%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU264+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n010.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 12:02:55 EDT 2023

% Result   : Theorem 43.90s 42.80s
% Output   : Proof 43.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU264+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n010.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 13:33:12 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 43.90/42.80  
% 43.90/42.80  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 43.90/42.80  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.90/42.80  %-----------------------------------------------------
% 43.90/42.80  ncf(matrix, plain, [(5522 ^ _527078) ^ [] : [relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5514 ^ [])], (5520 ^ _527078) ^ [] : [-(subset(5513 ^ [], 5514 ^ []))], (5518 ^ _527078) ^ [] : [-(relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5513 ^ []))], !, (3652 ^ _335846) ^ [] : [-(relation(3650 ^ []))], (498 ^ _335846) ^ [_352108, _352110, _352112, _352114] : [-(union_of_subsets(_352114, _352110) = union_of_subsets(_352112, _352108)), _352114 = _352112, _352110 = _352108], (3294 ^ _335846) ^ [_449529, _449531] : [element(_449529, powerset(_449531)), -(subset_complement(_449531, subset_complement(_449531, _449529)) = _449529)], (3636 ^ _335846) ^ [] : [-(ordinal(3622 ^ []))], (1605 ^ _335846) ^ [_391771, _391773, _391775] : [_391771 = unordered_pair(_391775, _391773), 1608 ^ _335846 : [(1609 ^ _335846) ^ [_391953] : [in(_391953, _391771), -(_391953 = _391775), -(_391953 = _391773)], (1619 ^ _335846) ^ [_392231] : [1620 ^ _335846 : [(1623 ^ _335846) ^ [] : [_392231 = _391773], (1621 ^ _335846) ^ [] : [_392231 = _391775]], -(in(_392231, _391771))]]], (1315 ^ _335846) ^ [_381789, _381791, _381793] : [relation_of2(_381789, _381793, _381791), -(subset(_381789, cartesian_product2(_381793, _381791)))], (3701 ^ _335846) ^ [_463382, _463384, _463386] : [relation_of2_as_subset(_463382, _463386, _463384), -(relation_of2(_463382, _463386, _463384))], (5323 ^ _335846) ^ [_516971, _516973] : [in(_516973, _516971), 5327 ^ _335846 : [(5330 ^ _335846) ^ [_517262] : [in(_517262, _516971), in(_517262, 5326 ^ [_516971, _516973])], (5328 ^ _335846) ^ [] : [-(in(5326 ^ [_516971, _516973], _516971))]]], (686 ^ _335846) ^ [_359043, _359045] : [in(_359045, _359043), in(_359043, _359045)], (594 ^ _335846) ^ [_355545, _355547] : [_355547 = _355545, -(relation_field(_355547) = relation_field(_355545))], (676 ^ _335846) ^ [_358515, _358517, _358519, _358521] : [-(unordered_pair(_358521, _358517) = unordered_pair(_358519, _358515)), _358521 = _358519, _358517 = _358515], (4244 ^ _335846) ^ [_481728, _481730] : [relation(_481728), function(_481728), 4251 ^ _335846 : [(4252 ^ _335846) ^ [_481974] : [relation(_481974), function(_481974), in(_481730, relation_dom(_481728)), -(apply(relation_composition(_481728, _481974), _481730) = apply(_481974, apply(_481728, _481730)))]]], (4761 ^ _335846) ^ [_498727] : [relation(_498727), 4764 ^ _335846 : [(4765 ^ _335846) ^ [_498874] : [relation(_498874), subset(relation_rng(_498727), relation_dom(_498874)), -(relation_dom(relation_composition(_498727, _498874)) = relation_dom(_498727))]]], (1824 ^ _335846) ^ [_399905] : [relation(_399905), 1827 ^ _335846 : [(1828 ^ _335846) ^ [_400063] : [relation(_400063), 1831 ^ _335846 : [(1832 ^ _335846) ^ [] : [subset(_399905, _400063), 1835 ^ _335846 : [(1836 ^ _335846) ^ [_400339, _400341] : [in(ordered_pair(_400341, _400339), _399905), -(in(ordered_pair(_400341, _400339), _400063))]]], (1842 ^ _335846) ^ [] : [1845 ^ _335846 : [(1848 ^ _335846) ^ [] : [in(ordered_pair(1843 ^ [_399905, _400063], 1844 ^ [_399905, _400063]), _400063)], (1846 ^ _335846) ^ [] : [-(in(ordered_pair(1843 ^ [_399905, _400063], 1844 ^ [_399905, _400063]), _399905))]], -(subset(_399905, _400063))]]]]], (4526 ^ _335846) ^ [_490847, _490849] : [-(subset(set_difference(_490849, _490847), _490849))], (1198 ^ _335846) ^ [_377444] : [relation(_377444), 1201 ^ _335846 : [(1208 ^ _335846) ^ [] : [is_transitive_in(_377444, relation_field(_377444)), -(transitive(_377444))], (1202 ^ _335846) ^ [] : [transitive(_377444), -(is_transitive_in(_377444, relation_field(_377444)))]]], (3216 ^ _335846) ^ [] : [-(empty(empty_set))], (2773 ^ _335846) ^ [_434425] : [relation(_434425), function(_434425), one_to_one(_434425), -(function_inverse(_434425) = relation_inverse(_434425))], (4314 ^ _335846) ^ [_483831] : [relation(_483831), 4317 ^ _335846 : [(4318 ^ _335846) ^ [_483981] : [relation(_483981), subset(_483831, _483981), 4325 ^ _335846 : [(4328 ^ _335846) ^ [] : [-(subset(relation_rng(_483831), relation_rng(_483981)))], (4326 ^ _335846) ^ [] : [-(subset(relation_dom(_483831), relation_dom(_483981)))]]]]], (3176 ^ _335846) ^ [_445754, _445756] : [-(relation(set_difference(_445756, _445754))), relation(_445756), relation(_445754)], (3673 ^ _335846) ^ [] : [-(relation(3671 ^ []))], (4354 ^ _335846) ^ [_485214, _485216] : [element(_485216, _485214), -(empty(_485214)), -(in(_485216, _485214))], (558 ^ _335846) ^ [_354250, _354252] : [_354252 = _354250, -(function_inverse(_354252) = function_inverse(_354250))], (1499 ^ _335846) ^ [_388192, _388194] : [-(_388192 = powerset(_388194)), 1503 ^ _335846 : [(1506 ^ _335846) ^ [] : [subset(1500 ^ [_388192, _388194], _388194)], (1504 ^ _335846) ^ [] : [-(in(1500 ^ [_388192, _388194], _388192))]], 1507 ^ _335846 : [(1510 ^ _335846) ^ [] : [in(1500 ^ [_388192, _388194], _388192)], (1508 ^ _335846) ^ [] : [-(subset(1500 ^ [_388192, _388194], _388194))]]], (2787 ^ _335846) ^ [_434789] : [relation(_434789), 2790 ^ _335846 : [(2797 ^ _335846) ^ [] : [is_reflexive_in(_434789, relation_field(_434789)), -(reflexive(_434789))], (2791 ^ _335846) ^ [] : [reflexive(_434789), -(is_reflexive_in(_434789, relation_field(_434789)))]]], (3351 ^ _335846) ^ [_451511, _451513] : [-(in(_451513, _451511)), -(disjoint(singleton(_451513), _451511))], (764 ^ _335846) ^ [_361506, _361508] : [-(set_union2(_361508, _361506) = set_union2(_361506, _361508))], (1998 ^ _335846) ^ [_406097] : [-(ordinal(_406097)), epsilon_transitive(_406097), epsilon_connected(_406097)], (4234 ^ _335846) ^ [_481429, _481431] : [relation(_481429), reflexive(_481429), -(reflexive(relation_restriction(_481429, _481431)))], (4200 ^ _335846) ^ [_480273] : [relation(_480273), -(subset(_480273, cartesian_product2(relation_dom(_480273), relation_rng(_480273))))], (2112 ^ _335846) ^ [_410414, _410416] : [-(_410414 = union(_410416)), 2125 ^ _335846 : [(2130 ^ _335846) ^ [] : [in(2113 ^ [_410414, _410416], _410414)], (2128 ^ _335846) ^ [] : [-(in(2124 ^ [_410414, _410416], _410416))], (2126 ^ _335846) ^ [] : [-(in(2113 ^ [_410414, _410416], 2124 ^ [_410414, _410416]))]], 2116 ^ _335846 : [(2119 ^ _335846) ^ [_410697] : [in(2113 ^ [_410414, _410416], _410697), in(_410697, _410416)], (2117 ^ _335846) ^ [] : [-(in(2113 ^ [_410414, _410416], _410414))]]], (3528 ^ _335846) ^ [_457680, _457682] : [in(_457682, _457680), -(subset(_457682, union(_457680)))], (3619 ^ _335846) ^ [] : [-(empty(3615 ^ []))], (2907 ^ _335846) ^ [] : [true___, -(true___)], (5336 ^ _335846) ^ [_517487, _517489] : [-(subset(_517489, set_union2(_517489, _517487)))], (1727 ^ _335846) ^ [_396041, _396043, _396045] : [_396041 = cartesian_product2(_396045, _396043), 1730 ^ _335846 : [(1743 ^ _335846) ^ [_396802] : [-(in(_396802, _396041)), 1744 ^ _335846 : [(1745 ^ _335846) ^ [_396932, _396934] : [in(_396934, _396045), in(_396932, _396043), _396802 = ordered_pair(_396934, _396932)]]], (1731 ^ _335846) ^ [_396242] : [in(_396242, _396041), 1736 ^ _335846 : [(1741 ^ _335846) ^ [] : [-(_396242 = ordered_pair(1734 ^ [_396041, _396043, _396045, _396242], 1735 ^ [_396041, _396043, _396045, _396242]))], (1739 ^ _335846) ^ [] : [-(in(1735 ^ [_396041, _396043, _396045, _396242], _396043))], (1737 ^ _335846) ^ [] : [-(in(1734 ^ [_396041, _396043, _396045, _396242], _396045))]]]]], (3602 ^ _335846) ^ [] : [-(relation(3598 ^ []))], (900 ^ _335846) ^ [_366258] : [relation(_366258), function(_366258), 907 ^ _335846 : [(908 ^ _335846) ^ [_366556, _366558] : [_366556 = relation_image(_366258, _366558), 911 ^ _335846 : [(923 ^ _335846) ^ [_367211] : [-(in(_367211, _366556)), 924 ^ _335846 : [(925 ^ _335846) ^ [_367324] : [in(_367324, relation_dom(_366258)), in(_367324, _366558), _367211 = apply(_366258, _367324)]]], (912 ^ _335846) ^ [_366756] : [in(_366756, _366556), 916 ^ _335846 : [(921 ^ _335846) ^ [] : [-(_366756 = apply(_366258, 915 ^ [_366258, _366556, _366558, _366756]))], (919 ^ _335846) ^ [] : [-(in(915 ^ [_366258, _366556, _366558, _366756], _366558))], (917 ^ _335846) ^ [] : [-(in(915 ^ [_366258, _366556, _366558, _366756], relation_dom(_366258)))]]]]], (937 ^ _335846) ^ [_367684, _367686] : [-(_367684 = relation_image(_366258, _367686)), 954 ^ _335846 : [(957 ^ _335846) ^ [] : [-(in(953 ^ [_366258, _367684, _367686], _367686))], (959 ^ _335846) ^ [] : [-(938 ^ [_366258, _367684, _367686] = apply(_366258, 953 ^ [_366258, _367684, _367686]))], (961 ^ _335846) ^ [] : [in(938 ^ [_366258, _367684, _367686], _367684)], (955 ^ _335846) ^ [] : [-(in(953 ^ [_366258, _367684, _367686], relation_dom(_366258)))]], 941 ^ _335846 : [(944 ^ _335846) ^ [_368004] : [in(_368004, relation_dom(_366258)), in(_368004, _367686), 938 ^ [_366258, _367684, _367686] = apply(_366258, _368004)], (942 ^ _335846) ^ [] : [-(in(938 ^ [_366258, _367684, _367686], _367684))]]]]], (3339 ^ _335846) ^ [_451078, _451080] : [in(_451080, _451078), -(set_union2(singleton(_451080), _451078) = _451078)], (1808 ^ _335846) ^ [_399199] : [1811 ^ _335846 : [(1812 ^ _335846) ^ [] : [-(in(1809 ^ [_399199], _399199))], (1816 ^ _335846) ^ [] : [in(1809 ^ [_399199], 1810 ^ [_399199])], (1820 ^ _335846) ^ [] : [in(1810 ^ [_399199], 1809 ^ [_399199])], (1818 ^ _335846) ^ [] : [1809 ^ [_399199] = 1810 ^ [_399199]], (1814 ^ _335846) ^ [] : [-(in(1810 ^ [_399199], _399199))]], -(epsilon_connected(_399199))], (3468 ^ _335846) ^ [_455640] : [relation(_455640), 3471 ^ _335846 : [(3472 ^ _335846) ^ [] : [connected(_455640), 3475 ^ _335846 : [(3476 ^ _335846) ^ [_455934, _455936] : [in(_455936, relation_field(_455640)), in(_455934, relation_field(_455640)), -(_455936 = _455934), -(in(ordered_pair(_455936, _455934), _455640)), -(in(ordered_pair(_455934, _455936), _455640))]]], (3494 ^ _335846) ^ [] : [3497 ^ _335846 : [(3498 ^ _335846) ^ [] : [-(in(3495 ^ [_455640], relation_field(_455640)))], (3502 ^ _335846) ^ [] : [3495 ^ [_455640] = 3496 ^ [_455640]], (3506 ^ _335846) ^ [] : [in(ordered_pair(3496 ^ [_455640], 3495 ^ [_455640]), _455640)], (3504 ^ _335846) ^ [] : [in(ordered_pair(3495 ^ [_455640], 3496 ^ [_455640]), _455640)], (3500 ^ _335846) ^ [] : [-(in(3496 ^ [_455640], relation_field(_455640)))]], -(connected(_455640))]]], (5251 ^ _335846) ^ [_514597] : [empty(_514597), -(_514597 = empty_set)], (548 ^ _335846) ^ [_353919, _353921, _353923, _353925] : [-(subset_complement(_353925, _353921) = subset_complement(_353923, _353919)), _353925 = _353923, _353921 = _353919], (1408 ^ _335846) ^ [_384936, _384938] : [-(_384936 = singleton(_384938)), 1412 ^ _335846 : [(1415 ^ _335846) ^ [] : [1409 ^ [_384936, _384938] = _384938], (1413 ^ _335846) ^ [] : [-(in(1409 ^ [_384936, _384938], _384936))]], 1416 ^ _335846 : [(1419 ^ _335846) ^ [] : [in(1409 ^ [_384936, _384938], _384936)], (1417 ^ _335846) ^ [] : [-(1409 ^ [_384936, _384938] = _384938)]]], (240 ^ _335846) ^ [_343454, _343456, _343458, _343460] : [-(is_well_founded_in(_343458, _343454)), is_well_founded_in(_343460, _343456), _343460 = _343458, _343456 = _343454], (5118 ^ _335846) ^ [_510476] : [relation(_510476), 5121 ^ _335846 : [(5128 ^ _335846) ^ [] : [is_well_founded_in(_510476, relation_field(_510476)), -(well_founded_relation(_510476))], (5122 ^ _335846) ^ [] : [well_founded_relation(_510476), -(is_well_founded_in(_510476, relation_field(_510476)))]]], (3588 ^ _335846) ^ [] : [-(relation(3586 ^ []))], (3597 ^ _335846) ^ [] : [-(ordinal(3591 ^ []))], (574 ^ _335846) ^ [_354855, _354857, _354859, _354861] : [-(ordered_pair(_354861, _354857) = ordered_pair(_354859, _354855)), _354861 = _354859, _354857 = _354855], (1648 ^ _335846) ^ [_393233] : [relation(_393233), 1651 ^ _335846 : [(1652 ^ _335846) ^ [] : [well_founded_relation(_393233), 1655 ^ _335846 : [(1656 ^ _335846) ^ [_393500] : [subset(_393500, relation_field(_393233)), -(_393500 = empty_set), 1664 ^ _335846 : [(1667 ^ _335846) ^ [] : [-(disjoint(fiber(_393233, 1663 ^ [_393233, _393500]), _393500))], (1665 ^ _335846) ^ [] : [-(in(1663 ^ [_393233, _393500], _393500))]]]]], (1669 ^ _335846) ^ [] : [-(well_founded_relation(_393233)), 1671 ^ _335846 : [(1676 ^ _335846) ^ [_394183] : [in(_394183, 1670 ^ [_393233]), disjoint(fiber(_393233, _394183), 1670 ^ [_393233])], (1674 ^ _335846) ^ [] : [1670 ^ [_393233] = empty_set], (1672 ^ _335846) ^ [] : [-(subset(1670 ^ [_393233], relation_field(_393233)))]]]]], (3290 ^ _335846) ^ [_449320, _449322] : [-(set_union2(_449322, _449322) = _449322)], (4594 ^ _335846) ^ [_493211, _493213] : [subset(_493213, singleton(_493211)), -(_493213 = empty_set), -(_493213 = singleton(_493211))], (3945 ^ _335846) ^ [_471891, _471893] : [relation(_471891), subset(_471893, relation_dom(_471891)), -(subset(_471893, relation_inverse_image(_471891, relation_image(_471891, _471893))))], (4868 ^ _335846) ^ [_502356, _502358] : [4869 ^ _335846 : [(4870 ^ _335846) ^ [_502429] : [in(_502429, set_intersection2(_502358, _502356))]], disjoint(_502358, _502356)], (2839 ^ _335846) ^ [] : [true___, -(true___)], (4112 ^ _335846) ^ [_477418] : [-(set_union2(_477418, empty_set) = _477418)], (3230 ^ _335846) ^ [_447495, _447497] : [3237 ^ _335846 : [(3240 ^ _335846) ^ [] : [-(function(relation_rng_restriction(_447497, _447495)))], (3238 ^ _335846) ^ [] : [-(relation(relation_rng_restriction(_447497, _447495)))]], relation(_447495), function(_447495)], (2995 ^ _335846) ^ [_440172, _440174] : [relation(_440172), -(relation(relation_rng_restriction(_440174, _440172)))], (4805 ^ _335846) ^ [_500196, _500198] : [element(_500196, powerset(powerset(_500198))), -(_500196 = empty_set), -(subset_difference(_500198, cast_to_subset(_500198), union_of_subsets(_500198, _500196)) = meet_of_subsets(_500198, complements_of_subsets(_500198, _500196)))], (3929 ^ _335846) ^ [_471354, _471356] : [-(subset(relation_image(_471354, relation_inverse_image(_471354, _471356)), _471356)), relation(_471354), function(_471354)], (5168 ^ _335846) ^ [_511905] : [relation(_511905), 5173 ^ _335846 : [(5176 ^ _335846) ^ [] : [relation_rng(_511905) = empty_set], (5174 ^ _335846) ^ [] : [relation_dom(_511905) = empty_set]], -(_511905 = empty_set)], (4212 ^ _335846) ^ [_480735, _480737] : [relation(_480735), function(_480735), 4219 ^ _335846 : [(4220 ^ _335846) ^ [_480984] : [relation(_480984), function(_480984), in(_480737, relation_dom(relation_composition(_480984, _480735))), -(apply(relation_composition(_480984, _480735), _480737) = apply(_480735, apply(_480984, _480737)))]]], (3128 ^ _335846) ^ [] : [-(ordinal(empty_set))], (768 ^ _335846) ^ [_361721, _361723] : [ordinal(_361723), ordinal(_361721), -(ordinal_subset(_361723, _361721)), -(ordinal_subset(_361721, _361723))], (4849 ^ _335846) ^ [_501664] : [-(set_difference(empty_set, _501664) = empty_set)], (4815 ^ _335846) ^ [_500536, _500538] : [element(_500536, powerset(powerset(_500538))), -(_500536 = empty_set), -(union_of_subsets(_500538, complements_of_subsets(_500538, _500536)) = subset_difference(_500538, cast_to_subset(_500538), meet_of_subsets(_500538, _500536)))], (3292 ^ _335846) ^ [_449417, _449419] : [-(set_intersection2(_449419, _449419) = _449419)], (3542 ^ _335846) ^ [_458216, _458218, _458220, _458222] : [-(in(ordered_pair(_458222, _458220), cartesian_product2(_458218, _458216))), in(_458222, _458218), in(_458220, _458216)], (1852 ^ _335846) ^ [_400988, _400990] : [subset(_400990, _400988), 