%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET065+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 11:55:16 EDT 2023

% Result   : Theorem 0.32s 1.37s
% Output   : Proof 0.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n028.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 19:26:48 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.32/1.37  
% 0.32/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.32/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/1.37  %-----------------------------------------------------
% 0.32/1.37  ncf(matrix, plain, [(713 ^ _103017) ^ [] : [member(null_class, universal_class)], (2 ^ _103017) ^ [_103161] : [-(_103161 = _103161)], (4 ^ _103017) ^ [_103268, _103270] : [_103270 = _103268, -(_103268 = _103270)], (10 ^ _103017) ^ [_103472, _103474, _103476] : [-(_103476 = _103472), _103476 = _103474, _103474 = _103472], (20 ^ _103017) ^ [_103785, _103787] : [-(inductive(_103785)), _103787 = _103785, inductive(_103787)], (30 ^ _103017) ^ [_104108, _104110, _104112, _104114] : [-(subclass(_104112, _104108)), subclass(_104114, _104110), _104114 = _104112, _104110 = _104108], (44 ^ _103017) ^ [_104552, _104554, _104556, _104558] : [-(disjoint(_104556, _104552)), disjoint(_104558, _104554), _104558 = _104556, _104554 = _104552], (58 ^ _103017) ^ [_104968, _104970] : [-(function(_104968)), _104970 = _104968, function(_104970)], (68 ^ _103017) ^ [_105271, _105273, _105275, _105277] : [-(member(_105275, _105271)), member(_105277, _105273), _105277 = _105275, _105273 = _105271], (82 ^ _103017) ^ [_105729, _105731, _105733, _105735] : [-(unordered_pair(_105735, _105731) = unordered_pair(_105733, _105729)), _105735 = _105733, _105731 = _105729], (92 ^ _103017) ^ [_106060, _106062] : [_106062 = _106060, -(first(_106062) = first(_106060))], (98 ^ _103017) ^ [_106278, _106280] : [_106280 = _106278, -(second(_106280) = second(_106278))], (104 ^ _103017) ^ [_106496, _106498] : [_106498 = _106496, -(complement(_106498) = complement(_106496))], (110 ^ _103017) ^ [_106742, _106744, _106746, _106748] : [-(intersection(_106748, _106744) = intersection(_106746, _106742)), _106748 = _106746, _106744 = _106742], (120 ^ _103017) ^ [_107073, _107075] : [_107075 = _107073, -(rotate(_107075) = rotate(_107073))], (126 ^ _103017) ^ [_107319, _107321, _107323, _107325] : [-(union(_107325, _107321) = union(_107323, _107319)), _107325 = _107323, _107321 = _107319], (136 ^ _103017) ^ [_107650, _107652] : [_107652 = _107650, -(successor(_107652) = successor(_107650))], (142 ^ _103017) ^ [_107868, _107870] : [_107870 = _107868, -(flip(_107870) = flip(_107868))], (148 ^ _103017) ^ [_108086, _108088] : [_108088 = _108086, -(domain_of(_108088) = domain_of(_108086))], (154 ^ _103017) ^ [_108304, _108306] : [_108306 = _108304, -(range_of(_108306) = range_of(_108304))], (160 ^ _103017) ^ [_108578, _108580, _108582, _108584, _108586, _108588] : [-(restrict(_108588, _108584, _108580) = restrict(_108586, _108582, _108578)), _108588 = _108586, _108584 = _108582, _108580 = _108578], (174 ^ _103017) ^ [_109038, _109040] : [_109040 = _109038, -(power_class(_109040) = power_class(_109038))], (180 ^ _103017) ^ [_109284, _109286, _109288, _109290] : [-(ordered_pair(_109290, _109286) = ordered_pair(_109288, _109284)), _109290 = _109288, _109286 = _109284], (190 ^ _103017) ^ [_109643, _109645, _109647, _109649] : [-(cross_product(_109649, _109645) = cross_product(_109647, _109643)), _109649 = _109647, _109645 = _109643], (200 ^ _103017) ^ [_110002, _110004, _110006, _110008] : [-(compose(_110008, _110004) = compose(_110006, _110002)), _110008 = _110006, _110004 = _110002], (210 ^ _103017) ^ [_110333, _110335] : [_110335 = _110333, -(inverse(_110335) = inverse(_110333))], (216 ^ _103017) ^ [_110551, _110553] : [_110553 = _110551, -(sum_class(_110553) = sum_class(_110551))], (222 ^ _103017) ^ [_110797, _110799, _110801, _110803] : [-(image(_110803, _110799) = image(_110801, _110797)), _110803 = _110801, _110799 = _110797], (232 ^ _103017) ^ [_111128, _111130] : [_111130 = _111128, -(singleton(_111130) = singleton(_111128))], (238 ^ _103017) ^ [_111354, _111356, _111358, _111360] : [-(apply(_111360, _111356) = apply(_111358, _111354)), _111360 = _111358, _111356 = _111354], (258 ^ _103017) ^ [_112116, _112118] : [260 ^ _103017 : [(261 ^ _103017) ^ [] : [-(member(259 ^ [_112116, _112118], _112118))], (263 ^ _103017) ^ [] : [member(259 ^ [_112116, _112118], _112116)]], -(subclass(_112118, _112116))], (248 ^ _103017) ^ [_111802, _111804] : [subclass(_111804, _111802), 251 ^ _103017 : [(252 ^ _103017) ^ [_111939] : [member(_111939, _111804), -(member(_111939, _111802))]]], (267 ^ _103017) ^ [_112444] : [-(subclass(_112444, universal_class))], (269 ^ _103017) ^ [_112580, _112582] : [_112582 = _112580, 272 ^ _103017 : [(273 ^ _103017) ^ [] : [-(subclass(_112582, _112580))], (275 ^ _103017) ^ [] : [-(subclass(_112580, _112582))]]], (277 ^ _103017) ^ [_112817, _112819] : [-(_112819 = _112817), subclass(_112819, _112817), subclass(_112817, _112819)], (287 ^ _103017) ^ [_113161, _113163, _113165] : [member(_113165, unordered_pair(_113163, _113161)), 290 ^ _103017 : [(291 ^ _103017) ^ [] : [-(member(_113165, universal_class))], (293 ^ _103017) ^ [] : [-(_113165 = _113163), -(_113165 = _113161)]]], (299 ^ _103017) ^ [_113506, _113508, _113510] : [-(member(_113510, unordered_pair(_113508, _113506))), member(_113510, universal_class), 304 ^ _103017 : [(305 ^ _103017) ^ [] : [_113510 = _113508], (307 ^ _103017) ^ [] : [_113510 = _113506]]], (311 ^ _103017) ^ [_113884, _113886] : [-(member(unordered_pair(_113886, _113884), universal_class))], (313 ^ _103017) ^ [_113967] : [-(singleton(_113967) = unordered_pair(_113967, _113967))], (315 ^ _103017) ^ [_114064, _114066] : [-(ordered_pair(_114066, _114064) = unordered_pair(singleton(_114066), unordered_pair(_114066, singleton(_114064))))], (317 ^ _103017) ^ [_114243, _114245, _114247, _114249] : [member(ordered_pair(_114249, _114247), cross_product(_114245, _114243)), 320 ^ _103017 : [(321 ^ _103017) ^ [] : [-(member(_114249, _114245))], (323 ^ _103017) ^ [] : [-(member(_114247, _114243))]]], (325 ^ _103017) ^ [_114508, _114510, _114512, _114514] : [-(member(ordered_pair(_114514, _114512), cross_product(_114510, _114508))), member(_114514, _114510), member(_114512, _114508)], (335 ^ _103017) ^ [_114841, _114843] : [342 ^ _103017 : [(343 ^ _103017) ^ [] : [-(first(ordered_pair(_114843, _114841)) = _114843)], (345 ^ _103017) ^ [] : [-(second(ordered_pair(_114843, _114841)) = _114841)]], member(_114843, universal_class), member(_114841, universal_class)], (347 ^ _103017) ^ [_115249, _115251, _115253] : [member(_115249, cross_product(_115253, _115251)), -(_115249 = ordered_pair(first(_115249), second(_115249)))], (353 ^ _103017) ^ [_115514, _115516] : [member(ordered_pair(_115516, _115514), element_relation), 356 ^ _103017 : [(357 ^ _103017) ^ [] : [-(member(_115514, universal_class))], (359 ^ _103017) ^ [] : [-(member(_115516, _115514))]]], (361 ^ _103017) ^ [_115757, _115759] : [-(member(ordered_pair(_115759, _115757), element_relation)), member(_115757, universal_class), member(_115759, _115757)], (371 ^ _103017) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _103017) ^ [_116160, _116162, _116164] : [member(_116160, intersection(_116164, _116162)), 376 ^ _103017 : [(377 ^ _103017) ^ [] : [-(member(_116160, _116164))], (379 ^ _103017) ^ [] : [-(member(_116160, _116162))]]], (381 ^ _103017) ^ [_116411, _116413, _116415] : [-(member(_116411, intersection(_116415, _116413))), member(_116411, _116415), member(_116411, _116413)], (391 ^ _103017) ^ [_116757, _116759] : [member(_116757, complement(_116759)), 394 ^ _103017 : [(395 ^ _103017) ^ [] : [-(member(_116757, universal_class))], (397 ^ _103017) ^ [] : [member(_116757, _116759)]]], (399 ^ _103017) ^ [_116999, _117001] : [-(member(_116999, complement(_117001))), member(_116999, universal_class), -(member(_116999, _117001))], (409 ^ _103017) ^ [_117306, _117308, _117310] : [-(restrict(_117308, _117310, _117306) = intersection(_117308, cross_product(_117310, _117306)))], (411 ^ _103017) ^ [_117397] : [member(_117397, null_class)], (413 ^ _103017) ^ [_117533, _117535] : [member(_117533, domain_of(_117535)), 416 ^ _103017 : [(417 ^ _103017) ^ [] : [-(member(_117533, universal_class))], (419 ^ _103017) ^ [] : [restrict(_117535, singleton(_117533), universal_class) = null_class]]], (421 ^ _103017) ^ [_117787, _117789] : [-(member(_117787, domain_of(_117789))), member(_117787, universal_class), -(restrict(_117789, singleton(_117787), universal_class) = null_class)], (431 ^ _103017) ^ [_118164, _118166, _118168, _118170] : [member(ordered_pair(ordered_pair(_118168, _118166), _118164), rotate(_118170)), 434 ^ _103017 : [(435 ^ _103017) ^ [] : [-(member(ordered_pair(ordered_pair(_118168, _118166), _118164), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _103017) ^ [] : [-(member(ordered_pair(ordered_pair(_118166, _118164), _118168), _118170))]]], (439 ^ _103017) ^ [_118457, _118459, _118461, _118463] : [-(member(ordered_pair(ordered_pair(_118461, _118459), _118457), rotate(_118463))), member(ordered_pair(ordered_pair(_118461, _118459), _118457), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118459, _118457), _118461), _118463)], (449 ^ _103017) ^ [_118789] : [-(subclass(rotate(_118789), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _103017) ^ [_118955, _118957, _118959, _118961] : [member(ordered_pair(ordered_pair(_118961, _118959), _118957), flip(_118955)), 454 ^ _103017 : [(455 ^ _103017) ^ [] : [-(member(ordered_pair(ordered_pair(_118961, _118959), _118957), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _103017) ^ [] : [-(member(ordered_pair(ordered_pair(_118959, _118961), _118957), _118955))]]], (459 ^ _103017) ^ [_119248, _119250, _119252, _119254] : [-(member(ordered_pair(ordered_pair(_119254, _119252), _119250), flip(_119248))), member(ordered_pair(ordered_pair(_119254, _119252), _119250), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_119252, _119254), _119250), _119248)], (469 ^ _103017) ^ [_119580] : [-(subclass(flip(_119580), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _103017) ^ [_120000, _120002, _120004] : [482 ^ _103017 : [(483 ^ _103017) ^ [] : [member(_120000, _120004)], (485 ^ _103017) ^ [] : [member(_120000, _120002)]], -(member(_120000, union(_120004, _120002)))], (471 ^ _103017) ^ [_119732, _119734, _119736] : [member(_119732, union(_119736, _119734)), -(member(_119732, _119736)), -(member(_119732, _119734))], (489 ^ _103017) ^ [_120271] : [-(successor(_120271) = union(_120271, singleton(_120271)))], (491 ^ _103017) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _103017) ^ [_120467, _120469] : [member(ordered_pair(_120469, _120467), successor_relation), 496 ^ _103017 : [(497 ^ _103017) ^ [] : [-(member(_120469, universal_class))], (499 ^ _103017) ^ [] : [-(member(_120467, universal_class))], (501 ^ _103017) ^ [] : [-(successor(_120469) = _120467)]]], (503 ^ _103017) ^ [_120788, _120790] : [-(member(ordered_pair(_120790, _120788), successor_relation)), member(_120790, universal_class), member(_120788, universal_class), successor(_120790) = _120788], (517 ^ _103017) ^ [_121159] : [-(inverse(_121159) = domain_of(flip(cross_product(_121159, universal_class))))], (519 ^ _103017) ^ [_121246] : [-(range_of(_121246) = domain_of(inverse(_121246)))], (521 ^ _103017) ^ [_121344, _121346] : [-(image(_121344, _121346) = range_of(restrict(_121344, _121346, universal_class)))], (523 ^ _103017) ^ [_121477] : [inductive(_121477), 526 ^ _103017 : [(527 ^ _103017) ^ [] : [-(member(null_class, _121477))], (529 ^ _103017) ^ [] : [-(subclass(image(successor_relation, _121477), _121477))]]], (531 ^ _103017) ^ [_121710] : [-(inductive(_121710)), member(null_class, _121710), subclass(image(successor_relation, _121710), _121710)], (542 ^ _103017) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _103017) ^ [] : [-(inductive(540 ^ []))], (546 ^ _103017) ^ [_122155] : [inductive(_122155), -(subclass(540 ^ [], _122155))], (552 ^ _103017) ^ [_122390, _122392] : [member(_122392, sum_class(_122390)), 556 ^ _103017 : [(557 ^ _103017) ^ [] : [-(member(_122392, 555 ^ [_122390, _122392]))], (559 ^ _103017) ^ [] : [-(member(555 ^ [_122390, _122392], _122390))]]], (561 ^ _103017) ^ [_122701, _122703] : [-(member(_122703, sum_class(_122701))), 562 ^ _103017 : [(563 ^ _103017) ^ [_122795] : [member(_122703, _122795), member(_122795, _122701)]]], (571 ^ _103017) ^ [_123055] : [member(_123055, universal_class), -(member(sum_class(_123055), universal_class))], (577 ^ _103017) ^ [_123292, _123294] : [member(_123294, power_class(_123292)), 580 ^ _103017 : [(581 ^ _103017) ^ [] : [-(member(_123294, universal_class))], (583 ^ _103017) ^ [] : [-(subclass(_123294, _123292))]]], (585 ^ _103017) ^ [_123533, _123535] : [-(member(_123535, power_class(_123533))), member(_123535, universal_class), subclass(_123535, _123533)], (595 ^ _103017) ^ [_123824] : [member(_123824, universal_class), -(member(power_class(_123824), universal_class))], (601 ^ _103017) ^ [_124017, _124019] : [-(subclass(compose(_124017, _124019), cross_product(universal_class, universal_class)))], (603 ^ _103017) ^ [_124186, _124188, _124190, _124192] : [member(ordered_pair(_124188, _124186), compose(_124190, _124192)), 606 ^ _103017 : [(607 ^ _103017) ^ [] : [-(member(_124188, universal_class))], (609 ^ _103017) ^ [] : [-(member(_124186, image(_124190, image(_124192, singleton(_124188)))))]]], (611 ^ _103017) ^ [_124467, _124469, _124471, _124473] : [-(member(ordered_pair(_124469, _124467), compose(_124471, _124473))), member(_124469, universal_class), member(_124467, image(_124471, image(_124473, singleton(_124469))))], (621 ^ _103017) ^ [_124831] : [member(_124831, identity_relation), 625 ^ _103017 : [(626 ^ _103017) ^ [] : [-(member(624 ^ [_124831], universal_class))], (628 ^ _103017) ^ [] : [-(_124831 = ordered_pair(624 ^ [_124831], 624 ^ [_124831]))]]], (630 ^ _103017) ^ [_125136] : [-(member(_125136, identity_relation)), 631 ^ _103017 : [(632 ^ _103017) ^ [_125229] : [member(_125229, universal_class), _125136 = ordered_pair(_125229, _125229)]]], (640 ^ _103017) ^ [_125512] : [function(_125512), 643 ^ _103017 : [(644 ^ _103017) ^ [] : [-(subclass(_125512, cross_product(universal_class, universal_class)))], (646 ^ _103017) ^ [] : [-(subclass(compose(_125512, inverse(_125512)), identity_relation))]]], (648 ^ _103017) ^ [_125749] : [-(function(_125749)), subclass(_125749, cross_product(universal_class, universal_class)), subclass(compose(_125749, inverse(_125749)), identity_relation)], (658 ^ _103017) ^ [_126048, _126050] : [-(member(image(_126048, _126050), universal_class)), member(_126050, universal_class), function(_126048)], (678 ^ _103017) ^ [_126695, _126697] : [680 ^ _103017 : [(681 ^ _103017) ^ [] : [-(member(679 ^ [_126695, _126697], _126697))], (683 ^ _103017) ^ [] : [-(member(679 ^ [_126695, _126697], _126695))]], -(disjoint(_126697, _126695))], (668 ^ _103017) ^ [_126380, _126382] : [disjoint(_126382, _126380), 671 ^ _103017 : [(672 ^ _103017) ^ [_126519] : [member(_126519, _126382), member(_126519, _126380)]]], (687 ^ _103017) ^ [_127043] : [-(_127043 = null_class), 691 ^ _103017 : [(692 ^ _103017) ^ [] : [-(member(690 ^ [_127043], universal_class))], (694 ^ _103017) ^ [] : [-(member(690 ^ [_127043], _127043))], (696 ^ _103017) ^ [] : [-(disjoint(690 ^ [_127043], _127043))]]], (698 ^ _103017) ^ [_127453, _127455] : [-(apply(_127455, _127453) = sum_class(image(_127455, singleton(_127453))))], (701 ^ _103017) ^ [] : [-(function(699 ^ []))], (703 ^ _103017) ^ [_127653] : [member(_127653, universal_class), -(_127653 = null_class), -(member(apply(699 ^ [], _127653), _127653))]], input).
% 0.32/1.37  ncf('1',plain,[member(null_class, universal_class)],start(713 ^ 0)).
% 0.32/1.37  ncf('1.1',plain,[-(member(null_class, universal_class)), 252 : member(null_class, 540 ^ []), 252 : subclass(540 ^ [], universal_class)],extension(248 ^ 1,bind([[_111802, _111804, _111939], [universal_class, 540 ^ [], null_class]]))).
% 0.32/1.37  ncf('1.1.1',plain,[-(member(null_class, 540 ^ [])), inductive(540 ^ [])],extension(523 ^ 4,bind([[_121477], [540 ^ []]]))).
% 0.32/1.37  ncf('1.1.1.1',plain,[-(inductive(540 ^ []))],extension(544 ^ 5)).
% 0.32/1.37  ncf('1.1.2',plain,[-(subclass(540 ^ [], universal_class))],extension(267 ^ 2,bind([[_112444], [540 ^ []]]))).
% 0.32/1.37  %-----------------------------------------------------
% 0.32/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------