%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 81.28s 78.88s
% Output   : Proof 81.28s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 19:12:14 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 81.28/78.88  
% 81.28/78.88  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 81.28/78.88  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.28/78.88  %-----------------------------------------------------
% 81.28/78.88  ncf(matrix, plain, [(1315 ^ _252963) ^ [] : [-(maps(1309 ^ [], 1310 ^ [], 1311 ^ []))], (1319 ^ _252963) ^ [] : [-(subset(1313 ^ [], 1311 ^ []))], (1323 ^ _252963) ^ [] : [subset(inverse_image2(1309 ^ [], 1312 ^ []), inverse_image2(1309 ^ [], 1313 ^ []))], (1321 ^ _252963) ^ [] : [-(subset(1312 ^ [], 1313 ^ []))], (1317 ^ _252963) ^ [] : [-(subset(1312 ^ [], 1311 ^ []))], !, (1112 ^ _200254) ^ [_242962, _242964, _242966, _242968, _242970] : [increasing(_242970, _242968, _242966, _242964, _242962), 1115 ^ _200254 : [(1116 ^ _200254) ^ [_243214, _243216, _243218, _243220] : [-(apply(_242962, _243218, _243214)), member(_243220, _242968), member(_243218, _242964), member(_243216, _242968), member(_243214, _242964), apply(_242966, _243220, _243216), apply(_242970, _243220, _243218), apply(_242970, _243216, _243214)]]], (1054 ^ _200254) ^ [_240654, _240656, _240658, _240660] : [-(member(_240654, image3(_240660, _240658, _240656))), member(_240654, _240656), 1059 ^ _200254 : [(1060 ^ _200254) ^ [_240848] : [member(_240848, _240658), apply(_240660, _240848, _240654)]]], (466 ^ _200254) ^ [_217161, _217163] : [subset(_217163, _217161), 469 ^ _200254 : [(470 ^ _200254) ^ [_217298] : [member(_217298, _217163), -(member(_217298, _217161))]]], (543 ^ _200254) ^ [_219732, _219734, _219736] : [544 ^ _200254 : [(547 ^ _200254) ^ [] : [member(_219736, _219732)], (545 ^ _200254) ^ [] : [member(_219736, _219734)]], -(member(_219736, union(_219734, _219732)))], (950 ^ _200254) ^ [_236631, _236633, _236635] : [-(one_to_one(_236635, _236633, _236631)), injective(_236635, _236633, _236631), surjective(_236635, _236633, _236631)], (1098 ^ _200254) ^ [_242395, _242397, _242399, _242401] : [-(member(_242395, inverse_image3(_242401, _242399, _242397))), member(_242395, _242397), 1103 ^ _200254 : [(1104 ^ _200254) ^ [_242589] : [member(_242589, _242399), apply(_242401, _242395, _242589)]]], (4 ^ _200254) ^ [_200485, _200487] : [_200487 = _200485, -(_200485 = _200487)], (639 ^ _200254) ^ [_223223, _223225, _223227] : [maps(_223227, _223225, _223223), 642 ^ _200254 : [(652 ^ _200254) ^ [_223841, _223843, _223845] : [member(_223845, _223225), member(_223843, _223223), member(_223841, _223223), -(_223843 = _223841), apply(_223227, _223845, _223843), apply(_223227, _223845, _223841)], (643 ^ _200254) ^ [_223451] : [member(_223451, _223225), 647 ^ _200254 : [(650 ^ _200254) ^ [] : [-(apply(_223227, _223451, 646 ^ [_223223, _223225, _223227, _223451]))], (648 ^ _200254) ^ [] : [-(member(646 ^ [_223223, _223225, _223227, _223451], _223223))]]]]], (561 ^ _200254) ^ [_220404, _220406, _220408] : [-(member(_220408, difference(_220404, _220406))), member(_220408, _220404), -(member(_220408, _220406))], (485 ^ _200254) ^ [_217861, _217863] : [equal_set(_217863, _217861), 488 ^ _200254 : [(491 ^ _200254) ^ [] : [-(subset(_217861, _217863))], (489 ^ _200254) ^ [] : [-(subset(_217863, _217861))]]], (571 ^ _200254) ^ [_220753, _220755] : [member(_220755, singleton(_220753)), -(_220755 = _220753)], (593 ^ _200254) ^ [_221446, _221448, _221450] : [594 ^ _200254 : [(597 ^ _200254) ^ [] : [_221450 = _221446], (595 ^ _200254) ^ [] : [_221450 = _221448]], -(member(_221450, unordered_pair(_221448, _221446)))], (236 ^ _200254) ^ [_208905, _208907, _208909, _208911, _208913, _208915] : [-(one_to_one(_208913, _208909, _208905)), one_to_one(_208915, _208911, _208907), _208915 = _208913, _208911 = _208909, _208907 = _208905], (210 ^ _200254) ^ [_207974, _207976, _207978, _207980, _207982, _207984, _207986, _207988, _207990, _207992] : [-(isomorphism(_207990, _207986, _207982, _207978, _207974)), isomorphism(_207992, _207988, _207984, _207980, _207976), _207992 = _207990, _207988 = _207986, _207984 = _207982, _207980 = _207978, _207976 = _207974], (2 ^ _200254) ^ [_200378] : [-(_200378 = _200378)], (942 ^ _200254) ^ [_236380, _236382, _236384] : [one_to_one(_236384, _236382, _236380), 945 ^ _200254 : [(948 ^ _200254) ^ [] : [-(surjective(_236384, _236382, _236380))], (946 ^ _200254) ^ [] : [-(injective(_236384, _236382, _236380))]]], (376 ^ _200254) ^ [_213712, _213714] : [_213714 = _213712, -(product(_213714) = product(_213712))], (100 ^ _200254) ^ [_203936, _203938, _203940, _203942, _203944, _203946] : [-(injective(_203944, _203940, _203936)), injective(_203946, _203942, _203938), _203946 = _203944, _203942 = _203940, _203938 = _203936], (1033 ^ _200254) ^ [_239784, _239786, _239788] : [-(member(_239784, image2(_239788, _239786))), 1034 ^ _200254 : [(1035 ^ _200254) ^ [_239882] : [member(_239882, _239786), apply(_239788, _239882, _239784)]]], (10 ^ _200254) ^ [_200689, _200691, _200693] : [-(_200693 = _200689), _200693 = _200691, _200691 = _200689], (807 ^ _200254) ^ [_230622, _230624, _230626, _230628] : [equal_maps(_230628, _230626, _230624, _230622), 810 ^ _200254 : [(811 ^ _200254) ^ [_230835, _230837, _230839] : [member(_230839, _230624), member(_230837, _230622), member(_230835, _230622), -(_230837 = _230835), apply(_230628, _230839, _230837), apply(_230626, _230839, _230835)]]], (1228 ^ _200254) ^ [_248784, _248786, _248788, _248790, _248792] : [isomorphism(_248792, _248790, _248788, _248786, _248784), 1231 ^ _200254 : [(1236 ^ _200254) ^ [_249196, _249198, _249200, _249202] : [1259 ^ _200254 : [(1266 ^ _200254) ^ [] : [apply(_248784, _249200, _249196), -(apply(_248788, _249202, _249198))], (1260 ^ _200254) ^ [] : [apply(_248788, _249202, _249198), -(apply(_248784, _249200, _249196))]], member(_249202, _248790), member(_249200, _248786), member(_249198, _248790), member(_249196, _248786), apply(_248792, _249202, _249200), apply(_248792, _249198, _249196)], (1234 ^ _200254) ^ [] : [-(one_to_one(_248792, _248790, _248786))], (1232 ^ _200254) ^ [] : [-(maps(_248792, _248790, _248786))]]], (354 ^ _200254) ^ [_212917, _212919] : [_212919 = _212917, -(singleton(_212919) = singleton(_212917))], (304 ^ _200254) ^ [_211128, _211130, _211132, _211134] : [-(subset(_211132, _211128)), subset(_211134, _211130), _211134 = _211132, _211130 = _211128], (533 ^ _200254) ^ [_219464, _219466, _219468] : [member(_219468, union(_219466, _219464)), -(member(_219468, _219466)), -(member(_219468, _219464))], (360 ^ _200254) ^ [_213163, _213165, _213167, _213169] : [-(unordered_pair(_213169, _213165) = unordered_pair(_213167, _213163)), _213169 = _213167, _213165 = _213163], (1004 ^ _200254) ^ [_238780, _238782, _238784, _238786, _238788] : [member(_238782, _238786), member(_238780, _238784), 1011 ^ _200254 : [(1018 ^ _200254) ^ [] : [apply(inverse_function(_238788, _238786, _238784), _238780, _238782), -(apply(_238788, _238782, _238780))], (1012 ^ _200254) ^ [] : [apply(_238788, _238782, _238780), -(apply(inverse_function(_238788, _238786, _238784), _238780, _238782))]]], (704 ^ _200254) ^ [_226028, _226030, _226032, _226034, _226036, _226038] : [compose_predicate(_226038, _226036, _226034, _226032, _226030, _226028), 707 ^ _200254 : [(708 ^ _200254) ^ [_226240, _226242] : [member(_226242, _226032), member(_226240, _226028), 715 ^ _200254 : [(727 ^ _200254) ^ [] : [-(apply(_226038, _226242, _226240)), 728 ^ _200254 : [(729 ^ _200254) ^ [_227085] : [member(_227085, _226030), apply(_226034, _226242, _227085), apply(_226036, _227085, _226240)]]], (716 ^ _200254) ^ [] : [apply(_226038, _226242, _226240), 720 ^ _200254 : [(725 ^ _200254) ^ [] : [-(apply(_226036, 719 ^ [_226028, _226030, _226032, _226034, _226036, _226038, _226240, _226242], _226240))], (723 ^ _200254) ^ [] : [-(apply(_226034, _226242, 719 ^ [_226028, _226030, _226032, _226034, _226036, _226038, _226240, _226242]))], (721 ^ _200254) ^ [] : [-(member(719 ^ [_226028, _226030, _226032, _226034, _226036, _226038, _226240, _226242], _226030))]]]]]]], (620 ^ _200254) ^ [_222463, _222465] : [member(_222465, product(_222463)), 623 ^ _200254 : [(624 ^ _200254) ^ [_222604] : [member(_222604, _222463), -(member(_222465, _222604))]]], (503 ^ _200254) ^ [_218428, _218430] : [member(_218430, power_set(_218428)), -(subset(_218430, _218428))], (1204 ^ _200254) ^ [_247064, _247066, _247068, _247070, _247072] : [1209 ^ _200254 : [(1214 ^ _200254) ^ [] : [-(member(1207 ^ [_247064, _247066, _247068, _247070, _247072], _247070))], (1220 ^ _200254) ^ [] : [-(apply(_247072, 1205 ^ [_247064, _247066, _247068, _247070, _247072], 1206 ^ [_247064, _247066, _247068, _247070, _247072]))], (1210 ^ _200254) ^ [] : [-(member(1205 ^ [_247064, _247066, _247068, _247070, _247072], _247070))], (1222 ^ _200254) ^ [] : [-(apply(_247072, 1207 ^ [_247064, _247066, _247068, _247070, _247072], 1208 ^ [_247064, _247066, _247068, _247070, _247072]))], (1216 ^ _200254) ^ [] : [-(member(1208 ^ [_247064, _247066, _247068, _247070, _247072], _247066))], (1218 ^ _200254) ^ [] : [-(apply(_247068, 1205 ^ [_247064, _247066, _247068, _247070, _247072], 1207 ^ [_247064, _247066, _247068, _247070, _247072]))], (1224 ^ _200254) ^ [] : [apply(_247064, 1208 ^ [_247064, _247066, _247068, _247070, _247072], 1206 ^ [_247064, _247066, _247068, _247070, _247072])], (1212 ^ _200254) ^ [] : [-(member(1206 ^ [_247064, _247066, _247068, _247070, _247072], _247066))]], -(decreasing(_247072, _247070, _247068, _247066, _247064))], (509 ^ _200254) ^ [_218594, _218596] : [subset(_218596, _218594), -(member(_218596, power_set(_218594)))], (833 ^ _200254) ^ [_231484, _231486, _231488, _231490] : [837 ^ _200254 : [(840 ^ _200254) ^ [] : [-(member(835 ^ [_231484, _231486, _231488, _231490], _231484))], (838 ^ _200254) ^ [] : [-(member(834 ^ [_231484, _231486, _231488, _231490], _231486))], (848 ^ _200254) ^ [] : [835 ^ [_231484, _231486, _231488, _231490] = 836 ^ [_231484, _231486, _231488, _231490]], (844 ^ _200254) ^ [] : [-(apply(_231490, 834 ^ [_231484, _231486, _231488, _231490], 835 ^ [_231484, _231486, _231488, _231490]))], (846 ^ _200254) ^ [] : [-(apply(_231488, 834 ^ [_231484, _231486, _231488, _231490], 836 ^ [_231484, _231486, _231488, _231490]))], (842 ^ _200254) ^ [] : [-(member(836 ^ [_231484, _231486, _231488, _231490], _231484))]], -(equal_maps(_231490, _231488, _231486, _231484))], (136 ^ _200254) ^ [_205182, _205184, _205186, _205188, _205190, _205192, _205194, _205196] : [-(inverse_predicate(_205194, _205190, _205186, _205182)), inverse_predicate(_205196, _205192, _205188, _205184), _205196 = _205194, _205192 = _205190, _205188 = _205186, _205184 = _205182], (862 ^ _200254) ^ [_232942, _232944] : [864 ^ _200254 : [(867 ^ _200254) ^ [] : [apply(_232944, 863 ^ [_232942, _232944], 863 ^ [_232942, _232944])], (865 ^ _200254) ^ [] : [-(member(863 ^ [_232942, _232944], _232942))]], -(identity(_232944, _232942))], (1272 ^ _200254) ^ [_250334, _250336, _250338, _250340, _250342] : [-(isomorphism(_250342, _250340, _250338, _250336, _250334)), maps(_250342, _250340, _250336), one_to_one(_250342, _250340, _250336), 1285 ^ _200254 : [(1290 ^ _200254) ^ [] : [-(member(1283 ^ [_250334, _250336, _250338, _250340, _250342], _250340))], (1296 ^ _200254) ^ [] : [-(apply(_250342, 1283 ^ [_250334, _250336, _250338, _250340, _250342], 1284 ^ [_250334, _250336, _250338, _250340, _250342]))], (1298 ^ _200254) ^ [] : [1299 ^ _200254 : [(1302 ^ _200254) ^ [] : [apply(_250334, 1282 ^ [_250334, _250336, _250338, _250340, _250342], 1284 ^ [_250334, _250336, _250338, _250340, _250342])], (1300 ^ _200254) ^ [] : [-(apply(_250338, 1281 ^ [_250334, _250336, _250338, _250340, _250342], 1283 ^ [_250334, _250336, _250338, _250340, _250342]))]], 1303 ^ _200254 : [(1306 ^ _200254) ^ [] : [apply(_250338, 1281 ^ [_250334, _250336, _250338, _250340, _250342], 1283 ^ [_250334, _250336, _250338, _250340, _250342])], (1304 ^ _200254) ^ [] : [-(apply(_250334, 1282 ^ [_250334, _250336, _250338, _250340, _250342], 1284 ^ [_250334, _250336, _250338, _250340, _250342]))]]], (1292 ^ _200254) ^ [] : [-(member(1284 ^ [_250334, _250336, _250338, _250340, _250342], _250336))], (1286 ^ _200254) ^ [] : [-(member(1281 ^ [_250334, _250336, _250338, _250340, _250342], _250340))], (1288 ^ _200254) ^ [] : [-(member(1282 ^ [_250334, _250336, _250338, _250340, _250342], _250336))], (1294 ^ _200254) ^ [] : [-(apply(_250342, 1281 ^ [_250334, _250336, _250338, _250340, _250342], 1282 ^ [_250334, _250336, _250338, _250340, _250342]))]]], (476 ^ _200254) ^ [_217475, _217477] : [478 ^ _200254 : [(481 ^ _200254) ^ [] : [member(477 ^ [_217475, _217477], _217475)], (479 ^ _200254) ^ [] : [-(member(477 ^ [_217475, _217477], _217477))]], -(subset(_217477, _217475))], (158 ^ _200254) ^ [_206000, _206002, _206004, _206006, _206008, _206010, _206012, _206014, _206016, _206018] : [-(increasing(_206016, _206012, _206008, _206004, _206000)), increasing(_206018, _206014, _206010, _206006, _206002), _206018 = _206016, _206014 = _206012, _206010 = _206008, _206006 = _206004, _206002 = _206000], (515 ^ _200254) ^ [_218853, _218855, _218857] : [member(_218857, intersection(_218855, _218853)), 518 ^ _200254 : [(521 ^ _200254) ^ [] : [-(member(_218857, _218853))], (519 ^ _200254) ^ [] : [-(member(_218857, _218855))]]], (577 ^ _200254) ^ [_220919, _220921] : [_220921 = _220919, -(member(_220921, singleton(_220919)))], (1087 ^ _200254) ^ [_241967, _241969, _241971, _241973] : [member(_241967, inverse_image3(_241973, _241971, _241969)), 1090 ^ _200254 : [(1096 ^ _200254) ^ [] : [-(apply(_241973, _241967, 1092 ^ [_241967, _241969, _241971, _241973]))], (1094 ^ _200254) ^ [] : [-(member(1092 ^ [_241967, _241969, _241971, _241973], _241971))], (1091 ^ _200254) ^ [] : [-(member(_241967, _241969))]]], (583 ^ _200254) ^ [_221178, _221180, _221182] : [member(_221182, unordered_pair(_221180, _221178)), -(_221182 = _221180), -(_221182 = _221178)], (929 ^ _200254) ^ [_235781, _235783, _235785] : [-(surjective(_235785, _235783, _235781)), 931 ^ _200254 : [(934 ^ _200254) ^ [_236032] : [member(_236032, _235783), apply(_235785, _236032, 930 ^ [_235781, _235783, _235785])], (932 ^ _200254) ^ [] : [-(member(930 ^ [_235781, _235783, _235785], _235781))]]], (20 ^ _200254) ^ [_201030, _201032, _201034, _201036] : [-(equal_set(_201034, _201030)), equal_set(_201036, _201032), _201036 = _201034, _201032 = _201030], (610 ^ _200254) ^ [_222086, _222088] : [-(member(_222088, sum(_222086))), 611 ^ _200254 : [(612 ^ _200254) ^ [_222180] : [member(_222180, _222086), member(_222088, _222180)]]], (324 ^ _200254) ^ [_211868, _211870, _211872, _211874] : [-(intersection(_211874, _211870) = intersection(_211872, _211868)), _211874 = _211872, _211870 = _211868], (334 ^ _200254) ^ [_212227, _212229, _212231, _212233] : [-(union(_212233, _212229) = union(_212231, _212227)), _212233 = _212231, _212229 = _212227], (984 ^ _200254) ^ [_237789, _237791, _237793, _237795] : [-(inverse_predicate(_237795, _237793, _237791, _237789)), 987 ^ _200254 : [(992 ^ _200254) ^ [] : [993 ^ _200254 : [(996 ^ _200254) ^ [] : [apply(_237795, 986 ^ [_237789, _237791, _237793, _237795], 985 ^ [_237789, _237791, _237793, _237795])], (994 ^ _200254) ^ [] : [-(apply(_237793, 985 ^ [_237789, _237791, _237793, _237795], 986 ^ [_237789, _237791, _237793, _237795]))]], 997 ^ _200254 : [(1000 ^ _200254) ^ [] : [apply(_237793, 985 ^ [_237789, _237791, _237793, _237795], 986 ^ [_237789, _237791, _237793, _237795])], (998 ^ _200254) ^ [] : [-(apply(_237795, 986 ^ [_237789, _237791, _237793, _237795], 985 ^ [_237789, _237791, _237793, _237795]))]]], (990 ^ _200254) ^ [] : [-(member(986 ^ [_237789, _237791, _237793, _237795], _237789))], (988 ^ _200254) ^ [] : [-(member(985 ^ [_237789, _237791, _237793, _237795], _237791))]]], (456 ^ _200254) ^ [_216723, _216725, _216727, _216729] : [-(inverse_image2(_216729, _216725) = inverse_image2(_216727, _216723)), _216729 = _216727, _216725 = _216723], (871 ^ _200254) ^ [_233352, _233354, _233356] : [injective(_233356, _233354, _233352), 874 ^ _200254 : [(875 ^ _200254) ^ [_233559, _233561, _233563] : [member(_233563, _233354), member(_233561, _233354), member(_233559, _233352), -(_233563 = _233561), apply(_233356, _233563, _233559), apply(_233356, _233561, _233559)]]], (382 ^ _200254) ^ [_214042, _214044, _214046, _214048, _214050, _214052, _214054, _214056, _214058, _214060] : [-(compose_function(_214060, _214056, _214052, _214048, _214044) = compose_function(_214058, _214054, _214050, _214046, _214042)), _214060 = _214058, _214056 = _214054, _214052 = _214050, _214048 = _214046, _214044 = _214042], (370 ^ _200254) ^ [_213494, _213496] : [_213496 = _213494, -(sum(_213496) = sum(_213494))], (286 ^ _200254) ^ [_210567, _210569, _210571, _210573, _210575, _210577] : [-(maps(_210575, _210571, _210567)), maps(_210577, _210573, _210569), _210577 = _210575, _210573 = _210571, _210569 = _210567], (118 ^ _200254) ^ [_204545, _204547, _204549, _204551, _204553, _204555] : [-(surjective(_204553, _204549, _204545)), surjective(_204555, _204551, _204547), _204555 = _204553, _204551 = _204549, _204547 = _204545], (404 ^ _200254) ^ [_214864, _214866, _214868, _214870, _214872, _214874] : [-(inverse_function(_214874, _214870, _214866) = inverse_function(_214872, _214868, _214864)), _214874 = _214872, _214870 = _214868, _214866 = _214864], (318 ^ _200254) ^ [_211622, _211624] : [_211624 = _211622, -(power_set(_211624) = power_set(_211622))], (630 ^ _200254) ^ [_222781, _222783] : [632 ^ _200254 : [(635 ^ _200254) ^ [] : [member(_222783, 631 ^ [_222781, _222783])], (633 ^ _200254) ^ [] : [-(member(631 ^ [_222781, _222783], _222781))]], -(member(_222783, product(_222781)))], (1068 ^ _200254) ^ [_241193, _241195, _241197] : [member(_241193, inverse_image2(_241197, _241195)), 1072 ^ _200254 : [(1075 ^ _200254) ^ [] : [-(apply(_241197, _241193, 1071 ^ [_241193, _241195, _241197]))], (1073 ^ _200254) ^ [] : [-(member(1071 ^ [_241193, _241195, _241197], _241195))]]], (553 ^ _200254) ^ [_220152, _220154, _220156] : [member(_220156, difference(_220152, _220154)), 556 ^ _200254 : [(559 ^ _200254) ^ [] : [member(_220156, _220154)], (557 ^ _200254) ^ [] : [-(member(_220156, _220152))]]], (1043 ^ _200254) ^ [_240226, _240228, _240230, _240232] : [member(_240226, image3(_240232, _240230, _240228)), 1046 ^ _200254 : [(1052 ^ _200254) ^ [] : [-(apply(_240232, 1048 ^ [_240226, _240228, _240230, _240232], _240226))], (1050 ^ _200254) ^ [] : [-(member(1048 ^ [_240226, _240228, _240230, _240232], _240230))], (1047 ^ _200254) ^ [] : [-(member(_240226, _240228))]]], (184 ^ _200254) ^ [_206987, _206989, _206991, _206993, _206995, _206997, _206999, _207001, _207003, _207005] : [-(decreasing(_207003, _206999, _206995, _206991, _206987)), decreasing(_207005, _207001, _206997, _206993, _206989), _207005 = _207003, _207001 = _206999, _206997 = _206995, _206993 = _206991, _206989 = _206987], (428 ^ _200254) ^ [_215739, _215741, _215743, _215745, _215747, _215749] : [-(image3(_215749, _215745, _215741) = image3(_215747, _215743, _215739)), _215749 = _215747, _215745 = _215743, _215741 = _215739], (774 ^ _200254) ^ [_229297, _229299, _229301, _229303, _229305, _229307, _229309] : [member(_229299, _229305), member(_229297, _229301), 781 ^ _200254 : [(793 ^ _200254) ^ [] : [-(apply(compose_function(_229309, _229307, _229305, _229303, _229301), _229299, _229297)), 794 ^ _200254 : [(795 ^ _200254) ^ [_230112] : [member(_230112, _229303), apply(_229307, _229299, _230112), apply(_229309, _230112, _229297)]]], (782 ^ _200254) ^ [] : [apply(compose_function(_229309, _229307, _229305, _229303, _229301), _229299, _229297), 786 ^ _200254 : [(791 ^ _200254) ^ [] : [-(apply(_229309, 785 ^ [_229297, _229299, _229301, _229303, _229305, _229307, _229309], _229297))], (789 ^ _200254) ^ [] : [-(apply(_229307, _229299, 785 ^ [_229297, _229299, _229301, _229303, _229305, _229307, _229309]))], (787 ^ _200254) ^ [] : [-(member(785 ^ [_229297, _229299, _229301, _229303, _229305, _229307, _229309], _229303))]]]]], (674 ^ _200254) ^ [_224468, _224470, _224472] : [-(maps(_224472, _224470, _224468)), 689 ^ _200254 : [(692 ^ _200254) ^ [] : [-(member(687 ^ [_224468, _224470, _224472], _224468))], (690 ^ _200254) ^ [] : [-(member(686 ^ [_224468, _224470, _224472], _224470))], (700 ^ _200254) ^ [] : [687 ^ [_224468, _224470, _224472] = 688 ^ [_224468, _224470, _224472]], (696 ^ _200254) ^ [] : [-(apply(_224472, 686 ^ [_224468, _224470, _224472], 687 ^ [_224468, _224470, _224472]))], (698 ^ _200254) ^ [] : [-(apply(_224472, 686 ^ [_224468, _224470, _224472], 688 ^ [_224468, _224470, _224472]))], (694 ^ _200254) ^ [] : [-(member(688 ^ [_224468, _224470, _224472], _224468))]], 678 ^ _200254 : [(681 ^ _200254) ^ [_224808] : [member(_224808, _224468), apply(_224472, 677 ^ [_224468, _224470, _224472], _224808)], (679 ^ _200254) ^ [] : [-(member(677 ^ [_224468, _224470, _224472], _224470))]]], (741 ^ _200254) ^ [_227503, _227505, _227507, _227509, _227511, _227513] : [-(compose_predicate(_227513, _227511, _227509, _227507, _227505, _227503)), 744 ^ _200254 : [(749 ^ _200254) ^ [] : [763 ^ _200254 : [(766 ^ _200254) ^ [] : [-(apply(_227509, 742 ^ [_227503, _227505, _227507, _227509, _227511, _227513], 762 ^ [_227503, _227505, _227507, _227509, _227511, _227513]))], (768 ^ _200254) ^ [] : [-(apply(_227511, 762 ^ [_227503, _227505, _227507, _227509, _227511, _227513], 743 ^ [_227503, _227505, _227507, _227509, _227511, _227513]))], (770 ^ _200254) ^ [] : [apply(_227513, 742 ^ [_227503, _227505, _227507, _227509, _227511, _227513], 743 ^ [_227503, _227505, _227507, _227509, _227511, _227513])], (764 ^ _200254) ^ [] : [-(member(762 ^ [_227503, _227505, _227507, _227509, _227511, _227513], _227505))]], 750 ^ _200254 : [(753 ^ _200254) ^ [_228228] : [member(_228228, _227505), apply(_227509, 742 ^ [_227503, _227505, _227507, _227509, _227511, _227513], _228228), apply(_227511, _228228, 743 ^ [_227503, _227505, _227507, _227509, _227511, _227513])], (751 ^ _200254) ^ [] : [-(apply(_227513, 742 ^ [_227503, _227505, _227507, _227509, _227511, _227513], 743 ^ [_227503, _227505, _227507, _227509, _227511, _227513]))]]], (747 ^ _200254) ^ [] : [-(member(743 ^ [_227503, _227505, _227507, _227509, _227511, _227513], _227503))], (745 ^ _200254) ^ [] : [-(member(742 ^ [_227503, _227505, _227507, _227509, _227511, _227513], _227507))]]], (551 ^ _200254) ^ [_220002] : [member(_220002, empty_set)], (960 ^ _200254) ^ [_237005, _237007, _237009, _237011] : [inverse_predicate(_237011, _237009, _237007, _237005), 963 ^ _200254 : [(964 ^ _200254) ^ [_237187, _237189] : [member(_237189, _237007), member(_237187, _237005), 971 ^ _200254 : [(978 ^ _200254) ^ [] : [apply(_237011, _237187, _237189), -(apply(_237009, _237189, _237187))], (972 ^ _200254) ^ [] : [apply(_237009, _237189, _237187), -(apply(_237011, _237187, _237189))]]]]], (418 ^ _200254) ^ [_215352, _215354, _215356, _215358] : [-(image2(_215358, _215354) = image2(_215356, _215352)), _215358 = _215356, _215354 = _215352], (897 ^ _200254) ^ [_234184, _234186, _234188] : [901 ^ _200254 : [(904 ^ _200254) ^ [] : [-(member(899 ^ [_234184, _234186, _234188], _234186))], (902 ^ _200254) ^ [] : [-(member(898 ^ [_234184, _234186, _234188], _234186))], (912 ^ _200254) ^ [] : [898 ^ [_234184, _234186, _234188] = 899 ^ [_234184, _234186, _234188]], (908 ^ _200254) ^ [] : [-(apply(_234188, 898 ^ [_234184, _234186, _234188], 900 ^ [_234184, _234186, _234188]))], (910 ^ _200254) ^ [] : [-(apply(_234188, 899 ^ [_234184, _234186, _234188], 900 ^ [_234184, _234186, _234188]))], (906 ^ _200254) ^ [] : [-(member(900 ^ [_234184, _234186, _234188], _234184))]], -(injective(_234188, _234186, _234184))], (86 ^ _200254) ^ [_203464, _203466, _203468, _203470] : [-(identity(_203468, _203464)), identity(_203470, _203466), _203470 = _203468, _203466 = _203464], (34 ^ _200254) ^ [_201586, _201588, _201590, _201592, _201594, _201596, _201598, _201600, _201602, _201604, _201606, _201608] : [-(compose_predicate(_201606, _201602, _201598, _201594, _201590, _201586)), compose_predicate(_201608, _201604, _201600, _201596, _201592, _201588), _201608 = _201606, _201604 = _201602, _201600 = _201598, _201596 = _201594, _201592 = _201590, _201588 = _201586], (601 ^ _200254) ^ [_221775, _221777] : [member(_221777, sum(_221775)), 605 ^ _200254 : [(608 ^ _200254) ^ [] : [-(member(_221777, 604 ^ [_221775, _221777]))], (606 ^ _200254) ^ [] : [-(member(604 ^ [_221775, _221777], _221775))]]], (493 ^ _200254) ^ [_218098, _218100] : [-(equal_set(_218100, _218098)), subset(_218100, _218098), subset(_218098, _218100)], (442 ^ _200254) ^ [_216255, _216257, _216259, _216261, _216263, _216265] : [-(inverse_image3(_216265, _216261, _216257) = inverse_image3(_216263, _216259, _216255)), _216265 = _216263, _216261 = _216259, _216257 = _216255], (268 ^ _200254) ^ [_209958, _209960, _209962, _209964, _209966, _209968] : [-(apply(_209966, _209962, _209958)), apply(_209968, _209964, _209960), _209968 = _209966, _209964 = _209962, _209960 = _209958], (254 ^ _200254) ^ [_209486, _209488, _209490, _209492] : [-(member(_209490, _209486)), member(_209492, _209488), _209492 = _209490, _209488 = _209486], (64 ^ _200254) ^ [_202730, _202732, _202734, _202736, _202738, _202740, _202742, _202744] : [-(equal_maps(_202742, _202738, _202734, _202730)), equal_maps(_202744, _202740, _202736, _202732), _202744 = _202742, _202740 = _202738, _202736 = _202734, _202732 = _202730], (916 ^ _200254) ^ [_235273, _235275, _235277] : [surjective(_235277, _235275, _235273), 919 ^ _200254 : [(920 ^ _200254) ^ [_235428] : [member(_235428, _235273), 924 ^ _200254 : [(927 ^ _200254) ^ [] : [-(apply(_235277, 923 ^ [_235273, _235275, _235277, _235428], _235428))], (925 ^ _200254) ^ [] : [-(member(923 ^ [_235273, _235275, _235277, _235428], _235275))]]]]], (1024 ^ _200254) ^ [_239452, _239454, _239456] : [member(_239452, image2(_239456, _239454)), 1028 ^ _200254 : [(1031 ^ _200254) ^ [] : [-(apply(_239456, 1027 ^ [_239452, _239454, _239456], _239452))], (1029 ^ _200254) ^ [] : [-(member(1027 ^ [_239452, _239454, _239456], _239454))]]], (1170 ^ _200254) ^ [_245883, _245885, _245887, _245889, _245891] : [decreasing(_245891, _245889, _245887, _245885, _245883), 1173 ^ _200254 : [(1174 ^ _200254) ^ [_246135, _246137, _246139, _246141] : [-(apply(_245883, _246135, _246139)), member(_246141, _245889), member(_246139, _245885), member(_246137, _245889), member(_246135, _245885), apply(_245887, _246141, _246137), apply(_245891, _246141, _246139), apply(_245891, _246137, _246135)]]], (1146 ^ _200254) ^ [_244143, _244145, _244147, _244149, _244151] : [1151 ^ _200254 : [(1156 ^ _200254) ^ [] : [-(member(1149 ^ [_244143, _244145, _244147, _244149, _244151], _244149))], (1162 ^ _200254) ^ [] : [-(apply(_244151, 1147 ^ [_244143, _244145, _244147, _244149, _244151], 1148 ^ [_244143, _244145, _244147, _244149, _244151]))], (1152 ^ _200254) ^ [] : [-(member(1147 ^ [_244143, _244145, _244147, _244149, _244151], _244149))], (1164 ^ _200254) ^ [] : [-(apply(_244151, 1149 ^ [_244143, _244145, _244147, _244149, _244151], 1150 ^ [_244143, _244145, _244147, _244149, _244151]))], (1158 ^ _200254) ^ [] : [-(member(1150 ^ [_244143, _244145, _244147, _244149, _244151], _244145))], (1160 ^ _200254) ^ [] : [-(apply(_244147, 1147 ^ [_244143, _244145, _244147, _244149, _244151], 1149 ^ [_244143, _244145, _244147, _244149, _244151]))], (1166 ^ _200254) ^ [] : [apply(_244143, 1148 ^ [_244143, _244145, _244147, _244149, _244151], 1150 ^ [_244143, _244145, _244147, _244149, _244151])], (1154 ^ _200254) ^ [] : [-(member(1148 ^ [_244143, _244145, _244147, _244149, _244151], _244145))]], -(increasing(_244151, _244149, _244147, _244145, _244143))], (523 ^ _200254) ^ [_219104, _219106, _219108] : [-(member(_219108, intersection(_219106, _219104))), member(_219108, _219106), member(_219108, _219104)], (1077 ^ _200254) ^ [_241525, _241527, _241529] : [-(member(_241525, inverse_image2(_241529, _241527))), 1078 ^ _200254 : [(1079 ^ _200254) ^ [_241623] : [member(_241623, _241527), apply(_241529, _241525, _241623)]]], (344 ^ _200254) ^ [_212586, _212588, _212590, _212592] : [-(difference(_212592, _212588) = difference(_212590, _212586)), _212592 = _212590, _212588 = _212586], (852 ^ _200254) ^ [_232625, _232627] : [identity(_232627, _232625), 855 ^ _200254 : [(856 ^ _200254) ^ [_232763] : [member(_232763, _232625), -(apply(_232627, _232763, _232763))]]]], input).
% 81.28/78.88  ncf('1',plain,[-(subset(1312 ^ [], 1313 ^ []))],start(1321 ^ 0)).
% 81.28/78.88  ncf('1.1',plain,[subset(1312 ^ [], 1313 ^ []), 470 : member(1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []], 1312 ^ []), 470 : -(member(1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []], 1313 ^ []))],extension(466 ^ 1,bind([[_217161, _217163, _217298], [1313 ^ [], 1312 ^ [], 1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []]]]))).
% 81.28/78.88  ncf('1.1.1',plain,[-(member(1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []], 1312 ^ [])), member(477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], inverse_image2(1309 ^ [], 1312 ^ []))],extension(1068 ^ 4,bind([[_241193, _241195, _241197], [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []]]))).
% 81.28/78.88  ncf('1.1.1.1',plain,[-(member(477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], inverse_image2(1309 ^ [], 1312 ^ []))), -(subset(inverse_image2(1309 ^ [], 1312 ^ []), inverse_image2(1309 ^ [], 1313 ^ [])))],extension(476 ^ 5,bind([[_217475, _217477], [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])]]))).
% 81.28/78.88  ncf('1.1.1.1.1',plain,[subset(inverse_image2(1309 ^ [], 1312 ^ []), inverse_image2(1309 ^ [], 1313 ^ []))],extension(1323 ^ 6)).
% 81.28/78.88  ncf('1.1.2',plain,[member(1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []], 1313 ^ []), 1079 : apply(1309 ^ [], 477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []]), 1079 : -(member(477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], inverse_image2(1309 ^ [], 1313 ^ [])))],extension(1077 ^ 4,bind([[_241525, _241527, _241529, _241623], [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1313 ^ [], 1309 ^ [], 1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []]]]))).
% 81.28/78.88  ncf('1.1.2.1',plain,[-(apply(1309 ^ [], 477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1071 ^ [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []])), member(477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], inverse_image2(1309 ^ [], 1312 ^ []))],extension(1068 ^ 7,bind([[_241193, _241195, _241197], [477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], 1312 ^ [], 1309 ^ []]]))).
% 81.28/78.88  ncf('1.1.2.1.1',plain,[-(member(477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], inverse_image2(1309 ^ [], 1312 ^ []))), -(subset(inverse_image2(1309 ^ [], 1312 ^ []), inverse_image2(1309 ^ [], 1313 ^ [])))],extension(476 ^ 8,bind([[_217475, _217477], [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])]]))).
% 81.28/78.88  ncf('1.1.2.1.1.1',plain,[subset(inverse_image2(1309 ^ [], 1312 ^ []), inverse_image2(1309 ^ [], 1313 ^ []))],extension(1323 ^ 9)).
% 81.28/78.88  ncf('1.1.2.2',plain,[member(477 ^ [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])], inverse_image2(1309 ^ [], 1313 ^ [])), -(subset(inverse_image2(1309 ^ [], 1312 ^ []), inverse_image2(1309 ^ [], 1313 ^ [])))],extension(476 ^ 5,bind([[_217475, _217477], [inverse_image2(1309 ^ [], 1313 ^ []), inverse_image2(1309 ^ [], 1312 ^ [])]]))).
% 81.28/78.88  ncf('1.1.2.2.1',plain,[subset(inverse_image2(1309 ^ [], 1312 ^ []), inverse_image2(1309 ^ [], 1313 ^ []))],extension(1323 ^ 6)).
% 81.28/78.88  %-----------------------------------------------------
% 81.28/78.88  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------