TSTP Solution File: SET734+4 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n031.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 11:56:21 EDT 2023
% Result : Theorem 16.04s 15.85s
% Output : Proof 16.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.11/0.12 % Command : nanocop.sh %s %d
% 0.11/0.33 % Computer : n031.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
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Thu May 18 19:13:25 EDT 2023
% 0.11/0.34 % CPUTime :
% 16.04/15.85
% 16.04/15.85 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 16.04/15.85 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.04/15.85 %-----------------------------------------------------
% 16.04/15.85 ncf(matrix, plain, [(1314 ^ _191433) ^ [] : [-(maps(1310 ^ [], 1311 ^ [], 1312 ^ []))], (1316 ^ _191433) ^ [] : [-(maps(1309 ^ [], 1312 ^ [], 1311 ^ []))], (1318 ^ _191433) ^ [] : [-(identity(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 1312 ^ []))], (1320 ^ _191433) ^ [] : [surjective(1310 ^ [], 1311 ^ [], 1312 ^ [])], (318 ^ _191433) ^ [_202821, _202823] : [_202823 = _202821, -(power_set(_202823) = power_set(_202821))], (324 ^ _191433) ^ [_203067, _203069, _203071, _203073] : [-(intersection(_203073, _203069) = intersection(_203071, _203067)), _203073 = _203071, _203069 = _203067], (334 ^ _191433) ^ [_203426, _203428, _203430, _203432] : [-(union(_203432, _203428) = union(_203430, _203426)), _203432 = _203430, _203428 = _203426], (344 ^ _191433) ^ [_203785, _203787, _203789, _203791] : [-(difference(_203791, _203787) = difference(_203789, _203785)), _203791 = _203789, _203787 = _203785], (354 ^ _191433) ^ [_204116, _204118] : [_204118 = _204116, -(singleton(_204118) = singleton(_204116))], (360 ^ _191433) ^ [_204362, _204364, _204366, _204368] : [-(unordered_pair(_204368, _204364) = unordered_pair(_204366, _204362)), _204368 = _204366, _204364 = _204362], (370 ^ _191433) ^ [_204693, _204695] : [_204695 = _204693, -(sum(_204695) = sum(_204693))], (376 ^ _191433) ^ [_204911, _204913] : [_204913 = _204911, -(product(_204913) = product(_204911))], (382 ^ _191433) ^ [_205185, _205187, _205189, _205191, _205193, _205195] : [-(inverse_function(_205195, _205191, _205187) = inverse_function(_205193, _205189, _205185)), _205195 = _205193, _205191 = _205189, _205187 = _205185], (396 ^ _191433) ^ [_205673, _205675, _205677, _205679] : [-(image2(_205679, _205675) = image2(_205677, _205673)), _205679 = _205677, _205675 = _205673], (406 ^ _191433) ^ [_206060, _206062, _206064, _206066, _206068, _206070] : [-(image3(_206070, _206066, _206062) = image3(_206068, _206064, _206060)), _206070 = _206068, _206066 = _206064, _206062 = _206060], (420 ^ _191433) ^ [_206548, _206550, _206552, _206554] : [-(inverse_image2(_206554, _206550) = inverse_image2(_206552, _206548)), _206554 = _206552, _206550 = _206548], (430 ^ _191433) ^ [_206935, _206937, _206939, _206941, _206943, _206945] : [-(inverse_image3(_206945, _206941, _206937) = inverse_image3(_206943, _206939, _206935)), _206945 = _206943, _206941 = _206939, _206937 = _206935], (444 ^ _191433) ^ [_207487, _207489, _207491, _207493, _207495, _207497, _207499, _207501, _207503, _207505] : [-(compose_function(_207505, _207501, _207497, _207493, _207489) = compose_function(_207503, _207499, _207495, _207491, _207487)), _207505 = _207503, _207501 = _207499, _207497 = _207495, _207493 = _207491, _207489 = _207487], (2 ^ _191433) ^ [_191577] : [-(_191577 = _191577)], (4 ^ _191433) ^ [_191684, _191686] : [_191686 = _191684, -(_191684 = _191686)], (10 ^ _191433) ^ [_191888, _191890, _191892] : [-(_191892 = _191888), _191892 = _191890, _191890 = _191888], (20 ^ _191433) ^ [_192229, _192231, _192233, _192235] : [-(equal_set(_192233, _192229)), equal_set(_192235, _192231), _192235 = _192233, _192231 = _192229], (34 ^ _191433) ^ [_192673, _192675, _192677, _192679] : [-(subset(_192677, _192673)), subset(_192679, _192675), _192679 = _192677, _192675 = _192673], (48 ^ _191433) ^ [_193229, _193231, _193233, _193235, _193237, _193239, _193241, _193243, _193245, _193247, _193249, _193251] : [-(compose_predicate(_193249, _193245, _193241, _193237, _193233, _193229)), compose_predicate(_193251, _193247, _193243, _193239, _193235, _193231), _193251 = _193249, _193247 = _193245, _193243 = _193241, _193239 = _193237, _193235 = _193233, _193231 = _193229], (78 ^ _191433) ^ [_194373, _194375, _194377, _194379, _194381, _194383, _194385, _194387] : [-(equal_maps(_194385, _194381, _194377, _194373)), equal_maps(_194387, _194383, _194379, _194375), _194387 = _194385, _194383 = _194381, _194379 = _194377, _194375 = _194373], (100 ^ _191433) ^ [_195135, _195137, _195139, _195141, _195143, _195145] : [-(injective(_195143, _195139, _195135)), injective(_195145, _195141, _195137), _195145 = _195143, _195141 = _195139, _195137 = _195135], (118 ^ _191433) ^ [_195772, _195774, _195776, _195778, _195780, _195782, _195784, _195786] : [-(inverse_predicate(_195784, _195780, _195776, _195772)), inverse_predicate(_195786, _195782, _195778, _195774), _195786 = _195784, _195782 = _195780, _195778 = _195776, _195774 = _195772], (140 ^ _191433) ^ [_196590, _196592, _196594, _196596, _196598, _196600, _196602, _196604, _196606, _196608] : [-(increasing(_196606, _196602, _196598, _196594, _196590)), increasing(_196608, _196604, _196600, _196596, _196592), _196608 = _196606, _196604 = _196602, _196600 = _196598, _196596 = _196594, _196592 = _196590], (166 ^ _191433) ^ [_197577, _197579, _197581, _197583, _197585, _197587, _197589, _197591, _197593, _197595] : [-(decreasing(_197593, _197589, _197585, _197581, _197577)), decreasing(_197595, _197591, _197587, _197583, _197579), _197595 = _197593, _197591 = _197589, _197587 = _197585, _197583 = _197581, _197579 = _197577], (192 ^ _191433) ^ [_198564, _198566, _198568, _198570, _198572, _198574, _198576, _198578, _198580, _198582] : [-(isomorphism(_198580, _198576, _198572, _198568, _198564)), isomorphism(_198582, _198578, _198574, _198570, _198566), _198582 = _198580, _198578 = _198576, _198574 = _198572, _198570 = _198568, _198566 = _198564], (218 ^ _191433) ^ [_199495, _199497, _199499, _199501, _199503, _199505] : [-(one_to_one(_199503, _199499, _199495)), one_to_one(_199505, _199501, _199497), _199505 = _199503, _199501 = _199499, _199497 = _199495], (236 ^ _191433) ^ [_200076, _200078, _200080, _200082] : [-(member(_200080, _200076)), member(_200082, _200078), _200082 = _200080, _200078 = _200076], (250 ^ _191433) ^ [_200548, _200550, _200552, _200554, _200556, _200558] : [-(apply(_200556, _200552, _200548)), apply(_200558, _200554, _200550), _200558 = _200556, _200554 = _200552, _200550 = _200548], (268 ^ _191433) ^ [_201157, _201159, _201161, _201163, _201165, _201167] : [-(maps(_201165, _201161, _201157)), maps(_201167, _201163, _201159), _201167 = _201165, _201163 = _201161, _201159 = _201157], (286 ^ _191433) ^ [_201738, _201740, _201742, _201744] : [-(identity(_201742, _201738)), identity(_201744, _201740), _201744 = _201742, _201740 = _201738], (300 ^ _191433) ^ [_202190, _202192, _202194, _202196, _202198, _202200] : [-(surjective(_202198, _202194, _202190)), surjective(_202200, _202196, _202192), _202200 = _202198, _202196 = _202194, _202192 = _202190], (476 ^ _191433) ^ [_208674, _208676] : [478 ^ _191433 : [(479 ^ _191433) ^ [] : [-(member(477 ^ [_208674, _208676], _208676))], (481 ^ _191433) ^ [] : [member(477 ^ [_208674, _208676], _208674)]], -(subset(_208676, _208674))], (466 ^ _191433) ^ [_208360, _208362] : [subset(_208362, _208360), 469 ^ _191433 : [(470 ^ _191433) ^ [_208497] : [member(_208497, _208362), -(member(_208497, _208360))]]], (485 ^ _191433) ^ [_209060, _209062] : [equal_set(_209062, _209060), 488 ^ _191433 : [(489 ^ _191433) ^ [] : [-(subset(_209062, _209060))], (491 ^ _191433) ^ [] : [-(subset(_209060, _209062))]]], (493 ^ _191433) ^ [_209297, _209299] : [-(equal_set(_209299, _209297)), subset(_209299, _209297), subset(_209297, _209299)], (503 ^ _191433) ^ [_209627, _209629] : [member(_209629, power_set(_209627)), -(subset(_209629, _209627))], (509 ^ _191433) ^ [_209793, _209795] : [subset(_209795, _209793), -(member(_209795, power_set(_209793)))], (515 ^ _191433) ^ [_210052, _210054, _210056] : [member(_210056, intersection(_210054, _210052)), 518 ^ _191433 : [(519 ^ _191433) ^ [] : [-(member(_210056, _210054))], (521 ^ _191433) ^ [] : [-(member(_210056, _210052))]]], (523 ^ _191433) ^ [_210303, _210305, _210307] : [-(member(_210307, intersection(_210305, _210303))), member(_210307, _210305), member(_210307, _210303)], (543 ^ _191433) ^ [_210931, _210933, _210935] : [544 ^ _191433 : [(545 ^ _191433) ^ [] : [member(_210935, _210933)], (547 ^ _191433) ^ [] : [member(_210935, _210931)]], -(member(_210935, union(_210933, _210931)))], (533 ^ _191433) ^ [_210663, _210665, _210667] : [member(_210667, union(_210665, _210663)), -(member(_210667, _210665)), -(member(_210667, _210663))], (551 ^ _191433) ^ [_211201] : [member(_211201, empty_set)], (553 ^ _191433) ^ [_211351, _211353, _211355] : [member(_211355, difference(_211351, _211353)), 556 ^ _191433 : [(557 ^ _191433) ^ [] : [-(member(_211355, _211351))], (559 ^ _191433) ^ [] : [member(_211355, _211353)]]], (561 ^ _191433) ^ [_211603, _211605, _211607] : [-(member(_211607, difference(_211603, _211605))), member(_211607, _211603), -(member(_211607, _211605))], (571 ^ _191433) ^ [_211952, _211954] : [member(_211954, singleton(_211952)), -(_211954 = _211952)], (577 ^ _191433) ^ [_212118, _212120] : [_212120 = _212118, -(member(_212120, singleton(_212118)))], (593 ^ _191433) ^ [_212645, _212647, _212649] : [594 ^ _191433 : [(595 ^ _191433) ^ [] : [_212649 = _212647], (597 ^ _191433) ^ [] : [_212649 = _212645]], -(member(_212649, unordered_pair(_212647, _212645)))], (583 ^ _191433) ^ [_212377, _212379, _212381] : [member(_212381, unordered_pair(_212379, _212377)), -(_212381 = _212379), -(_212381 = _212377)], (601 ^ _191433) ^ [_212974, _212976] : [member(_212976, sum(_212974)), 605 ^ _191433 : [(606 ^ _191433) ^ [] : [-(member(604 ^ [_212974, _212976], _212974))], (608 ^ _191433) ^ [] : [-(member(_212976, 604 ^ [_212974, _212976]))]]], (610 ^ _191433) ^ [_213285, _213287] : [-(member(_213287, sum(_213285))), 611 ^ _191433 : [(612 ^ _191433) ^ [_213379] : [member(_213379, _213285), member(_213287, _213379)]]], (630 ^ _191433) ^ [_213980, _213982] : [632 ^ _191433 : [(633 ^ _191433) ^ [] : [-(member(631 ^ [_213980, _213982], _213980))], (635 ^ _191433) ^ [] : [member(_213982, 631 ^ [_213980, _213982])]], -(member(_213982, product(_213980)))], (620 ^ _191433) ^ [_213662, _213664] : [member(_213664, product(_213662)), 623 ^ _191433 : [(624 ^ _191433) ^ [_213803] : [member(_213803, _213662), -(member(_213664, _213803))]]], (674 ^ _191433) ^ [_215667, _215669, _215671] : [-(maps(_215671, _215669, _215667)), 689 ^ _191433 : [(690 ^ _191433) ^ [] : [-(member(686 ^ [_215667, _215669, _215671], _215669))], (692 ^ _191433) ^ [] : [-(member(687 ^ [_215667, _215669, _215671], _215667))], (694 ^ _191433) ^ [] : [-(member(688 ^ [_215667, _215669, _215671], _215667))], (696 ^ _191433) ^ [] : [-(apply(_215671, 686 ^ [_215667, _215669, _215671], 687 ^ [_215667, _215669, _215671]))], (698 ^ _191433) ^ [] : [-(apply(_215671, 686 ^ [_215667, _215669, _215671], 688 ^ [_215667, _215669, _215671]))], (700 ^ _191433) ^ [] : [687 ^ [_215667, _215669, _215671] = 688 ^ [_215667, _215669, _215671]]], 678 ^ _191433 : [(679 ^ _191433) ^ [] : [-(member(677 ^ [_215667, _215669, _215671], _215669))], (681 ^ _191433) ^ [_216007] : [member(_216007, _215667), apply(_215671, 677 ^ [_215667, _215669, _215671], _216007)]]], (639 ^ _191433) ^ [_214422, _214424, _214426] : [maps(_214426, _214424, _214422), 642 ^ _191433 : [(643 ^ _191433) ^ [_214650] : [member(_214650, _214424), 647 ^ _191433 : [(648 ^ _191433) ^ [] : [-(member(646 ^ [_214422, _214424, _214426, _214650], _214422))], (650 ^ _191433) ^ [] : [-(apply(_214426, _214650, 646 ^ [_214422, _214424, _214426, _214650]))]]], (652 ^ _191433) ^ [_215040, _215042, _215044] : [member(_215044, _214424), member(_215042, _214422), member(_215040, _214422), -(_215042 = _215040), apply(_214426, _215044, _215042), apply(_214426, _215044, _215040)]]], (741 ^ _191433) ^ [_218702, _218704, _218706, _218708, _218710, _218712] : [-(compose_predicate(_218712, _218710, _218708, _218706, _218704, _218702)), 