%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n019.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 11:56:23 EDT 2023

% Result   : Theorem 5.34s 5.52s
% Output   : Proof 5.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.14/0.34  % Computer : n019.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May 18 19:00:12 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 5.34/5.52  
% 5.34/5.52  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 5.34/5.52  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.34/5.52  %-----------------------------------------------------
% 5.34/5.52  ncf(matrix, plain, [(1313 ^ _185793) ^ [] : [-(maps(1309 ^ [], 1310 ^ [], 1311 ^ []))], (1315 ^ _185793) ^ [] : [equal_set(image2(1309 ^ [], empty_set), empty_set)], (318 ^ _185793) ^ [_197181, _197183] : [_197183 = _197181, -(power_set(_197183) = power_set(_197181))], (324 ^ _185793) ^ [_197427, _197429, _197431, _197433] : [-(intersection(_197433, _197429) = intersection(_197431, _197427)), _197433 = _197431, _197429 = _197427], (334 ^ _185793) ^ [_197786, _197788, _197790, _197792] : [-(union(_197792, _197788) = union(_197790, _197786)), _197792 = _197790, _197788 = _197786], (344 ^ _185793) ^ [_198145, _198147, _198149, _198151] : [-(difference(_198151, _198147) = difference(_198149, _198145)), _198151 = _198149, _198147 = _198145], (354 ^ _185793) ^ [_198476, _198478] : [_198478 = _198476, -(singleton(_198478) = singleton(_198476))], (360 ^ _185793) ^ [_198722, _198724, _198726, _198728] : [-(unordered_pair(_198728, _198724) = unordered_pair(_198726, _198722)), _198728 = _198726, _198724 = _198722], (370 ^ _185793) ^ [_199053, _199055] : [_199055 = _199053, -(sum(_199055) = sum(_199053))], (376 ^ _185793) ^ [_199271, _199273] : [_199273 = _199271, -(product(_199273) = product(_199271))], (382 ^ _185793) ^ [_199601, _199603, _199605, _199607, _199609, _199611, _199613, _199615, _199617, _199619] : [-(compose_function(_199619, _199615, _199611, _199607, _199603) = compose_function(_199617, _199613, _199609, _199605, _199601)), _199619 = _199617, _199615 = _199613, _199611 = _199609, _199607 = _199605, _199603 = _199601], (404 ^ _185793) ^ [_200423, _200425, _200427, _200429, _200431, _200433] : [-(inverse_function(_200433, _200429, _200425) = inverse_function(_200431, _200427, _200423)), _200433 = _200431, _200429 = _200427, _200425 = _200423], (418 ^ _185793) ^ [_200939, _200941, _200943, _200945, _200947, _200949] : [-(image3(_200949, _200945, _200941) = image3(_200947, _200943, _200939)), _200949 = _200947, _200945 = _200943, _200941 = _200939], (432 ^ _185793) ^ [_201427, _201429, _201431, _201433] : [-(inverse_image2(_201433, _201429) = inverse_image2(_201431, _201427)), _201433 = _201431, _201429 = _201427], (456 ^ _185793) ^ [_202282, _202284, _202286, _202288] : [-(image2(_202288, _202284) = image2(_202286, _202282)), _202288 = _202286, _202284 = _202282], (442 ^ _185793) ^ [_201814, _201816, _201818, _201820, _201822, _201824] : [-(inverse_image3(_201824, _201820, _201816) = inverse_image3(_201822, _201818, _201814)), _201824 = _201822, _201820 = _201818, _201816 = _201814], (2 ^ _185793) ^ [_185937] : [-(_185937 = _185937)], (4 ^ _185793) ^ [_186044, _186046] : [_186046 = _186044, -(_186044 = _186046)], (10 ^ _185793) ^ [_186248, _186250, _186252] : [-(_186252 = _186248), _186252 = _186250, _186250 = _186248], (20 ^ _185793) ^ [_186589, _186591, _186593, _186595] : [-(subset(_186593, _186589)), subset(_186595, _186591), _186595 = _186593, _186591 = _186589], (34 ^ _185793) ^ [_187145, _187147, _187149, _187151, _187153, _187155, _187157, _187159, _187161, _187163, _187165, _187167] : [-(compose_predicate(_187165, _187161, _187157, _187153, _187149, _187145)), compose_predicate(_187167, _187163, _187159, _187155, _187151, _187147), _187167 = _187165, _187163 = _187161, _187159 = _187157, _187155 = _187153, _187151 = _187149, _187147 = _187145], (64 ^ _185793) ^ [_188289, _188291, _188293, _188295, _188297, _188299, _188301, _188303] : [-(equal_maps(_188301, _188297, _188293, _188289)), equal_maps(_188303, _188299, _188295, _188291), _188303 = _188301, _188299 = _188297, _188295 = _188293, _188291 = _188289], (86 ^ _185793) ^ [_189023, _189025, _189027, _189029] : [-(identity(_189027, _189023)), identity(_189029, _189025), _189029 = _189027, _189025 = _189023], (100 ^ _185793) ^ [_189495, _189497, _189499, _189501, _189503, _189505] : [-(injective(_189503, _189499, _189495)), injective(_189505, _189501, _189497), _189505 = _189503, _189501 = _189499, _189497 = _189495], (118 ^ _185793) ^ [_190104, _190106, _190108, _190110, _190112, _190114] : [-(surjective(_190112, _190108, _190104)), surjective(_190114, _190110, _190106), _190114 = _190112, _190110 = _190108, _190106 = _190104], (136 ^ _185793) ^ [_190741, _190743, _190745, _190747, _190749, _190751, _190753, _190755] : [-(inverse_predicate(_190753, _190749, _190745, _190741)), inverse_predicate(_190755, _190751, _190747, _190743), _190755 = _190753, _190751 = _190749, _190747 = _190745, _190743 = _190741], (158 ^ _185793) ^ [_191559, _191561, _191563, _191565, _191567, _191569, _191571, _191573, _191575, _191577] : [-(increasing(_191575, _191571, _191567, _191563, _191559)), increasing(_191577, _191573, _191569, _191565, _191561), _191577 = _191575, _191573 = _191571, _191569 = _191567, _191565 = _191563, _191561 = _191559], (184 ^ _185793) ^ [_192546, _192548, _192550, _192552, _192554, _192556, _192558, _192560, _192562, _192564] : [-(decreasing(_192562, _192558, _192554, _192550, _192546)), decreasing(_192564, _192560, _192556, _192552, _192548), _192564 = _192562, _192560 = _192558, _192556 = _192554, _192552 = _192550, _192548 = _192546], (210 ^ _185793) ^ [_193533, _193535, _193537, _193539, _193541, _193543, _193545, _193547, _193549, _193551] : [-(isomorphism(_193549, _193545, _193541, _193537, _193533)), isomorphism(_193551, _193547, _193543, _193539, _193535), _193551 = _193549, _193547 = _193545, _193543 = _193541, _193539 = _193537, _193535 = _193533], (236 ^ _185793) ^ [_194464, _194466, _194468, _194470, _194472, _194474] : [-(one_to_one(_194472, _194468, _194464)), one_to_one(_194474, _194470, _194466), _194474 = _194472, _194470 = _194468, _194466 = _194464], (254 ^ _185793) ^ [_195045, _195047, _195049, _195051] : [-(member(_195049, _195045)), member(_195051, _195047), _195051 = _195049, _195047 = _195045], (268 ^ _185793) ^ [_195517, _195519, _195521, _195523, _195525, _195527] : [-(apply(_195525, _195521, _195517)), apply(_195527, _195523, _195519), _195527 = _195525, _195523 = _195521, _195519 = _195517], (304 ^ _185793) ^ [_196687, _196689, _196691, _196693] : [-(equal_set(_196691, _196687)), equal_set(_196693, _196689), _196693 = _196691, _196689 = _196687], (286 ^ _185793) ^ [_196126, _196128, _196130, _196132, _196134, _196136] : [-(maps(_196134, _196130, _196126)), maps(_196136, _196132, _196128), _196136 = _196134, _196132 = _196130, _196128 = _196126], (476 ^ _185793) ^ [_203034, _203036] : [478 ^ _185793 : [(479 ^ _185793) ^ [] : [-(member(477 ^ [_203034, _203036], _203036))], (481 ^ _185793) ^ [] : [member(477 ^ [_203034, _203036], _203034)]], -(subset(_203036, _203034))], (466 ^ _185793) ^ [_202720, _202722] : [subset(_202722, _202720), 469 ^ _185793 : [(470 ^ _185793) ^ [_202857] : [member(_202857, _202722), -(member(_202857, _202720))]]], (485 ^ _185793) ^ [_203420, _203422] : [equal_set(_203422, _203420), 488 ^ _185793 : [(489 ^ _185793) ^ [] : [-(subset(_203422, _203420))], (491 ^ _185793) ^ [] : [-(subset(_203420, _203422))]]], (493 ^ _185793) ^ [_203657, _203659] : [-(equal_set(_203659, _203657)), subset(_203659, _203657), subset(_203657, _203659)], (503 ^ _185793) ^ [_203987, _203989] : [member(_203989, power_set(_203987)), -(subset(_203989, _203987))], (509 ^ _185793) ^ [_204153, _204155] : [subset(_204155, _204153), -(member(_204155, power_set(_204153)))], (515 ^ _185793) ^ [_204412, _204414, _204416] : [member(_204416, intersection(_204414, _204412)), 518 ^ _185793 : [(519 ^ _185793) ^ [] : [-(member(_204416, _204414))], (521 ^ _185793) ^ [] : [-(member(_204416, _204412))]]], (523 ^ _185793) ^ [_204663, _204665, _204667] : [-(member(_204667, intersection(_204665, _204663))), member(_204667, _204665), member(_204667, _204663)], (543 ^ _185793) ^ [_205291, _205293, _205295] : [544 ^ _185793 : [(545 ^ _185793) ^ [] : [member(_205295, _205293)], (547 ^ _185793) ^ [] : [member(_205295, _205291)]], -(member(_205295, union(_205293, _205291)))], (533 ^ _185793) ^ [_205023, _205025, _205027] : [member(_205027, union(_205025, _205023)), -(member(_205027, _205025)), -(member(_205027, _205023))], (551 ^ _185793) ^ [_205561] : [member(_205561, empty_set)], (553 ^ _185793) ^ [_205711, _205713, _205715] : [member(_205715, difference(_205711, _205713)), 556 ^ _185793 : [(557 ^ _185793) ^ [] : [-(member(_205715, _205711))], (559 ^ _185793) ^ [] : [member(_205715, _205713)]]], (561 ^ _185793) ^ [_205963, _205965, _205967] : [-(member(_205967, difference(_205963, _205965))), member(_205967, _205963), -(member(_205967, _205965))], (571 ^ _185793) ^ [_206312, _206314] : [member(_206314, singleton(_206312)), -(_206314 = _206312)], (577 ^ _185793) ^ [_206478, _206480] : [_206480 = _206478, -(member(_206480, singleton(_206478)))], (593 ^ _185793) ^ [_207005, _207007, _207009] : [594 ^ _185793 : [(595 ^ _185793) ^ [] : [_207009 = _207007], (597 ^ _185793) ^ [] : [_207009 = _207005]], -(member(_207009, unordered_pair(_207007, _207005)))], (583 ^ _185793) ^ [_206737, _206739, _206741] : [member(_206741, unordered_pair(_206739, _206737)), -(_206741 = _206739), -(_206741 = _206737)], (601 ^ _185793) ^ [_207334, _207336] : [member(_207336, sum(_207334)), 605 ^ _185793 : [(606 ^ _185793) ^ [] : [-(member(604 ^ [_207334, _207336], _207334))], (608 ^ _185793) ^ [] : [-(member(_207336, 604 ^ [_207334, _207336]))]]], (610 ^ _185793) ^ [_207645, _207647] : [-(member(_207647, sum(_207645))), 611 ^ _185793 : [(612 ^ _185793) ^ [_207739] : [member(_207739, _207645), member(_207647, _207739)]]], (630 ^ _185793) ^ [_208340, _208342] : [632 ^ _185793 : [(633 ^ _185793) ^ [] : [-(member(631 ^ [_208340, _208342], _208340))], (635 ^ _185793) ^ [] : [member(_208342, 631 ^ [_208340, _208342])]], -(member(_208342, product(_208340)))], (620 ^ _185793) ^ [_208022, _208024] : [member(_208024, product(_208022)), 623 ^ _185793 : [(624 ^ _185793) ^ [_208163] : [member(_208163, _208022), -(member(_208024, _208163))]]], (674 ^ _185793) ^ [_210027, _210029, _210031] : [-(maps(_210031, _210029, _210027)), 689 ^ _185793 : [(690 ^ _185793) ^ [] : [-(member(686 ^ [_210027, _210029, _210031], _210029))], (692 ^ _185793) ^ [] : [-(member(687 ^ [_210027, _210029, _210031], _210027))], (694 ^ _185793) ^ [] : [-(member(688 ^ [_210027, _210029, _210031], _210027))], (696 ^ _185793) ^ [] : [-(apply(_210031, 686 ^ [_210027, _210029, _210031], 687 ^ [_210027, _210029, _210031]))], (698 ^ _185793) ^ [] : [-(apply(_210031, 686 ^ [_210027, _210029, _210031], 688 ^ [_210027, _210029, _210031]))], (700 ^ _185793) ^ [] : [687 ^ [_210027, _210029, _210031] = 688 ^ [_210027, _210029, _210031]]], 678 ^ _185793 : [(679 ^ _185793) ^ [] : [-(member(677 ^ [_210027, _210029, _210031], _210029))], (681 ^ _185793) ^ [_210367] : [member(_210367, _210027), apply(_210031, 677 ^ [_210027, _210029, _210031], _210367)]]], (639 ^ _185793) ^ [_208782, _208784, _208786] : [maps(_208786, _208784, _208782), 642 ^ _185793 : [(643 ^ _185793) ^ [_209010] : [member(_209010, _208784), 647 ^ _185793 : [(648 ^ _185793) ^ [] : [-(member(646 ^ [_208782, _208784, _208786, _209010], _208782))], (650 ^ _185793) ^ [] : [-(apply(_208786, _209010, 646 ^ [_208782, _208784, _208786, _209010]))]]], (652 ^ _185793) ^ [_209400, _209402, _209404] : [member(_209404, _208784), member(_209402, _208782), member(_209400, _208782), -(_209402 = _209400), apply(_208786, _209404, _209402), apply(_208786, _209404, _209400)]]], (741 ^ _185793) ^ [_213062, _213064, _213066, _213068, _213070, _213072] : [-(compose_predicate(_213072, _213070, _213068, _213066, _213064, _213062)), 744 ^ _185793 : [(745 ^ _185793) ^ [] : [-(member(742 ^ [_213062, _213064, _213066, _213068, _213070, _213072], _213066))], (747 ^ _185793) ^ [] : [-(member(743 ^ [_213062, _213064, _213066, _213068, _213070, _213072], _213062))], (749 ^ _185793) ^ [] : [763 ^ _185793 : [(764 ^ _185793) ^ [] : [-(member(762 ^ [_213062, _213064, _213066, _213068, _213070, _213072], _213064))], (766 ^ _185793) ^ [] : [-(apply(_213068, 742 ^ [_213062, _213064, _213066, _213068, _213070, _213072], 762 ^ [_213062, _213064, _213066, _213068, _213070, _213072]))], (768 ^ _185793) ^ [] : [-(apply(_213070, 762 ^ [_213062, _213064, _213066, _213068, _213070, _213072], 743 ^ [_213062, _213064, _213066, _213068, _213070, _213072]))], (770 ^ _185793) ^ [] : [apply(_213072, 742 ^ [_213062, _213064, _213066, _213068, _213070, _213072], 743 ^ [_213062, _213064, _213066, _213068, _213070, _213072])]], 750 ^ _185793 : [(751 ^ _185793) ^ [] : [-(apply(_213072, 742 ^ [_213062, _213064, _213066, _213068, _213070, _213072], 743 ^ [_213062, _213064, _213066, _213068, _213070, _213072]))], (753 ^ _185793) ^ [_213787] : [member(_213787, _213064), apply(_213068, 742 ^ [_213062, _213064, _213066, _213068, _213070, _213072], _213787), apply(_213070, _213787, 743 ^ [_213062, _213064, _213066, _213068, _213070, _213072])]]]]], (704 ^ _185793) ^ [_211587, _211589, _211591, _211593, _211595, _211597] : [compose_predicate(_211597, _211595, _211593, _211591, _211589, _211587), 707 ^ _185793 : [(708 ^ _185793) ^ [_211799, _211801] : [member(_211801, _211591), member(_211799, _211587), 715 ^ _185793 : [(716 ^ _185793) ^ [] : [apply(_211597, _211801, _211799), 720 ^ _185793 : [(721 ^ _185793) ^ [] : [-(member(719 ^ [_211587, _211589, _211591, _211593, _211595, _211597, _211799, _211801], _211589))], (723 ^ _185793) ^ [] : [-(apply(_211593, _211801, 719 ^ [_211587, _211589, _211591, _211593, _211595, _211597, _211799, _211801]))], (725 ^ _185793) ^ [] : [-(apply(_211595, 719 ^ [_211587, _211589, _211591, _211593, _211595, _211597, _211799, _211801], _211799))]]], (727 ^ _185793) ^ [] : [-(apply(_211597, _211801, _211799)), 728 ^ _185793 : [(729 ^ _185793) ^ [_212644] : [member(_212644, _211589), apply(_211593, _211801, _212644), apply(_211595, _212644, _211799)]]]]]]], (774 ^ _185793) ^ [_214856, _214858, _214860, _214862, _214864, _214866, _214868] : [member(_214858, _214864), member(_214856, _214860), 781 ^ _185793 : [(782 ^ _185793) ^ [] : [apply(compose_function(_214868, _214866, _214864, _214862, _214860), _214858, _214856), 786 ^ _185793 : [(787 ^ _185793) ^ [] : [-(member(785 ^ [_214856, _214858, _214860, _214862, _214864, _214866, _214868], _214862))], (789 ^ _185793) ^ [] : [-(apply(_214866, _214858, 785 ^ [_214856, _214858, _214860, _214862, _214864, _214866, _214868]))], (791 ^ _185793) ^ [] : [-(apply(_214868, 785 ^ [_214856, _214858, _214860, _214862, _214864, _214866, _214868], _214856))]]], (793 ^ _185793) ^ [] : [-(apply(compose_function(_214868, _214866, _214864, _214862, _214860), _214858, _214856)), 794 ^ _185793 : [(795 ^ _185793) ^ [_215671] : [member(_215671, _214862), apply(_214866, _214858, _215671), apply(_214868, _215671, _214856)]]]]], (833 ^ _185793) ^ [_217043, _217045, _217047, _217049] : [837 ^ _185793 : [(838 ^ _185793) ^ [] : [-(member(834 ^ [_217043, _217045, _217047, _217049], _217045))], (840 ^ _185793) ^ [] : [-(member(835 ^ [_217043, _217045, _217047, _217049], _217043))], (842 ^ _185793) ^ [] : [-(member(836 ^ [_217043, _217045, _217047, _217049], _217043))], (844 ^ _185793) ^ [] : [-(apply(_217049, 834 ^ [_217043, _217045, _217047, _217049], 835 ^ [_217043, _217045, _217047, _217049]))], (846 ^ _185793) ^ [] : [-(apply(_217047, 834 ^ [_217043, _217045, _217047, _217049], 836 ^ [_217043, _217045, _217047, _217049]))], (848 ^ _185793) ^ [] : [835 ^ [_217043, _217045, _217047, _217049] = 836 ^ [_217043, _217045, _217047, _217049]]], -(equal_maps(_217049, _217047, _217045, _217043))], (807 ^ _185793) ^ [_216181, _216183, _216185, _216187] : [equal_maps(_216187, _216185, _216183, _216181), 810 ^ _185793 : [(811 ^ _185793) ^ [_216394, _216396, _216398] : [member(_216398, _216183), member(_216396, _216181), member(_216394, _216181), -(_216396 = _216394), apply(_216187, _216398, _216396), apply(_216185, _216398, _216394)]]], (862 ^ _185793) ^ [_218501, _218503] : [864 ^ _185793 : [(865 ^ _185793) ^ [] : [-(member(863 ^ [_218501, _218503], _218501))], (867 ^ _185793) ^ [] : [apply(_218503, 863 ^ [_218501, _218503], 863 ^ [_218501, _218503])]], -(identity(_218503, _218501))], (852 ^ _185793) ^ [_218184, _218186] : [identity(_218186, _218184), 855 ^ _185793 : [(856 ^ _185793) ^ [_218322] : [member(_218322, _218184), -(apply(_218186, _218322, _218322))]]], (897 ^ _185793) ^ [_219743, _219745, _219747] : [901 ^ _185793 : [(902 ^ _185793) ^ [] : [-(member(898 ^ [_219743, _219745, _219747], _219745))], (904 ^ _185793) ^ [] : [-(member(899 ^ [_219743, _219745, _219747], _219745))], (906 ^ _185793) ^ [] : [-(member(900 ^ [_219743, _219745, _219747], _219743))], (908 ^ _185793) ^ [] : [-(apply(_219747, 898 ^ [_219743, _219745, _219747], 900 ^ [_219743, _219745, _219747]))], (910 ^ _185793) ^ [] : [-(apply(_219747, 899 ^ [_219743, _219745, _219747], 900 ^ [_219743, _219745, _219747]))], (912 ^ _185793) ^ [] : [898 ^ [_219743, _219745, _219747] = 899 ^ [_219743, _219745, _219747]]], -(injective(_219747, _219745, _219743))], (871 ^ _185793) ^ [_218911, _218913, _218915] : [injective(_218915, _218913, _218911), 874 ^ _185793 : [(875 ^ _185793) ^ [_219118, _219120, _219122] : [member(_219122, _218913), member(_219120, _218913), member(_219118, _218911), -(_219122 = _219120), apply(_218915, _219122, _219118), apply(_218915, _219120, _219118)]]], (916 ^ _185793) ^ [_220832, _220834, _220836] : [surjective(_220836, _220834, _220832), 919 ^ _185793 : [(920 ^ _185793) ^ [_220987] : [member(_220987, _220832), 924 ^ _185793 : [(925 ^ _185793) ^ [] : [-(member(923 ^ [_220832, _220834, _220836, _220987], _220834))], (927 ^ _185793) ^ [] : [-(apply(_220836, 923 ^ [_220832, _220834, _220836, _220987], _220987))]]]]], (929 ^ _185793) ^ [_221340, _221342, _221344] : [-(surjective(_221344, _221342, _221340)), 931 ^ _185793 : [(932 ^ _185793) ^ [] : [-(member(930 ^ [_221340, _221342, _221344], _221340))], (934 ^ _185793) ^ [_221591] : [member(_221591, _221342), apply(_221344, _221591, 930 ^ [_221340, _221342, _221344])]]], (942 ^ _185793) ^ [_221939, _221941, _221943] : [one_to_one(_221943, _221941, _221939), 945 ^ _185793 : [(946 ^ _185793) ^ [] : [-(injective(_221943, _221941, _221939))], (948 ^ _185793) ^ [] : [-(surjective(_221943, _221941, _221939))]]], (950 ^ _185793) ^ [_222190, _222192, _222194] : [-(one_to_one(_222194, _222192, _222190)), injective(_222194, _222192, _222190), surjective(_222194, _222192, _222190)], (984 ^ _185793) ^ [_223348, _223350, _223352, _223354] : [-(inverse_predicate(_223354, _223352, _223350, _223348)), 987 ^ _185793 : [(988 ^ _185793) ^ [] : [-(member(985 ^ [_223348, _223350, _223352, _223354], _223350))], (990 ^ _185793) ^ [] : [-(member(986 ^ [_223348, _223350, _223352, _223354], _223348))], (992 ^ _185793) ^ [] : [993 ^ _185793 : [(994 ^ _185793) ^ [] : [-(apply(_223352, 985 ^ [_223348, _223350, _223352, _223354], 986 ^ [_223348, _223350, _223352, _223354]))], (996 ^ _185793) ^ [] : [apply(_223354, 986 ^ [_223348, _223350, _223352, _223354], 985 ^ [_223348, _223350, _223352, _223354])]], 997 ^ _185793 : [(998 ^ _185793) ^ [] : [-(apply(_223354, 986 ^ [_223348, _223350, _223352, _223354], 985 ^ [_223348, _223350, _223352, _223354]))], (1000 ^ _185793) ^ [] : [apply(_223352, 985 ^ [_223348, _223350, _223352, _223354], 986 ^ [_223348, _223350, _223352, _223354])]]]]], (960 ^ _185793) ^ [_222564, _222566, _222568, _222570] : [inverse_predicate(_222570, _222568, _222566, _222564), 963 ^ _185793 : [(964 ^ _185793) ^ [_222746, _222748] : [member(_222748, _222566), member(_222746, _222564), 971 ^ _185793 : [(972 ^ _185793) ^ [] : [apply(_222568, _222748, _222746), -(apply(_222570, _222746, _222748))], (978 ^ _185793) ^ [] : [apply(_222570, _222746, _222748), -(apply(_222568, _222748, _222746))]]]]], (1004 ^ _185793) ^ [_224339, _224341, _224343, _224345, _224347] : [member(_224341, _224345), member(_224339, _224343), 1011 ^ _185793 : [(1012 ^ _185793) ^ [] : [apply(_224347, _224341, _224339), -(apply(inverse_function(_224347, _224345, _224343), _224339, _224341))], (1018 ^ _185793) ^ [] : [apply(inverse_function(_224347, _224345, _224343), _224339, _224341), -(apply(_224347, _224341, _224339))]]], (1024 ^ _185793) ^ [_225011, _225013, _225015] : [member(_225011, image2(_225015, _225013)), 1028 ^ _185793 : [(1029 ^ _185793) ^ [] : [-(member(1027 ^ [_225011, _225013, _225015], _225013))], (1031 ^ _185793) ^ [] : [-(apply(_225015, 1027 ^ [_225011, _225013, _225015], _225011))]]], (1033 ^ _185793) ^ [_225343, _225345, _225347] : [-(member(_225343, image2(_225347, _225345))), 1034 ^ _185793 : [(1035 ^ _185793) ^ [_225441] : [member(_225441, _225345), apply(_225347, _225441, _225343)]]], (1043 ^ _185793) ^ [_225785, _225787, _225789, _225791] : [member(_225785, image3(_225791, _225789, _225787)), 1046 ^ _185793 : [(1047 ^ _185793) ^ [] : [-(member(_225785, _225787))], (1050 ^ _185793) ^ [] : [-(member(1048 ^ [_225785, _225787, _225789, _225791], _225789))], (1052 ^ _185793) ^ [] : [-(apply(_225791, 1048 ^ [_225785, _225787, _225789, _225791], _225785))]]], (1054 ^ _185793) ^ [_226213, _226215, _226217, _226219] : [-(member(_226213, image3(_226219, _226217, _226215))), member(_226213, _226215), 1059 ^ _185793 : [(1060 ^ _185793) ^ [_226407] : [member(_226407, _226217), apply(_226219, _226407, _226213)]]], (1068 ^ _185793) ^ [_226752, _226754, _226756] : [member(_226752, inverse_image2(_226756, _226754)), 1072 ^ _185793 : [(1073 ^ _185793) ^ [] : [-(member(1071 ^ [_226752, _226754, _226756], _226754))], (1075 ^ _185793) ^ [] : [-(apply(_226756, _226752, 1071 ^ [_226752, _226754, _226756]))]]], (1077 ^ _185793) ^ [_227084, _227086, _227088] : [-(member(_227084, inverse_image2(_227088, _227086))), 1078 ^ _185793 : [(1079 ^ _185793) ^ [_227182] : [member(_227182, _227086), apply(_227088, _227084, _227182)]]], (1087 ^ _185793) ^ [_227526, _227528, _227530, _227532] : [member(_227526, inverse_image3(_227532, _227530, _227528)), 1090 ^ _185793 : [(1091 ^ _185793) ^ [] : [-(member(_227526, _227528))], (1094 ^ _185793) ^ [] : [-(member(1092 ^ [_227526, _227528, _227530, _227532], _227530))], (1096 ^ _185793) ^ [] : [-(apply(_227532, _227526, 1092 ^ [_227526, _227528, _227530, _227532]))]]], (1098 ^ _185793) ^ [_227954, _227956, _227958, _227960] : [-(member(_227954, inverse_image3(_227960, _227958, _227956))), member(_227954, _227956), 