TSTP Solution File: SEU206+2 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SEU206+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n017.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 12:02:39 EDT 2023
% Result : Theorem 71.62s 69.80s
% Output : Proof 71.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU206+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n017.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 12:18:30 EDT 2023
% 0.12/0.33 % CPUTime :
% 71.62/69.80
% 71.62/69.80 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 71.62/69.80 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.62/69.80 %-----------------------------------------------------
% 71.62/69.80 ncf(matrix, plain, [(2732 ^ _496417) ^ [] : [relation_image(2728 ^ [], relation_dom(2728 ^ [])) = relation_rng(2728 ^ [])], (2730 ^ _496417) ^ [] : [-(relation(2728 ^ []))], !, (2376 ^ _399050) ^ [_482708] : [relation(_482708), 2379 ^ _399050 : [(2380 ^ _399050) ^ [_482855] : [relation(_482855), subset(relation_dom(_482708), relation_rng(_482855)), -(relation_rng(relation_composition(_482855, _482708)) = relation_rng(_482708))]]], (2203 ^ _399050) ^ [_476742, _476744] : [subset(_476744, _476742), -(set_difference(_476744, _476742) = empty_set)], (350 ^ _399050) ^ [_411276] : [empty(_411276), -(relation(_411276))], (332 ^ _399050) ^ [_410536, _410538] : [_410538 = _410536, -(relation_rng(_410538) = relation_rng(_410536))], (86 ^ _399050) ^ [_401897, _401899, _401901, _401903] : [-(are_equipotent(_401901, _401897)), are_equipotent(_401903, _401899), _401903 = _401901, _401899 = _401897], (48 ^ _399050) ^ [_400714, _400716, _400718, _400720] : [-(disjoint(_400718, _400714)), disjoint(_400720, _400716), _400720 = _400718, _400716 = _400714], (2300 ^ _399050) ^ [_480150, _480152] : [element(_480150, powerset(_480152)), 2303 ^ _399050 : [(2304 ^ _399050) ^ [_480302] : [element(_480302, powerset(_480152)), 2307 ^ _399050 : [(2314 ^ _399050) ^ [] : [subset(_480150, subset_complement(_480152, _480302)), -(disjoint(_480150, _480302))], (2308 ^ _399050) ^ [] : [disjoint(_480150, _480302), -(subset(_480150, subset_complement(_480152, _480302)))]]]]], (2667 ^ _399050) ^ [_492482, _492484] : [in(_492484, _492482), -(subset(_492484, union(_492482)))], (1406 ^ _399050) ^ [] : [true___, -(true___)], (1337 ^ _399050) ^ [_447928, _447930] : [element(_447928, powerset(powerset(_447930))), 1340 ^ _399050 : [(1341 ^ _399050) ^ [_448108] : [element(_448108, powerset(powerset(_447930))), 1344 ^ _399050 : [(1345 ^ _399050) ^ [] : [_448108 = complements_of_subsets(_447930, _447928), 1348 ^ _399050 : [(1349 ^ _399050) ^ [_448396] : [element(_448396, powerset(_447930)), 1352 ^ _399050 : [(1359 ^ _399050) ^ [] : [in(subset_complement(_447930, _448396), _447928), -(in(_448396, _448108))], (1353 ^ _399050) ^ [] : [in(_448396, _448108), -(in(subset_complement(_447930, _448396), _447928))]]]]], (1365 ^ _399050) ^ [] : [-(_448108 = complements_of_subsets(_447930, _447928)), 1367 ^ _399050 : [(1370 ^ _399050) ^ [] : [1371 ^ _399050 : [(1374 ^ _399050) ^ [] : [in(subset_complement(_447930, 1366 ^ [_447928, _447930, _448108]), _447928)], (1372 ^ _399050) ^ [] : [-(in(1366 ^ [_447928, _447930, _448108], _448108))]], 1375 ^ _399050 : [(1378 ^ _399050) ^ [] : [in(1366 ^ [_447928, _447930, _448108], _448108)], (1376 ^ _399050) ^ [] : [-(in(subset_complement(_447930, 1366 ^ [_447928, _447930, _448108]), _447928))]]], (1368 ^ _399050) ^ [] : [-(element(1366 ^ [_447928, _447930, _448108], powerset(_447930)))]]]]]]], (1697 ^ _399050) ^ [_458715, _458717] : [element(_458715, powerset(powerset(_458717))), -(complements_of_subsets(_458717, complements_of_subsets(_458717, _458715)) = _458715)], (326 ^ _399050) ^ [_410338, _410340] : [_410340 = _410338, -(relation_dom(_410340) = relation_dom(_410338))], (2360 ^ _399050) ^ [_482185, _482187] : [element(_482185, powerset(powerset(_482187))), -(_482185 = empty_set), complements_of_subsets(_482187, _482185) = empty_set], (410 ^ _399050) ^ [_413457, _413459] : [_413459 = _413457, 413 ^ _399050 : [(416 ^ _399050) ^ [] : [-(subset(_413457, _413459))], (414 ^ _399050) ^ [] : [-(subset(_413459, _413457))]]], (418 ^ _399050) ^ [_413694, _413696] : [-(_413696 = _413694), subset(_413696, _413694), subset(_413694, _413696)], (1707 ^ _399050) ^ [_459117, _459119] : [in(_459119, _459117), -(set_union2(singleton(_459119), _459117) = _459117)], (1550 ^ _399050) ^ [] : [true___, -(true___)], (1279 ^ _399050) ^ [_445412] : [relation(_445412), 1282 ^ _399050 : [(1283 ^ _399050) ^ [_445597] : [relation(_445597), 1286 ^ _399050 : [(1287 ^ _399050) ^ [_445778] : [relation(_445778), 1290 ^ _399050 : [(1291 ^ _399050) ^ [] : [_445778 = relation_composition(_445412, _445597), 1294 ^ _399050 : [(1304 ^ _399050) ^ [_446498, _446500] : [-(in(ordered_pair(_446500, _446498), _445778)), 1305 ^ _399050 : [(1306 ^ _399050) ^ [_446611] : [in(ordered_pair(_446500, _446611), _445412), in(ordered_pair(_446611, _446498), _445597)]]], (1295 ^ _399050) ^ [_446113, _446115] : [in(ordered_pair(_446115, _446113), _445778), 1299 ^ _399050 : [(1302 ^ _399050) ^ [] : [-(in(ordered_pair(1298 ^ [_445412, _445597, _445778, _446113, _446115], _446113), _445597))], (1300 ^ _399050) ^ [] : [-(in(ordered_pair(_446115, 1298 ^ [_445412, _445597, _445778, _446113, _446115]), _445412))]]]]], (1314 ^ _399050) ^ [] : [-(_445778 = relation_composition(_445412, _445597)), 1328 ^ _399050 : [(1333 ^ _399050) ^ [] : [in(ordered_pair(1315 ^ [_445412, _445597, _445778], 1316 ^ [_445412, _445597, _445778]), _445778)], (1331 ^ _399050) ^ [] : [-(in(ordered_pair(1327 ^ [_445412, _445597, _445778], 1316 ^ [_445412, _445597, _445778]), _445597))], (1329 ^ _399050) ^ [] : [-(in(ordered_pair(1315 ^ [_445412, _445597, _445778], 1327 ^ [_445412, _445597, _445778]), _445412))]], 1319 ^ _399050 : [(1322 ^ _399050) ^ [_447242] : [in(ordered_pair(1315 ^ [_445412, _445597, _445778], _447242), _445412), in(ordered_pair(_447242, 1316 ^ [_445412, _445597, _445778]), _445597)], (1320 ^ _399050) ^ [] : [-(in(ordered_pair(1315 ^ [_445412, _445597, _445778], 1316 ^ [_445412, _445597, _445778]), _445778))]]]]]]]]], (1605 ^ _399050) ^ [_455696, _455698] : [-(empty(_455698)), empty(set_union2(_455698, _455696))], (2 ^ _399050) ^ [_399174] : [-(_399174 = _399174)], (2535 ^ _399050) ^ [_488022, _488024] : [set_difference(_488024, singleton(_488022)) = _488024, in(_488022, _488024)], (2491 ^ _399050) ^ [_486668, _486670] : [subset(_486670, _486668), proper_subset(_486668, _486670)], (1779 ^ _399050) ^ [_461582, _461584] : [1780 ^ _399050 : [(1783 ^ _399050) ^ [] : [_461584 = singleton(_461582)], (1781 ^ _399050) ^ [] : [_461584 = empty_set]], -(subset(_461584, singleton(_461582)))], (1703 ^ _399050) ^ [_458929, _458931] : [proper_subset(_458931, _458931)], (2298 ^ _399050) ^ [_480032, _480034] : [-(set_difference(set_union2(_480034, _480032), _480032) = set_difference(_480034, _480032))], (2645 ^ _399050) ^ [_491699, _491701, _491703] : [-(subset(set_union2(_491703, _491699), _491701)), subset(_491703, _491701), subset(_491699, _491701)], (2120 ^ _399050) ^ [_473737, _473739, _473741] : [subset(_473741, _473739), -(subset(set_intersection2(_473741, _473737), set_intersection2(_473739, _473737)))], (1508 ^ _399050) ^ [_452522, _452524] : [element(_452522, powerset(powerset(_452524))), -(element(union_of_subsets(_452524, _452522), powerset(_452524)))], (1942 ^ _399050) ^ [_467344, _467346] : [relation(_467344), -(subset(relation_rng(relation_rng_restriction(_467346, _467344)), relation_rng(_467344)))], (2346 ^ _399050) ^ [_481712] : [relation(_481712), 2349 ^ _399050 : [(2350 ^ _399050) ^ [_481859] : [relation(_481859), subset(relation_rng(_481712), relation_dom(_481859)), -(relation_dom(relation_composition(_481712, _481859)) = relation_dom(_481712))]]], (1456 ^ _399050) ^ [] : [true___, -(true___)], (1444 ^ _399050) ^ [] : [true___, -(true___)], (1948 ^ _399050) ^ [_467580, _467582, _467584] : [subset(_467584, _467582), 1951 ^ _399050 : [(1954 ^ _399050) ^ [] : [-(subset(cartesian_product2(_467580, _467584), cartesian_product2(_467580, _467582)))], (1952 ^ _399050) ^ [] : [-(subset(cartesian_product2(_467584, _467580), cartesian_product2(_467582, _467580)))]]], (1480 ^ _399050) ^ [_451781] : [relation(_451781), -(relation(relation_inverse(_451781)))], (1438 ^ _399050) ^ [] : [true___, -(true___)], (1685 ^ _399050) ^ [_458293, _458295] : [element(_458293, powerset(_458295)), -(subset_complement(_458295, subset_complement(_458295, _458293)) = _458293)], (2487 ^ _399050) ^ [] : [-(relation_dom(empty_set) = empty_set)], (1843 ^ _399050) ^ [_463861] : [-(element(1841 ^ [_463861], powerset(_463861)))], (1611 ^ _399050) ^ [_455896, _455898] : [empty(unordered_pair(_455898, _455896))], (1743 ^ _399050) ^ [_460375, _460377] : [subset(_460377, _460375), -(set_difference(_460377, _460375) = empty_set)], (1840 ^ _399050) ^ [] : [-(relation(1836 ^ []))], (1474 ^ _399050) ^ [] : [true___, -(true___)], (242 ^ _399050) ^ [_407340, _407342, _407344, _407346] : [-(set_union2(_407346, _407342) = set_union2(_407344, _407340)), _407346 = _407344, _407342 = _407340], (1436 ^ _399050) ^ [_450746] : [-(element(cast_to_subset(_450746), powerset(_450746)))], (2593 ^ _399050) ^ [_489974, _489976] : [-(subset(_489976, set_union2(_489976, _489974)))], (836 ^ _399050) ^ [_428717, _428719, _428721] : [-(_428717 = unordered_pair(_428721, _428719)), 840 ^ _399050 : [(845 ^ _399050) ^ [] : [837 ^ [_428717, _428719, _428721] = _428719], (843 ^ _399050) ^ [] : [837 ^ [_428717, _428719, _428721] = _428721], (841 ^ _399050) ^ [] : [-(in(837 ^ [_428717, _428719, _428721], _428717))]], 846 ^ _399050 : [(847 ^ _399050) ^ [] : [-(837 ^ [_428717, _428719, _428721] = _428721), -(837 ^ [_428717, _428719, _428721] = _428719)], (853 ^ _399050) ^ [] : [in(837 ^ [_428717, _428719, _428721], _428717)]]], (1643 ^ _399050) ^ [_456900] : [empty(relation_rng(_456900)), -(empty(_456900)), relation(_456900)], (698 ^ _399050) ^ [_424076] : [_424076 = empty_set, 701 ^ _399050 : [(702 ^ _399050) ^ [_424189] : [in(_424189, _424076)]]], (2267 ^ _399050) ^ [_478944, _478946] : [subset(_478946, _478944), -(element(_478946, powerset(_478944)))], (1577 ^ _399050) ^ [_454794, _454796] : [-(relation(set_intersection2(_454796, _454794))), relation(_454796), relation(_454794)], (782 ^ _399050) ^ [_427079, _427081] : [-(empty(_427081)), 785 ^ _399050 : [(792 ^ _399050) ^ [] : [in(_427079, _427081), -(element(_427079, _427081))], (786 ^ _399050) ^ [] : [element(_427079, _427081), -(in(_427079, _427081))]]], (2189 ^ _399050) ^ [_476246] : [relation(_476246), 2192 ^ _399050 : [(2195 ^ _399050) ^ [] : [-(relation_dom(_476246) = relation_rng(relation_inverse(_476246)))], (2193 ^ _399050) ^ [] : [-(relation_rng(_476246) = relation_dom(relation_inverse(_476246)))]]], (2161 ^ _399050) ^ [_475182, _475184, _475186] : [relation(_475182), in(ordered_pair(_475186, _475184), _475182), 2168 ^ _399050 : [(2171 ^ _399050) ^ [] : [-(in(_475184, relation_field(_475182)))], (2169 ^ _399050) ^ [] : [-(in(_475186, relation_field(_475182)))]]], (1424 ^ _399050) ^ [] : [true___, -(true___)], (2561 ^ _399050) ^ [_488900] : [-(relation_dom(identity_relation(_488900)) = _488900)], (2507 ^ _399050) ^ [_487186] : [relation(_487186), 2512 ^ _399050 : [(2515 ^ _399050) ^ [] : [relation_rng(_487186) = empty_set], (2513 ^ _399050) ^ [] : [relation_dom(_487186) = empty_set]], -(_487186 = empty_set)], (1227 ^ _399050) ^ [_443533] : [relation(_443533), 1230 ^ _399050 : [(1231 ^ _399050) ^ [_443693] : [relation(_443693), 1234 ^ _399050 : [(1235 ^ _399050) ^ [] : [_443693 = relation_inverse(_443533), 1238 ^ _399050 : [(1245 ^ _399050) ^ [_444192, _444194] : [in(ordered_pair(_444192, _444194), _443533), -(in(ordered_pair(_444194, _444192), _443693))], (1239 ^ _399050) ^ [_444002, _444004] : [in(ordered_pair(_444004, _444002), _443693), -(in(ordered_pair(_444002, _444004), _443533))]]], (1251 ^ _399050) ^ [] : [-(_443693 = relation_inverse(_443533)), 1256 ^ _399050 : [(1259 ^ _399050) ^ [] : [in(ordered_pair(1253 ^ [_443533, _443693], 1252 ^ [_443533, _443693]), _443533)], (1257 ^ _399050) ^ [] : [-(in(ordered_pair(1252 ^ [_443533, _443693], 1253 ^ [_443533, _443693]), _443693))]], 1260 ^ _399050 : [(1263 ^ _399050) ^ [] : [in(ordered_pair(1252 ^ [_443533, _443693], 1253 ^ [_443533, _443693]), _443693)], (1261 ^ _399050) ^ [] : [-(in(ordered_pair(1253 ^ [_443533, _443693], 1252 ^ [_443533, _443693]), _443533))]]]]]]], (2239 ^ _399050) ^ [_477967, _477969] : [-(set_union2(_477969, set_difference(_477967, _477969)) = set_union2(_477969, _477967))], (1133 ^ _399050) ^ [_440081, _440083, _440085] : [_440081 = set_difference(_440085, _440083), 1136 ^ _399050 : [(1145 ^ _399050) ^ [_440525] : [-(in(_440525, _440081)), in(_440525, _440085), -(in(_440525, _440083))], (1137 ^ _399050) ^ [_440265] : [in(_440265, _440081), 1140 ^ _399050 : [(1143 ^ _399050) ^ [] : [in(_440265, _440083)], (1141 ^ _399050) ^ [] : [-(in(_440265, _440085))]]]]], (1991 ^ _399050) ^ [_469233, _469235] : [in(_469233, 1977 ^ [_469235]), -(in(powerset(_469233), 1977 ^ [_469235]))], (930 ^ _399050) ^ [_432287, _432289, _432291] : [-(_432287 = cartesian_product2(_432291, _432289)), 948 ^ _399050 : [(951 ^ _399050) ^ [] : [-(in(947 ^ [_432287, _432289, _432291], _432289))], (953 ^ _399050) ^ [] : [-(931 ^ [_432287, _432289, _432291] = ordered_pair(946 ^ [_432287, _432289, _432291], 947 ^ [_432287, _432289, _432291]))], (955 ^ _399050) ^ [] : [in(931 ^ [_432287, _432289, _432291], _432287)], (949 ^ _399050) ^ [] : [-(in(946 ^ [_432287, _432289, _432291], _432291))]], 934 ^ _399050 : [(937 ^ _399050) ^ [_432625, _432627] : [in(_432627, _432291), in(_432625, _432289), 931 ^ [_432287, _432289, _432291] = ordered_pair(_432627, _432625)], (935 ^ _399050) ^ [] : [-(in(931 ^ [_432287, _432289, _432291], _432287))]]], (2555 ^ _399050) ^ [_488691, _488693] : [subset(singleton(_488693), singleton(_488691)), -(_488693 = _488691)], (156 ^ _399050) ^ [_404206, _404208] : [_404208 = _404206, -(relation_inverse(_404208) = relation_inverse(_404206))], (1155 ^ _399050) ^ [_440812, _440814, _440816] : [-(_440812 = set_difference(_440816, _440814)), 1167 ^ _399050 : [(1172 ^ _399050) ^ [] : [in(1156 ^ [_440812, _440814, _440816], _440812)], (1170 ^ _399050) ^ [] : [in(1156 ^ [_440812, _440814, _440816], _440814)], (1168 ^ _399050) ^ [] : [-(in(1156 ^ [_440812, _440814, _440816], _440816))]], 1159 ^ _399050 : [(1162 ^ _399050) ^ [] : [in(1156 ^ [_440812, _440814, _440816], _440816), -(in(1156 ^ [_440812, _440814, _440816], _440814))], (1160 ^ _399050) ^ [] : [-(in(1156 ^ [_440812, _440814, _440816], _440812))]]], (959 ^ _399050) ^ [_433521] : [relation(_433521), 962 ^ _399050 : [(963 ^ _399050) ^ [_433679] : [relation(_433679), 966 ^ _399050 : [(967 ^ _399050) ^ [] : [subset(_433521, _433679), 970 ^ _399050 : [(971 ^ _399050) ^ [_433955, _433957] : [in(ordered_pair(_433957, _433955), _433521), -(in(ordered_pair(_433957, _433955), _433679))]]], (977 ^ _399050) ^ [] : [980 ^ _399050 : [(983 ^ _399050) ^ [] : [in(ordered_pair(978 ^ [_433521, _433679], 979 ^ [_433521, _433679]), _433679)], (981 ^ _399050) ^ [] : [-(in(ordered_pair(978 ^ [_433521, _433679], 979 ^ [_433521, _433679]), _433521))]], -(subset(_433521, _433679))]]]]], (362 ^ _399050) ^ [_411776, _411778] : [relation(_411776), 365 ^ _399050 : [(366 ^ _399050) ^ [] : [_411776 = identity_relation(_411778), 369 ^ _399050 : [(378 ^ _399050) ^ [_412349, _412351] : [-(in(ordered_pair(_412351, _412349), _411776)), in(_412351, _411778), _412351 = _412349], (370 ^ _399050) ^ [_412086, _412088] : [in(ordered_pair(_412088, _412086), _411776), 373 ^ _399050 : [(376 ^ _399050) ^ [] : [-(_412088 = _412086)], (374 ^ _399050) ^ [] : [-(in(_412088, _411778))]]]]], (388 ^ _399050) ^ [] : [-(_411776 = identity_relation(_411778)), 401 ^ _399050 : [(406 ^ _399050) ^ [] : [in(ordered_pair(389 ^ [_411776, _411778], 390 ^ [_411776, _411778]), _411776)], (404 ^ _399050) ^ [] : [-(389 ^ [_411776, _411778] = 390 ^ [_411776, _411778])], (402 ^ _399050) ^ [] : [-(in(389 ^ [_411776, _411778], _411778))]], 393 ^ _399050 : [(396 ^ _399050) ^ [] : [in(389 ^ [_411776, _411778], _411778), 389 ^ [_411776, _411778] = 390 ^ [_411776, _411778]], (394 ^ _399050) ^ [] : [-(in(ordered_pair(389 ^ [_411776, _411778], 390 ^ [_411776, _411778]), _411776))]]]]], (1486 ^ _399050) ^ [] : [true___, -(true___)], (704 ^ _399050) ^ [_424255] : [-(in(705 ^ [_424255], _424255)), -(_424255 = empty_set)], (2489 ^ _399050) ^ [] : [-(relation_rng(empty_set) = empty_set)], (344 ^ _399050) ^ [_411079, _411081] : [proper_subset(_411081, _411079), proper_subset(_411079, _411081)], (1845 ^ _399050) ^ [_463912] : [-(empty(1841 ^ [_463912]))], (1691 ^ _399050) ^ [_458505] : [relation(_458505), -(relation_inverse(relation_inverse(_458505)) = _458505)], (1908 ^ _399050) ^ [_466253, _466255, _466257] : [relation(_466253), 1911 ^ _399050 : [(1920 ^ _399050) ^ [] : [-(in(_466257, relation_rng(relation_rng_restriction(_466255, _466253)))), in(_466257, _466255), in(_466257, relation_rng(_466253))], (1912 ^ _399050) ^ [] : [in(_466257, relation_rng(relation_rng_restriction(_466255, _466253))), 1915 ^ _399050 : [(1918 ^ _399050) ^ [] : [-(in(_466257, relation_rng(_466253)))], (1916 ^ _399050) ^ [] : [-(in(_466257, _466255))]]]]], (1661 ^ _399050) ^ [_457442] : [empty(_457442), 1664 ^ _399050 : [(1667 ^ _399050) ^ [] : [-(relation(relation_rng(_457442)))], (1665 ^ _399050) ^ [] : [-(empty(relation_rng(_457442)))]]], (1823 ^ _399050) ^ [] : [-(relation(1819 ^ []))], (1821 ^ _399050) ^ [] : [-(empty(1819 ^ []))], (1872 ^ _399050) ^ [_464901, _464903] : [-(subset(_464903, _464903))], (2173 ^ _399050) ^ [_475594, _475596, _475598] : [subset(_475598, _475596), -(subset(set_difference(_475598, _475594), set_difference(_475596, _475594)))], (140 ^ _399050) ^ [_403657, _403659, _403661, _403663] : [-(cartesian_product2(_403663, _403659) = cartesian_product2(_403661, _403657)), _403663 = _403661, _403659 = _403657], (300 ^ _399050) ^ [_409402, _409404] : [_409404 = _409402, -(singleton(_409404) = singleton(_409402))], (1725 ^ _399050) ^ [_459796, _459798] : [subset(singleton(_459798), _459796), -(in(_459798, _459796))], (2104 ^ _399050) ^ [_473178] : [relation(_473178), 2107 ^ _399050 : [(2108 ^ _399050) ^ [_473328] : [relation(_473328), subset(_473178, _473328), 2115 ^ _399050 : [(2118 ^ _399050) ^ [] : [-(subset(relation_rng(_473178), relation_rng(_473328)))], (2116 ^ _399050) ^ [] : [-(subset(relation_dom(_473178), relation_dom(_473328)))]]]]], (1862 ^ _399050) ^ [_464585, _464587, _464589] : [-(subset_difference(_464589, _464587, _464585) = set_difference(_464587, _464585)), element(_464587, powerset(_464589)), element(_464585, powerset(_464589))], (2007 ^ _399050) ^ [_469787, _469789, _469791] : [relation(_469787), -(relation_dom_restriction(relation_rng_restriction(_469791, _469787), _469789) = relation_rng_restriction(_469791, relation_dom_restriction(_469787, _469789)))], (124 ^ _399050) ^ [_403052, _403054] : [_403054 = _403052, -(set_meet(_403054) = set_meet(_403052))], (581 ^ _399050) ^ [_419911] : [relation(_419911), 584 ^ _399050 : [(585 ^ _399050) ^ [_420059] : [in(_420059, _419911), -(_420059 = ordered_pair(588 ^ [_419911, _420059], 589 ^ [_419911, _420059]))]]], (1213 ^ _399050) ^ [_443010, _443012] : [element(_443010, powerset(_443012)), -(subset_complement(_443012, _443010) = set_difference(_443012, _443010))], (1972 ^ _399050) ^ [_468484, _468486] : [subset(_468486, _468484), -(set_union2(_468486, _468484) = _468484)], (1176 ^ _399050) ^ [_441555] : [relation(_441555), 1179 ^ _399050 : [(1180 ^ _399050) ^ [_441736] : [_441736 = relation_rng(_441555), 1183 ^ _399050 : [(1191 ^ _399050) ^ [_442160] : [1192 ^ _399050 : [(1193 ^ _399050) ^ [_442239] : [in(ordered_pair(_442239, _442160), _441555)]], -(in(_442160, _441736))], (1184 ^ _399050) ^ [_441916] : [in(_441916, _441736), -(in(ordered_pair(1187 ^ [_441555, _441736, _441916], _441916), _441555))]]], (1197 ^ _399050) ^ [_442367] : [-(_442367 = relation_rng(_441555)), 1201 ^ _399050 : [(1204 ^ _399050) ^ [_442630] : [in(ordered_pair(_442630, 1198 ^ [_441555, _442367]), _441555)], (1202 ^ _399050) ^ [] : [-(in(1198 ^ [_441555, _442367], _442367))]], 1206 ^ _399050 : [(1209 ^ _399050) ^ [] : [in(1198 ^ [_441555, _442367], _442367)], (1207 ^ _399050) ^ [] : [-(in(ordered_pair(1205 ^ [_441555, _442367], 1198 ^ [_441555, _442367]), _441555))]]]]], (2068 ^ _399050) ^ [_471992, _471994] : [in(_471994, _471992), -(element(_471994, _471992))], (2565 ^ _399050) ^ [_489089, _489091, _489093, _489095] : [relation(_489089), 2568 ^ _399050 : [(2577 ^ _399050) ^ [] : [-(in(ordered_pair(_489095, _489093), relation_composition(identity_relation(_489091), _489089))), in(_489095, _489091), in(ordered_pair(_489095, _489093), _489089)], (2569 ^ _399050) ^ [] : [in(ordered_pair(_489095, _489093), relation_composition(identity_relation(_489091), _489089)), 2572 ^ _399050 : [(2575 ^ _399050) ^ [] : [-(in(ordered_pair(_489095, _489093), _489089))], (2573 ^ _399050) ^ [] : [-(in(_489095, _489091))]]]]], (2685 ^ _399050) ^ [_493113] : [-(union(powerset(_493113)) = _493113)], (1587 ^ _399050) ^ [_455063] : [empty(powerset(_455063))], (100 ^ _399050) ^ [_402341, _402343, _402345, _402347] : [-(in(_402345, _402341)), in(_402347, _402343), _402347 = _402345, _402343 = _402341], (2424 ^ _399050) ^ [_484392, _484394] : [-(disjoint(_484394, _484392)), -(in(2427 ^ [_484392, _484394], set_intersection2(_484394, _484392)))], (2282 ^ _399050) ^ [_479494, _479496] : [disjoint(_479496, _479494), 2283 ^ _399050 : [(2284 ^ _399050) ^ [_479586] : [in(_479586, _479496), in(_479586, _479494)]]], (1468 ^ _399050) ^ [] : [true___, -(true___)], (72 ^ _399050) ^ [_401453, _401455, _401457, _401459] : [-(subset(_401457, _401453)), subset(_401459, _401455), _401459 = _401457, _401455 = _401453], (1633 ^ _399050) ^ [_456623] : [empty(relation_dom(_456623)), -(empty(_456623)), relation(_456623)], (1653 ^ _399050) ^ [_457177] : [empty(_457177), 1656 ^ _399050 : [(1659 ^ _399050) ^ [] : [-(relation(relation_dom(_457177)))], (1657 ^ _399050) ^ [] : [-(empty(relation_dom(_457177)))]]], (798 ^ _399050) ^ [_427492, _427494] : [empty(_427494), 801 ^ _399050 : [(808 ^ _399050) ^ [] : [empty(_427492), -(element(_427492, _427494))], (802 ^ _399050) ^ [] : [element(_427492, _427494), -(empty(_427492))]]], (1956 ^ _399050) ^ [_467897, _467899] : [relation(_467897), -(relation_rng(relation_rng_restriction(_467899, _467897)) = set_intersection2(relation_rng(_467897), _467899))], (727 ^ _399050) ^ [_425067, _425069] : [-(_425067 = powerset(_425069)), 731 ^ _399050 : [(734 ^ _399050) ^ [] : [subset(728 ^ [_425067, _425069], _425069)], (732 ^ _399050) ^ [] : [-(in(728 ^ [_425067, _425069], _425067))]], 735 ^ _399050 : [(738 ^ _399050) ^ [] : [in(728 ^ [_425067, _425069], _425067)], (736 ^ _399050) ^ [] : [-(subset(728 ^ [_425067, _425069], _425069))]]], (1450 ^ _399050) ^ [] : [true___, -(true___)], (1522 ^ _399050) ^ [_453071, _453073, _453075] : [-(element(subset_difference(_453075, _453073, _453071), powerset(_453075))), element(_453073, powerset(_453075)), element(_453071, powerset(_453075))], (2197 ^ _399050) ^ [_476574, _476576] : [set_difference(_476576, _476574) = empty_set, -(subset(_476576, _476574))], (1705 ^ _399050) ^ [_459008] : [singleton(_459008) = empty_set], (683 ^ _399050) ^ [_423525, _423527] : [-(_423525 = singleton(_423527)), 687 ^ _399050 : [(690 ^ _399050) ^ [] : [684 ^ [_423525, _423527] = _423527], (688 ^ _399050) ^ [] : [-(in(684 ^ [_423525, _423527], _423525))]], 691 ^ _399050 : [(694 ^ _399050) ^ [] : [in(684 ^ [_423525, _423527], _423525)], (692 ^ _399050) ^ [] : [-(684 ^ [_423525, _423527] = _423527)]]], (1825 ^ _399050) ^ [_463239] : [-(empty(_463239)), 1829 ^ _399050 : [(1832 ^ _399050) ^ [] : [empty(1828 ^ [_463239])], (1830 ^ _399050) ^ [] : [-(element(1828 ^ [_463239], powerset(_463239)))]]], (196 ^ _399050) ^ [_405658, _405660] : [_405660 = _405658, -(cast_to_subset(_405660) = cast_to_subset(_405658))], (997 ^ _399050) ^ [_434918, _434920] : [999 ^ _399050 : [(1002 ^ _399050) ^ [] : [in(998 ^ [_434918, _434920], _434918)], (1000 ^ _399050) ^ [] : [-(in(998 ^ [_434918, _434920], _434920))]], -(subset(_434920, _434918))], (252 ^ _399050) ^ [_407699, _407701, _407703, _407705] : [-(set_intersection2(_407705, _407701) = set_intersection2(_407703, _407699)), _407705 = _407703, _407701 = _407699], (1400 ^ _399050) ^ [] : [true___, -(true___)], (1681 ^ _399050) ^ [_458084, _458086] : [-(set_union2(_458086, _458086) = _458086)], (1936 ^ _399050) ^ [_467130, _467132] : [relation(_467130), -(subset(relation_rng_restriction(_467132, _467130), _467130))], (2629 ^ _399050) ^ [_491174, _491176] : [relation(_491174), -(subset(relation_dom_restriction(_491174, _491176), _491174))], (1619 ^ _399050) ^ [] : [-(empty(empty_set))], (1412 ^ _399050) ^ [] : [true___, -(true___)], (987 ^ _399050) ^ [_434604, _434606] : [subset(_434606, _434604), 990 ^ _399050 : [(991 ^ _399050) ^ [_434741] : [in(_434741, _434606), -(in(_434741, _434604))]]], (857 ^ _399050) ^ [_429511, _429513, _429515] : [_429511 = set_union2(_429515, _429513), 860 ^ _399050 : [(861 ^ _399050) ^ [_429693] : [in(_429693, _429511), -(in(_429693, _429515)), -(in(_429693, _429513))], (871 ^ _399050) ^ [_429971] : [872 ^ _399050 : [(875 ^ _399050) ^ [] : [in(_429971, _429513)], (873 ^ _399050) ^ [] : [in(_429971, _429515)]], -(in(_429971, _429511))]]], (288 ^ _399050) ^ [_408966, _408968] : [_408968 = _408966, -(union(_408968) = union(_408966))], (814 ^ _399050) ^ [_427992, _427994, _427996] : [_427992 = unordered_pair(_427996, _427994), 817 ^ _399050 : [(818 ^ _399050) ^ [_428174] : [in(_428174, _427992), -(_428174 = _427996), -(_428174 = _427994)], (828 ^ _399050) ^ [_428452] : [829 ^ _399050 : [(832 ^ _399050) ^ [] : [_428452 = _427994], (830 ^ _399050) ^ [] : [_428452 = _427996]], -(in(_428452, _427992))]]], (1713 ^ _399050) ^ [_459337, _459339] : [disjoint(singleton(_459339), _459337), in(_459339, _459337)], (1221 ^ _399050) ^ [_443327] : [relation(_443327), -(relation_field(_443327) = set_union2(relation_dom(_443327), relation_rng(_443327)))], (62 ^ _399050) ^ [_401130, _401132] : [-(empty(_401130)), _401132 = _401130, empty(_401132)], (2054 ^ _399050) ^ [_471470, _471472] : [-(subset(set_intersection2(_471472, _471470), _471472))], (1962 ^ _399050) ^ [_468153, _468155, _468157, _468159] : [-(subset(cartesian_product2(_468159, _468155), cartesian_product2(_468157, _468153))), subset(_468159, _468157), subset(_468155, _468153)], (356 ^ _399050) ^ [_411461, _411463] : [-(unordered_pair(_411463, _411461) = unordered_pair(_411461, _411463))], (2688 ^ _399050) ^ [_493354] : [-(in(_493354, 2686 ^ [_493354]))], (1930 ^ _399050) ^ [_466912, _466914] : [relation(_466912), -(subset(relation_rng(relation_rng_restriction(_466914, _466912)), _466914))], (212 ^ _399050) ^ [_406263, _406265, _406267, _406269] : [-(subset_complement(_406269, _406265) = subset_complement(_406267, _406263)), _406269 = _406267, _406265 = _406263], (2179 ^ _399050) ^ [_475850, _475852, _475854, _475856] : [ordered_pair(_475856, _475854) = ordered_pair(_475852, _475850), 2182 ^ _399050 : [(2185 ^ _399050) ^ [] : [-(_475854 = _475850)], (2183 ^ _399050) ^ [] : [-(_475856 = _475852)]]], (1769 ^ _399050) ^ [_461322, _461324] : [subset(_461324, singleton(_461322)), -(_461324 = empty_set), -(_461324 = singleton(_461322))], (2159 ^ _399050) ^ [_475061] : [-(subset(empty_set, _475061))], (172 ^ _399050) ^ [_404811, _404813, _404815, _404817] : [-(complements_of_subsets(_404817, _404813) = complements_of_subsets(_404815, _404811)), _404817 = _404815, _404813 = _404811], (1811 ^ _399050) ^ [_462745, _462747] : [1813 ^ _399050 : [(1816 ^ _399050) ^ [] : [in(1812 ^ [_462745, _462747], _462745)], (1814 ^ _399050) ^ [] : [-(in(1812 ^ [_462745, _462747], _462747))]], -(element(_462747, powerset(_462745)))], (358 ^ _399050) ^ [_411561, _411563] : [-(set_union2(_411563, _411561) = set_union2(_411561, _411563))], (1462 ^ _399050) ^ [_451333, _451335] : [element(_451333, powerset(_451335)), -(element(subset_complement(_451335, _451333), powerset(_451335)))], (360 ^ _399050) ^ [_411661, _411663] : [-(set_intersection2(_411663, _411661) = set_intersection2(_411661, _411663))], (1787 ^ _399050) ^ [_461876, _461878] : [in(_461878, _461876), -(subset(_461878, union(_461876)))], (1028 ^ _399050) ^ [_436043, _436045, _436047] : [-(_436043 = set_intersection2(_436047, _436045)), 1040 ^ _399050 : [(1045 ^ _399050) ^ [] : [in(1029 ^ [_436043, _436045, _436047], _436043)], (1043 ^ _399050) ^ [] : [-(in(1029 ^ [_436043, _436045, _436047], _436045))], (1041 ^ _399050) ^ [] : [-(in(1029 ^ [_436043, _436045, _436047], _436047))]], 1032 ^ _399050 : [(1035 ^ _399050) ^ [] : [in(1029 ^ [_436043, _436045, _436047], _436047), in(1029 ^ [_436043, _436045, _436047], _436045)], (1033 ^ _399050) ^ [] : [-(in(1029 ^ [_436043, _436045, _436047], _436043))]]], (1589 ^ _399050) ^ [] : [-(empty(empty_set))], (114 ^ _399050) ^ [_402737, _402739] : [-(relation(_402737)), _402739 = _402737, relation(_402739)], (1898 ^ _399050) ^ [_465903, _465905, _465907, _465909] : [unordered_pair(_465909, _465907) = unordered_pair(_465905, _465903), -(_465909 = _465905), -(_465909 = _465903)], (2400 ^ _399050) ^ [_483521, _483523] : [element(_483521, powerset(powerset(_483523))), -(_483521 = empty_set), -(union_of_subsets(_483523, complements_of_subsets(_483523, _483521)) = subset_difference(_483523, cast_to_subset(_483523), meet_of_subsets(_483523, _483521)))], (1086 ^ _399050) ^ [_438208] : [-(cast_to_subset(_438208) = _438208)], (2661 ^ _399050) ^ [_492254, _492256] : [relation(_492254), -(relation_dom(relation_dom_restriction(_492254, _492256)) = set_intersection2(relation_dom(_492254), _492256))], (1418 ^ _399050) ^ [] : [true___, -(true___)], (602 ^ _399050) ^ [_420800, _420802] : [-(_420802 = empty_set), 605 ^ _399050 : [(606 ^ _399050) ^ [] : [_420800 = set_meet(_420802), 609 ^ _399050 : [(610 ^ _399050) ^ [_421098] : [in(_421098, _420800), 613 ^ _399050 : [(614 ^ _399050) ^ [_421243] : [in(_421243, _420802), -(in(_421098, _421243))]]], (620 ^ _399050) ^ [_421428] : [622 ^ _399050 : [(625 ^ _399050) ^ [] : [in(_421428, 621 ^ [_420800, _420802, _421428])], (623 ^ _399050) ^ [] : [-(in(621 ^ [_420800, _420802, _421428], _420802))]], -(in(_421428, _420800))]]], (629 ^ _399050) ^ [] : [-(_420800 = set_meet(_420802)), 633 ^ _399050 : [(639 ^ _399050) ^ [] : [in(630 ^ [_420800, _420802], 635 ^ [_420800, _420802])], (637 ^ _399050) ^ [] : [-(in(635 ^ [_420800, _420802], _420802))], (634 ^ _399050) ^ [] : [-(in(630 ^ [_420800, _420802], _420800))]], 640 ^ _399050 : [(641 ^ _399050) ^ [_422202] : [in(_422202, _420802), -(in(630 ^ [_420800, _420802], _422202))], (647 ^ _399050) ^ [] : [in(630 ^ [_420800, _420802], _420800)]]]]], (2259 ^ _399050) ^ [_478639] : [-(set_difference(_478639, empty_set) = _478639)], (34 ^ _399050) ^ [_400270, _400272, _400274, _400276] : [-(proper_subset(_400274, _400270)), proper_subset(_400276, _400272), _400276 = _400274, _400272 = _400270], (1731 ^ _399050) ^ [_459962, _459964] : [in(_459964, _459962), -(subset(singleton(_459964), _459962))], (1267 ^ _399050) ^ [_445040, _445042] : [disjoint(_445042, _445040), -(set_intersection2(_445042, _445040) = empty_set)], (2519 ^ _399050) ^ [_487539] : [relation(_487539), 2522 ^ _399050 : [(2529 ^ _399050) ^ [] : [relation_rng(_487539) = empty_set, -(relation_dom(_487539) = empty_set)], (2523 ^ _399050) ^ [] : [relation_dom(_487539) = empty_set, -(relation_rng(_487539) = empty_set)]]], (1848 ^ _399050) ^ [] : [empty(1846 ^ [])], (2655 ^ _399050) ^ [_492028, _492030, _492032] : [singleton(_492032) = unordered_pair(_492030, _492028), -(_492032 = _492030)], (2251 ^ _399050) ^ [_478374, _478376] : [2252 ^ _399050 : [(2255 ^ _399050) ^ [] : [_478376 = singleton(_478374)], (2253 ^ _399050) ^ [] : [_478376 = empty_set]], -(subset(_478376, singleton(_478374)))], (2541 ^ _399050) ^ [_488195, _488197] : [-(in(_488195, _488197)), -(set_difference(_488197, singleton(_488195)) = _488197)], (1498 ^ _399050) ^ [_452223, _452225] : [-(relation(relation_composition(_452225, _452223))), relation(_452225), relation(_452223)], (2547 ^ _399050) ^ [_488391] : [-(unordered_pair(_488391, _488391) = singleton(_488391))], (879 ^ _399050) ^ [_430236, _430238, _430240] : [-(_430236 = set_union2(_430240, _430238)), 883 ^ _399050 : [(888 ^ _399050) ^ [] : [in(880 ^ [_430236, _430238, _430240], _430238)], (886 ^ _399050) ^ [] : [in(880 ^ [_430236, _430238, _430240], _430240)], (884 ^ _399050) ^ [] : [-(in(880 ^ [_430236, _430238, _430240], _430236))]], 889 ^ _399050 : [(890 ^ _399050) ^ [] : [-(in(880 ^ [_430236, _430238, _430240], _430240)), -(in(880 ^ [_430236, _430238, _430240], _430238))], (896 ^ _399050) ^ [] : [in(880 ^ [_430236, _430238, _430240], _430236)]]], (2370 ^ _399050) ^ [_482502, _482504] : [in(_482504, _482502), -(set_union2(singleton(_482504), _482502) = _482502)], (222 ^ _399050) ^ [_406622, _406624, _406626, _406628] : [-(ordered_pair(_406628, _406624) = ordered_pair(_406626, _406622)), _406628 = _406626, _406624 = _406622], (150 ^ _399050) ^ [_403988, _403990] : [_403990 = _403988, -(relation_field(_403990) = relation_field(_403988))], (278 ^ _399050) ^ [_408635, _408637, _408639, _408641] : [-(relation_dom_restriction(_408641, _408637) = relation_dom_restriction(_408639, _408635)), _408641 = _408639, _408637 = _408635], (2013 ^ _399050) ^ [_470039, _470041, _470043] : [relation(_470039), 2016 ^ _399050 : [(2028 ^ _399050) ^ [] : [-(in(_470043, relation_image(_470039, _470041))), 2029 ^ _399050 : [(2030 ^ _399050) ^ [_470640] : [in(_470640, relation_dom(_470039)), in(ordered_pair(_470640, _470043), _470039), in(_470640, _470041)]]], (2017 ^ _399050) ^ [] : [in(_470043, relation_image(_470039, _470041)), 2021 ^ _399050 : [(2026 ^ _399050) ^ [] : [-(in(2020 ^ [_470039, _470041, _470043], _470041))], (2024 ^ _399050) ^ [] : [-(in(ordered_pair(2020 ^ [_470039, _470041, _470043], _470043), _470039))], (2022 ^ _399050) ^ [] : [-(in(2020 ^ [_470039, _470041, _470043], relation_dom(_470039)))]]]]], (2437 ^ _399050) ^ [_484852] : [-(_484852 = empty_set), 2440 ^ _399050 : [(2441 ^ _399050) ^ [_485012] : [element(_485012, powerset(_484852)), 2444 ^ _399050 : [(2445 ^ _399050) ^ [_485166] : [element(_485166, _484852), -(in(_485166, _485012)), -(in(_485166, subset_complement(_484852, _485012)))]]]]], (2261 ^ _399050) ^ [_478778, _478780] : [element(_478780, powerset(_478778)), -(subset(_478780, _478778))], (593 ^ _399050) ^ [_420372] : [595 ^ _399050 : [(598 ^ _399050) ^ [_420609, _420611] : [594 ^ [_420372] = ordered_pair(_420611, _420609)], (596 ^ _399050) ^ [] : [-(in(594 ^ [_420372], _420372))]], -(relation(_420372))], (1856 ^ _399050) ^ [_464343, _464345] : [element(_464343, powerset(powerset(_464345))), -(meet_of_subsets(_464345, _464343) = set_meet(_464343))], (1382 ^ _399050) ^ [_449519, _449521] : [proper_subset(_449521, _449519), 1385 ^ _399050 : [(1388 ^ _399050) ^ [] : [_449521 = _449519], (1386 ^ _399050) ^ [] : [-(subset(_449521, _449519))]]], (1603 ^ _399050) ^ [_455588] : [empty(singleton(_455588))], (2098 ^ _399050) ^ [_472976] : [relation(_472976), -(subset(_472976, cartesian_product2(relation_dom(_472976), relation_rng(_472976))))], (1219 ^ _399050) ^ [_443221, _443223] : [-(ordered_pair(_443223, _443221) = unordered_pair(unordered_pair(_443223, _443221), singleton(_443223)))], (1623 ^ _399050) ^ [_456331, _456333] : [empty(cartesian_product2(_456333, _456331)), -(empty(_456333)), -(empty(_456331))], (1979 ^ _399050) ^ [_468806] : [-(in(_468806, 1977 ^ [_468806]))], (1719 ^ _399050) ^ [_459550, _459552] : [-(in(_459552, _459550)), -(disjoint(singleton(_459552), _459550))], (1390 ^ _399050) ^ [_449757, _449759] : [-(proper_subset(_449759, _449757)), subset(_449759, _449757), -(_449759 = _449757)], (667 ^ _399050) ^ [_423004, _423006] : [_423004 = singleton(_423006), 670 ^ _399050 : [(677 ^ _399050) ^ [_423346] : [_423346 = _423006, -(in(_423346, _423004))], (671 ^ _399050) ^ [_423174] : [in(_423174, _423004), -(_423174 = _423006)]]], (316 ^ _399050) ^ [_410007, _410009, _410011, _410013] : [-(relation_image(_410013, _410009) = relation_image(_410011, _410007)), _410013 = _410011, _410009 = _410007], (1563 ^ _399050) ^ [_454304] : [-(element(1561 ^ [_454304], _454304))], (2713 ^ _399050) ^ [_494300, _494302] : [subset(_494300, 2686 ^ [_494302]), -(are_equipotent(_494300, 2686 ^ [_494302])), -(in(_494300, 2686 ^ [_494302]))], (2042 ^ _399050) ^ [_471037, _471039] : [relation(_471037), -(subset(relation_image(_471037, _471039), relation_rng(_471037)))], (532 ^ _399050) ^ [_417863] : [relation(_417863), 535 ^ _399050 : [(536 ^ _399050) ^ [_418070, _418072] : [_418070 = relation_image(_417863, _418072), 539 ^ _399050 : [(549 ^ _399050) ^ [_418616] : [-(in(_418616, _418070)), 550 ^ _399050 : [(551 ^ _399050) ^ [_418721] : [in(ordered_pair(_418721, _418616), _417863), in(_418721, _418072)]]], (540 ^ _399050) ^ [_418262] : [in(_418262, _418070), 544 ^ _399050 : [(547 ^ _399050) ^ [] : [-(in(543 ^ [_417863, _418070, _418072, _418262], _418072))], (545 ^ _399050) ^ [] : [-(in(ordered_pair(543 ^ [_417863, _418070, _418072, _418262], _418262), _417863))]]]]], (559 ^ _399050) ^ [_418976, _418978] : [-(_418976 = relation_image(_417863, _418978)), 572 ^ _399050 : [(577 ^ _399050) ^ [] : [in(560 ^ [_417863, _418976, _418978], _418976)], (575 ^ _399050) ^ [] : [-(in(571 ^ [_417863, _418976, _418978], _418978))], (573 ^ _399050) ^ [] : [-(in(ordered_pair(571 ^ [_417863, _418976, _418978], 560 ^ [_417863, _418976, _418978]), _417863))]], 563 ^ _399050 : [(566 ^ _399050) ^ [_419280] : [in(ordered_pair(_419280, 560 ^ [_417863, _418976, _418978]), _417863), in(_419280, _418978)], (564 ^ _399050) ^ [] : [-(in(560 ^ [_417863, _418976, _418978], _418976))]]]]], (232 ^ _399050) ^ [_406981, _406983, _406985, _406987] : [-(set_difference(_406987, _406983) = set_difference(_406985, _406981)), _406987 = _406985, _406983 = _406981], (2595 ^ _399050) ^ [_490115, _490117] : [disjoint(_490117, _490115), -(set_difference(_490117, _490115) = _490117)], (1981 ^ _399050) ^ [_468918, _468920, _468922] : [-(in(_468918, 1977 ^ [_468922])), in(_468920, 1977 ^ [_468922]), subset(_468918, _468920)], (1516 ^ _399050) ^ [_452829, _452831] : [element(_452829, powerset(powerset(_452831))), -(element(meet_of_subsets(_452831, _452829), powerset(_452831)))], (2673 ^ _399050) ^ [_492696, _492698] : [relation(_492696), -(relation_dom_restriction(_492696, _492698) = relation_composition(identity_relation(_492698), _492696))], (2229 ^ _399050) ^ [_477665, _477667, _477669] : [-(subset(unordered_pair(_477669, _477667), _477665)), in(_477669, _477665), in(_477667, _477665)], (2209 ^ _399050) ^ [_476989, _476991] : [subset(singleton(_476991), _476989), -(in(_476991, _476989))], (1593 ^ _399050) ^ [_455319, _455321] : [-(relation(set_union2(_455321, _455319))), relation(_455321), relation(_455319)], (1430 ^ _399050) ^ [] : [true___, -(true___)], (294 ^ _399050) ^ [_409184, _409186] : [_409186 = _409184, -(powerset(_409186) = powerset(_409184))], (2074 ^ _399050) ^ [_472216, _472218, _472220] : [-(subset(_472220, _472216)), subset(_472220, _472218), subset(_472218, _472216)], (1532 ^ _399050) ^ [_453400, _453402] : [relation(_453402), -(relation(relation_dom_restriction(_453402, _453400)))], (2215 ^ _399050) ^ [_477155, _477157] : [in(_477157, _477155), -(subset(singleton(_477157), _477155))], (2587 ^ _399050) ^ [_489782, _489784] : [in(_489784, _489782), empty(_489782)], (1111 ^ _399050) ^ [_439191, _439193] : [-(_439191 = union(_439193)), 1124 ^ _399050 : [(1129 ^ _399050) ^ [] : [in(1112 ^ [_439191, _439193], _439191)], (1127 ^ _399050) ^ [] : [-(in(1123 ^ [_439191, _439193], _439193))], (1125 ^ _399050) ^ [] : [-(in(1112 ^ [_439191, _439193], 1123 ^ [_439191, _439193]))]], 1115 ^ _399050 : [(1118 ^ _399050) ^ [_439474] : [in(1112 ^ [_439191, _439193], _439474), in(_439474, _439193)], (1116 ^ _399050) ^ [] : [-(in(1112 ^ [_439191, _439193], _439191))]]], (1880 ^ _399050) ^ [_465277, _465279, _465281, _465283] : [in(ordered_pair(_465283, _465281), cartesian_product2(_465279, _465277)), 1883 ^ _399050 : [(1886 ^ _399050) ^ [] : [-(in(_465281, _465277))], (1884 ^ _399050) ^ [] : [-(in(_465283, _465279))]]], (2412 ^ _399050) ^ [_483935] : [-(set_difference(empty_set, _483935) = empty_set)], (2690 ^ _399050) ^ [_493466, _493468, _493470] : [-(in(_493466, 2686 ^ [_493470])), in(_493468, 2686 ^ [_493470]), subset(_493466, _493468)], (2273 ^ _399050) ^ [_479180, _479182] : [-(disjoint(_479182, _479180)), 2277 ^ _399050 : [(2280 ^ _399050) ^ [] : [-(in(2276 ^ [_479180, _479182], _479180))], (2278 ^ _399050) ^ [] : [-(in(2276 ^ [_479180, _479182], _479182))]]], (2477 ^ _399050) ^ [_486250, _486252, _486254] : [in(_486254, _486252), element(_486252, powerset(_486250)), empty(_486250)], (2431 ^ _399050) ^ [_484627, _484629] : [2432 ^ _399050 : [(2433 ^ _399050) ^ [_484700] : [in(_484700, set_intersection2(_484629, _484627))]], disjoint(_484629, _484627)], (2679 ^ _399050) ^ [_492920, _492922] : [relation(_492920), -(subset(relation_rng(relation_dom_restriction(_492920, _492922)), relation_rng(_492920)))], (1565 ^ _399050) ^ [_454416, _454418] : [1572 ^ _399050 : [(1575 ^ _399050) ^ [] : [-(relation(relation_composition(_454416, _454418)))], (1573 ^ _399050) ^ [] : [-(empty(relation_composition(_454416, _454418)))]], empty(_454418), relation(_454416)], (182 ^ _399050) ^ [_405198, _405200, _405202, _405204, _405206, _405208] : [-(subset_difference(_405208, _405204, _405200) = subset_difference(_405206, _405202, _405198)), _405208 = _405206, _405204 = _405202, _405200 = _405198], (2084 ^ _399050) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (480 ^ _399050) ^ [_415940, _415942] : [relation(_415940), 483 ^ _399050 : [(484 ^ _399050) ^ [_416111] : [relation(_416111), 487 ^ _399050 : [(488 ^ _399050) ^ [] : [_416111 = relation_rng_restriction(_415942, _415940), 491 ^ _399050 : [(500 ^ _399050) ^ [_416717, _416719] : [-(in(ordered_pair(_416719, _416717), _416111)), in(_416717, _415942), in(ordered_pair(_416719, _416717), _415940)], (492 ^ _399050) ^ [_416438, _416440] : [in(ordered_pair(_416440, _416438), _416111), 495 ^ _399050 : [(498 ^ _399050) ^ [] : [-(in(ordered_pair(_416440, _416438), _415940))], (496 ^ _399050) ^ [] : [-(in(_416438, _415942))]]]]], (510 ^ _399050) ^ [] : [-(_416111 = relation_rng_restriction(_415942, _415940)), 523 ^ _399050 : [(528 ^ _399050) ^ [] : [in(ordered_pair(511 ^ [_415940, _415942, _416111], 512 ^ [_415940, _415942, _416111]), _416111)], (526 ^ _399050) ^ [] : [-(in(ordered_pair(511 ^ [_415940, _415942, _416111], 512 ^ [_415940, _415942, _416111]), _415940))], (524 ^ _399050) ^ [] : [-(in(512 ^ [_415940, _415942, _416111], _415942))]], 515 ^ _399050 : [(518 ^ _399050) ^ [] : [in(512 ^ [_415940, _415942, _416111], _415942), in(ordered_pair(511 ^ [_415940, _415942, _416111], 512 ^ [_415940, _415942, _416111]), _415940)], (516 ^ _399050) ^ [] : [-(in(ordered_pair(511 ^ [_415940, _415942, _416111], 512 ^ [_415940, _415942, _416111]), _416111))]]]]]]], (1669 ^ _399050) ^ [_457721, _457723] : [1676 ^ _399050 : [(1679 ^ _399050) ^ [] : [-(relation(relation_composition(_457723, _457721)))], (1677 ^ _399050) ^ [] : [-(empty(relation_composition(_457723, _457721)))]], empty(_457723), relation(_457721)], (2126 ^ _399050) ^ [_473965, _473967] : [subset(_473967, _473965), -(set_intersection2(_473967, _473965) = _473967)], (162 ^ _399050) ^ [_404452, _404454, _404456, _404458] : [-(union_of_subsets(_404458, _404454) = union_of_subsets(_404456, _404452)), _404458 = _404456, _404454 = _404452], (1591 ^ _399050) ^ [_455208, _455210] : [empty(ordered_pair(_455210, _455208))], (1835 ^ _399050) ^ [] : [-(empty(1833 ^ []))], (262 ^ _399050) ^ [_408058, _408060, _408062, _408064] : [-(relation_composition(_408064, _408060) = relation_composition(_408062, _408058)), _408064 = _408062, _408060 = _408058], (2700 ^ _399050) ^ [_493781, _493783] : [in(_493781, 2686 ^ [_493783]), 2704 ^ _399050 : [(2707 ^ _399050) ^ [_494093] : [subset(_494093, _493781), -(in(_494093, 2703 ^ [_493781, _493783]))], (2705 ^ _399050) ^ [] : [-(in(2703 ^ [_493781, _493783], 2686 ^ [_493783]))]]], (2635 ^ _399050) ^ [_491388, _491390] : [empty(_491390), -(_491390 = _491388), empty(_491388)], (1492 ^ _399050) ^ [] : [true___, -(true___)], (2410 ^ _399050) ^ [_483846, _483848] : [-(set_difference(_483848, set_difference(_483848, _483846)) = set_intersection2(_483848, _483846))], (2497 ^ _399050) ^ [_486891, _486893, _486895] : [-(disjoint(_486895, _486891)), subset(_486895, _486893), disjoint(_486893, _486891)], (2292 ^ _399050) ^ [_479843] : [subset(_479843, empty_set), -(_479843 = empty_set)], (2320 ^ _399050) ^ [_480786] : [relation(_480786), 2323 ^ _399050 : [(2324 ^ _399050) ^ [_480923] : [relation(_480923), -(subset(relation_dom(relation_composition(_480786, _480923)), relation_dom(_480786)))]]], (2048 ^ _399050) ^ [_471255, _471257] : [relation(_471255), -(relation_image(_471255, _471257) = relation_image(_471255, set_intersection2(relation_dom(_471255), _471257)))], (338 ^ _399050) ^ [_410868, _410870] : [in(_410870, _410868), in(_410868, _410870)], (742 ^ _399050) ^ [_425589] : [relation(_425589), 745 ^ _399050 : [(746 ^ _399050) ^ [_425747] : [relation(_425747), 749 ^ _399050 : [(750 ^ _399050) ^ [] : [_425589 = _425747, 753 ^ _399050 : [(760 ^ _399050) ^ [_426242, _426244] : [in(ordered_pair(_426244, _426242), _425747), -(in(ordered_pair(_426244, _426242), _425589))], (754 ^ _399050) ^ [_426052, _426054] : [in(ordered_pair(_426054, _426052), _425589), -(in(ordered_pair(_426054, _426052), _425747))]]], (766 ^ _399050) ^ [] : [-(_425589 = _425747), 771 ^ _399050 : [(774 ^ _399050) ^ [] : [in(ordered_pair(767 ^ [_425589, _425747], 768 ^ [_425589, _425747]), _425747)], (772 ^ _399050) ^ [] : [-(in(ordered_pair(767 ^ [_425589, _425747], 768 ^ [_425589, _425747]), _425589))]], 775 ^ _399050 : [(778 ^ _399050) ^ [] : [in(ordered_pair(767 ^ [_425589, _425747], 768 ^ [_425589, _425747]), _425589)], (776 ^ _399050) ^ [] : [-(in(ordered_pair(767 ^ [_425589, _425747], 768 ^ [_425589, _425747]), _425747))]]]]]]], (1801 ^ _399050) ^ [_462412, _462414, _462416, _462418] : [-(in(ordered_pair(_462418, _462416), cartesian_product2(_462414, _462412))), in(_462418, _462414), in(_462416, _462412)], (1621 ^ _399050) ^ [] : [-(relation(empty_set))], (1683 ^ _399050) ^ [_458181, _458183] : [-(set_intersection2(_458183, _458183) = _458183)], (900 ^ _399050) ^ [_431030, _431032, _431034] : [_431030 = cartesian_product2(_431034, _431032), 903 ^ _399050 : [(916 ^ _399050) ^ [_431791] : [-(in(_431791, _431030)), 917 ^ _399050 : [(918 ^ _399050) ^ [_431921, _431923] : [in(_431923, _431034), in(_431921, _431032), _431791 = ordered_pair(_431923, _431921)]]], (904 ^ _399050) ^ [_431231] : [in(_431231, _431030), 909 ^ _399050 : [(914 ^ _399050) ^ [] : [-(_431231 = ordered_pair(907 ^ [_431030, _431032, _431034, _431231], 908 ^ [_431030, _431032, _431034, _431231]))], (912 ^ _399050) ^ [] : [-(in(908 ^ [_431030, _431032, _431034, _431231], _431032))], (910 ^ _399050) ^ [] : [-(in(907 ^ [_431030, _431032, _431034, _431231], _431034))]]]]], (1514 ^ _399050) ^ [_452721] : [-(relation(identity_relation(_452721)))], (2241 ^ _399050) ^ [_478114, _478116] : [subset(_478116, singleton(_478114)), -(_478116 = empty_set), -(_478116 = singleton(_478114))], (2330 ^ _399050) ^ [_481138] : [relation(_481138), 2333 ^ _399050 : [(2334 ^ _399050) ^ [_481275] : [relation(_481275), -(subset(relation_rng(relation_composition(_481138, _481275)), relation_rng(_481275)))]]], (1874 ^ _399050) ^ [_465010, _465012] : [disjoint(_465012, _465010), -(disjoint(_465010, _465012))], (2056 ^ _399050) ^ [_471596, _471598, _471600] : [-(subset(_471600, set_intersection2(_471598, _471596))), subset(_471600, _471598), subset(_471600, _471596)], (1793 ^ _399050) ^ [_462147, _462149, _462151, _462153] : [in(ordered_pair(_462153, _462151), cartesian_product2(_462149, _462147)), 1796 ^ _399050 : [(1799 ^ _399050) ^ [] : [-(in(_462151, _462147))], (1797 ^ _399050) ^ [] : [-(in(_462153, _462149))]]], (2134 ^ _399050) ^ [_474262, _474264] : [element(_474264, _474262), -(empty(_474262)), -(in(_474264, _474262))], (1850 ^ _399050) ^ [_464115, _464117] : [element(_464115, powerset(powerset(_464117))), -(union_of_subsets(_464117, _464115) = union(_464115))], (651 ^ _399050) ^ [_422507, _422509] : [_422509 = empty_set, 654 ^ _399050 : [(661 ^ _399050) ^ [] : [_422507 = empty_set, -(_422507 = set_meet(_422509))], (655 ^ _399050) ^ [] : [_422507 = set_meet(_422509), -(_422507 = empty_set)]]], (2563 ^ _399050) ^ [_488948] : [-(relation_rng(identity_relation(_488948)) = _488948)], (2144 ^ _399050) ^ [_474560, _474562] : [-(_474562 = _474560), 2148 ^ _399050 : [(2151 ^ _399050) ^ [] : [in(2145 ^ [_474560, _474562], _474560)], (2149 ^ _399050) ^ [] : [-(in(2145 ^ [_474560, _474562], _474562))]], 2152 ^ _399050 : [(2155 ^ _399050) ^ [] : [in(2145 ^ [_474560, _474562], _474562)], (2153 ^ _399050) ^ [] : [-(in(2145 ^ [_474560, _474562], _474560))]]], (2221 ^ _399050) ^ [_477414, _477416, _477418] : [subset(unordered_pair(_477418, _477416), _477414), 2224 ^ _399050 : [(2227 ^ _399050) ^ [] : [-(in(_477416, _477414))], (2225 ^ _399050) ^ [] : [-(in(_477418, _477414))]]], (2414 ^ _399050) ^ [_484059, _484061, _484063] : [-(element(_484063, _484059)), in(_484063, _484061), element(_484061, powerset(_484059))], (428 ^ _399050) ^ [_413981] : [relation(_413981), 431 ^ _399050 : [(432 ^ _399050) ^ [_414167, _414169] : [relation(_414167), 435 ^ _399050 : [(436 ^ _399050) ^ [] : [_414167 = relation_dom_restriction(_413981, _414169), 439 ^ _399050 : [(448 ^ _399050) ^ [_414771, _414773] : [-(in(ordered_pair(_414773, _414771), _414167)), in(_414773, _414169), in(ordered_pair(_414773, _414771), _413981)], (440 ^ _399050) ^ [_414492, _414494] : [in(ordered_pair(_414494, _414492), _414167), 443 ^ _399050 : [(446 ^ _399050) ^ [] : [-(in(ordered_pair(_414494, _414492), _413981))], (444 ^ _399050) ^ [] : [-(in(_414494, _414169))]]]]], (458 ^ _399050) ^ [] : [-(_414167 = relation_dom_restriction(_413981, _414169)), 471 ^ _399050 : [(476 ^ _399050) ^ [] : [in(ordered_pair(459 ^ [_413981, _414167, _414169], 460 ^ [_413981, _414167, _414169]), _414167)], (474 ^ _399050) ^ [] : [-(in(ordered_pair(459 ^ [_413981, _414167, _414169], 460 ^ [_413981, _414167, _414169]), _413981))], (472 ^ _399050) ^ [] : [-(in(459 ^ [_413981, _414167, _414169], _414169))]], 463 ^ _399050 : [(466 ^ _399050) ^ [] : [in(459 ^ [_413981, _414167, _414169], _414169), in(ordered_pair(459 ^ [_413981, _414167, _414169], 460 ^ [_413981, _414167, _414169]), _413981)], (464 ^ _399050) ^ [] : [-(in(ordered_pair(459 ^ [_413981, _414167, _414169], 460 ^ [_413981, _414167, _414169]), _414167))]]]]]]], (1759 ^ _399050) ^ [_460973, _460975, _460977] : [subset(_460977, _460975), -(in(_460973, _460977)), -(subset(_460977, set_difference(_460975, singleton(_460973))))], (272 ^ _399050) ^ [_408389, _408391] : [_408391 = _408389, -(identity_relation(_408391) = identity_relation(_408389))], (2455 ^ _399050) ^ [_485512, _485514, _485516] : [element(_485512, powerset(_485516)), in(_485514, subset_complement(_485516, _485512)), in(_485514, _485512)], (1049 ^ _399050) ^ [_436782] : [relation(_436782), 1052 ^ _399050 : [(1053 ^ _399050) ^ [_436963] : [_436963 = relation_dom(_436782), 1056 ^ _399050 : [(1064 ^ _399050) ^ [_437387] : [1065 ^ _399050 : [(1066 ^ _399050) ^ [_437466] : [in(ordered_pair(_437387, _437466), _436782)]], -(in(_437387, _436963))], (1057 ^ _399050) ^ [_437143] : [in(_437143, _436963), -(in(ordered_pair(_437143, 1060 ^ [_436782, _436963, _437143]), _436782))]]], (1070 ^ _399050) ^ [_437594] : [-(_437594 = relation_dom(_436782)), 1074 ^ _399050 : [(1077 ^ _399050) ^ [_437857] : [in(ordered_pair(1071 ^ [_436782, _437594], _437857), _436782)], (1075 ^ _399050) ^ [] : [-(in(1071 ^ [_436782, _437594], _437594))]], 1079 ^ _399050 : [(1082 ^ _399050) ^ [] : [in(1071 ^ [_436782, _437594], _437594)], (1080 ^ _399050) ^ [] : [-(in(ordered_pair(1071 ^ [_436782, _437594], 1078 ^ [_436782, _437594]), _436782))]]]]], (4 ^ _399050) ^ [_399281, _399283] : [_399283 = _399281, -(_399281 = _399283)], (2465 ^ _399050) ^ [_485818] : [relation(_485818), -(in(ordered_pair(2470 ^ [_485818], 2471 ^ [_485818]), _485818)), -(_485818 = empty_set)], (2340 ^ _399050) ^ [_481504, _481506] : [subset(_481506, _481504), -(_481504 = set_union2(_481506, set_difference(_481504, _481506)))], (1749 ^ _399050) ^ [_460593, _460595] : [element(_460593, powerset(_460595)), 1752 ^ _399050 : [(1753 ^ _399050) ^ [_460734] : [in(_460734, _460593), -(in(_460734, _460595))]]], (1556 ^ _399050) ^ [] : [true___, -(true___)], (1544 ^ _399050) ^ [_453844, _453846] : [relation(_453844), -(relation(relation_rng_restriction(_453846, _453844)))], (711 ^ _399050) ^ [_424546, _424548] : [_424546 = powerset(_424548), 714 ^ _399050 : [(721 ^ _399050) ^ [_424888] : [subset(_424888, _424548), -(in(_424888, _424546))], (715 ^ _399050) ^ [_424716] : [in(_424716, _424546), -(subset(_424716, _424548))]]], (1088 ^ _399050) ^ [_438346, _438348] : [_438346 = union(_438348), 1091 ^ _399050 : [(1101 ^ _399050) ^ [_438854] : [-(in(_438854, _438346)), 1102 ^ _399050 : [(1103 ^ _399050) ^ [_438952] : [in(_438854, _438952), in(_438952, _438348)]]], (1092 ^ _399050) ^ [_438527] : [in(_438527, _438346), 1096 ^ _399050 : [(1099 ^ _399050) ^ [] : [-(in(1095 ^ [_438346, _438348, _438527], _438348))], (1097 ^ _399050) ^ [] : [-(in(_438527, 1095 ^ [_438346, _438348, _438527]))]]]]], (2601 ^ _399050) ^ [_490283, _490285] : [set_difference(_490285, _490283) = _490285, -(disjoint(_490285, _490283))], (1538 ^ _399050) ^ [_453612, _453614] : [element(_453612, powerset(powerset(_453614))), -(element(complements_of_subsets(_453614, _453612), powerset(powerset(_453614))))], (202 ^ _399050) ^ [_405904, _405906, _405908, _405910] : [-(meet_of_subsets(_405910, _405906) = meet_of_subsets(_405908, _405904)), _405910 = _405908, _405906 = _405904], (306 ^ _399050) ^ [_409648, _409650, _409652, _409654] : [-(unordered_pair(_409654, _409650) = unordered_pair(_409652, _409648)), _409654 = _409652, _409650 = _409648], (2723 ^ _399050) ^ [_494634, _494636, _494638] : [singleton(_494638) = unordered_pair(_494636, _494634), -(_494636 = _494634)], (1838 ^ _399050) ^ [] : [empty(1836 ^ [])], (1613 ^ _399050) ^ [_456007, _456009] : [-(empty(_456009)), empty(set_union2(_456007, _456009))], (1273 ^ _399050) ^ [_445208, _445210] : [set_intersection2(_445210, _445208) = empty_set, -(disjoint(_445210, _445208))], (2086 ^ _399050) ^ [_472592, _472594, _472596] : [relation(_472592), in(ordered_pair(_472596, _472594), _472592), 2093 ^ _399050 : [(2096 ^ _399050) ^ [] : [-(in(_472594, relation_rng(_472592)))], (2094 ^ _399050) ^ [] : [-(in(_472596, relation_dom(_472592)))]]], (2132 ^ _399050) ^ [_474152] : [-(set_intersection2(_474152, empty_set) = empty_set)], (2607 ^ _399050) ^ [_490515, _490517, _490519] : [relation(_490515), 2610 ^ _399050 : [(2619 ^ _399050) ^ [] : [-(in(_490519, relation_dom(relation_dom_restriction(_490515, _490517)))), in(_490519, _490517), in(_490519, relation_dom(_490515))], (2611 ^ _399050) ^ [] : [in(_490519, relation_dom(relation_dom_restriction(_490515, _490517))), 2614 ^ _399050 : [(2617 ^ _399050) ^ [] : [-(in(_490519, relation_dom(_490515)))], (2615 ^ _399050) ^ [] : [-(in(_490519, _490517))]]]]], (10 ^ _399050) ^ [_399485, _399487, _399489] : [-(_399489 = _399485), _399489 = _399487, _399487 = _399485], (2390 ^ _399050) ^ [_483181, _483183] : [element(_483181, powerset(powerset(_483183))), -(_483181 = empty_set), -(subset_difference(_483183, cast_to_subset(_483183), union_of_subsets(_483183, _483181)) = meet_of_subsets(_483183, complements_of_subsets(_483183, _483181)))], (1006 ^ _399050) ^ [_435318, _435320, _435322] : [_435318 = set_intersection2(_435322, _435320), 1009 ^ _399050 : [(1018 ^ _399050) ^ [_435759] : [-(in(_435759, _435318)), in(_435759, _435322), in(_435759, _435320)], (1010 ^ _399050) ^ [_435500] : [in(_435500, _435318), 1013 ^ _399050 : [(1016 ^ _399050) ^ [] : [-(in(_435500, _435320))], (1014 ^ _399050) ^ [] : [-(in(_435500, _435322))]]]]], (1888 ^ _399050) ^ [_465542, _465544, _465546, _465548] : [-(in(ordered_pair(_465548, _465546), cartesian_product2(_465544, _465542))), in(_465548, _465544), in(_465546, _465542)], (2187 ^ _399050) ^ [_476148, _476150] : [-(subset(set_difference(_476150, _476148), _476150))], (20 ^ _399050) ^ [_399826, _399828, _399830, _399832] : [-(element(_399830, _399826)), element(_399832, _399828), _399832 = _399830, _399828 = _399826], (2066 ^ _399050) ^ [_471882] : [-(set_union2(_471882, empty_set) = _471882)], (2549 ^ _399050) ^ [_488489] : [empty(_488489), -(_488489 = empty_set)], (1737 ^ _399050) ^ [_460207, _460209] : [set_difference(_460209, _460207) = empty_set, -(subset(_460209, _460207))], (1997 ^ _399050) ^ [_469433, _469435] : [subset(_469433, 1977 ^ [_469435]), -(are_equipotent(_469433, 1977 ^ [_469435])), -(in(_469433, 1977 ^ [_469435]))], (130 ^ _399050) ^ [_403298, _403300, _403302, _403304] : [-(relation_rng_restriction(_403304, _403300) = relation_rng_restriction(_403302, _403298)), _403304 = _403302, _403300 = _403298]], input).
% 71.62/69.80 ncf('1',plain,[-(relation(2728 ^ []))],start(2730 ^ 0)).
% 71.62/69.80 ncf('1.1',plain,[relation(2728 ^ []), 1180 : relation_rng(2728 ^ []) = relation_rng(2728 ^ []), 1184 : in(560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], relation_rng(2728 ^ [])), 1184 : -(in(ordered_pair(1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]], 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]), 2728 ^ []))],extension(1176 ^ 1,bind([[_441555, _441736, _441916], [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]]]))).
% 71.62/69.80 ncf('1.1.1',plain,[-(relation_rng(2728 ^ []) = relation_rng(2728 ^ [])), 2728 ^ [] = 2728 ^ []],extension(332 ^ 4,bind([[_410536, _410538], [2728 ^ [], 2728 ^ []]]))).
% 71.62/69.80 ncf('1.1.1.1',plain,[-(2728 ^ [] = 2728 ^ [])],extension(2 ^ 5,bind([[_399174], [2728 ^ []]]))).
% 71.62/69.80 ncf('1.1.2',plain,[-(in(560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], relation_rng(2728 ^ []))), 559 : -(relation_rng(2728 ^ []) = relation_image(2728 ^ [], relation_dom(2728 ^ []))), 573 : -(in(ordered_pair(571 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]), 2728 ^ [])), 559 : relation(2728 ^ [])],extension(532 ^ 6,bind([[_417863, _418976, _418978], [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]]))).
% 71.62/69.80 ncf('1.1.2.1',plain,[relation_rng(2728 ^ []) = relation_image(2728 ^ [], relation_dom(2728 ^ [])), -(relation_image(2728 ^ [], relation_dom(2728 ^ [])) = relation_rng(2728 ^ []))],extension(4 ^ 9,bind([[_399281, _399283], [relation_image(2728 ^ [], relation_dom(2728 ^ [])), relation_rng(2728 ^ [])]]))).
% 71.62/69.80 ncf('1.1.2.1.1',plain,[relation_image(2728 ^ [], relation_dom(2728 ^ [])) = relation_rng(2728 ^ [])],extension(2732 ^ 10)).
% 71.62/69.80 ncf('1.1.2.2',plain,[in(ordered_pair(571 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]), 2728 ^ []), -(in(560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], relation_rng(2728 ^ [])))],extension(1191 ^ 11,bind([[_442160, _442239], [560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], 571 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]]]))).
% 71.62/69.80 ncf('1.1.2.2.1',plain,[in(560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], relation_rng(2728 ^ []))],reduction('1.1')).
% 71.62/69.80 ncf('1.1.2.3',plain,[-(relation(2728 ^ []))],reduction('1')).
% 71.62/69.80 ncf('1.1.3',plain,[in(ordered_pair(1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]], 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]), 2728 ^ []), 566 : in(1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]], relation_dom(2728 ^ [])), 566 : -(relation_rng(2728 ^ []) = relation_image(2728 ^ [], relation_dom(2728 ^ []))), 577 : in(560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], relation_rng(2728 ^ [])), 559 : relation(2728 ^ [])],extension(532 ^ 6,bind([[_417863, _418976, _418978, _419280], [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ []), 1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]]]]))).
% 71.62/69.80 ncf('1.1.3.1',plain,[-(in(1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]], relation_dom(2728 ^ []))), relation(2728 ^ []), in(ordered_pair(1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]], 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]), 2728 ^ [])],extension(2086 ^ 11,bind([[_472592, _472594, _472596], [2728 ^ [], 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], 1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]]]]))).
% 71.62/69.80 ncf('1.1.3.1.1',plain,[-(relation(2728 ^ []))],reduction('1')).
% 71.62/69.80 ncf('1.1.3.1.2',plain,[-(in(ordered_pair(1187 ^ [2728 ^ [], relation_rng(2728 ^ []), 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]], 560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])]), 2728 ^ []))],reduction('1.1')).
% 71.62/69.80 ncf('1.1.3.2',plain,[relation_rng(2728 ^ []) = relation_image(2728 ^ [], relation_dom(2728 ^ [])), -(relation_image(2728 ^ [], relation_dom(2728 ^ [])) = relation_rng(2728 ^ []))],extension(4 ^ 9,bind([[_399281, _399283], [relation_image(2728 ^ [], relation_dom(2728 ^ [])), relation_rng(2728 ^ [])]]))).
% 71.62/69.80 ncf('1.1.3.2.1',plain,[relation_image(2728 ^ [], relation_dom(2728 ^ [])) = relation_rng(2728 ^ [])],extension(2732 ^ 10)).
% 71.62/69.80 ncf('1.1.3.3',plain,[-(in(560 ^ [2728 ^ [], relation_rng(2728 ^ []), relation_dom(2728 ^ [])], relation_rng(2728 ^ [])))],lemmata('[1].x')).
% 71.62/69.80 ncf('1.1.3.4',plain,[-(relation(2728 ^ []))],reduction('1')).
% 71.62/69.80 %-----------------------------------------------------
% 71.62/69.80 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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