744 ^ _191433 : [(745 ^ _191433) ^ [] : [-(member(742 ^ [_218702, _218704, _218706, _218708, _218710, _218712], _218706))], (747 ^ _191433) ^ [] : [-(member(743 ^ [_218702, _218704, _218706, _218708, _218710, _218712], _218702))], (749 ^ _191433) ^ [] : [763 ^ _191433 : [(764 ^ _191433) ^ [] : [-(member(762 ^ [_218702, _218704, _218706, _218708, _218710, _218712], _218704))], (766 ^ _191433) ^ [] : [-(apply(_218708, 742 ^ [_218702, _218704, _218706, _218708, _218710, _218712], 762 ^ [_218702, _218704, _218706, _218708, _218710, _218712]))], (768 ^ _191433) ^ [] : [-(apply(_218710, 762 ^ [_218702, _218704, _218706, _218708, _218710, _218712], 743 ^ [_218702, _218704, _218706, _218708, _218710, _218712]))], (770 ^ _191433) ^ [] : [apply(_218712, 742 ^ [_218702, _218704, _218706, _218708, _218710, _218712], 743 ^ [_218702, _218704, _218706, _218708, _218710, _218712])]], 750 ^ _191433 : [(751 ^ _191433) ^ [] : [-(apply(_218712, 742 ^ [_218702, _218704, _218706, _218708, _218710, _218712], 743 ^ [_218702, _218704, _218706, _218708, _218710, _218712]))], (753 ^ _191433) ^ [_219427] : [member(_219427, _218704), apply(_218708, 742 ^ [_218702, _218704, _218706, _218708, _218710, _218712], _219427), apply(_218710, _219427, 743 ^ [_218702, _218704, _218706, _218708, _218710, _218712])]]]]], (704 ^ _191433) ^ [_217227, _217229, _217231, _217233, _217235, _217237] : [compose_predicate(_217237, _217235, _217233, _217231, _217229, _217227), 707 ^ _191433 : [(708 ^ _191433) ^ [_217439, _217441] : [member(_217441, _217231), member(_217439, _217227), 715 ^ _191433 : [(716 ^ _191433) ^ [] : [apply(_217237, _217441, _217439), 720 ^ _191433 : [(721 ^ _191433) ^ [] : [-(member(719 ^ [_217227, _217229, _217231, _217233, _217235, _217237, _217439, _217441], _217229))], (723 ^ _191433) ^ [] : [-(apply(_217233, _217441, 719 ^ [_217227, _217229, _217231, _217233, _217235, _217237, _217439, _217441]))], (725 ^ _191433) ^ [] : [-(apply(_217235, 719 ^ [_217227, _217229, _217231, _217233, _217235, _217237, _217439, _217441], _217439))]]], (727 ^ _191433) ^ [] : [-(apply(_217237, _217441, _217439)), 728 ^ _191433 : [(729 ^ _191433) ^ [_218284] : [member(_218284, _217229), apply(_217233, _217441, _218284), apply(_217235, _218284, _217439)]]]]]]], (774 ^ _191433) ^ [_220496, _220498, _220500, _220502, _220504, _220506, _220508] : [member(_220498, _220504), member(_220496, _220500), 781 ^ _191433 : [(782 ^ _191433) ^ [] : [apply(compose_function(_220508, _220506, _220504, _220502, _220500), _220498, _220496), 786 ^ _191433 : [(787 ^ _191433) ^ [] : [-(member(785 ^ [_220496, _220498, _220500, _220502, _220504, _220506, _220508], _220502))], (789 ^ _191433) ^ [] : [-(apply(_220506, _220498, 785 ^ [_220496, _220498, _220500, _220502, _220504, _220506, _220508]))], (791 ^ _191433) ^ [] : [-(apply(_220508, 785 ^ [_220496, _220498, _220500, _220502, _220504, _220506, _220508], _220496))]]], (793 ^ _191433) ^ [] : [-(apply(compose_function(_220508, _220506, _220504, _220502, _220500), _220498, _220496)), 794 ^ _191433 : [(795 ^ _191433) ^ [_221311] : [member(_221311, _220502), apply(_220506, _220498, _221311), apply(_220508, _221311, _220496)]]]]], (833 ^ _191433) ^ [_222683, _222685, _222687, _222689] : [837 ^ _191433 : [(838 ^ _191433) ^ [] : [-(member(834 ^ [_222683, _222685, _222687, _222689], _222685))], (840 ^ _191433) ^ [] : [-(member(835 ^ [_222683, _222685, _222687, _222689], _222683))], (842 ^ _191433) ^ [] : [-(member(836 ^ [_222683, _222685, _222687, _222689], _222683))], (844 ^ _191433) ^ [] : [-(apply(_222689, 834 ^ [_222683, _222685, _222687, _222689], 835 ^ [_222683, _222685, _222687, _222689]))], (846 ^ _191433) ^ [] : [-(apply(_222687, 834 ^ [_222683, _222685, _222687, _222689], 836 ^ [_222683, _222685, _222687, _222689]))], (848 ^ _191433) ^ [] : [835 ^ [_222683, _222685, _222687, _222689] = 836 ^ [_222683, _222685, _222687, _222689]]], -(equal_maps(_222689, _222687, _222685, _222683))], (807 ^ _191433) ^ [_221821, _221823, _221825, _221827] : [equal_maps(_221827, _221825, _221823, _221821), 810 ^ _191433 : [(811 ^ _191433) ^ [_222034, _222036, _222038] : [member(_222038, _221823), member(_222036, _221821), member(_222034, _221821), -(_222036 = _222034), apply(_221827, _222038, _222036), apply(_221825, _222038, _222034)]]], (862 ^ _191433) ^ [_224141, _224143] : [864 ^ _191433 : [(865 ^ _191433) ^ [] : [-(member(863 ^ [_224141, _224143], _224141))], (867 ^ _191433) ^ [] : [apply(_224143, 863 ^ [_224141, _224143], 863 ^ [_224141, _224143])]], -(identity(_224143, _224141))], (852 ^ _191433) ^ [_223824, _223826] : [identity(_223826, _223824), 855 ^ _191433 : [(856 ^ _191433) ^ [_223962] : [member(_223962, _223824), -(apply(_223826, _223962, _223962))]]], (897 ^ _191433) ^ [_225383, _225385, _225387] : [901 ^ _191433 : [(902 ^ _191433) ^ [] : [-(member(898 ^ [_225383, _225385, _225387], _225385))], (904 ^ _191433) ^ [] : [-(member(899 ^ [_225383, _225385, _225387], _225385))], (906 ^ _191433) ^ [] : [-(member(900 ^ [_225383, _225385, _225387], _225383))], (908 ^ _191433) ^ [] : [-(apply(_225387, 898 ^ [_225383, _225385, _225387], 900 ^ [_225383, _225385, _225387]))], (910 ^ _191433) ^ [] : [-(apply(_225387, 899 ^ [_225383, _225385, _225387], 900 ^ [_225383, _225385, _225387]))], (912 ^ _191433) ^ [] : [898 ^ [_225383, _225385, _225387] = 899 ^ [_225383, _225385, _225387]]], -(injective(_225387, _225385, _225383))], (871 ^ _191433) ^ [_224551, _224553, _224555] : [injective(_224555, _224553, _224551), 874 ^ _191433 : [(875 ^ _191433) ^ [_224758, _224760, _224762] : [member(_224762, _224553), member(_224760, _224553), member(_224758, _224551), -(_224762 = _224760), apply(_224555, _224762, _224758), apply(_224555, _224760, _224758)]]], (916 ^ _191433) ^ [_226472, _226474, _226476] : [surjective(_226476, _226474, _226472), 919 ^ _191433 : [(920 ^ _191433) ^ [_226627] : [member(_226627, _226472), 924 ^ _191433 : [(925 ^ _191433) ^ [] : [-(member(923 ^ [_226472, _226474, _226476, _226627], _226474))], (927 ^ _191433) ^ [] : [-(apply(_226476, 923 ^ [_226472, _226474, _226476, _226627], _226627))]]]]], (929 ^ _191433) ^ [_226980, _226982, _226984] : [-(surjective(_226984, _226982, _226980)), 931 ^ _191433 : [(932 ^ _191433) ^ [] : [-(member(930 ^ [_226980, _226982, _226984], _226980))], (934 ^ _191433) ^ [_227231] : [member(_227231, _226982), apply(_226984, _227231, 930 ^ [_226980, _226982, _226984])]]], (942 ^ _191433) ^ [_227579, _227581, _227583] : [one_to_one(_227583, _227581, _227579), 945 ^ _191433 : [(946 ^ _191433) ^ [] : [-(injective(_227583, _227581, _227579))], (948 ^ _191433) ^ [] : [-(surjective(_227583, _227581, _227579))]]], (950 ^ _191433) ^ [_227830, _227832, _227834] : [-(one_to_one(_227834, _227832, _227830)), injective(_227834, _227832, _227830), surjective(_227834, _227832, _227830)], (984 ^ _191433) ^ [_228988, _228990, _228992, _228994] : [-(inverse_predicate(_228994, _228992, _228990, _228988)), 987 ^ _191433 : [(988 ^ _191433) ^ [] : [-(member(985 ^ [_228988, _228990, _228992, _228994], _228990))], (990 ^ _191433) ^ [] : [-(member(986 ^ [_228988, _228990, _228992, _228994], _228988))], (992 ^ _191433) ^ [] : [993 ^ _191433 : [(994 ^ _191433) ^ [] : [-(apply(_228992, 985 ^ [_228988, _228990, _228992, _228994], 986 ^ [_228988, _228990, _228992, _228994]))], (996 ^ _191433) ^ [] : [apply(_228994, 986 ^ [_228988, _228990, _228992, _228994], 985 ^ [_228988, _228990, _228992, _228994])]], 997 ^ _191433 : [(998 ^ _191433) ^ [] : [-(apply(_228994, 986 ^ [_228988, _228990, _228992, _228994], 985 ^ [_228988, _228990, _228992, _228994]))], (1000 ^ _191433) ^ [] : [apply(_228992, 985 ^ [_228988, _228990, _228992, _228994], 986 ^ [_228988, _228990, _228992, _228994])]]]]], (960 ^ _191433) ^ [_228204, _228206, _228208, _228210] : [inverse_predicate(_228210, _228208, _228206, _228204), 963 ^ _191433 : [(964 ^ _191433) ^ [_228386, _228388] : [member(_228388, _228206), member(_228386, _228204), 971 ^ _191433 : [(972 ^ _191433) ^ [] : [apply(_228208, _228388, _228386), -(apply(_228210, _228386, _228388))], (978 ^ _191433) ^ [] : [apply(_228210, _228386, _228388), -(apply(_228208, _228388, _228386))]]]]], (1004 ^ _191433) ^ [_229979, _229981, _229983, _229985, _229987] : [member(_229981, _229985), member(_229979, _229983), 1011 ^ _191433 : [(1012 ^ _191433) ^ [] : [apply(_229987, _229981, _229979), -(apply(inverse_function(_229987, _229985, _229983), _229979, _229981))], (1018 ^ _191433) ^ [] : [apply(inverse_function(_229987, _229985, _229983), _229979, _229981), -(apply(_229987, _229981, _229979))]]], (1024 ^ _191433) ^ [_230651, _230653, _230655] : [member(_230651, image2(_230655, _230653)), 1028 ^ _191433 : [(1029 ^ _191433) ^ [] : [-(member(1027 ^ [_230651, _230653, _230655], _230653))], (1031 ^ _191433) ^ [] : [-(apply(_230655, 1027 ^ [_230651, _230653, _230655], _230651))]]], (1033 ^ _191433) ^ [_230983, _230985, _230987] : [-(member(_230983, image2(_230987, _230985))), 1034 ^ _191433 : [(1035 ^ _191433) ^ [_231081] : [member(_231081, _230985), apply(_230987, _231081, _230983)]]], (1043 ^ _191433) ^ [_231425, _231427, _231429, _231431] : [member(_231425, image3(_231431, _231429, _231427)), 1046 ^ _191433 : [(1047 ^ _191433) ^ [] : [-(member(_231425, _231427))], (1050 ^ _191433) ^ [] : [-(member(1048 ^ [_231425, _231427, _231429, _231431], _231429))], (1052 ^ _191433) ^ [] : [-(apply(_231431, 1048 ^ [_231425, _231427, _231429, _231431], _231425))]]], (1054 ^ _191433) ^ [_231853, _231855, _231857, _231859] : [-(member(_231853, image3(_231859, _231857, _231855))), member(_231853, _231855), 1059 ^ _191433 : [(1060 ^ _191433) ^ [_232047] : [member(_232047, _231857), apply(_231859, _232047, _231853)]]], (1068 ^ _191433) ^ [_232392, _232394, _232396] : [member(_232392, inverse_image2(_232396, _232394)), 1072 ^ _191433 : [(1073 ^ _191433) ^ [] : [-(member(1071 ^ [_232392, _232394, _232396], _232394))], (1075 ^ _191433) ^ [] : [-(apply(_232396, _232392, 1071 ^ [_232392, _232394, _232396]))]]], (1077 ^ _191433) ^ [_232724, _232726, _232728] : [-(member(_232724, inverse_image2(_232728, _232726))), 1078 ^ _191433 : [(1079 ^ _191433) ^ [_232822] : [member(_232822, _232726), apply(_232728, _232724, _232822)]]], (1087 ^ _191433) ^ [_233166, _233168, _233170, _233172] : [member(_233166, inverse_image3(_233172, _233170, _233168)), 1090 ^ _191433 : [(1091 ^ _191433) ^ [] : [-(member(_233166, _233168))], (1094 ^ _191433) ^ [] : [-(member(1092 ^ [_233166, _233168, _233170, _233172], _233170))], (1096 ^ _191433) ^ [] : [-(apply(_233172, _233166, 1092 ^ [_233166, _233168, _233170, _233172]))]]], (1098 ^ _191433) ^ [_233594, _233596, _233598, _233600] : [-(member(_233594, inverse_image3(_233600, _233598, _233596))), member(_233594, _233596), 1103 ^ _191433 : [(1104 ^ _191433) ^ [_233788] : [member(_233788, _233598), apply(_233600, _233594, _233788)]]], (1146 ^ _191433) ^ [_235342, _235344, _235346, _235348, _235350] : [1151 ^ _191433 : [(1152 ^ _191433) ^ [] : [-(member(1147 ^ [_235342, _235344, _235346, _235348, _235350], _235348))], (1154 ^ _191433) ^ [] : [-(member(1148 ^ [_235342, _235344, _235346, _235348, _235350], _235344))], (1156 ^ _191433) ^ [] : [-(member(1149 ^ [_235342, _235344, _235346, _235348, _235350], _235348))], (1158 ^ _191433) ^ [] : [-(member(1150 ^ [_235342, _235344, _235346, _235348, _235350], _235344))], (1160 ^ _191433) ^ [] : [-(apply(_235346, 1147 ^ [_235342, _235344, _235346, _235348, _235350], 1149 ^ [_235342, _235344, _235346, _235348, _235350]))], (1162 ^ _191433) ^ [] : [-(apply(_235350, 1147 ^ [_235342, _235344, _235346, _235348, _235350], 1148 ^ [_235342, _235344, _235346, _235348, _235350]))], (1164 ^ _191433) ^ [] : [-(apply(_235350, 1149 ^ [_235342, _235344, _235346, _235348, _235350], 1150 ^ [_235342, _235344, _235346, _235348, _235350]))], (1166 ^ _191433) ^ [] : [apply(_235342, 1148 ^ [_235342, _235344, _235346, _235348, _235350], 1150 ^ [_235342, _235344, _235346, _235348, _235350])]], -(increasing(_235350, _235348, _235346, _235344, _235342))], (1112 ^ _191433) ^ [_234161, _234163, _234165, _234167, _234169] : [increasing(_234169, _234167, _234165, _234163, _234161), 1115 ^ _191433 : [(1116 ^ _191433) ^ [_234413, _234415, _234417, _234419] : [-(apply(_234161, _234417, _234413)), member(_234419, _234167), member(_234417, _234163), member(_234415, _234167), member(_234413, _234163), apply(_234165, _234419, _234415), apply(_234169, _234419, _234417), apply(_234169, _234415, _234413)]]], (1204 ^ _191433) ^ [_238263, _238265, _238267, _238269, _238271] : [1209 ^ _191433 : [(1210 ^ _191433) ^ [] : [-(member(1205 ^ [_238263, _238265, _238267, _238269, _238271], _238269))], (1212 ^ _191433) ^ [] : [-(member(1206 ^ [_238263, _238265, _238267, _238269, _238271], _238265))], (1214 ^ _191433) ^ [] : [-(member(1207 ^ [_238263, _238265, _238267, _238269, _238271], _238269))], (1216 ^ _191433) ^ [] : [-(member(1208 ^ [_238263, _238265, _238267, _238269, _238271], _238265))], (1218 ^ _191433) ^ [] : [-(apply(_238267, 1205 ^ [_238263, _238265, _238267, _238269, _238271], 1207 ^ [_238263, _238265, _238267, _238269, _238271]))], (1220 ^ _191433) ^ [] : [-(apply(_238271, 1205 ^ [_238263, _238265, _238267, _238269, _238271], 1206 ^ [_238263, _238265, _238267, _238269, _238271]))], (1222 ^ _191433) ^ [] : [-(apply(_238271, 1207 ^ [_238263, _238265, _238267, _238269, _238271], 1208 ^ [_238263, _238265, _238267, _238269, _238271]))], (1224 ^ _191433) ^ [] : [apply(_238263, 1208 ^ [_238263, _238265, _238267, _238269, _238271], 1206 ^ [_238263, _238265, _238267, _238269, _238271])]], -(decreasing(_238271, _238269, _238267, _238265, _238263))], (1170 ^ _191433) ^ [_237082, _237084, _237086, _237088, _237090] : [decreasing(_237090, _237088, _237086, _237084, _237082), 1173 ^ _191433 : [(1174 ^ _191433) ^ [_237334, _237336, _237338, _237340] : [-(apply(_237082, _237334, _237338)), member(_237340, _237088), member(_237338, _237084), member(_237336, _237088), member(_237334, _237084), apply(_237086, _237340, _237336), apply(_237090, _237340, _237338), apply(_237090, _237336, _237334)]]], (1272 ^ _191433) ^ [_241533, _241535, _241537, _241539, _241541] : [-(isomorphism(_241541, _241539, _241537, _241535, _241533)), maps(_241541, _241539, _241535), one_to_one(_241541, _241539, _241535), 1285 ^ _191433 : [(1286 ^ _191433) ^ [] : [-(member(1281 ^ [_241533, _241535, _241537, _241539, _241541], _241539))], (1288 ^ _191433) ^ [] : [-(member(1282 ^ [_241533, _241535, _241537, _241539, _241541], _241535))], (1290 ^ _191433) ^ [] : [-(member(1283 ^ [_241533, _241535, _241537, _241539, _241541], _241539))], (1292 ^ _191433) ^ [] : [-(member(1284 ^ [_241533, _241535, _241537, _241539, _241541], _241535))], (1294 ^ _191433) ^ [] : [-(apply(_241541, 1281 ^ [_241533, _241535, _241537, _241539, _241541], 1282 ^ [_241533, _241535, _241537, _241539, _241541]))], (1296 ^ _191433) ^ [] : [-(apply(_241541, 1283 ^ [_241533, _241535, _241537, _241539, _241541], 1284 ^ [_241533, _241535, _241537, _241539, _241541]))], (1298 ^ _191433) ^ [] : [1299 ^ _191433 : [(1300 ^ _191433) ^ [] : [-(apply(_241537, 1281 ^ [_241533, _241535, _241537, _241539, _241541], 1283 ^ [_241533, _241535, _241537, _241539, _241541]))], (1302 ^ _191433) ^ [] : [apply(_241533, 1282 ^ [_241533, _241535, _241537, _241539, _241541], 1284 ^ [_241533, _241535, _241537, _241539, _241541])]], 1303 ^ _191433 : [(1304 ^ _191433) ^ [] : [-(apply(_241533, 1282 ^ [_241533, _241535, _241537, _241539, _241541], 1284 ^ [_241533, _241535, _241537, _241539, _241541]))], (1306 ^ _191433) ^ [] : [apply(_241537, 1281 ^ [_241533, _241535, _241537, _241539, _241541], 1283 ^ [_241533, _241535, _241537, _241539, _241541])]]]]], (1228 ^ _191433) ^ [_239983, _239985, _239987, _239989, _239991] : [isomorphism(_239991, _239989, _239987, _239985, _239983), 1231 ^ _191433 : [(1232 ^ _191433) ^ [] : [-(maps(_239991, _239989, _239985))], (1234 ^ _191433) ^ [] : [-(one_to_one(_239991, _239989, _239985))], (1236 ^ _191433) ^ [_240395, _240397, _240399, _240401] : [1259 ^ _191433 : [(1260 ^ _191433) ^ [] : [apply(_239987, _240401, _240397), -(apply(_239983, _240399, _240395))], (1266 ^ _191433) ^ [] : [apply(_239983, _240399, _240395), -(apply(_239987, _240401, _240397))]], member(_240401, _239989), member(_240399, _239985), member(_240397, _239989), member(_240395, _239985), apply(_239991, _240401, _240399), apply(_239991, _240397, _240395)]]]], input).