1103 ^ _185793 : [(1104 ^ _185793) ^ [_228148] : [member(_228148, _227958), apply(_227960, _227954, _228148)]]], (1146 ^ _185793) ^ [_229702, _229704, _229706, _229708, _229710] : [1151 ^ _185793 : [(1152 ^ _185793) ^ [] : [-(member(1147 ^ [_229702, _229704, _229706, _229708, _229710], _229708))], (1154 ^ _185793) ^ [] : [-(member(1148 ^ [_229702, _229704, _229706, _229708, _229710], _229704))], (1156 ^ _185793) ^ [] : [-(member(1149 ^ [_229702, _229704, _229706, _229708, _229710], _229708))], (1158 ^ _185793) ^ [] : [-(member(1150 ^ [_229702, _229704, _229706, _229708, _229710], _229704))], (1160 ^ _185793) ^ [] : [-(apply(_229706, 1147 ^ [_229702, _229704, _229706, _229708, _229710], 1149 ^ [_229702, _229704, _229706, _229708, _229710]))], (1162 ^ _185793) ^ [] : [-(apply(_229710, 1147 ^ [_229702, _229704, _229706, _229708, _229710], 1148 ^ [_229702, _229704, _229706, _229708, _229710]))], (1164 ^ _185793) ^ [] : [-(apply(_229710, 1149 ^ [_229702, _229704, _229706, _229708, _229710], 1150 ^ [_229702, _229704, _229706, _229708, _229710]))], (1166 ^ _185793) ^ [] : [apply(_229702, 1148 ^ [_229702, _229704, _229706, _229708, _229710], 1150 ^ [_229702, _229704, _229706, _229708, _229710])]], -(increasing(_229710, _229708, _229706, _229704, _229702))], (1112 ^ _185793) ^ [_228521, _228523, _228525, _228527, _228529] : [increasing(_228529, _228527, _228525, _228523, _228521), 1115 ^ _185793 : [(1116 ^ _185793) ^ [_228773, _228775, _228777, _228779] : [-(apply(_228521, _228777, _228773)), member(_228779, _228527), member(_228777, _228523), member(_228775, _228527), member(_228773, _228523), apply(_228525, _228779, _228775), apply(_228529, _228779, _228777), apply(_228529, _228775, _228773)]]], (1204 ^ _185793) ^ [_232623, _232625, _232627, _232629, _232631] : [1209 ^ _185793 : [(1210 ^ _185793) ^ [] : [-(member(1205 ^ [_232623, _232625, _232627, _232629, _232631], _232629))], (1212 ^ _185793) ^ [] : [-(member(1206 ^ [_232623, _232625, _232627, _232629, _232631], _232625))], (1214 ^ _185793) ^ [] : [-(member(1207 ^ [_232623, _232625, _232627, _232629, _232631], _232629))], (1216 ^ _185793) ^ [] : [-(member(1208 ^ [_232623, _232625, _232627, _232629, _232631], _232625))], (1218 ^ _185793) ^ [] : [-(apply(_232627, 1205 ^ [_232623, _232625, _232627, _232629, _232631], 1207 ^ [_232623, _232625, _232627, _232629, _232631]))], (1220 ^ _185793) ^ [] : [-(apply(_232631, 1205 ^ [_232623, _232625, _232627, _232629, _232631], 1206 ^ [_232623, _232625, _232627, _232629, _232631]))], (1222 ^ _185793) ^ [] : [-(apply(_232631, 1207 ^ [_232623, _232625, _232627, _232629, _232631], 1208 ^ [_232623, _232625, _232627, _232629, _232631]))], (1224 ^ _185793) ^ [] : [apply(_232623, 1208 ^ [_232623, _232625, _232627, _232629, _232631], 1206 ^ [_232623, _232625, _232627, _232629, _232631])]], -(decreasing(_232631, _232629, _232627, _232625, _232623))], (1170 ^ _185793) ^ [_231442, _231444, _231446, _231448, _231450] : [decreasing(_231450, _231448, _231446, _231444, _231442), 1173 ^ _185793 : [(1174 ^ _185793) ^ [_231694, _231696, _231698, _231700] : [-(apply(_231442, _231694, _231698)), member(_231700, _231448), member(_231698, _231444), member(_231696, _231448), member(_231694, _231444), apply(_231446, _231700, _231696), apply(_231450, _231700, _231698), apply(_231450, _231696, _231694)]]], (1272 ^ _185793) ^ [_235893, _235895, _235897, _235899, _235901] : [-(isomorphism(_235901, _235899, _235897, _235895, _235893)), maps(_235901, _235899, _235895), one_to_one(_235901, _235899, _235895), 1285 ^ _185793 : [(1286 ^ _185793) ^ [] : [-(member(1281 ^ [_235893, _235895, _235897, _235899, _235901], _235899))], (1288 ^ _185793) ^ [] : [-(member(1282 ^ [_235893, _235895, _235897, _235899, _235901], _235895))], (1290 ^ _185793) ^ [] : [-(member(1283 ^ [_235893, _235895, _235897, _235899, _235901], _235899))], (1292 ^ _185793) ^ [] : [-(member(1284 ^ [_235893, _235895, _235897, _235899, _235901], _235895))], (1294 ^ _185793) ^ [] : [-(apply(_235901, 1281 ^ [_235893, _235895, _235897, _235899, _235901], 1282 ^ [_235893, _235895, _235897, _235899, _235901]))], (1296 ^ _185793) ^ [] : [-(apply(_235901, 1283 ^ [_235893, _235895, _235897, _235899, _235901], 1284 ^ [_235893, _235895, _235897, _235899, _235901]))], (1298 ^ _185793) ^ [] : [1299 ^ _185793 : [(1300 ^ _185793) ^ [] : [-(apply(_235897, 1281 ^ [_235893, _235895, _235897, _235899, _235901], 1283 ^ [_235893, _235895, _235897, _235899, _235901]))], (1302 ^ _185793) ^ [] : [apply(_235893, 1282 ^ [_235893, _235895, _235897, _235899, _235901], 1284 ^ [_235893, _235895, _235897, _235899, _235901])]], 1303 ^ _185793 : [(1304 ^ _185793) ^ [] : [-(apply(_235893, 1282 ^ [_235893, _235895, _235897, _235899, _235901], 1284 ^ [_235893, _235895, _235897, _235899, _235901]))], (1306 ^ _185793) ^ [] : [apply(_235897, 1281 ^ [_235893, _235895, _235897, _235899, _235901], 1283 ^ [_235893, _235895, _235897, _235899, _235901])]]]]], (1228 ^ _185793) ^ [_234343, _234345, _234347, _234349, _234351] : [isomorphism(_234351, _234349, _234347, _234345, _234343), 1231 ^ _185793 : [(1232 ^ _185793) ^ [] : [-(maps(_234351, _234349, _234345))], (1234 ^ _185793) ^ [] : [-(one_to_one(_234351, _234349, _234345))], (1236 ^ _185793) ^ [_234755, _234757, _234759, _234761] : [1259 ^ _185793 : [(1260 ^ _185793) ^ [] : [apply(_234347, _234761, _234757), -(apply(_234343, _234759, _234755))], (1266 ^ _185793) ^ [] : [apply(_234343, _234759, _234755), -(apply(_234347, _234761, _234757))]], member(_234761, _234349), member(_234759, _234345), member(_234757, _234349), member(_234755, _234345), apply(_234351, _234761, _234759), apply(_234351, _234757, _234755)]]]], input).
% 5.34/5.52  ncf('1',plain,[equal_set(image2(1309 ^ [], empty_set), empty_set)],start(1315 ^ 0)).
% 5.34/5.52  ncf('1.1',plain,[-(equal_set(image2(1309 ^ [], empty_set), empty_set)), subset(image2(1309 ^ [], empty_set), empty_set), subset(empty_set, image2(1309 ^ [], empty_set))],extension(493 ^ 1,bind([[_203657, _203659], [empty_set, image2(1309 ^ [], empty_set)]]))).
% 5.34/5.52  ncf('1.1.1',plain,[-(subset(image2(1309 ^ [], empty_set), empty_set)), 479 : -(member(477 ^ [empty_set, image2(1309 ^ [], empty_set)], image2(1309 ^ [], empty_set)))],extension(476 ^ 2,bind([[_203034, _203036], [empty_set, image2(1309 ^ [], empty_set)]]))).
% 5.34/5.52  ncf('1.1.1.1',plain,[member(477 ^ [empty_set, image2(1309 ^ [], empty_set)], image2(1309 ^ [], empty_set)), 1029 : -(member(1027 ^ [477 ^ [empty_set, image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []], empty_set))],extension(1024 ^ 5,bind([[_225011, _225013, _225015], [477 ^ [empty_set, image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []]]))).
% 5.34/5.52  ncf('1.1.1.1.1',plain,[member(1027 ^ [477 ^ [empty_set, image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []], empty_set)],extension(551 ^ 8,bind([[_205561], [1027 ^ [477 ^ [empty_set, image2(1309 ^ [], empty_set)], empty_set, 1309 ^ []]]]))).
% 5.34/5.52  ncf('1.1.2',plain,[-(subset(empty_set, image2(1309 ^ [], empty_set))), 479 : -(member(477 ^ [image2(1309 ^ [], empty_set), empty_set], empty_set))],extension(476 ^ 2,bind([[_203034, _203036], [image2(1309 ^ [], empty_set), empty_set]]))).
% 5.34/5.52  ncf('1.1.2.1',plain,[member(477 ^ [image2(1309 ^ [], empty_set), empty_set], empty_set)],extension(551 ^ 5,bind([[_205561], [477 ^ [image2(1309 ^ [], empty_set), empty_set]]]))).
% 5.34/5.52  %-----------------------------------------------------
% 5.34/5.52  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------