%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n007.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 11:56:24 EDT 2023

% Result   : Theorem 5.25s 5.52s
% Output   : Proof 5.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.13/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May 18 19:03:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 5.25/5.52  
% 5.25/5.52  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 5.25/5.52  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.25/5.52  %-----------------------------------------------------
% 5.25/5.52  ncf(matrix, plain, [(1313 ^ _185809) ^ [] : [-(maps(1309 ^ [], 1310 ^ [], 1311 ^ []))], (1315 ^ _185809) ^ [] : [equal_set(inverse_image2(1309 ^ [], empty_set), empty_set)], (318 ^ _185809) ^ [_197197, _197199] : [_197199 = _197197, -(power_set(_197199) = power_set(_197197))], (324 ^ _185809) ^ [_197443, _197445, _197447, _197449] : [-(intersection(_197449, _197445) = intersection(_197447, _197443)), _197449 = _197447, _197445 = _197443], (334 ^ _185809) ^ [_197802, _197804, _197806, _197808] : [-(union(_197808, _197804) = union(_197806, _197802)), _197808 = _197806, _197804 = _197802], (344 ^ _185809) ^ [_198161, _198163, _198165, _198167] : [-(difference(_198167, _198163) = difference(_198165, _198161)), _198167 = _198165, _198163 = _198161], (354 ^ _185809) ^ [_198492, _198494] : [_198494 = _198492, -(singleton(_198494) = singleton(_198492))], (360 ^ _185809) ^ [_198738, _198740, _198742, _198744] : [-(unordered_pair(_198744, _198740) = unordered_pair(_198742, _198738)), _198744 = _198742, _198740 = _198738], (370 ^ _185809) ^ [_199069, _199071] : [_199071 = _199069, -(sum(_199071) = sum(_199069))], (376 ^ _185809) ^ [_199287, _199289] : [_199289 = _199287, -(product(_199289) = product(_199287))], (382 ^ _185809) ^ [_199617, _199619, _199621, _199623, _199625, _199627, _199629, _199631, _199633, _199635] : [-(compose_function(_199635, _199631, _199627, _199623, _199619) = compose_function(_199633, _199629, _199625, _199621, _199617)), _199635 = _199633, _199631 = _199629, _199627 = _199625, _199623 = _199621, _199619 = _199617], (404 ^ _185809) ^ [_200439, _200441, _200443, _200445, _200447, _200449] : [-(inverse_function(_200449, _200445, _200441) = inverse_function(_200447, _200443, _200439)), _200449 = _200447, _200445 = _200443, _200441 = _200439], (418 ^ _185809) ^ [_200927, _200929, _200931, _200933] : [-(image2(_200933, _200929) = image2(_200931, _200927)), _200933 = _200931, _200929 = _200927], (428 ^ _185809) ^ [_201314, _201316, _201318, _201320, _201322, _201324] : [-(image3(_201324, _201320, _201316) = image3(_201322, _201318, _201314)), _201324 = _201322, _201320 = _201318, _201316 = _201314], (456 ^ _185809) ^ [_202298, _202300, _202302, _202304] : [-(inverse_image2(_202304, _202300) = inverse_image2(_202302, _202298)), _202304 = _202302, _202300 = _202298], (442 ^ _185809) ^ [_201830, _201832, _201834, _201836, _201838, _201840] : [-(inverse_image3(_201840, _201836, _201832) = inverse_image3(_201838, _201834, _201830)), _201840 = _201838, _201836 = _201834, _201832 = _201830], (2 ^ _185809) ^ [_185953] : [-(_185953 = _185953)], (4 ^ _185809) ^ [_186060, _186062] : [_186062 = _186060, -(_186060 = _186062)], (10 ^ _185809) ^ [_186264, _186266, _186268] : [-(_186268 = _186264), _186268 = _186266, _186266 = _186264], (20 ^ _185809) ^ [_186605, _186607, _186609, _186611] : [-(subset(_186609, _186605)), subset(_186611, _186607), _186611 = _186609, _186607 = _186605], (34 ^ _185809) ^ [_187161, _187163, _187165, _187167, _187169, _187171, _187173, _187175, _187177, _187179, _187181, _187183] : [-(compose_predicate(_187181, _187177, _187173, _187169, _187165, _187161)), compose_predicate(_187183, _187179, _187175, _187171, _187167, _187163), _187183 = _187181, _187179 = _187177, _187175 = _187173, _187171 = _187169, _187167 = _187165, _187163 = _187161], (64 ^ _185809) ^ [_188305, _188307, _188309, _188311, _188313, _188315, _188317, _188319] : [-(equal_maps(_188317, _188313, _188309, _188305)), equal_maps(_188319, _188315, _188311, _188307), _188319 = _188317, _188315 = _188313, _188311 = _188309, _188307 = _188305], (86 ^ _185809) ^ [_189039, _189041, _189043, _189045] : [-(identity(_189043, _189039)), identity(_189045, _189041), _189045 = _189043, _189041 = _189039], (100 ^ _185809) ^ [_189511, _189513, _189515, _189517, _189519, _189521] : [-(injective(_189519, _189515, _189511)), injective(_189521, _189517, _189513), _189521 = _189519, _189517 = _189515, _189513 = _189511], (118 ^ _185809) ^ [_190120, _190122, _190124, _190126, _190128, _190130] : [-(surjective(_190128, _190124, _190120)), surjective(_190130, _190126, _190122), _190130 = _190128, _190126 = _190124, _190122 = _190120], (136 ^ _185809) ^ [_190757, _190759, _190761, _190763, _190765, _190767, _190769, _190771] : [-(inverse_predicate(_190769, _190765, _190761, _190757)), inverse_predicate(_190771, _190767, _190763, _190759), _190771 = _190769, _190767 = _190765, _190763 = _190761, _190759 = _190757], (158 ^ _185809) ^ [_191575, _191577, _191579, _191581, _191583, _191585, _191587, _191589, _191591, _191593] : [-(increasing(_191591, _191587, _191583, _191579, _191575)), increasing(_191593, _191589, _191585, _191581, _191577), _191593 = _191591, _191589 = _191587, _191585 = _191583, _191581 = _191579, _191577 = _191575], (184 ^ _185809) ^ [_192562, _192564, _192566, _192568, _192570, _192572, _192574, _192576, _192578, _192580] : [-(decreasing(_192578, _192574, _192570, _192566, _192562)), decreasing(_192580, _192576, _192572, _192568, _192564), _192580 = _192578, _192576 = _192574, _192572 = _192570, _192568 = _192566, _192564 = _192562], (210 ^ _185809) ^ [_193549, _193551, _193553, _193555, _193557, _193559, _193561, _193563, _193565, _193567] : [-(isomorphism(_193565, _193561, _193557, _193553, _193549)), isomorphism(_193567, _193563, _193559, _193555, _193551), _193567 = _193565, _193563 = _193561, _193559 = _193557, _193555 = _193553, _193551 = _193549], (236 ^ _185809) ^ [_194480, _194482, _194484, _194486, _194488, _194490] : [-(one_to_one(_194488, _194484, _194480)), one_to_one(_194490, _194486, _194482), _194490 = _194488, _194486 = _194484, _194482 = _194480], (254 ^ _185809) ^ [_195061, _195063, _195065, _195067] : [-(member(_195065, _195061)), member(_195067, _195063), _195067 = _195065, _195063 = _195061], (268 ^ _185809) ^ [_195533, _195535, _195537, _195539, _195541, _195543] : [-(apply(_195541, _195537, _195533)), apply(_195543, _195539, _195535), _195543 = _195541, _195539 = _195537, _195535 = _195533], (304 ^ _185809) ^ [_196703, _196705, _196707, _196709] : [-(equal_set(_196707, _196703)), equal_set(_196709, _196705), _196709 = _196707, _196705 = _196703], (286 ^ _185809) ^ [_196142, _196144, _196146, _196148, _196150, _196152] : [-(maps(_196150, _196146, _196142)), maps(_196152, _196148, _196144), _196152 = _196150, _196148 = _196146, _196144 = _196142], (476 ^ _185809) ^ [_203050, _203052] : [478 ^ _185809 : [(479 ^ _185809) ^ [] : [-(member(477 ^ [_203050, _203052], _203052))], (481 ^ _185809) ^ [] : [member(477 ^ [_203050, _203052], _203050)]], -(subset(_203052, _203050))], (466 ^ _185809) ^ [_202736, _202738] : [subset(_202738, _202736), 469 ^ _185809 : [(470 ^ _185809) ^ [_202873] : [member(_202873, _202738), -(member(_202873, _202736))]]], (485 ^ _185809) ^ [_203436, _203438] : [equal_set(_203438, _203436), 488 ^ _185809 : [(489 ^ _185809) ^ [] : [-(subset(_203438, _203436))], (491 ^ _185809) ^ [] : [-(subset(_203436, _203438))]]], (493 ^ _185809) ^ [_203673, _203675] : [-(equal_set(_203675, _203673)), subset(_203675, _203673), subset(_203673, _203675)], (503 ^ _185809) ^ [_204003, _204005] : [member(_204005, power_set(_204003)), -(subset(_204005, _204003))], (509 ^ _185809) ^ [_204169, _204171] : [subset(_204171, _204169), -(member(_204171, power_set(_204169)))], (515 ^ _185809) ^ [_204428, _204430, _204432] : [member(_204432, intersection(_204430, _204428)), 518 ^ _185809 : [(519 ^ _185809) ^ [] : [-(member(_204432, _204430))], (521 ^ _185809) ^ [] : [-(member(_204432, _204428))]]], (523 ^ _185809) ^ [_204679, _204681, _204683] : [-(member(_204683, intersection(_204681, _204679))), member(_204683, _204681), member(_204683, _204679)], (543 ^ _185809) ^ [_205307, _205309, _205311] : [544 ^ _185809 : [(545 ^ _185809) ^ [] : [member(_205311, _205309)], (547 ^ _185809) ^ [] : [member(_205311, _205307)]], -(member(_205311, union(_205309, _205307)))], (533 ^ _185809) ^ [_205039, _205041, _205043] : [member(_205043, union(_205041, _205039)), -(member(_205043, _205041)), -(member(_205043, _205039))], (551 ^ _185809) ^ [_205577] : [member(_205577, empty_set)], (553 ^ _185809) ^ [_205727, _205729, _205731] : [member(_205731, difference(_205727, _205729)), 556 ^ _185809 : [(557 ^ _185809) ^ [] : [-(member(_205731, _205727))], (559 ^ _185809) ^ [] : [member(_205731, _205729)]]], (561 ^ _185809) ^ [_205979, _205981, _205983] : [-(member(_205983, difference(_205979, _205981))), member(_205983, _205979), -(member(_205983, _205981))], (571 ^ _185809) ^ [_206328, _206330] : [member(_206330, singleton(_206328)), -(_206330 = _206328)], (577 ^ _185809) ^ [_206494, _206496] : [_206496 = _206494, -(member(_206496, singleton(_206494)))], (593 ^ _185809) ^ [_207021, _207023, _207025] : [594 ^ _185809 : [(595 ^ _185809) ^ [] : [_207025 = _207023], (597 ^ _185809) ^ [] : [_207025 = _207021]], -(member(_207025, unordered_pair(_207023, _207021)))], (583 ^ _185809) ^ [_206753, _206755, _206757] : [member(_206757, unordered_pair(_206755, _206753)), -(_206757 = _206755), -(_206757 = _206753)], (601 ^ _185809) ^ [_207350, _207352] : [member(_207352, sum(_207350)), 605 ^ _185809 : [(606 ^ _185809) ^ [] : [-(member(604 ^ [_207350, _207352], _207350))], (608 ^ _185809) ^ [] : [-(member(_207352, 604 ^ [_207350, _207352]))]]], (610 ^ _185809) ^ [_207661, _207663] : [-(member(_207663, sum(_207661))), 611 ^ _185809 : [(612 ^ _185809) ^ [_207755] : [member(_207755, _207661), member(_207663, _207755)]]], (630 ^ _185809) ^ [_208356, _208358] : [632 ^ _185809 : [(633 ^ _185809) ^ [] : [-(member(631 ^ [_208356, _208358], _208356))], (635 ^ _185809) ^ [] : [member(_208358, 631 ^ [_208356, _208358])]], -(member(_208358, product(_208356)))], (620 ^ _185809) ^ [_208038, _208040] : [member(_208040, product(_208038)), 623 ^ _185809 : [(624 ^ _185809) ^ [_208179] : [member(_208179, _208038), -(member(_208040, _208179))]]], (674 ^ _185809) ^ [_210043, _210045, _210047] : [-(maps(_210047, _210045, _210043)), 689 ^ _185809 : [(690 ^ _185809) ^ [] : [-(member(686 ^ [_210043, _210045, _210047], _210045))], (692 ^ _185809) ^ [] : [-(member(687 ^ [_210043, _210045, _210047], _210043))], (694 ^ _185809) ^ [] : [-(member(688 ^ [_210043, _210045, _210047], _210043))], (696 ^ _185809) ^ [] : [-(apply(_210047, 686 ^ [_210043, _210045, _210047], 687 ^ [_210043, _210045, _210047]))], (698 ^ _185809) ^ [] : [-(apply(_210047, 686 ^ [_210043, _210045, _210047], 688 ^ [_210043, _210045, _210047]))], (700 ^ _185809) ^ [] : [687 ^ [_210043, _210045, _210047] = 688 ^ [_210043, _210045, _210047]]], 678 ^ _185809 : [(679 ^ _185809) ^ [] : [-(member(677 ^ [_210043, _210045, _210047], _210045))], (681 ^ _185809) ^ [_210383] : [member(_210383, _210043), apply(_210047, 677 ^ [_210043, _210045, _210047], _210383)]]], (639 ^ _185809) ^ [_208798, _208800, _208802] : [maps(_208802, _208800, _208798), 642 ^ _185809 : [(643 ^ _185809) ^ [_209026] : [member(_209026, _208800), 647 ^ _185809 : [(648 ^ _185809) ^ [] : [-(member(646 ^ [_208798, _208800, _208802, _209026], _208798))], (650 ^ _185809) ^ [] : [-(apply(_208802, _209026, 646 ^ [_208798, _208800, _208802, _209026]))]]], (652 ^ _185809) ^ [_209416, _209418, _209420] : [member(_209420, _208800), member(_209418, _208798), member(_209416, _208798), -(_209418 = _209416), apply(_208802, _209420, _209418), apply(_208802, _209420, _209416)]]], (741 ^ _185809) ^ [_213078, _213080, _213082, _213084, _213086, _213088] : [-(compose_predicate(_213088, _213086, _213084, _213082, _213080, _213078)), 744 ^ _185809 : [(745 ^ _185809) ^ [] : [-(member(742 ^ [_213078, _213080, _213082, _213084, _213086, _213088], _213082))], (747 ^ _185809) ^ [] : [-(member(743 ^ [_213078, _213080, _213082, _213084, _213086, _213088], _213078))], (749 ^ _185809) ^ [] : [763 ^ _185809 : [(764 ^ _185809) ^ [] : [-(member(762 ^ [_213078, _213080, _213082, _213084, _213086, _213088], _213080))], (766 ^ _185809) ^ [] : [-(apply(_213084, 742 ^ [_213078, _213080, _213082, _213084, _213086, _213088], 762 ^ [_213078, _213080, _213082, _213084, _213086, _213088]))], (768 ^ _185809) ^ [] : [-(apply(_213086, 762 ^ [_213078, _213080, _213082, _213084, _213086, _213088], 743 ^ [_213078, _213080, _213082, _213084, _213086, _213088]))], (770 ^ _185809) ^ [] : [apply(_213088, 742 ^ [_213078, _213080, _213082, _213084, _213086, _213088], 743 ^ [_213078, _213080, _213082, _213084, _213086, _213088])]], 750 ^ _185809 : [(751 ^ _185809) ^ [] : [-(apply(_213088, 742 ^ [_213078, _213080, _213082, _213084, _213086, _213088], 743 ^ [_213078, _213080, _213082, _213084, _213086, _213088]))], (753 ^ _185809) ^ [_213803] : [member(_213803, _213080), apply(_213084, 742 ^ [_213078, _213080, _213082, _213084, _213086, _213088], _213803), apply(_213086, _213803, 743 ^ [_213078, _213080, _213082, _213084, _213086, _213088])]]]]], (704 ^ _185809) ^ [_211603, _211605, _211607, _211609, _211611, _211613] : [compose_predicate(_211613, _211611, _211609, _211607, _211605, _211603), 707 ^ _185809 : [(708 ^ _185809) ^ [_211815, _211817] : [member(_211817, _211607), member(_211815, _211603), 715 ^ _185809 : [(716 ^ _185809) ^ [] : [apply(_211613, _211817, _211815), 720 ^ _185809 : [(721 ^ _185809) ^ [] : [-(member(719 ^ [_211603, _211605, _211607, _211609, _211611, _211613, _211815, _211817], _211605))], (723 ^ _185809) ^ [] : [-(apply(_211609, _211817, 719 ^ [_211603, _211605, _211607, _211609, _211611, _211613, _211815, _211817]))], (725 ^ _185809) ^ [] : [-(apply(_211611, 719 ^ [_211603, _211605, _211607, _211609, _211611, _211613, _211815, _211817], _211815))]]], (727 ^ _185809) ^ [] : [-(apply(_211613, _211817, _211815)), 728 ^ _185809 : [(729 ^ _185809) ^ [_212660] : [member(_212660, _211605), apply(_211609, _211817, _212660), apply(_211611, _212660, _211815)]]]]]]], (774 ^ _185809) ^ [_214872, _214874, _214876, _214878, _214880, _214882, _214884] : [member(_214874, _214880), member(_214872, _214876), 781 ^ _185809 : [(782 ^ _185809) ^ [] : [apply(compose_function(_214884, _214882, _214880, _214878, _214876), _214874, _214872), 786 ^ _185809 : [(787 ^ _185809) ^ [] : [-(member(785 ^ [_214872, _214874, _214876, _214878, _214880, _214882, _214884], _214878))], (789 ^ _185809) ^ [] : [-(apply(_214882, _214874, 785 ^ [_214872, _214874, _214876, _214878, _214880, _214882, _214884]))], (791 ^ _185809) ^ [] : [-(apply(_214884, 785 ^ [_214872, _214874, _214876, _214878, _214880, _214882, _214884], _214872))]]], (793 ^ _185809) ^ [] : [-(apply(compose_function(_214884, _214882, _214880, _214878, _214876), _214874, _214872)), 794 ^ _185809 : [(795 ^ _185809) ^ [_215687] : [member(_215687, _214878), apply(_214882, _214874, _215687), apply(_214884, _215687, _214872)]]]]], (833 ^ _185809) ^ [_217059, _217061, _217063, _217065] : [837 ^ _185809 : [(838 ^ _185809) ^ [] : [-(member(834 ^ [_217059, _217061, _217063, _217065], _217061))], (840 ^ _185809) ^ [] : [-(member(835 ^ [_217059, _217061, _217063, _217065], _217059))], (842 ^ _185809) ^ [] : [-(member(836 ^ [_217059, _217061, _217063, _217065], _217059))], (844 ^ _185809) ^ [] : [-(apply(_217065, 834 ^ [_217059, _217061, _217063, _217065], 835 ^ [_217059, _217061, _217063, _217065]))], (846 ^ _185809) ^ [] : [-(apply(_217063, 834 ^ [_217059, _217061, _217063, _217065], 836 ^ [_217059, _217061, _217063, _217065]))], (848 ^ _185809) ^ [] : [835 ^ [_217059, _217061, _217063, _217065] = 836 ^ [_217059, _217061, _217063, _217065]]], -(equal_maps(_217065, _217063, _217061, _217059))], (807 ^ _185809) ^ [_216197, _216199, _216201, _216203] : [equal_maps(_216203, _216201, _216199, _216197), 810 ^ _185809 : [(811 ^ _185809) ^ [_216410, _216412, _216414] : [member(_216414, _216199), member(_216412, _216197), member(_216410, _216197), -(_216412 = _216410), apply(_216203, _216414, _216412), apply(_216201, _216414, _216410)]]], (862 ^ _185809) ^ [_218517, _218519] : [864 ^ _185809 : [(865 ^ _185809) ^ [] : [-(member(863 ^ [_218517, _218519], _218517))], (867 ^ _185809) ^ [] : [apply(_218519, 863 ^ [_218517, _218519], 863 ^ [_218517, _218519])]], -(identity(_218519, _218517))], (852 ^ _185809) ^ [_218200, _218202] : [identity(_218202, _218200), 855 ^ _185809 : [(856 ^ _185809) ^ [_218338] : [member(_218338, _218200), -(apply(_218202, _218338, _218338))]]], (897 ^ _185809) ^ [_219759, _219761, _219763] : [901 ^ _185809 : [(902 ^ _185809) ^ [] : [-(member(898 ^ [_219759, _219761, _219763], _219761))], (904 ^ _185809) ^ [] : [-(member(899 ^ [_219759, _219761, _219763], _219761))], (906 ^ _185809) ^ [] : [-(member(900 ^ [_219759, _219761, _219763], _219759))], (908 ^ _185809) ^ [] : [-(apply(_219763, 898 ^ [_219759, _219761, _219763], 900 ^ [_219759, _219761, _219763]))], (910 ^ _185809) ^ [] : [-(apply(_219763, 899 ^ [_219759, _219761, _219763], 900 ^ [_219759, _219761, _219763]))], (912 ^ _185809) ^ [] : [898 ^ [_219759, _219761, _219763] = 899 ^ [_219759, _219761, _219763]]], -(injective(_219763, _219761, _219759))], (871 ^ _185809) ^ [_218927, _218929, _218931] : [injective(_218931, _218929, _218927), 874 ^ _185809 : [(875 ^ _185809) ^ [_219134, _219136, _219138] : [member(_219138, _218929), member(_219136, _218929), member(_219134, _218927), -(_219138 = _219136), apply(_218931, _219138, _219134), apply(_218931, _219136, _219134)]]], (916 ^ _185809) ^ [_220848, _220850, _220852] : [surjective(_220852, _220850, _220848), 919 ^ _185809 : [(920 ^ _185809) ^ [_221003] : [member(_221003, _220848), 924 ^ _185809 : [(925 ^ _185809) ^ [] : [-(member(923 ^ [_220848, _220850, _220852, _221003], _220850))], (927 ^ _185809) ^ [] : [-(apply(_220852, 923 ^ [_220848, _220850, _220852, _221003], _221003))]]]]], (929 ^ _185809) ^ [_221356, _221358, _221360] : [-(surjective(_221360, _221358, _221356)), 931 ^ _185809 : [(932 ^ _185809) ^ [] : [-(member(930 ^ [_221356, _221358, _221360], _221356))], (934 ^ _185809) ^ [_221607] : [member(_221607, _221358), apply(_221360, _221607, 930 ^ [_221356, _221358, _221360])]]], (942 ^ _185809) ^ [_221955, _221957, _221959] : [one_to_one(_221959, _221957, _221955), 945 ^ _185809 : [(946 ^ _185809) ^ [] : [-(injective(_221959, _221957, _221955))], (948 ^ _185809) ^ [] : [-(surjective(_221959, _221957, _221955))]]], (950 ^ _185809) ^ [_222206, _222208, _222210] : [-(one_to_one(_222210, _222208, _222206)), injective(_222210, _222208, _222206), surjective(_222210, _222208, _222206)], (984 ^ _185809) ^ [_223364, _223366, _223368, _223370] : [-(inverse_predicate(_223370, _223368, _223366, _223364)), 987 ^ _185809 : [(988 ^ _185809) ^ [] : [-(member(985 ^ [_223364, _223366, _223368, _223370], _223366))], (990 ^ _185809) ^ [] : [-(member(986 ^ [_223364, _223366, _223368, _223370], _223364))], (992 ^ _185809) ^ [] : [993 ^ _185809 : [(994 ^ _185809) ^ [] : [-(apply(_223368, 985 ^ [_223364, _223366, _223368, _223370], 986 ^ [_223364, _223366, _223368, _223370]))], (996 ^ _185809) ^ [] : [apply(_223370, 986 ^ [_223364, _223366, _223368, _223370], 985 ^ [_223364, _223366, _223368, _223370])]], 997 ^ _185809 : [(998 ^ _185809) ^ [] : [-(apply(_223370, 986 ^ [_223364, _223366, _223368, _223370], 985 ^ [_223364, _223366, _223368, _223370]))], (1000 ^ _185809) ^ [] : [apply(_223368, 985 ^ [_223364, _223366, _223368, _223370], 986 ^ [_223364, _223366, _223368, _223370])]]]]], (960 ^ _185809) ^ [_222580, _222582, _222584, _222586] : [inverse_predicate(_222586, _222584, _222582, _222580), 963 ^ _185809 : [(964 ^ _185809) ^ [_222762, _222764] : [member(_222764, _222582), member(_222762, _222580), 971 ^ _185809 : [(972 ^ _185809) ^ [] : [apply(_222584, _222764, _222762), -(apply(_222586, _222762, _222764))], (978 ^ _185809) ^ [] : [apply(_222586, _222762, _222764), -(apply(_222584, _222764, _222762))]]]]], (1004 ^ _185809) ^ [_224355, _224357, _224359, _224361, _224363] : [member(_224357, _224361), member(_224355, _224359), 1011 ^ _185809 : [(1012 ^ _185809) ^ [] : [apply(_224363, _224357, _224355), -(apply(inverse_function(_224363, _224361, _224359), _224355, _224357))], (1018 ^ _185809) ^ [] : [apply(inverse_function(_224363, _224361, _224359), _224355, _224357), -(apply(_224363, _224357, _224355))]]], (1024 ^ _185809) ^ [_225027, _225029, _225031] : [member(_225027, image2(_225031, _225029)), 1028 ^ _185809 : [(1029 ^ _185809) ^ [] : [-(member(1027 ^ [_225027, _225029, _225031], _225029))], (1031 ^ _185809) ^ [] : [-(apply(_225031, 1027 ^ [_225027, _225029, _225031], _225027))]]], (1033 ^ _185809) ^ [_225359, _225361, _225363] : [-(member(_225359, image2(_225363, _225361))), 1034 ^ _185809 : [(1035 ^ _185809) ^ [_225457] : [member(_225457, _225361), apply(_225363, _225457, _225359)]]], (1043 ^ _185809) ^ [_225801, _225803, _225805, _225807] : [member(_225801, image3(_225807, _225805, _225803)), 1046 ^ _185809 : [(1047 ^ _185809) ^ [] : [-(member(_225801, _225803))], (1050 ^ _185809) ^ [] : [-(member(1048 ^ [_225801, _225803, _225805, _225807], _225805))], (1052 ^ _185809) ^ [] : [-(apply(_225807, 1048 ^ [_225801, _225803, _225805, _225807], _225801))]]], (1054 ^ _185809) ^ [_226229, _226231, _226233, _226235] : [-(member(_226229, image3(_226235, _226233, _226231))), member(_226229, _226231), 1059 ^ _185809 : [(1060 ^ _185809) ^ [_226423] : [member(_226423, _226233), apply(_226235, _226423, _226229)]]], (1068 ^ _185809) ^ [_226768, _226770, _226772] : [member(_226768, inverse_image2(_226772, _226770)), 1072 ^ _185809 : [(1073 ^ _185809) ^ [] : [-(member(1071 ^ [_226768, _226770, _226772], _226770))], (1075 ^ _185809) ^ [] : [-(apply(_226772, _226768, 1071 ^ [_226768, _226770, _226772]))]]], (1077 ^ _185809) ^ [_227100, _227102, _227104] : [-(member(_227100, inverse_image2(_227104, _227102))), 1078 ^ _185809 : [(1079 ^ _185809) ^ [_227198] : [member(_227198, _227102), apply(_227104, _227100, _227198)]]], (1087 ^ _185809) ^ [_227542, _227544, _227546, _227548] : [member(_227542, inverse_image3(_227548, _227546, _227544)), 1090 ^ _185809 : [(1091 ^ _185809) ^ [] : [-(member(_227542, _227544))], (1094 ^ _185809) ^ [] : [-(member(1092 ^ [_227542, _227544, _227546, _227548], _227546))], (1096 ^ _185809) ^ [] : [-(apply(_227548, _227542, 1092 ^ [_227542, _227544, _227546, _227548]))]]], (1098 ^ _185809) ^ [_227970, _227972, _227974, _227976] : [-(member(_227970, inverse_image3(_227976, _227974, _227972))), member(_227970, _227972), 1103 ^ _185809 : [(1104 ^ _185809) ^ [_228164] : [member(_228164, _227974), apply(_227976, _227970, _228164)]]], (1146 ^ _185809) ^ [_229718, _229720, _229722, _229724, _229726] : [1151 ^ _185809 : [(1152 ^ _185809) ^ [] : [-(member(1147 ^ [_229718, _229720, _229722, _229724, _229726], _229724))], (1154 ^ _185809) ^ [] : [-(member(1148 ^ [_229718, _229720, _229722, _229724, _229726], _229720))], (1156 ^ _185809) ^ [] : [-(member(1149 ^ [_229718, _229720, _229722, _229724, _229726], _229724))], (1158 ^ _185809) ^ [] : [-(member(1150 ^ [_229718, _229720, _229722, _229724, _229726], _229720))], (1160 ^ _185809) ^ [] : [-(apply(_229722, 1147 ^ [_229718, _229720, _229722, _229724, _229726], 1149 ^ [_229718, _229720, _229722, _229724, _229726]))], (1162 ^ _185809) ^ [] : [-(apply(_229726, 1147 ^ [_229718, _229720, _229722, _229724, _229726], 1148 ^ [_229718, _229720, _229722, _229724, _229726]))], (1164 ^ _185809) ^ [] : [-(apply(_229726, 1149 ^ [_229718, _229720, _229722, _229724, _229726], 1150 ^ [_229718, _229720, _229722, _229724, _229726]))], (1166 ^ _185809) ^ [] : [apply(_229718, 1148 ^ [_229718, _229720, _229722, _229724, _229726], 1150 ^ [_229718, _229720, _229722, _229724, _229726])]], -(increasing(_229726, _229724, _229722, _229720, _229718))], (1112 ^ _185809) ^ [_228537, _228539, _228541, _228543, _228545] : [increasing(_228545, _228543, _228541, _228539, _228537), 1115 ^ _185809 : [(1116 ^ _185809) ^ [_228789, _228791, _228793, _228795] : [-(apply(_228537, _228793, _228789)), member(_228795, _228543), member(_228793, _228539), member(_228791, _228543), member(_228789, _228539), apply(_228541, _228795, _228791), apply(_228545, _228795, _228793), apply(_228545, _228791, _228789)]]], (1204 ^ _185809) ^ [_232639, _232641, _232643, _232645, _232647] : [1209 ^ _185809 : [(1210 ^ _185809) ^ [] : [-(member(1205 ^ [_232639, _232641, _232643, _232645, _232647], _232645))], (1212 ^ _185809) ^ [] : [-(member(1206 ^ [_232639, _232641, _232643, _232645, _232647], _232641))], (1214 ^ _185809) ^ [] : [-(member(1207 ^ [_232639, _232641, _232643, _232645, _232647], _232645))], (1216 ^ _185809) ^ [] : [-(member(1208 ^ [_232639, _232641, _232643, _232645, _232647], _232641))], (1218 ^ _185809) ^ [] : [-(apply(_232643, 1205 ^ [_232639, _232641, _232643, _232645, _232647], 1207 ^ [_232639, _232641, _232643, _232645, _232647]))], (1220 ^ _185809) ^ [] : [-(apply(_232647, 1205 ^ [_232639, _232641, _232643, _232645, _232647], 1206 ^ [_232639, _232641, _232643, _232645, _232647]))], (1222 ^ _185809) ^ [] : [-(apply(_232647, 1207 ^ [_232639, _232641, _232643, _232645, _232647], 1208 ^ [_232639, _232641, _232643, _232645, _232647]))], (1224 ^ _185809) ^ [] : [apply(_232639, 1208 ^ [_232639, _232641, _232643, _232645, _232647], 1206 ^ [_232639, _232641, _232643, _232645, _232647])]], -(decreasing(_232647, _232645, _232643, _232641, _232639))], (1170 ^ _185809) ^ [_231458, _231460, _231462, _231464, _231466] : [decreasing(_231466, _231464, _231462, _231460, _231458), 1173 ^ _185809 : [(1174 ^ _185809) ^ [_231710, _231712, _231714, _231716] : [-(apply(_231458, _231710, _231714)), member(_231716, _231464), member(_231714, _231460), member(_231712, _231464), member(_231710, _231460), apply(_231462, _231716, _231712), apply(_231466, _231716, _231714), apply(_231466, _231712, _231710)]]], (1272 ^ _185809) ^ [_235909, _235911, _235913, _235915, _235917] : [-(isomorphism(_235917, _235915, _235913, _235911, _235909)), maps(_235917, _235915, _235911), one_to_one(_235917, _235915, _235911), 1285 ^ _185809 : [(1286 ^ _185809) ^ [] : [-(member(1281 ^ [_235909, _235911, _235913, _235915, _235917], _235915))], (1288 ^ _185809) ^ [] : [-(member(1282 ^ [_235909, _235911, _235913, _235915, _235917], _235911))], (1290 ^ _185809) ^ [] : [-(member(1283 ^ [_235909, _235911, _235913, _235915, _235917], _235915))], (1292 ^ _185809) ^ [] : [-(member(1284 ^ [_235909, _235911, _235913, _235915, _235917], _235911))], (1294 ^ _185809) ^ [] : [-(apply(_235917, 1281 ^ [_235909, _235911, _235913, _235915, _235917], 1282 ^ [_235909, _235911, _235913, _235915, _235917]))], (1296 ^ _185809) ^ [] : [-(apply(_235917, 1283 ^ [_235909, _235911, _235913, _235915, _235917], 1284 ^ [_235909, _235911, _235913, _235915, _235917]))], (1298 ^ _185809) ^ [] : [1299 ^ _185809 : [(1300 ^ _185809) ^ [] : [-(apply(_235913, 1281 ^ [_235909, _235911, _235913, _235915, _235917], 1283 ^ [_235909, _235911, _235913, _235915, _235917]))], (1302 ^ _185809) ^ [] : [apply(_235909, 1282 ^ [_235909, _235911, _235913, _235915, _235917], 1284 ^ [_235909, _235911, _235913, _235915, _235917])]], 1303 ^ _185809 : [(1304 ^ _185809) ^ [] : [-(apply(_235909, 1282 ^ [_235909, _235911, _235913, _235915, _235917], 1284 ^ [_235909, _235911, _235913, _235915, _235917]))], (1306 ^ _185809) ^ [] : [apply(_235913, 1281 ^ [_235909, _235911, _235913, _235915, _235917], 1283 ^ [_235909, _235911, _235913, _235915, _235917])]]]]], (1228 ^ _185809) ^ [_234359, _234361, _234363, _234365, _234367] : [isomorphism(_234367, _234365, _234363, _234361, _234359), 1231 ^ _185809 : [(1232 ^ _185809) ^ [] : [-(maps(_234367, _234365, _234361))], (1234 ^ _185809) ^ [] : [-(one_to_one(_234367, _234365, _234361))], (1236 ^ _185809) ^ [_234771, _234773, _234775, _234777] : [1259 ^ _185809 : [(1260 ^ _185809) ^ [] : [apply(_234363, _234777, _234773), -(apply(_234359, _234775, _234771))], (1266 ^ _185809) ^ [] : [apply(_234359, _234775, _234771), -(apply(_234363, _234777, _234773))]], member(_234777, _234365), member(_234775, _234361), member(_234773, _234365), member(_234771, _234361), apply(_234367, _234777, _234775), apply(_234367, _234773, _234771)]]]], input).
% 5.25/5.52  ncf('1',plain,[equal_set(inverse_image2(1309 ^ [], empty_set), empty_set)],start(1315 ^ 0)).
% 5.25/5.52  ncf('1.1',plain,[-(equal_set(inverse_image2(1309 ^ [], empty_set), empty_set)), subset(inverse_image2(1309 ^ [], empty_set), empty_set), subset(empty_set, inverse_image2(1309 ^ [], empty_set))],extension(493 ^ 1,bind([[_203673, _203675], [empty_set, inverse_image2(1309 ^ [], empty_set)]]))).
% 5.25/5.52  ncf('1.1.1',plain,[-(subset(inverse_image2(1309 ^ [], empty_set), empty_set)), 479 : -(member(477 ^ [empty_set, inverse_image2(1309 ^ [], empty_set)], inverse_image2(1309 ^ [], empty_set)))],extension(476 ^ 2,bind([[_203050, _203052], [empty_set, inverse_image2(1309 ^ [], empty_set)]]))).
% 5.25/5.52  ncf('1.1.1.1',plain,[member(477 ^ [empty_set, inverse_image2(1309 ^ [], empty_set)], inverse_image2(1309 ^ [], empty_set)), 1073 : -(member(1071 ^ [477 ^ [empty_set, inverse_image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []], empty_set))],extension(1068 ^ 5,bind([[_226768, _226770, _226772], [477 ^ [empty_set, inverse_image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []]]))).
% 5.25/5.52  ncf('1.1.1.1.1',plain,[member(1071 ^ [477 ^ [empty_set, inverse_image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []], empty_set)],extension(551 ^ 8,bind([[_205577], [1071 ^ [477 ^ [empty_set, inverse_image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []]]]))).
% 5.25/5.52  ncf('1.1.2',plain,[-(subset(empty_set, inverse_image2(1309 ^ [], empty_set))), 479 : -(member(477 ^ [inverse_image2(1309 ^ [], empty_set), empty_set], empty_set))],extension(476 ^ 2,bind([[_203050, _203052], [inverse_image2(1309 ^ [], empty_set), empty_set]]))).
% 5.25/5.52  ncf('1.1.2.1',plain,[member(477 ^ [inverse_image2(1309 ^ [], empty_set), empty_set], empty_set)],extension(551 ^ 5,bind([[_205577], [477 ^ [inverse_image2(1309 ^ [], empty_set), empty_set]]]))).
% 5.25/5.52  %-----------------------------------------------------
% 5.25/5.52  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------