% 16.04/15.85 ncf('1',plain,[surjective(1310 ^ [], 1311 ^ [], 1312 ^ [])],start(1320 ^ 0)).
% 16.04/15.85 ncf('1.1',plain,[-(surjective(1310 ^ [], 1311 ^ [], 1312 ^ [])), 934 : member(785 ^ [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [], 1311 ^ [], 1312 ^ [], 1309 ^ [], 1310 ^ []], 1311 ^ []), 934 : apply(1310 ^ [], 785 ^ [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [], 1311 ^ [], 1312 ^ [], 1309 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []])],extension(929 ^ 1,bind([[_226980, _226982, _226984, _227231], [1312 ^ [], 1311 ^ [], 1310 ^ [], 785 ^ [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [], 1311 ^ [], 1312 ^ [], 1309 ^ [], 1310 ^ []]]]))).
% 16.04/15.85 ncf('1.1.1',plain,[-(member(785 ^ [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [], 1311 ^ [], 1312 ^ [], 1309 ^ [], 1310 ^ []], 1311 ^ [])), 782 : apply(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]), 782 : member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []), 782 : member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [])],extension(774 ^ 4,bind([[_220496, _220498, _220500, _220502, _220504, _220506, _220508], [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [], 1311 ^ [], 1312 ^ [], 1309 ^ [], 1310 ^ []]]))).
% 16.04/15.85 ncf('1.1.1.1',plain,[-(apply(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []])), 856 : member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []), 856 : identity(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 1312 ^ [])],extension(852 ^ 7,bind([[_223824, _223826, _223962], [1312 ^ [], compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]]]))).
% 16.04/15.85 ncf('1.1.1.1.1',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []))],extension(932 ^ 10)).
% 16.04/15.85 ncf('1.1.1.1.2',plain,[-(identity(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 1312 ^ []))],extension(1318 ^ 8)).
% 16.04/15.85 ncf('1.1.1.2',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [])), member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []] = 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [] = 1312 ^ []],extension(236 ^ 5,bind([[_200076, _200078, _200080, _200082], [1312 ^ [], 1312 ^ [], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]]]))).
% 16.04/15.85 ncf('1.1.1.2.1',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []))],extension(932 ^ 6)).
% 16.04/15.85 ncf('1.1.1.2.2',plain,[-(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []] = 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []])],extension(2 ^ 6,bind([[_191577], [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]]]))).
% 16.04/15.85 ncf('1.1.1.2.3',plain,[-(1312 ^ [] = 1312 ^ [])],extension(2 ^ 6,bind([[_191577], [1312 ^ []]]))).
% 16.04/15.85 ncf('1.1.1.3',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []))],lemmata('[1, 1].x')).
% 16.04/15.85 ncf('1.1.2',plain,[-(apply(1310 ^ [], 785 ^ [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [], 1311 ^ [], 1312 ^ [], 1309 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []])), 782 : apply(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]), 782 : member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []), 782 : member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [])],extension(774 ^ 4,bind([[_220496, _220498, _220500, _220502, _220504, _220506, _220508], [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [], 1311 ^ [], 1312 ^ [], 1309 ^ [], 1310 ^ []]]))).
% 16.04/15.85 ncf('1.1.2.1',plain,[-(apply(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []])), 856 : member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []), 856 : identity(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 1312 ^ [])],extension(852 ^ 7,bind([[_223824, _223826, _223962], [1312 ^ [], compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]]]))).
% 16.04/15.85 ncf('1.1.2.1.1',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []))],extension(932 ^ 10)).
% 16.04/15.85 ncf('1.1.2.1.2',plain,[-(identity(compose_function(1310 ^ [], 1309 ^ [], 1312 ^ [], 1311 ^ [], 1312 ^ []), 1312 ^ []))],extension(1318 ^ 8)).
% 16.04/15.85 ncf('1.1.2.2',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [])), member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []), 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []] = 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ [] = 1312 ^ []],extension(236 ^ 5,bind([[_200076, _200078, _200080, _200082], [1312 ^ [], 1312 ^ [], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]]]))).
% 16.04/15.85 ncf('1.1.2.2.1',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []))],extension(932 ^ 6)).
% 16.04/15.85 ncf('1.1.2.2.2',plain,[-(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []] = 930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []])],extension(2 ^ 6,bind([[_191577], [930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []]]]))).
% 16.04/15.85 ncf('1.1.2.2.3',plain,[-(1312 ^ [] = 1312 ^ [])],extension(2 ^ 6,bind([[_191577], [1312 ^ []]]))).
% 16.04/15.85 ncf('1.1.2.3',plain,[-(member(930 ^ [1312 ^ [], 1311 ^ [], 1310 ^ []], 1312 ^ []))],lemmata('[1, 1].x')).
% 16.04/15.85 %-----------------------------------------------------
% 16.04/15.85 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------