 : [(581 ^ _104469) ^ [] : [-(member(_124746, universal_class))], (583 ^ _104469) ^ [] : [-(subclass(_124746, _124744))]]], (585 ^ _104469) ^ [_124985, _124987] : [-(member(_124987, power_class(_124985))), member(_124987, universal_class), subclass(_124987, _124985)], (595 ^ _104469) ^ [_125276] : [member(_125276, universal_class), -(member(power_class(_125276), universal_class))], (601 ^ _104469) ^ [_125469, _125471] : [-(subclass(compose(_125469, _125471), cross_product(universal_class, universal_class)))], (603 ^ _104469) ^ [_125638, _125640, _125642, _125644] : [member(ordered_pair(_125640, _125638), compose(_125642, _125644)), 606 ^ _104469 : [(607 ^ _104469) ^ [] : [-(member(_125640, universal_class))], (609 ^ _104469) ^ [] : [-(member(_125638, image(_125642, image(_125644, singleton(_125640)))))]]], (611 ^ _104469) ^ [_125919, _125921, _125923, _125925] : [-(member(ordered_pair(_125921, _125919), compose(_125923, _125925))), member(_125921, universal_class), member(_125919, image(_125923, image(_125925, singleton(_125921))))], (621 ^ _104469) ^ [_126283] : [member(_126283, identity_relation), 625 ^ _104469 : [(626 ^ _104469) ^ [] : [-(member(624 ^ [_126283], universal_class))], (628 ^ _104469) ^ [] : [-(_126283 = ordered_pair(624 ^ [_126283], 624 ^ [_126283]))]]], (630 ^ _104469) ^ [_126588] : [-(member(_126588, identity_relation)), 631 ^ _104469 : [(632 ^ _104469) ^ [_126681] : [member(_126681, universal_class), _126588 = ordered_pair(_126681, _126681)]]], (640 ^ _104469) ^ [_126964] : [function(_126964), 643 ^ _104469 : [(644 ^ _104469) ^ [] : [-(subclass(_126964, cross_product(universal_class, universal_class)))], (646 ^ _104469) ^ [] : [-(subclass(compose(_126964, inverse(_126964)), identity_relation))]]], (648 ^ _104469) ^ [_127201] : [-(function(_127201)), subclass(_127201, cross_product(universal_class, universal_class)), subclass(compose(_127201, inverse(_127201)), identity_relation)], (658 ^ _104469) ^ [_127500, _127502] : [-(member(image(_127500, _127502), universal_class)), member(_127502, universal_class), function(_127500)], (678 ^ _104469) ^ [_128147, _128149] : [680 ^ _104469 : [(681 ^ _104469) ^ [] : [-(member(679 ^ [_128147, _128149], _128149))], (683 ^ _104469) ^ [] : [-(member(679 ^ [_128147, _128149], _128147))]], -(disjoint(_128149, _128147))], (668 ^ _104469) ^ [_127832, _127834] : [disjoint(_127834, _127832), 671 ^ _104469 : [(672 ^ _104469) ^ [_127971] : [member(_127971, _127834), member(_127971, _127832)]]], (687 ^ _104469) ^ [_128495] : [-(_128495 = null_class), 691 ^ _104469 : [(692 ^ _104469) ^ [] : [-(member(690 ^ [_128495], universal_class))], (694 ^ _104469) ^ [] : [-(member(690 ^ [_128495], _128495))], (696 ^ _104469) ^ [] : [-(disjoint(690 ^ [_128495], _128495))]]], (698 ^ _104469) ^ [_128905, _128907] : [-(apply(_128907, _128905) = sum_class(image(_128907, singleton(_128905))))], (701 ^ _104469) ^ [] : [-(function(699 ^ []))], (703 ^ _104469) ^ [_129105] : [member(_129105, universal_class), -(_129105 = null_class), -(member(apply(699 ^ [], _129105), _129105))]], input).
% 0.34/1.38  ncf('1',plain,[member(721 ^ [712 ^ []], universal_class), 712 ^ [] = singleton(721 ^ [712 ^ []])],start(714 ^ 0,bind([[_129761], [721 ^ [712 ^ []]]]))).
% 0.34/1.38  ncf('1.1',plain,[-(member(721 ^ [712 ^ []], universal_class)), 712 ^ [] = 712 ^ []],extension(720 ^ 1,bind([[_129920], [712 ^ []]]))).
% 0.34/1.38  ncf('1.1.1',plain,[-(712 ^ [] = 712 ^ [])],extension(2 ^ 2,bind([[_104613], [712 ^ []]]))).
% 0.34/1.38  ncf('1.2',plain,[-(712 ^ [] = singleton(721 ^ [712 ^ []])), 712 ^ [] = 712 ^ []],extension(720 ^ 1,bind([[_129920], [712 ^ []]]))).
% 0.34/1.38  ncf('1.2.1',plain,[-(712 ^ [] = 712 ^ [])],extension(2 ^ 2,bind([[_104613], [712 ^ []]]))).
% 0.34/1.38  %-----------------------------------------------------
% 0.34/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------