%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SET055+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n002.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 11:55:13 EDT 2023
% Result : Theorem 0.32s 1.36s
% Output : Proof 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET055+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.06/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n002.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 19:06:19 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.32/1.36
% 0.32/1.36 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.32/1.36 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/1.36 %-----------------------------------------------------
% 0.32/1.36 ncf(matrix, plain, [(714 ^ _101971) ^ [] : [712 ^ [] = 712 ^ []], (2 ^ _101971) ^ [_102115] : [-(_102115 = _102115)], (4 ^ _101971) ^ [_102222, _102224] : [_102224 = _102222, -(_102222 = _102224)], (10 ^ _101971) ^ [_102426, _102428, _102430] : [-(_102430 = _102426), _102430 = _102428, _102428 = _102426], (20 ^ _101971) ^ [_102739, _102741] : [-(inductive(_102739)), _102741 = _102739, inductive(_102741)], (30 ^ _101971) ^ [_103062, _103064, _103066, _103068] : [-(subclass(_103066, _103062)), subclass(_103068, _103064), _103068 = _103066, _103064 = _103062], (44 ^ _101971) ^ [_103506, _103508, _103510, _103512] : [-(disjoint(_103510, _103506)), disjoint(_103512, _103508), _103512 = _103510, _103508 = _103506], (58 ^ _101971) ^ [_103922, _103924] : [-(function(_103922)), _103924 = _103922, function(_103924)], (68 ^ _101971) ^ [_104225, _104227, _104229, _104231] : [-(member(_104229, _104225)), member(_104231, _104227), _104231 = _104229, _104227 = _104225], (82 ^ _101971) ^ [_104683, _104685, _104687, _104689] : [-(unordered_pair(_104689, _104685) = unordered_pair(_104687, _104683)), _104689 = _104687, _104685 = _104683], (92 ^ _101971) ^ [_105014, _105016] : [_105016 = _105014, -(first(_105016) = first(_105014))], (98 ^ _101971) ^ [_105232, _105234] : [_105234 = _105232, -(second(_105234) = second(_105232))], (104 ^ _101971) ^ [_105450, _105452] : [_105452 = _105450, -(complement(_105452) = complement(_105450))], (110 ^ _101971) ^ [_105696, _105698, _105700, _105702] : [-(intersection(_105702, _105698) = intersection(_105700, _105696)), _105702 = _105700, _105698 = _105696], (120 ^ _101971) ^ [_106027, _106029] : [_106029 = _106027, -(rotate(_106029) = rotate(_106027))], (126 ^ _101971) ^ [_106273, _106275, _106277, _106279] : [-(union(_106279, _106275) = union(_106277, _106273)), _106279 = _106277, _106275 = _106273], (136 ^ _101971) ^ [_106604, _106606] : [_106606 = _106604, -(successor(_106606) = successor(_106604))], (142 ^ _101971) ^ [_106822, _106824] : [_106824 = _106822, -(flip(_106824) = flip(_106822))], (148 ^ _101971) ^ [_107040, _107042] : [_107042 = _107040, -(domain_of(_107042) = domain_of(_107040))], (154 ^ _101971) ^ [_107258, _107260] : [_107260 = _107258, -(range_of(_107260) = range_of(_107258))], (160 ^ _101971) ^ [_107532, _107534, _107536, _107538, _107540, _107542] : [-(restrict(_107542, _107538, _107534) = restrict(_107540, _107536, _107532)), _107542 = _107540, _107538 = _107536, _107534 = _107532], (174 ^ _101971) ^ [_107992, _107994] : [_107994 = _107992, -(power_class(_107994) = power_class(_107992))], (180 ^ _101971) ^ [_108238, _108240, _108242, _108244] : [-(ordered_pair(_108244, _108240) = ordered_pair(_108242, _108238)), _108244 = _108242, _108240 = _108238], (190 ^ _101971) ^ [_108597, _108599, _108601, _108603] : [-(cross_product(_108603, _108599) = cross_product(_108601, _108597)), _108603 = _108601, _108599 = _108597], (200 ^ _101971) ^ [_108956, _108958, _108960, _108962] : [-(compose(_108962, _108958) = compose(_108960, _108956)), _108962 = _108960, _108958 = _108956], (210 ^ _101971) ^ [_109287, _109289] : [_109289 = _109287, -(inverse(_109289) = inverse(_109287))], (216 ^ _101971) ^ [_109505, _109507] : [_109507 = _109505, -(sum_class(_109507) = sum_class(_109505))], (222 ^ _101971) ^ [_109751, _109753, _109755, _109757] : [-(image(_109757, _109753) = image(_109755, _109751)), _109757 = _109755, _109753 = _109751], (232 ^ _101971) ^ [_110082, _110084] : [_110084 = _110082, -(singleton(_110084) = singleton(_110082))], (238 ^ _101971) ^ [_110308, _110310, _110312, _110314] : [-(apply(_110314, _110310) = apply(_110312, _110308)), _110314 = _110312, _110310 = _110308], (258 ^ _101971) ^ [_111070, _111072] : [260 ^ _101971 : [(261 ^ _101971) ^ [] : [-(member(259 ^ [_111070, _111072], _111072))], (263 ^ _101971) ^ [] : [member(259 ^ [_111070, _111072], _111070)]], -(subclass(_111072, _111070))], (248 ^ _101971) ^ [_110756, _110758] : [subclass(_110758, _110756), 251 ^ _101971 : [(252 ^ _101971) ^ [_110893] : [member(_110893, _110758), -(member(_110893, _110756))]]], (267 ^ _101971) ^ [_111398] : [-(subclass(_111398, universal_class))], (269 ^ _101971) ^ [_111534, _111536] : [_111536 = _111534, 272 ^ _101971 : [(273 ^ _101971) ^ [] : [-(subclass(_111536, _111534))], (275 ^ _101971) ^ [] : [-(subclass(_111534, _111536))]]], (277 ^ _101971) ^ [_111771, _111773] : [-(_111773 = _111771), subclass(_111773, _111771), subclass(_111771, _111773)], (287 ^ _101971) ^ [_112115, _112117, _112119] : [member(_112119, unordered_pair(_112117, _112115)), 290 ^ _101971 : [(291 ^ _101971) ^ [] : [-(member(_112119, universal_class))], (293 ^ _101971) ^ [] : [-(_112119 = _112117), -(_112119 = _112115)]]], (299 ^ _101971) ^ [_112460, _112462, _112464] : [-(member(_112464, unordered_pair(_112462, _112460))), member(_112464, universal_class), 304 ^ _101971 : [(305 ^ _101971) ^ [] : [_112464 = _112462], (307 ^ _101971) ^ [] : [_112464 = _112460]]], (311 ^ _101971) ^ [_112838, _112840] : [-(member(unordered_pair(_112840, _112838), universal_class))], (313 ^ _101971) ^ [_112921] : [-(singleton(_112921) = unordered_pair(_112921, _112921))], (315 ^ _101971) ^ [_113018, _113020] : [-(ordered_pair(_113020, _113018) = unordered_pair(singleton(_113020), unordered_pair(_113020, singleton(_113018))))], (317 ^ _101971) ^ [_113197, _113199, _113201, _113203] : [member(ordered_pair(_113203, _113201), cross_product(_113199, _113197)), 320 ^ _101971 : [(321 ^ _101971) ^ [] : [-(member(_113203, _113199))], (323 ^ _101971) ^ [] : [-(member(_113201, _113197))]]], (325 ^ _101971) ^ [_113462, _113464, _113466, _113468] : [-(member(ordered_pair(_113468, _113466), cross_product(_113464, _113462))), member(_113468, _113464), member(_113466, _113462)], (335 ^ _101971) ^ [_113795, _113797] : [342 ^ _101971 : [(343 ^ _101971) ^ [] : [-(first(ordered_pair(_113797, _113795)) = _113797)], (345 ^ _101971) ^ [] : [-(second(ordered_pair(_113797, _113795)) = _113795)]], member(_113797, universal_class), member(_113795, universal_class)], (347 ^ _101971) ^ [_114203, _114205, _114207] : [member(_114203, cross_product(_114207, _114205)), -(_114203 = ordered_pair(first(_114203), second(_114203)))], (353 ^ _101971) ^ [_114468, _114470] : [member(ordered_pair(_114470, _114468), element_relation), 356 ^ _101971 : [(357 ^ _101971) ^ [] : [-(member(_114468, universal_class))], (359 ^ _101971) ^ [] : [-(member(_114470, _114468))]]], (361 ^ _101971) ^ [_114711, _114713] : [-(member(ordered_pair(_114713, _114711), element_relation)), member(_114711, universal_class), member(_114713, _114711)], (371 ^ _101971) ^ [] : [-(subclass(element_relation, cross_product(universal_class, universal_class)))], (373 ^ _101971) ^ [_115114, _115116, _115118] : [member(_115114, intersection(_115118, _115116)), 376 ^ _101971 : [(377 ^ _101971) ^ [] : [-(member(_115114, _115118))], (379 ^ _101971) ^ [] : [-(member(_115114, _115116))]]], (381 ^ _101971) ^ [_115365, _115367, _115369] : [-(member(_115365, intersection(_115369, _115367))), member(_115365, _115369), member(_115365, _115367)], (391 ^ _101971) ^ [_115711, _115713] : [member(_115711, complement(_115713)), 394 ^ _101971 : [(395 ^ _101971) ^ [] : [-(member(_115711, universal_class))], (397 ^ _101971) ^ [] : [member(_115711, _115713)]]], (399 ^ _101971) ^ [_115953, _115955] : [-(member(_115953, complement(_115955))), member(_115953, universal_class), -(member(_115953, _115955))], (409 ^ _101971) ^ [_116260, _116262, _116264] : [-(restrict(_116262, _116264, _116260) = intersection(_116262, cross_product(_116264, _116260)))], (411 ^ _101971) ^ [_116351] : [member(_116351, null_class)], (413 ^ _101971) ^ [_116487, _116489] : [member(_116487, domain_of(_116489)), 416 ^ _101971 : [(417 ^ _101971) ^ [] : [-(member(_116487, universal_class))], (419 ^ _101971) ^ [] : [restrict(_116489, singleton(_116487), universal_class) = null_class]]], (421 ^ _101971) ^ [_116741, _116743] : [-(member(_116741, domain_of(_116743))), member(_116741, universal_class), -(restrict(_116743, singleton(_116741), universal_class) = null_class)], (431 ^ _101971) ^ [_117118, _117120, _117122, _117124] : [member(ordered_pair(ordered_pair(_117122, _117120), _117118), rotate(_117124)), 434 ^ _101971 : [(435 ^ _101971) ^ [] : [-(member(ordered_pair(ordered_pair(_117122, _117120), _117118), cross_product(cross_product(universal_class, universal_class), universal_class)))], (437 ^ _101971) ^ [] : [-(member(ordered_pair(ordered_pair(_117120, _117118), _117122), _117124))]]], (439 ^ _101971) ^ [_117411, _117413, _117415, _117417] : [-(member(ordered_pair(ordered_pair(_117415, _117413), _117411), rotate(_117417))), member(ordered_pair(ordered_pair(_117415, _117413), _117411), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_117413, _117411), _117415), _117417)], (449 ^ _101971) ^ [_117743] : [-(subclass(rotate(_117743), cross_product(cross_product(universal_class, universal_class), universal_class)))], (451 ^ _101971) ^ [_117909, _117911, _117913, _117915] : [member(ordered_pair(ordered_pair(_117915, _117913), _117911), flip(_117909)), 454 ^ _101971 : [(455 ^ _101971) ^ [] : [-(member(ordered_pair(ordered_pair(_117915, _117913), _117911), cross_product(cross_product(universal_class, universal_class), universal_class)))], (457 ^ _101971) ^ [] : [-(member(ordered_pair(ordered_pair(_117913, _117915), _117911), _117909))]]], (459 ^ _101971) ^ [_118202, _118204, _118206, _118208] : [-(member(ordered_pair(ordered_pair(_118208, _118206), _118204), flip(_118202))), member(ordered_pair(ordered_pair(_118208, _118206), _118204), cross_product(cross_product(universal_class, universal_class), universal_class)), member(ordered_pair(ordered_pair(_118206, _118208), _118204), _118202)], (469 ^ _101971) ^ [_118534] : [-(subclass(flip(_118534), cross_product(cross_product(universal_class, universal_class), universal_class)))], (481 ^ _101971) ^ [_118954, _118956, _118958] : [482 ^ _101971 : [(483 ^ _101971) ^ [] : [member(_118954, _118958)], (485 ^ _101971) ^ [] : [member(_118954, _118956)]], -(member(_118954, union(_118958, _118956)))], (471 ^ _101971) ^ [_118686, _118688, _118690] : [member(_118686, union(_118690, _118688)), -(member(_118686, _118690)), -(member(_118686, _118688))], (489 ^ _101971) ^ [_119225] : [-(successor(_119225) = union(_119225, singleton(_119225)))], (491 ^ _101971) ^ [] : [-(subclass(successor_relation, cross_product(universal_class, universal_class)))], (493 ^ _101971) ^ [_119421, _119423] : [member(ordered_pair(_119423, _119421), successor_relation), 496 ^ _101971 : [(497 ^ _101971) ^ [] : [-(member(_119423, universal_class))], (499 ^ _101971) ^ [] : [-(member(_119421, universal_class))], (501 ^ _101971) ^ [] : [-(successor(_119423) = _119421)]]], (503 ^ _101971) ^ [_119742, _119744] : [-(member(ordered_pair(_119744, _119742), successor_relation)), member(_119744, universal_class), member(_119742, universal_class), successor(_119744) = _119742], (517 ^ _101971) ^ [_120113] : [-(inverse(_120113) = domain_of(flip(cross_product(_120113, universal_class))))], (519 ^ _101971) ^ [_120200] : [-(range_of(_120200) = domain_of(inverse(_120200)))], (521 ^ _101971) ^ [_120298, _120300] : [-(image(_120298, _120300) = range_of(restrict(_120298, _120300, universal_class)))], (523 ^ _101971) ^ [_120431] : [inductive(_120431), 526 ^ _101971 : [(527 ^ _101971) ^ [] : [-(member(null_class, _120431))], (529 ^ _101971) ^ [] : [-(subclass(image(successor_relation, _120431), _120431))]]], (531 ^ _101971) ^ [_120664] : [-(inductive(_120664)), member(null_class, _120664), subclass(image(successor_relation, _120664), _120664)], (542 ^ _101971) ^ [] : [-(member(540 ^ [], universal_class))], (544 ^ _101971) ^ [] : [-(inductive(540 ^ []))], (546 ^ _101971) ^ [_121109] : [inductive(_121109), -(subclass(540 ^ [], _121109))], (552 ^ _101971) ^ [_121344, _121346] : [member(_121346, sum_class(_121344)), 556 ^ _101971 : [(557 ^ _101971) ^ [] : [-(member(_121346, 555 ^ [_121344, _121346]))], (559 ^ _101971) ^ [] : [-(member(555 ^ [_121344, _121346], _121344))]]], (561 ^ _101971) ^ [_121655, _121657] : [-(member(_121657, sum_class(_121655))), 562 ^ _101971 : [(563 ^ _101971) ^ [_121749] : [member(_121657, _121749), member(_121749, _121655)]]], (571 ^ _101971) ^ [_122009] : [member(_122009, universal_class), -(member(sum_class(_122009), universal_class))], (577 ^ _101971) ^ [_122246, _122248] : [member(_122248, power_class(_122246)), 580 ^ _101971 : [(581 ^ _101971) ^ [] : [-(member(_122248, universal_class))], (583 ^ _101971) ^ [] : [-(subclass(_122248, _122246))]]], (585 ^ _101971) ^ [_122487, _122489] : [-(member(_122489, power_class(_122487))), member(_122489, universal_class), subclass(_122489, _122487)], (595 ^ _101971) ^ [_122778] : [member(_122778, universal_class), -(member(power_class(_122778), universal_class))], (601 ^ _101971) ^ [_122971, _122973] : [-(subclass(compose(_122971, _122973), cross_product(universal_class, universal_class)))], (603 ^ _101971) ^ [_123140, _123142, _123144, _123146] : [member(ordered_pair(_123142, _123140), compose(_123144, _123146)), 606 ^ _101971 : [(607 ^ _101971) ^ [] : [-(member(_123142, universal_class))], (609 ^ _101971) ^ [] : [-(member(_123140, image(_123144, image(_123146, singleton(_123142)))))]]], (611 ^ _101971) ^ [_123421, _123423, _123425, _123427] : [-(member(ordered_pair(_123423, _123421), compose(_123425, _123427))), member(_123423, universal_class), member(_123421, image(_123425, image(_123427, singleton(_123423))))], (621 ^ _101971) ^ [_123785] : [member(_123785, identity_relation), 625 ^ _101971 : [(626 ^ _101971) ^ [] : [-(member(624 ^ [_123785], universal_class))], (628 ^ _101971) ^ [] : [-(_123785 = ordered_pair(624 ^ [_123785], 624 ^ [_123785]))]]], (630 ^ _101971) ^ [_124090] : [-(member(_124090, identity_relation)), 631 ^ _101971 : [(632 ^ _101971) ^ [_124183] : [member(_124183, universal_class), _124090 = ordered_pair(_124183, _124183)]]], (640 ^ _101971) ^ [_124466] : [function(_124466), 643 ^ _101971 : [(644 ^ _101971) ^ [] : [-(subclass(_124466, cross_product(universal_class, universal_class)))], (646 ^ _101971) ^ [] : [-(subclass(compose(_124466, inverse(_124466)), identity_relation))]]], (648 ^ _101971) ^ [_124703] : [-(function(_124703)), subclass(_124703, cross_product(universal_class, universal_class)), subclass(compose(_124703, inverse(_124703)), identity_relation)], (658 ^ _101971) ^ [_125002, _125004] : [-(member(image(_125002, _125004), universal_class)), member(_125004, universal_class), function(_125002)], (678 ^ _101971) ^ [_125649, _125651] : [680 ^ _101971 : [(681 ^ _101971) ^ [] : [-(member(679 ^ [_125649, _125651], _125651))], (683 ^ _101971) ^ [] : [-(member(679 ^ [_125649, _125651], _125649))]], -(disjoint(_125651, _125649))], (668 ^ _101971) ^ [_125334, _125336] : [disjoint(_125336, _125334), 671 ^ _101971 : [(672 ^ _101971) ^ [_125473] : [member(_125473, _125336), member(_125473, _125334)]]], (687 ^ _101971) ^ [_125997] : [-(_125997 = null_class), 691 ^ _101971 : [(692 ^ _101971) ^ [] : [-(member(690 ^ [_125997], universal_class))], (694 ^ _101971) ^ [] : [-(member(690 ^ [_125997], _125997))], (696 ^ _101971) ^ [] : [-(disjoint(690 ^ [_125997], _125997))]]], (698 ^ _101971) ^ [_126407, _126409] : [-(apply(_126409, _126407) = sum_class(image(_126409, singleton(_126407))))], (701 ^ _101971) ^ [] : [-(function(699 ^ []))], (703 ^ _101971) ^ [_126607] : [member(_126607, universal_class), -(_126607 = null_class), -(member(apply(699 ^ [], _126607), _126607))]], input).
% 0.32/1.36 ncf('1',plain,[712 ^ [] = 712 ^ []],start(714 ^ 0)).
% 0.32/1.36 ncf('1.1',plain,[-(712 ^ [] = 712 ^ [])],extension(2 ^ 1,bind([[_102115], [712 ^ []]]))).
% 0.32/1.36 %-----------------------------------------------------
% 0.32/1.36 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------