1855 ^ _335846 : [(1856 ^ _335846) ^ [_401125] : [in(_401125, _400990), -(in(_401125, _400988))]]], (3118 ^ _335846) ^ [] : [-(function(empty_set))], (492 ^ _335846) ^ [_351862, _351864] : [_351864 = _351862, -(succ(_351864) = succ(_351862))], (4152 ^ _335846) ^ [_478833, _478835] : [relation(_478833), function(_478833), 4159 ^ _335846 : [(4160 ^ _335846) ^ [_479083] : [relation(_479083), function(_479083), 4167 ^ _335846 : [(4176 ^ _335846) ^ [] : [-(in(_478835, relation_dom(relation_composition(_479083, _478833)))), in(_478835, relation_dom(_479083)), in(apply(_479083, _478835), relation_dom(_478833))], (4168 ^ _335846) ^ [] : [in(_478835, relation_dom(relation_composition(_479083, _478833))), 4171 ^ _335846 : [(4174 ^ _335846) ^ [] : [-(in(apply(_479083, _478835), relation_dom(_478833)))], (4172 ^ _335846) ^ [] : [-(in(_478835, relation_dom(_479083)))]]]]]]], (4030 ^ _335846) ^ [_474768, _474770, _474772] : [relation(_474768), 4033 ^ _335846 : [(4042 ^ _335846) ^ [] : [-(in(_474772, relation_restriction(_474768, _474770))), in(_474772, _474768), in(_474772, cartesian_product2(_474770, _474770))], (4034 ^ _335846) ^ [] : [in(_474772, relation_restriction(_474768, _474770)), 4037 ^ _335846 : [(4040 ^ _335846) ^ [] : [-(in(_474772, cartesian_product2(_474770, _474770)))], (4038 ^ _335846) ^ [] : [-(in(_474772, _474768))]]]]], (626 ^ _335846) ^ [_356727, _356729, _356731, _356733] : [-(relation_composition(_356733, _356729) = relation_composition(_356731, _356727)), _356733 = _356731, _356729 = _356727], (3458 ^ _335846) ^ [_455334, _455336, _455338] : [subset(_455338, _455336), -(in(_455334, _455338)), -(subset(_455338, set_difference(_455336, singleton(_455334))))], (4130 ^ _335846) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (3835 ^ _335846) ^ [_467935, _467937, _467939, _467941] : [-(subset(cartesian_product2(_467941, _467937), cartesian_product2(_467939, _467935))), subset(_467941, _467939), subset(_467937, _467935)], (3771 ^ _335846) ^ [_465685, _465687, _465689, _465691] : [unordered_pair(_465691, _465689) = unordered_pair(_465687, _465685), -(_465691 = _465687), -(_465691 = _465685)], (3624 ^ _335846) ^ [] : [-(relation(3622 ^ []))], (704 ^ _335846) ^ [_359637] : [ordinal(_359637), 707 ^ _335846 : [(710 ^ _335846) ^ [] : [-(epsilon_connected(_359637))], (708 ^ _335846) ^ [] : [-(epsilon_transitive(_359637))]]], (482 ^ _335846) ^ [_351531, _351533, _351535, _351537] : [-(relation_restriction(_351537, _351533) = relation_restriction(_351535, _351531)), _351537 = _351535, _351533 = _351531], (3242 ^ _335846) ^ [_447859] : [empty(relation_dom(_447859)), -(empty(_447859)), relation(_447859)], (4520 ^ _335846) ^ [_490642, _490644] : [in(_490642, _490644), -(apply(identity_relation(_490644), _490642) = _490642)], (3939 ^ _335846) ^ [_471661, _471663] : [relation(_471661), -(relation_image(_471661, _471663) = relation_image(_471661, set_intersection2(relation_dom(_471661), _471663)))], (1627 ^ _335846) ^ [_392496, _392498, _392500] : [-(_392496 = unordered_pair(_392500, _392498)), 1631 ^ _335846 : [(1636 ^ _335846) ^ [] : [1628 ^ [_392496, _392498, _392500] = _392498], (1634 ^ _335846) ^ [] : [1628 ^ [_392496, _392498, _392500] = _392500], (1632 ^ _335846) ^ [] : [-(in(1628 ^ [_392496, _392498, _392500], _392496))]], 1637 ^ _335846 : [(1638 ^ _335846) ^ [] : [-(1628 ^ [_392496, _392498, _392500] = _392500), -(1628 ^ [_392496, _392498, _392500] = _392498)], (1644 ^ _335846) ^ [] : [in(1628 ^ [_392496, _392498, _392500], _392496)]]], (2461 ^ _335846) ^ [_422753] : [relation(_422753), 2464 ^ _335846 : [(2465 ^ _335846) ^ [_422974] : [relation(_422974), 2468 ^ _335846 : [(2469 ^ _335846) ^ [_423191] : [relation(_423191), function(_423191), 2476 ^ _335846 : [(2477 ^ _335846) ^ [] : [relation_isomorphism(_422753, _422974, _423191), 2480 ^ _335846 : [(2481 ^ _335846) ^ [] : [-(relation_dom(_423191) = relation_field(_422753))], (2485 ^ _335846) ^ [] : [-(one_to_one(_423191))], (2497 ^ _335846) ^ [_424236, _424238] : [-(in(ordered_pair(_424238, _424236), _422753)), in(_424238, relation_field(_422753)), in(_424236, relation_field(_422753)), in(ordered_pair(apply(_423191, _424238), apply(_423191, _424236)), _422974)], (2487 ^ _335846) ^ [_423857, _423859] : [in(ordered_pair(_423859, _423857), _422753), 2490 ^ _335846 : [(2495 ^ _335846) ^ [] : [-(in(ordered_pair(apply(_423191, _423859), apply(_423191, _423857)), _422974))], (2493 ^ _335846) ^ [] : [-(in(_423857, relation_field(_422753)))], (2491 ^ _335846) ^ [] : [-(in(_423859, relation_field(_422753)))]]], (2483 ^ _335846) ^ [] : [-(relation_rng(_423191) = relation_field(_422974))]]], (2511 ^ _335846) ^ [] : [-(relation_isomorphism(_422753, _422974, _423191)), relation_dom(_423191) = relation_field(_422753), relation_rng(_423191) = relation_field(_422974), one_to_one(_423191), 2540 ^ _335846 : [(2543 ^ _335846) ^ [] : [-(in(2525 ^ [_422753, _422974, _423191], relation_field(_422753)))], (2545 ^ _335846) ^ [] : [-(in(ordered_pair(apply(_423191, 2524 ^ [_422753, _422974, _423191]), apply(_423191, 2525 ^ [_422753, _422974, _423191])), _422974))], (2547 ^ _335846) ^ [] : [in(ordered_pair(2524 ^ [_422753, _422974, _423191], 2525 ^ [_422753, _422974, _423191]), _422753)], (2541 ^ _335846) ^ [] : [-(in(2524 ^ [_422753, _422974, _423191], relation_field(_422753)))]], 2528 ^ _335846 : [(2531 ^ _335846) ^ [] : [in(2524 ^ [_422753, _422974, _423191], relation_field(_422753)), in(2525 ^ [_422753, _422974, _423191], relation_field(_422753)), in(ordered_pair(apply(_423191, 2524 ^ [_422753, _422974, _423191]), apply(_423191, 2525 ^ [_422753, _422974, _423191])), _422974)], (2529 ^ _335846) ^ [] : [-(in(ordered_pair(2524 ^ [_422753, _422974, _423191], 2525 ^ [_422753, _422974, _423191]), _422753))]]]]]]]]], (5108 ^ _335846) ^ [_510180, _510182, _510184] : [in(_510184, _510182), element(_510182, powerset(_510180)), empty(_510180)], (3829 ^ _335846) ^ [_467679, _467681] : [relation(_467679), -(relation_rng(relation_rng_restriction(_467681, _467679)) = set_intersection2(relation_rng(_467679), _467681))], (3142 ^ _335846) ^ [_444693, _444695] : [-(empty(_444695)), empty(set_union2(_444695, _444693))], (3663 ^ _335846) ^ [] : [-(epsilon_connected(3657 ^ []))], (3632 ^ _335846) ^ [] : [-(epsilon_transitive(3622 ^ []))], (2217 ^ _335846) ^ [_413793] : [relation(_413793), function(_413793), 2224 ^ _335846 : [(2225 ^ _335846) ^ [_414065] : [_414065 = relation_rng(_413793), 2228 ^ _335846 : [(2238 ^ _335846) ^ [_414595] : [-(in(_414595, _414065)), 2239 ^ _335846 : [(2240 ^ _335846) ^ [_414698] : [in(_414698, relation_dom(_413793)), _414595 = apply(_413793, _414698)]]], (2229 ^ _335846) ^ [_414253] : [in(_414253, _414065), 2233 ^ _335846 : [(2236 ^ _335846) ^ [] : [-(_414253 = apply(_413793, 2232 ^ [_413793, _414065, _414253]))], (2234 ^ _335846) ^ [] : [-(in(2232 ^ [_413793, _414065, _414253], relation_dom(_413793)))]]]]], (2248 ^ _335846) ^ [_414947] : [-(_414947 = relation_rng(_413793)), 2261 ^ _335846 : [(2266 ^ _335846) ^ [] : [in(2249 ^ [_413793, _414947], _414947)], (2264 ^ _335846) ^ [] : [-(2249 ^ [_413793, _414947] = apply(_413793, 2260 ^ [_413793, _414947]))], (2262 ^ _335846) ^ [] : [-(in(2260 ^ [_413793, _414947], relation_dom(_413793)))]], 2252 ^ _335846 : [(2255 ^ _335846) ^ [_415242] : [in(_415242, relation_dom(_413793)), 2249 ^ [_413793, _414947] = apply(_413793, _415242)], (2253 ^ _335846) ^ [] : [-(in(2249 ^ [_413793, _414947], _414947))]]]]], (3743 ^ _335846) ^ [_464603, _464605] : [-(subset(_464605, _464605))], (3252 ^ _335846) ^ [_448136] : [empty(relation_rng(_448136)), -(empty(_448136)), relation(_448136)], (446 ^ _335846) ^ [_350236, _350238, _350240, _350242] : [-(relation_rng_restriction(_350242, _350238) = relation_rng_restriction(_350240, _350236)), _350242 = _350240, _350238 = _350236], (3534 ^ _335846) ^ [_457951, _457953, _457955, _457957] : [in(ordered_pair(_457957, _457955), cartesian_product2(_457953, _457951)), 3537 ^ _335846 : [(3540 ^ _335846) ^ [] : [-(in(_457955, _457951))], (3538 ^ _335846) ^ [] : [-(in(_457957, _457953))]]], (3668 ^ _335846) ^ [] : [-(relation(3666 ^ []))], (3406 ^ _335846) ^ [_453546, _453548] : [set_difference(_453548, _453546) = empty_set, -(subset(_453548, _453546))], (2 ^ _335846) ^ [_335970] : [-(_335970 = _335970)], (148 ^ _335846) ^ [_340603, _340605] : [-(being_limit_ordinal(_340603)), _340605 = _340603, being_limit_ordinal(_340605)], (2973 ^ _335846) ^ [_439399, _439401, _439403] : [-(element(subset_difference(_439403, _439401, _439399), powerset(_439403))), element(_439401, powerset(_439403)), element(_439399, powerset(_439403))], (4636 ^ _335846) ^ [_494599, _494601] : [-(disjoint(_494601, _494599)), 4640 ^ _335846 : [(4643 ^ _335846) ^ [] : [-(in(4639 ^ [_494599, _494601], _494599))], (4641 ^ _335846) ^ [] : [-(in(4639 ^ [_494599, _494601], _494601))]]], (216 ^ _335846) ^ [_342715, _342717, _342719, _342721] : [-(element(_342719, _342715)), element(_342721, _342717), _342721 = _342719, _342717 = _342715], (4346 ^ _335846) ^ [_484917, _484919] : [subset(_484919, _484917), -(set_intersection2(_484919, _484917) = _484919)], (2045 ^ _335846) ^ [_407809] : [relation(_407809), 2048 ^ _335846 : [(2049 ^ _335846) ^ [_408009] : [is_antisymmetric_in(_407809, _408009), 2052 ^ _335846 : [(2053 ^ _335846) ^ [_408191, _408193] : [-(_408193 = _408191), in(_408193, _408009), in(_408191, _408009), in(ordered_pair(_408193, _408191), _407809), in(ordered_pair(_408191, _408193), _407809)]]], (2071 ^ _335846) ^ [_408677] : [2074 ^ _335846 : [(2075 ^ _335846) ^ [] : [-(in(2072 ^ [_407809, _408677], _408677))], (2079 ^ _335846) ^ [] : [-(in(ordered_pair(2072 ^ [_407809, _408677], 2073 ^ [_407809, _408677]), _407809))], (2083 ^ _335846) ^ [] : [2072 ^ [_407809, _408677] = 2073 ^ [_407809, _408677]], (2081 ^ _335846) ^ [] : [-(in(ordered_pair(2073 ^ [_407809, _408677], 2072 ^ [_407809, _408677]), _407809))], (2077 ^ _335846) ^ [] : [-(in(2073 ^ [_407809, _408677], _408677))]], -(is_antisymmetric_in(_407809, _408677))]]], (4663 ^ _335846) ^ [_495555] : [ordinal(_495555), 4666 ^ _335846 : [(4667 ^ _335846) ^ [] : [being_limit_ordinal(_495555), 4670 ^ _335846 : [(4671 ^ _335846) ^ [_495801] : [ordinal(_495801), in(_495801, _495555), -(in(succ(_495801), _495555))]]], (4681 ^ _335846) ^ [] : [4683 ^ _335846 : [(4688 ^ _335846) ^ [] : [in(succ(4682 ^ [_495555]), _495555)], (4686 ^ _335846) ^ [] : [-(in(4682 ^ [_495555], _495555))], (4684 ^ _335846) ^ [] : [-(ordinal(4682 ^ [_495555]))]], -(being_limit_ordinal(_495555))]]], (3845 ^ _335846) ^ [_468280, _468282, _468284] : [relation_of2_as_subset(_468280, _468284, _468282), 3848 ^ _335846 : [(3851 ^ _335846) ^ [] : [-(subset(relation_rng(_468280), _468282))], (3849 ^ _335846) ^ [] : [-(subset(relation_dom(_468280), _468284))]]], (4592 ^ _335846) ^ [_493064, _493066] : [-(set_union2(_493066, set_difference(_493064, _493066)) = set_union2(_493066, _493064))], (5257 ^ _335846) ^ [_514799, _514801] : [subset(singleton(_514801), singleton(_514799)), -(_514801 = _514799)], (2087 ^ _335846) ^ [_409431] : [-(cast_to_subset(_409431) = _409431)], (2925 ^ _335846) ^ [] : [true___, -(true___)], (2355 ^ _335846) ^ [_418826] : [being_limit_ordinal(_418826), -(_418826 = union(_418826))], (62 ^ _335846) ^ [_337954, _337956, _337958, _337960] : [-(is_reflexive_in(_337958, _337954)), is_reflexive_in(_337960, _337956), _337960 = _337958, _337956 = _337954], (4066 ^ _335846) ^ [_475838, _475840, _475842] : [relation(_475838), subset(_475842, _475840), -(subset(relation_inverse_image(_475838, _475842), relation_inverse_image(_475838, _475840)))], (3058 ^ _335846) ^ [] : [-(relation_empty_yielding(empty_set))], (692 ^ _335846) ^ [_359254, _359256] : [proper_subset(_359256, _359254), proper_subset(_359254, _359256)], (3188 ^ _335846) ^ [_446148, _446150] : [-(empty(_446150)), empty(set_union2(_446148, _446150))], (5088 ^ _335846) ^ [_509582, _509584] : [relation(_509582), function(_509582), 5103 ^ _335846 : [(5106 ^ _335846) ^ [] : [-(_509584 = apply(relation_composition(function_inverse(_509582), _509582), _509584))], (5104 ^ _335846) ^ [] : [-(_509584 = apply(_509582, apply(function_inverse(_509582), _509584)))]], one_to_one(_509582), in(_509584, relation_rng(_509582))], (10 ^ _335846) ^ [_336281, _336283, _336285] : [-(_336285 = _336281), _336285 = _336283, _336283 = _336281], (4612 ^ _335846) ^ [_493736] : [-(set_difference(_493736, empty_set) = _493736)], (752 ^ _335846) ^ [_361080] : [empty(_361080), 755 ^ _335846 : [(760 ^ _335846) ^ [] : [-(ordinal(_361080))], (758 ^ _335846) ^ [] : [-(epsilon_connected(_361080))], (756 ^ _335846) ^ [] : [-(epsilon_transitive(_361080))]]], (4379 ^ _335846) ^ [_486013] : [-(subset(empty_set, _486013))], (5372 ^ _335846) ^ [_518687, _518689] : [relation(_518687), -(subset(relation_dom_restriction(_518687, _518689), _518687))], (3114 ^ _335846) ^ [] : [-(relation(empty_set))], (2845 ^ _335846) ^ [] : [true___, -(true___)], (3677 ^ _335846) ^ [] : [-(function(3671 ^ []))], (3306 ^ _335846) ^ [_449951, _449953] : [element(_449951, powerset(powerset(_449953))), -(complements_of_subsets(_449953, complements_of_subsets(_449953, _449951)) = _449951)], (1017 ^ _335846) ^ [_370737] : [relation(_370737), 1020 ^ _335846 : [(1027 ^ _335846) ^ [] : [is_antisymmetric_in(_370737, relation_field(_370737)), -(antisymmetric(_370737))], (1021 ^ _335846) ^ [] : [antisymmetric(_370737), -(is_antisymmetric_in(_370737, relation_field(_370737)))]]], (1084 ^ _335846) ^ [_372975] : [relation(_372975), 1087 ^ _335846 : [(1088 ^ _335846) ^ [_373182, _373184] : [_373182 = relation_image(_372975, _373184), 1091 ^ _335846 : [(1101 ^ _335846) ^ [_373728] : [-(in(_373728, _373182)), 1102 ^ _335846 : [(1103 ^ _335846) ^ [_373833] : [in(ordered_pair(_373833, _373728), _372975), in(_373833, _373184)]]], (1092 ^ _335846) ^ [_373374] : [in(_373374, _373182), 1096 ^ _335846 : [(1099 ^ _335846) ^ [] : [-(in(1095 ^ [_372975, _373182, _373184, _373374], _373184))], (1097 ^ _335846) ^ [] : [-(in(ordered_pair(1095 ^ [_372975, _373182, _373184, _373374], _373374), _372975))]]]]], (1111 ^ _335846) ^ [_374088, _374090] : [-(_374088 = relation_image(_372975, _374090)), 1124 ^ _335846 : [(1129 ^ _335846) ^ [] : [in(1112 ^ [_372975, _374088, _374090], _374088)], (1127 ^ _335846) ^ [] : [-(in(1123 ^ [_372975, _374088, _374090], _374090))], (1125 ^ _335846) ^ [] : [-(in(ordered_pair(1123 ^ [_372975, _374088, _374090], 1112 ^ [_372975, _374088, _374090]), _372975))]], 1115 ^ _335846 : [(1118 ^ _335846) ^ [_374392] : [in(ordered_pair(_374392, 1112 ^ [_372975, _374088, _374090]), _372975), in(_374392, _374090)], (1116 ^ _335846) ^ [] : [-(in(1112 ^ [_372975, _374088, _374090], _374088))]]]]], (1292 ^ _335846) ^ [_380867] : [relation(_380867), 1295 ^ _335846 : [(1296 ^ _335846) ^ [_381041] : [is_reflexive_in(_380867, _381041), 1299 ^ _335846 : [(1300 ^ _335846) ^ [_381183] : [in(_381183, _381041), -(in(ordered_pair(_381183, _381183), _380867))]]], (1306 ^ _335846) ^ [_381366] : [1308 ^ _335846 : [(1311 ^ _335846) ^ [] : [in(ordered_pair(1307 ^ [_380867, _381366], 1307 ^ [_380867, _381366]), _380867)], (1309 ^ _335846) ^ [] : [-(in(1307 ^ [_380867, _381366], _381366))]], -(is_reflexive_in(_380867, _381366))]]], (2827 ^ _335846) ^ [] : [true___, -(true___)], (1862 ^ _335846) ^ [_401302, _401304] : [1864 ^ _335846 : [(1867 ^ _335846) ^ [] : [in(1863 ^ [_401302, _401304], _401302)], (1865 ^ _335846) ^ [] : [-(in(1863 ^ [_401302, _401304], _401304))]], -(subset(_401304, _401302))], (4548 ^ _335846) ^ [_491688, _491690] : [subset(singleton(_491690), _491688), -(in(_491690, _491688))], (5452 ^ _335846) ^ [_521195, _521197] : [in(_521197, _521195), -(subset(_521197, union(_521195)))], (3685 ^ _335846) ^ [_462766, _462768] : [element(_462766, powerset(powerset(_462768))), -(meet_of_subsets(_462768, _462766) = set_meet(_462766))], (3112 ^ _335846) ^ [_443768] : [-(function(identity_relation(_443768)))], (3520 ^ _335846) ^ [_457386, _457388] : [3521 ^ _335846 : [(3524 ^ _335846) ^ [] : [_457388 = singleton(_457386)], (3522 ^ _335846) ^ [] : [_457388 = empty_set]], -(subset(_457388, singleton(_457386)))], (406 ^ _335846) ^ [_348812, _348814, _348816, _348818, _348820, _348822] : [-(unordered_triple(_348822, _348818, _348814) = unordered_triple(_348820, _348816, _348812)), _348822 = _348820, _348818 = _348816, _348814 = _348812], (4082 ^ _335846) ^ [_476368, _476370] : [-(subset(set_intersection2(_476370, _476368), _476370))], (3124 ^ _335846) ^ [] : [-(epsilon_transitive(empty_set))], (3654 ^ _335846) ^ [] : [-(function(3650 ^ []))], (1182 ^ _335846) ^ [_377013] : [relation(_377013), 1185 ^ _335846 : [(1192 ^ _335846) ^ [] : [is_connected_in(_377013, relation_field(_377013)), -(connected(_377013))], (1186 ^ _335846) ^ [] : [connected(_377013), -(is_connected_in(_377013, relation_field(_377013)))]]], (5060 ^ _335846) ^ [_508711] : [relation(_508711), function(_508711), one_to_one(_508711), 5071 ^ _335846 : [(5074 ^ _335846) ^ [] : [-(relation_dom(_508711) = relation_rng(function_inverse(_508711)))], (5072 ^ _335846) ^ [] : [-(relation_rng(_508711) = relation_dom(function_inverse(_508711)))]]], (3628 ^ _335846) ^ [] : [-(one_to_one(3622 ^ []))], (4604 ^ _335846) ^ [_493471, _493473] : [4605 ^ _335846 : [(4608 ^ _335846) ^ [] : [_493473 = singleton(_493471)], (4606 ^ _335846) ^ [] : [_493473 = empty_set]], -(subset(_493473, singleton(_493471)))], (4286 ^ _335846) ^ [_482993] : [ordinal(_482993), 4289 ^ _335846 : [(4290 ^ _335846) ^ [_483143] : [ordinal(_483143), -(in(_482993, _483143)), -(_482993 = _483143), -(in(_483143, _482993))]]], (3032 ^ _335846) ^ [_441276, _441278] : [-(relation_of2_as_subset(3030 ^ [_441276, _441278], _441278, _441276))], (2857 ^ _335846) ^ [] : [true___, -(true___)], (1283 ^ _335846) ^ [_380473] : [1285 ^ _335846 : [(1288 ^ _335846) ^ [_380710, _380712] : [1284 ^ [_380473] = ordered_pair(_380712, _380710)], (1286 ^ _335846) ^ [] : [-(in(1284 ^ [_380473], _380473))]], -(relation(_380473))], (5281 ^ _335846) ^ [_515625, _515627, _515629] : [relation(_515625), function(_515625), in(_515627, _515629), -(apply(relation_dom_restriction(_515625, _515629), _515627) = apply(_515625, _515627))], (2943 ^ _335846) ^ [] : [true___, -(true___)], (3108 ^ _335846) ^ [_443621, _443623] : [empty(ordered_pair(_443623, _443621))], (4406 ^ _335846) ^ [_486948, _486950] : [relation(_486948), well_founded_relation(_486948), -(well_founded_relation(relation_restriction(_486948, _486950)))], (3186 ^ _335846) ^ [_446037, _446039] : [empty(unordered_pair(_446039, _446037))], (838 ^ _335846) ^ [_364026, _364028] : [-(_364028 = _364026), subset(_364028, _364026), subset(_364026, _364028)], (5317 ^ _335846) ^ [_516764, _516766] : [in(_516766, _516764), empty(_516764)], (2875 ^ _335846) ^ [] : [true___, -(true___)], (830 ^ _335846) ^ [_363789, _363791] : [_363791 = _363789, 833 ^ _335846 : [(836 ^ _335846) ^ [] : [-(subset(_363789, _363791))], (834 ^ _335846) ^ [] : [-(subset(_363791, _363789))]]], (3769 ^ _335846) ^ [_465548] : [-(in(_465548, succ(_465548)))], (965 ^ _335846) ^ [_368814, _368816] : [relation(_368814), 968 ^ _335846 : [(969 ^ _335846) ^ [_368985] : [relation(_368985), 972 ^ _335846 : [(973 ^ _335846) ^ [] : [_368985 = relation_rng_restriction(_368816, _368814), 976 ^ _335846 : [(985 ^ _335846) ^ [_369591, _369593] : [-(in(ordered_pair(_369593, _369591), _368985)), in(_369591, _368816), in(ordered_pair(_369593, _369591), _368814)], (977 ^ _335846) ^ [_369312, _369314] : [in(ordered_pair(_369314, _369312), _368985), 980 ^ _335846 : [(983 ^ _335846) ^ [] : [-(in(ordered_pair(_369314, _369312), _368814))], (981 ^ _335846) ^ [] : [-(in(_369312, _368816))]]]]], (995 ^ _335846) ^ [] : [-(_368985 = relation_rng_restriction(_368816, _368814)), 1008 ^ _335846 : [(1013 ^ _335846) ^ [] : [in(ordered_pair(996 ^ [_368814, _368816, _368985], 997 ^ [_368814, _368816, _368985]), _368985)], (1011 ^ _335846) ^ [] : [-(in(ordered_pair(996 ^ [_368814, _368816, _368985], 997 ^ [_368814, _368816, _368985]), _368814))], (1009 ^ _335846) ^ [] : [-(in(997 ^ [_368814, _368816, _368985], _368816))]], 1000 ^ _335846 : [(1003 ^ _335846) ^ [] : [in(997 ^ [_368814, _368816, _368985], _368816), in(ordered_pair(996 ^ [_368814, _368816, _368985], 997 ^ [_368814, _368816, _368985]), _368814)], (1001 ^ _335846) ^ [] : [-(in(ordered_pair(996 ^ [_368814, _368816, _368985], 997 ^ [_368814, _368816, _368985]), _368985))]]]]]]], (3019 ^ _335846) ^ [_440755, _440757, _440759] : [relation_of2_as_subset(_440755, _440759, _440757), -(element(_440755, powerset(cartesian_product2(_440759, _440757))))], (476 ^ _335846) ^ [_351285, _351287] : [_351287 = _351285, -(relation_inverse(_351287) = relation_inverse(_351285))], (3894 ^ _335846) ^ [_470138, _470140, _470142] : [relation(_470138), 3897 ^ _335846 : [(3909 ^ _335846) ^ [] : [-(in(_470142, relation_image(_470138, _470140))), 3910 ^ _335846 : [(3911 ^ _335846) ^ [_470739] : [in(_470739, relation_dom(_470138)), in(ordered_pair(_470739, _470142), _470138), in(_470739, _470140)]]], (3898 ^ _335846) ^ [] : [in(_470142, relation_image(_470138, _470140)), 3902 ^ _335846 : [(3907 ^ _335846) ^ [] : [-(in(3901 ^ [_470138, _470140, _470142], _470140))], (3905 ^ _335846) ^ [] : [-(in(ordered_pair(3901 ^ [_470138, _470140, _470142], _470142), _470138))], (3903 ^ _335846) ^ [] : [-(in(3901 ^ [_470138, _470140, _470142], relation_dom(_470138)))]]]]], (5388 ^ _335846) ^ [_519212, _519214, _519216] : [relation(_519212), function(_519212), 5395 ^ _335846 : [(5404 ^ _335846) ^ [] : [-(in(ordered_pair(_519216, _519214), _519212)), in(_519216, relation_dom(_519212)), _519214 = apply(_519212, _519216)], (5396 ^ _335846) ^ [] : [in(ordered_pair(_519216, _519214), _519212), 5399 ^ _335846 : [(5402 ^ _335846) ^ [] : [-(_519214 = apply(_519212, _519216))], (5400 ^ _335846) ^ [] : [-(in(_519216, relation_dom(_519212)))]]]]], (3985 ^ _335846) ^ [_473149] : [relation(_473149), 3988 ^ _335846 : [(3989 ^ _335846) ^ [_473289] : [relation(_473289), -(relation_rng(relation_composition(_473149, _473289)) = relation_image(_473289, relation_rng(_473149)))]]], (610 ^ _335846) ^ [_356150, _356152, _356154, _356156] : [-(set_intersection2(_356156, _356152) = set_intersection2(_356154, _356150)), _356156 = _356154, _356152 = _356150], (5277 ^ _335846) ^ [_515450] : [-(relation_dom(identity_relation(_515450)) = _515450)], (508 ^ _335846) ^ [_352467, _352469, _352471, _352473] : [-(complements_of_subsets(_352473, _352469) = complements_of_subsets(_352471, _352467)), _352473 = _352471, _352469 = _352467], (5473 ^ _335846) ^ [_522067] : [-(in(_522067, 5471 ^ [_522067]))], (420 ^ _335846) ^ [_349272, _349274] : [_349274 = _349272, -(set_meet(_349274) = set_meet(_349272))], (4352 ^ _335846) ^ [_485104] : [-(set_intersection2(_485104, empty_set) = empty_set)], (2551 ^ _335846) ^ [_426063, _426065] : [disjoint(_426065, _426063), -(set_intersection2(_426065, _426063) = empty_set)], (762 ^ _335846) ^ [_361406, _361408] : [-(unordered_pair(_361408, _361406) = unordered_pair(_361406, _361408))], (158 ^ _335846) ^ [_340898, _340900] : [-(reflexive(_340898)), _340900 = _340898, reflexive(_340900)], (2307 ^ _335846) ^ [_417274, _417276] : [element(_417274, powerset(_417276)), -(subset_complement(_417276, _417274) = set_difference(_417276, _417274))], (4861 ^ _335846) ^ [_502121, _502123] : [-(disjoint(_502123, _502121)), -(in(4864 ^ [_502121, _502123], set_intersection2(_502123, _502121)))], (564 ^ _335846) ^ [_354496, _354498, _354500, _354502] : [-(set_difference(_354502, _354498) = set_difference(_354500, _354496)), _354502 = _354500, _354498 = _354496], (3595 ^ _335846) ^ [] : [-(epsilon_connected(3591 ^ []))], (302 ^ _335846) ^ [_345348, _345350] : [-(function(_345348)), _345350 = _345348, function(_345350)], (3094 ^ _335846) ^ [_443207, _443209] : [-(relation(set_intersection2(_443209, _443207))), relation(_443209), relation(_443207)], (312 ^ _335846) ^ [_345671, _345673, _345675, _345677] : [-(well_orders(_345675, _345671)), well_orders(_345677, _345673), _345677 = _345675, _345673 = _345671], (5350 ^ _335846) ^ [_518028, _518030, _518032] : [relation(_518028), 5353 ^ _335846 : [(5362 ^ _335846) ^ [] : [-(in(_518032, relation_dom(relation_dom_restriction(_518028, _518030)))), in(_518032, _518030), in(_518032, relation_dom(_518028))], (5354 ^ _335846) ^ [] : [in(_518032, relation_dom(relation_dom_restriction(_518028, _518030))), 5357 ^ _335846 : [(5360 ^ _335846) ^ [] : [-(in(_518032, relation_dom(_518028)))], (5358 ^ _335846) ^ [] : [-(in(_518032, _518030))]]]]], (4304 ^ _335846) ^ [_483546, _483548] : [relation(_483546), transitive(_483546), -(transitive(relation_restriction(_483546, _483548)))], (5024 ^ _335846) ^ [_507606, _507608, _507610] : [element(_507606, powerset(_507610)), in(_507608, subset_complement(_507610, _507606)), in(_507608, _507606)], (4453 ^ _335846) ^ [_488426] : [ordinal(_488426), 4456 ^ _335846 : [(4457 ^ _335846) ^ [_488564] : [ordinal(_488564), 4460 ^ _335846 : [(4467 ^ _335846) ^ [] : [ordinal_subset(succ(_488426), _488564), -(in(_488426, _488564))], (4461 ^ _335846) ^ [] : [in(_488426, _488564), -(ordinal_subset(succ(_488426), _488564))]]]]], (4052 ^ _335846) ^ [_475424, _475426] : [relation(_475424), -(_475426 = empty_set), subset(_475426, relation_rng(_475424)), relation_inverse_image(_475424, _475426) = empty_set], (664 ^ _335846) ^ [_358071, _358073] : [_358073 = _358071, -(powerset(_358073) = powerset(_358071))], (4473 ^ _335846) ^ [_489049, _489051, _489053] : [subset(_489053, _489051), -(subset(set_difference(_489053, _489049), set_difference(_489051, _489049)))], (2089 ^ _335846) ^ [_409569, _409571] : [_409569 = union(_409571), 2092 ^ _335846 : [(2102 ^ _335846) ^ [_410077] : [-(in(_410077, _409569)), 2103 ^ _335846 : [(2104 ^ _335846) ^ [_410175] : [in(_410077, _410175), in(_410175, _409571)]]], (2093 ^ _335846) ^ [_409750] : [in(_409750, _409569), 2097 ^ _335846 : [(2100 ^ _335846) ^ [] : [-(in(2096 ^ [_409569, _409571, _409750], _409571))], (2098 ^ _335846) ^ [] : [-(in(_409750, 2096 ^ [_409569, _409571, _409750]))]]]]], (4084 ^ _335846) ^ [_476480, _476482] : [relation(_476480), -(relation_restriction(_476480, _476482) = relation_rng_restriction(_476482, relation_dom_restriction(_476480, _476482)))], (518 ^ _335846) ^ [_352854, _352856, _352858, _352860, _352862, _352864] : [-(subset_difference(_352864, _352860, _352856) = subset_difference(_352862, _352858, _352854)), _352864 = _352862, _352860 = _352858, _352856 = _352854], (1684 ^ _335846) ^ [_394522, _394524, _394526] : [_394522 = set_union2(_394526, _394524), 1687 ^ _335846 : [(1688 ^ _335846) ^ [_394704] : [in(_394704, _394522), -(in(_394704, _394526)), -(in(_394704, _394524))], (1698 ^ _335846) ^ [_394982] : [1699 ^ _335846 : [(1702 ^ _335846) ^ [] : [in(_394982, _394524)], (1700 ^ _335846) ^ [] : [in(_394982, _394526)]], -(in(_394982, _394522))]]], (3590 ^ _335846) ^ [] : [-(function(3586 ^ []))], (5263 ^ _335846) ^ [_515031, _515033, _515035] : [relation(_515031), function(_515031), in(_515033, relation_dom(relation_dom_restriction(_515031, _515035))), -(apply(relation_dom_restriction(_515031, _515035), _515033) = apply(_515031, _515033))], (3552 ^ _335846) ^ [_458549, _458551] : [3554 ^ _335846 : [(3557 ^ _335846) ^ [] : [in(3553 ^ [_458549, _458551], _458549)], (3555 ^ _335846) ^ [] : [-(in(3553 ^ [_458549, _458551], _458551))]], -(element(_458551, powerset(_458549)))], (4 ^ _335846) ^ [_336077, _336079] : [_336079 = _336077, -(_336077 = _336079)], (4186 ^ _335846) ^ [_479847] : [epsilon_transitive(_479847), 4189 ^ _335846 : [(4190 ^ _335846) ^ [_479983] : [ordinal(_479983), proper_subset(_479847, _479983), -(in(_479847, _479983))]]], (5138 ^ _335846) ^ [_511029, _511031] : [subset(_511031, _511029), proper_subset(_511029, _511031)], (3130 ^ _335846) ^ [_444316, _444318] : [-(relation(set_union2(_444318, _444316))), relation(_444318), relation(_444316)], (436 ^ _335846) ^ [_349877, _349879, _349881, _349883] : [-(relation_inverse_image(_349883, _349879) = relation_inverse_image(_349881, _349877)), _349883 = _349881, _349879 = _349877], (3646 ^ _335846) ^ [_461498] : [-(empty(3642 ^ [_461498]))], (1871 ^ _335846) ^ [_401645] : [relation(_401645), 1874 ^ _335846 : [(1875 ^ _335846) ^ [_401842] : [is_well_founded_in(_401645, _401842), 1878 ^ _335846 : [(1879 ^ _335846) ^ [_402007] : [subset(_402007, _401842), -(_402007 = empty_set), 1887 ^ _335846 : [(1890 ^ _335846) ^ [] : [-(disjoint(fiber(_401645, 1886 ^ [_401645, _401842, _402007]), _402007))], (1888 ^ _335846) ^ [] : [-(in(1886 ^ [_401645, _401842, _402007], _402007))]]]]], (1892 ^ _335846) ^ [_402448] : [-(is_well_founded_in(_401645, _402448)), 1894 ^ _335846 : [(1899 ^ _335846) ^ [_402790] : [in(_402790, 1893 ^ [_401645, _402448]), disjoint(fiber(_401645, _402790), 1893 ^ [_401645, _402448])], (1897 ^ _335846) ^ [] : [1893 ^ [_401645, _402448] = empty_set], (1895 ^ _335846) ^ [] : [-(subset(1893 ^ [_401645, _402448], _402448))]]]]], (2008 ^ _335846) ^ [_406368] : [relation(_406368), 2011 ^ _335846 : [(2012 ^ _335846) ^ [_406549] : [_406549 = relation_dom(_406368), 2015 ^ _335846 : [(2023 ^ _335846) ^ [_406973] : [2024 ^ _335846 : [(2025 ^ _335846) ^ [_407052] : [in(ordered_pair(_406973, _407052), _406368)]], -(in(_406973, _406549))], (2016 ^ _335846) ^ [_406729] : [in(_406729, _406549), -(in(ordered_pair(_406729, 2019 ^ [_406368, _406549, _406729]), _406368))]]], (2029 ^ _335846) ^ [_407180] : [-(_407180 = relation_dom(_406368)), 2033 ^ _335846 : [(2036 ^ _335846) ^ [_407443] : [in(ordered_pair(2030 ^ [_406368, _407180], _407443), _406368)], (2034 ^ _335846) ^ [] : [-(in(2030 ^ [_406368, _407180], _407180))]], 2038 ^ _335846 : [(2041 ^ _335846) ^ [] : [in(2030 ^ [_406368, _407180], _407180)], (2039 ^ _335846) ^ [] : [-(in(ordered_pair(2030 ^ [_406368, _407180], 2037 ^ [_406368, _407180]), _406368))]]]]], (2174 ^ _335846) ^ [_412319, _412321, _412323] : [_412319 = set_difference(_412323, _412321), 2177 ^ _335846 : [(2186 ^ _335846) ^ [_412763] : [-(in(_412763, _412319)), in(_412763, _412323), -(in(_412763, _412321))], (2178 ^ _335846) ^ [_412503] : [in(_412503, _412319), 2181 ^ _335846 : [(2184 ^ _335846) ^ [] : [in(_412503, _412321)], (2182 ^ _335846) ^ [] : [-(in(_412503, _412323))]]]]], (2913 ^ _335846) ^ [_437661, _437663] : [element(_437661, powerset(_437663)), -(element(subset_complement(_437663, _437661), powerset(_437663)))], (3126 ^ _335846) ^ [] : [-(epsilon_connected(empty_set))], (3630 ^ _335846) ^ [] : [-(empty(3622 ^ []))], (4624 ^ _335846) ^ [_494197, _494199] : [element(_494199, powerset(_494197)), -(subset(_494199, _494197))], (3218 ^ _335846) ^ [] : [-(relation(empty_set))], (3270 ^ _335846) ^ [_448678] : [empty(_448678), 3273 ^ _335846 : [(3276 ^ _335846) ^ [] : [-(relation(relation_rng(_448678)))], (3274 ^ _335846) ^ [] : [-(empty(relation_rng(_448678)))]]], (3600 ^ _335846) ^ [] : [-(empty(3598 ^ []))], (5249 ^ _335846) ^ [_514499] : [-(unordered_pair(_514499, _514499) = singleton(_514499))], (4715 ^ _335846) ^ [_497165, _497167] : [element(_497165, powerset(_497167)), 4718 ^ _335846 : [(4719 ^ _335846) ^ [_497317] : [element(_497317, powerset(_497167)), 4722 ^ _335846 : [(4729 ^ _335846) ^ [] : [subset(_497165, subset_complement(_497167, _497317)), -(disjoint(_497165, _497317))], (4723 ^ _335846) ^ [] : [disjoint(_497165, _497317), -(subset(_497165, subset_complement(_497167, _497317)))]]]]], (2863 ^ _335846) ^ [_436410] : [2870 ^ _335846 : [(2873 ^ _335846) ^ [] : [-(function(function_inverse(_436410)))], (2871 ^ _335846) ^ [] : [-(relation(function_inverse(_436410)))]], relation(_436410), function(_436410)], (2803 ^ _335846) ^ [] : [true___, -(true___)], (3975 ^ _335846) ^ [_472836, _472838, _472840, _472842] : [relation_of2_as_subset(_472836, _472838, _472842), subset(relation_rng(_472836), _472840), -(relation_of2_as_subset(_472836, _472838, _472840))], (1321 ^ _335846) ^ [_381965, _381967, _381969] : [subset(_381965, cartesian_product2(_381969, _381967)), -(relation_of2(_381965, _381969, _381967))], (718 ^ _335846) ^ [_360108, _360110, _360112] : [element(_360108, powerset(cartesian_product2(_360112, _360110))), -(relation(_360108))], (1269 ^ _335846) ^ [_379883] : [-(succ(_379883) = set_union2(_379883, singleton(_379883)))], (5440 ^ _335846) ^ [_520741, _520743, _520745] : [singleton(_520745) = unordered_pair(_520743, _520741), -(_520745 = _520743)], (2983 ^ _335846) ^ [_439728, _439730] : [relation(_439730), -(relation(relation_dom_restriction(_439730, _439728)))], (5295 ^ _335846) ^ [_516071, _516073, _516075, _516077] : [relation(_516071), 5298 ^ _335846 : [(5307 ^ _335846) ^ [] : [-(in(ordered_pair(_516077, _516075), relation_composition(identity_relation(_516073), _516071))), in(_516077, _516073), in(ordered_pair(_516077, _516075), _516071)], (5299 ^ _335846) ^ [] : [in(ordered_pair(_516077, _516075), relation_composition(identity_relation(_516073), _516071)), 5302 ^ _335846 : [(5305 ^ _335846) ^ [] : [-(in(ordered_pair(_516077, _516075), _516071))], (5303 ^ _335846) ^ [] : [-(in(_516077, _516073))]]]]], (3955 ^ _335846) ^ [_472190] : [relation(_472190), -(relation_image(_472190, relation_dom(_472190)) = relation_rng(_472190))], (1573 ^ _335846) ^ [_390858, _390860] : [-(empty(_390860)), 1576 ^ _335846 : [(1583 ^ _335846) ^ [] : [in(_390858, _390860), -(element(_390858, _390860))], (1577 ^ _335846) ^ [] : [element(_390858, _390860), -(in(_390858, _390860))]]], (388 ^ _335846) ^ [_348045, _348047, _348049, _348051, _348053, _348055] : [-(relation_of2_as_subset(_348053, _348049, _348045)), relation_of2_as_subset(_348055, _348051, _348047), _348055 = _348053, _348051 = _348049, _348047 = _348045], (1483 ^ _335846) ^ [_387671, _387673] : [_387671 = powerset(_387673), 1486 ^ _335846 : [(1493 ^ _335846) ^ [_388013] : [subset(_388013, _387673), -(in(_388013, _387671))], (1487 ^ _335846) ^ [_387841] : [in(_387841, _387671), -(subset(_387841, _387673))]]], (4528 ^ _335846) ^ [_490945] : [relation(_490945), 4531 ^ _335846 : [(4534 ^ _335846) ^ [] : [-(relation_dom(_490945) = relation_rng(relation_inverse(_490945)))], (4532 ^ _335846) ^ [] : [-(relation_rng(_490945) = relation_dom(relation_inverse(_490945)))]]], (3923 ^ _335846) ^ [_471136, _471138] : [relation(_471136), -(subset(relation_image(_471136, _471138), relation_rng(_471136)))], (1990 ^ _335846) ^ [_405874] : [ordinal(_405874), 1993 ^ _335846 : [(1996 ^ _335846) ^ [] : [-(epsilon_connected(_405874))], (1994 ^ _335846) ^ [] : [-(epsilon_transitive(_405874))]]], (3001 ^ _335846) ^ [] : [true___, -(true___)], (336 ^ _335846) ^ [_346382, _346384] : [-(relation(_346382)), _346384 = _346382, relation(_346384)], (2833 ^ _335846) ^ [] : [true___, -(true___)], (4393 ^ _335846) ^ [_486518] : [-(ordinal(_486518)), 4395 ^ _335846 : [(4398 ^ _335846) ^ [] : [ordinal(4394 ^ [_486518]), subset(4394 ^ [_486518], _486518)], (4396 ^ _335846) ^ [] : [-(in(4394 ^ [_486518], _486518))]]], (782 ^ _335846) ^ [_362108, _362110] : [relation(_362108), 785 ^ _335846 : [(786 ^ _335846) ^ [] : [_362108 = identity_relation(_362110), 789 ^ _335846 : [(798 ^ _335846) ^ [_362681, _362683] : [-(in(ordered_pair(_362683, _362681), _362108)), in(_362683, _362110), _362683 = _362681], (790 ^ _335846) ^ [_362418, _362420] : [in(ordered_pair(_362420, _362418), _362108), 793 ^ _335846 : [(796 ^ _335846) ^ [] : [-(_362420 = _362418)], (794 ^ _335846) ^ [] : [-(in(_362420, _362110))]]]]], (808 ^ _335846) ^ [] : [-(_362108 = identity_relation(_362110)), 821 ^ _335846 : [(826 ^ _335846) ^ [] : [in(ordered_pair(809 ^ [_362108, _362110], 810 ^ [_362108, _362110]), _362108)], (824 ^ _335846) ^ [] : [-(809 ^ [_362108, _362110] = 810 ^ [_362108, _362110])], (822 ^ _335846) ^ [] : [-(in(809 ^ [_362108, _362110], _362110))]], 813 ^ _335846 : [(816 ^ _335846) ^ [] : [in(809 ^ [_362108, _362110], _362110), 809 ^ [_362108, _362110] = 810 ^ [_362108, _362110]], (814 ^ _335846) ^ [] : [-(in(ordered_pair(809 ^ [_362108, _362110], 810 ^ [_362108, _362110]), _362108))]]]]], (2821 ^ _335846) ^ [] : [true___, -(true___)], (86 ^ _335846) ^ [_338665, _338667] : [-(relation_empty_yielding(_338665)), _338667 = _338665, relation_empty_yielding(_338667)], (3412 ^ _335846) ^ [_453714, _453716] : [subset(_453716, _453714), -(set_difference(_453716, _453714) = empty_set)], (3337 ^ _335846) ^ [_450969] : [singleton(_450969) = empty_set], (1376 ^ _335846) ^ [_383918, _383920] : [_383920 = empty_set, 1379 ^ _335846 : [(1386 ^ _335846) ^ [] : [_383918 = empty_set, -(_383918 = set_meet(_383920))], (1380 ^ _335846) ^ [] : [_383918 = set_meet(_383920), -(_383918 = empty_set)]]], (3621 ^ _335846) ^ [] : [-(function(3615 ^ []))], (1907 ^ _335846) ^ [_403148, _403150, _403152] : [_403148 = set_intersection2(_403152, _403150), 1910 ^ _335846 : [(1919 ^ _335846) ^ [_403589] : [-(in(_403589, _403148)), in(_403589, _403152), in(_403589, _403150)], (1911 ^ _335846) ^ [_403330] : [in(_403330, _403148), 1914 ^ _335846 : [(1917 ^ _335846) ^ [] : [-(in(_403330, _403150))], (1915 ^ _335846) ^ [] : [-(in(_403330, _403152))]]]]], (766 ^ _335846) ^ [_361606, _361608] : [-(set_intersection2(_361608, _361606) = set_intersection2(_361606, _361608))], (712 ^ _335846) ^ [_359894] : [empty(_359894), -(relation(_359894))], (3060 ^ _335846) ^ [_442199, _442201] : [3067 ^ _335846 : [(3070 ^ _335846) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_442201, _442199)))], (3068 ^ _335846) ^ [] : [-(relation(relation_dom_restriction(_442201, _442199)))]], relation(_442201), relation_empty_yielding(_442201)], (3751 ^ _335846) ^ [_464979, _464981, _464983, _464985] : [in(ordered_pair(_464985, _464983), cartesian_product2(_464981, _464979)), 3754 ^ _335846 : [(3757 ^ _335846) ^ [] : [-(in(_464983, _464979))], (3755 ^ _335846) ^ [] : [-(in(_464985, _464981))]]], (5344 ^ _335846) ^ [_517796, _517798] : [set_difference(_517798, _517796) = _517798, -(disjoint(_517798, _517796))], (1476 ^ _335846) ^ [_387380] : [-(in(1477 ^ [_387380], _387380)), -(_387380 = empty_set)], (5508 ^ _335846) ^ [_523347, _523349, _523351] : [singleton(_523351) = unordered_pair(_523349, _523347), -(_523349 = _523347)], (1589 ^ _335846) ^ [_391271, _391273] : [empty(_391273), 1592 ^ _335846 : [(1599 ^ _335846) ^ [] : [empty(_391271), -(element(_391271, _391273))], (1593 ^ _335846) ^ [] : [element(_391271, _391273), -(empty(_391271))]]], (2763 ^ _335846) ^ [_434135, _434137] : [-(proper_subset(_434137, _434135)), subset(_434137, _434135), -(_434137 = _434135)], (5144 ^ _335846) ^ [_511224] : [relation(_511224), function(_511224), one_to_one(_511224), -(one_to_one(function_inverse(_511224)))], (96 ^ _335846) ^ [_339016, _339018, _339020, _339022, _339024, _339026] : [-(relation_of2(_339024, _339020, _339016)), relation_of2(_339026, _339022, _339018), _339026 = _339024, _339022 = _339020, _339018 = _339016], (4416 ^ _335846) ^ [_487247, _487249] : [ordinal(_487247), subset(_487249, _487247), -(_487249 = empty_set), 4428 ^ _335846 : [(4433 ^ _335846) ^ [_487799] : [ordinal(_487799), in(_487799, _487249), -(ordinal_subset(4427 ^ [_487247, _487249], _487799))], (4431 ^ _335846) ^ [] : [-(in(4427 ^ [_487247, _487249], _487249))], (4429 ^ _335846) ^ [] : [-(ordinal(4427 ^ [_487247, _487249]))]]], (620 ^ _335846) ^ [_356481, _356483] : [_356483 = _356481, -(relation_dom(_356483) = relation_dom(_356481))], (5034 ^ _335846) ^ [_507912] : [relation(_507912), 5037 ^ _335846 : [(5038 ^ _335846) ^ [_508068] : [relation(_508068), 5041 ^ _335846 : [(5042 ^ _335846) ^ [_508220] : [relation(_508220), function(_508220), -(well_ordering(_508068)), well_ordering(_507912), relation_isomorphism(_507912, _508068, _508220)]]]]], (3116 ^ _335846) ^ [] : [-(relation_empty_yielding(empty_set))], (5208 ^ _335846) ^ [_513139, _513141] : [relation(_513139), function(_513139), 5215 ^ _335846 : [(5216 ^ _335846) ^ [_513406] : [relation(_513406), function(_513406), 5223 ^ _335846 : [(5236 ^ _335846) ^ [] : [-(_513139 = relation_dom_restriction(_513406, _513141)), relation_dom(_513139) = set_intersection2(relation_dom(_513406), _513141), 5242 ^ _335846 : [(5245 ^ _335846) ^ [] : [apply(_513139, 5241 ^ [_513139, _513141, _513406]) = apply(_513406, 5241 ^ [_513139, _513141, _513406])], (5243 ^ _335846) ^ [] : [-(in(5241 ^ [_513139, _513141, _513406], relation_dom(_513139)))]]], (5224 ^ _335846) ^ [] : [_513139 = relation_dom_restriction(_513406, _513141), 5227 ^ _335846 : [(5230 ^ _335846) ^ [_513860] : [in(_513860, relation_dom(_513139)), -(apply(_513139, _513860) = apply(_513406, _513860))], (5228 ^ _335846) ^ [] : [-(relation_dom(_513139) = set_intersection2(relation_dom(_513406), _513141))]]]]]]], (1786 ^ _335846) ^ [_398561] : [epsilon_connected(_398561), 1789 ^ _335846 : [(1790 ^ _335846) ^ [_398737, _398739] : [in(_398739, _398561), in(_398737, _398561), -(in(_398739, _398737)), -(_398739 = _398737), -(in(_398737, _398739))]]], (3745 ^ _335846) ^ [_464712, _464714] : [disjoint(_464714, _464712), -(disjoint(_464712, _464714))], (5076 ^ _335846) ^ [_509164] : [relation(_509164), -(in(ordered_pair(5081 ^ [_509164], 5082 ^ [_509164]), _509164)), -(_509164 = empty_set)], (360 ^ _335846) ^ [_347149, _347151, _347153, _347155] : [-(in(_347153, _347149)), in(_347155, _347151), _347155 = _347153, _347151 = _347149], (3106 ^ _335846) ^ [] : [-(empty(empty_set))], (636 ^ _335846) ^ [_357058, _357060] : [_357060 = _357058, -(identity_relation(_357060) = identity_relation(_357058))], (230 ^ _335846) ^ [_343131, _343133] : [-(well_founded_relation(_343131)), _343133 = _343131, well_founded_relation(_343133)], (138 ^ _335846) ^ [_340308, _340310] : [-(ordinal(_340308)), _340310 = _340308, ordinal(_340310)], (3312 ^ _335846) ^ [_450165, _450167] : [proper_subset(_450167, _450167)], (2851 ^ _335846) ^ [] : [true___, -(true___)], (5338 ^ _335846) ^ [_517628, _517630] : [disjoint(_517630, _517628), -(set_difference(_517630, _517628) = _517630)], (1214 ^ _335846) ^ [_377946, _377948, _377950, _377952] : [_377946 = unordered_triple(_377952, _377950, _377948), 1217 ^ _335846 : [(1218 ^ _335846) ^ [_378148] : [in(_378148, _377946), -(_378148 = _377952), -(_378148 = _377950), -(_378148 = _377948)], (1232 ^ _335846) ^ [_378548] : [1233 ^ _335846 : [(1238 ^ _335846) ^ [] : [_378548 = _377948], (1236 ^ _335846) ^ [] : [_378548 = _377950], (1234 ^ _335846) ^ [] : [_378548 = _377952]], -(in(_378548, _377946))]]], (2965 ^ _335846) ^ [_439049] : [-(relation(identity_relation(_439049)))], (2809 ^ _335846) ^ [] : [true___, -(true___)], (3164 ^ _335846) ^ [_445326] : [ordinal(_445326), 3167 ^ _335846 : [(3170 ^ _335846) ^ [] : [-(epsilon_transitive(succ(_445326)))], (3172 ^ _335846) ^ [] : [-(epsilon_connected(succ(_445326)))], (3174 ^ _335846) ^ [] : [-(ordinal(succ(_445326)))], (3168 ^ _335846) ^ [] : [empty(succ(_445326))]]], (4266 ^ _335846) ^ [_482413, _482415] : [ordinal(_482413), in(_482415, _482413), -(ordinal(_482415))], (2367 ^ _335846) ^ [_419178] : [relation(_419178), -(relation_field(_419178) = set_union2(relation_dom(_419178), relation_rng(_419178)))], (5196 ^ _335846) ^ [_512741, _512743] : [set_difference(_512743, singleton(_512741)) = _512743, in(_512741, _512743)], (4827 ^ _335846) ^ [_500965] : [relation(_500965), 4830 ^ _335846 : [(4831 ^ _335846) ^ [_501120] : [relation(_501120), 4834 ^ _335846 : [(4835 ^ _335846) ^ [_501271] : [relation(_501271), function(_501271), relation_isomorphism(_500965, _501120, _501271), -(relation_isomorphism(_501120, _500965, function_inverse(_501271)))]]]]], (1757 ^ _335846) ^ [_397298, _397300, _397302] : [-(_397298 = cartesian_product2(_397302, _397300)), 1775 ^ _335846 : [(1778 ^ _335846) ^ [] : [-(in(1774 ^ [_397298, _397300, _397302], _397300))], (1780 ^ _335846) ^ [] : [-(1758 ^ [_397298, _397300, _397302] = ordered_pair(1773 ^ [_397298, _397300, _397302], 1774 ^ [_397298, _397300, _397302]))], (1782 ^ _335846) ^ [] : [in(1758 ^ [_397298, _397300, _397302], _397298)], (1776 ^ _335846) ^ [] : [-(in(1773 ^ [_397298, _397300, _397302], _397302))]], 1761 ^ _335846 : [(1764 ^ _335846) ^ [_397636, _397638] : [in(_397638, _397302), in(_397636, _397300), 1758 ^ [_397298, _397300, _397302] = ordered_pair(_397638, _397636)], (1762 ^ _335846) ^ [] : [-(in(1758 ^ [_397298, _397300, _397302], _397298))]]], (3713 ^ _335846) ^ [_463776, _463778] : [ordinal(_463778), ordinal(_463776), 3720 ^ _335846 : [(3727 ^ _335846) ^ [] : [subset(_463778, _463776), -(ordinal_subset(_463778, _463776))], (3721 ^ _335846) ^ [] : [ordinal_subset(_463778, _463776), -(subset(_463778, _463776))]]], (3691 ^ _335846) ^ [_463008, _463010, _463012] : [-(subset_difference(_463012, _463010, _463008) = set_difference(_463010, _463008)), element(_463010, powerset(_463012)), element(_463008, powerset(_463012))], (3707 ^ _335846) ^ [_463554, _463556, _463558] : [relation_of2(_463554, _463558, _463556), -(relation_of2_as_subset(_463554, _463558, _463556))], (2937 ^ _335846) ^ [] : [true___, -(true___)], (2710 ^ _335846) ^ [_432306, _432308] : [element(_432306, powerset(powerset(_432308))), 2713 ^ _335846 : [(2714 ^ _335846) ^ [_432486] : [element(_432486, powerset(powerset(_432308))), 2717 ^ _335846 : [(2718 ^ _335846) ^ [] : [_432486 = complements_of_subsets(_432308, _432306), 2721 ^ _335846 : [(2722 ^ _335846) ^ [_432774] : [element(_432774, powerset(_432308)), 2725 ^ _335846 : [(2732 ^ _335846) ^ [] : [in(subset_complement(_432308, _432774), _432306), -(in(_432774, _432486))], (2726 ^ _335846) ^ [] : [in(_432774, _432486), -(in(subset_complement(_432308, _432774), _432306))]]]]], (2738 ^ _335846) ^ [] : [-(_432486 = complements_of_subsets(_432308, _432306)), 2740 ^ _335846 : [(2743 ^ _335846) ^ [] : [2744 ^ _335846 : [(2747 ^ _335846) ^ [] : [in(subset_complement(_432308, 2739 ^ [_432306, _432308, _432486]), _432306)], (2745 ^ _335846) ^ [] : [-(in(2739 ^ [_432306, _432308, _432486], _432486))]], 2748 ^ _335846 : [(2751 ^ _335846) ^ [] : [in(2739 ^ [_432306, _432308, _432486], _432486)], (2749 ^ _335846) ^ [] : [-(in(subset_complement(_432308, 2739 ^ [_432306, _432308, _432486]), _432306))]]], (2741 ^ _335846) ^ [] : [-(element(2739 ^ [_432306, _432308, _432486], powerset(_432308)))]]]]]]], (4090 ^ _335846) ^ [_476720, _476722, _476724] : [relation(_476720), in(_476724, relation_field(relation_restriction(_476720, _476722))), 4097 ^ _335846 : [(4100 ^ _335846) ^ [] : [-(in(_476724, _476722))], (4098 ^ _335846) ^ [] : [-(in(_476724, relation_field(_476720)))]]], (4206 ^ _335846) ^ [_480503, _480505, _480507] : [relation(_480503), -(subset(fiber(relation_restriction(_480503, _480507), _480505), fiber(_480503, _480505)))], (1514 ^ _335846) ^ [_388743] : [epsilon_transitive(_388743), 1517 ^ _335846 : [(1518 ^ _335846) ^ [_388874] : [in(_388874, _388743), -(subset(_388874, _388743))]]], (3860 ^ _335846) ^ [_468905] : [-(in(_468905, 3858 ^ [_468905]))], (4630 ^ _335846) ^ [_494363, _494365] : [subset(_494365, _494363), -(element(_494365, powerset(_494363)))], (3220 ^ _335846) ^ [_447189, _447191] : [empty(cartesian_product2(_447191, _447189)), -(empty(_447191)), -(empty(_447189))], (3675 ^ _335846) ^ [] : [-(relation_empty_yielding(3671 ^ []))], (2883 ^ _335846) ^ [] : [true___, -(true___)], (1470 ^ _335846) ^ [_387201] : [_387201 = empty_set, 1473 ^ _335846 : [(1474 ^ _335846) ^ [_387314] : [in(_387314, _387201)]]], (2557 ^ _335846) ^ [_426231, _426233] : [set_intersection2(_426233, _426231) = empty_set, -(disjoint(_426233, _426231))], (2959 ^ _335846) ^ [_438850, _438852] : [element(_438850, powerset(powerset(_438852))), -(element(union_of_subsets(_438852, _438850), powerset(_438852)))], (3394 ^ _335846) ^ [_453135, _453137] : [subset(singleton(_453137), _453135), -(in(_453137, _453135))], (3046 ^ _335846) ^ [_441757] : [empty(_441757), 3049 ^ _335846 : [(3052 ^ _335846) ^ [] : [-(relation(relation_inverse(_441757)))], (3050 ^ _335846) ^ [] : [-(empty(relation_inverse(_441757)))]]], (1929 ^ _335846) ^ [_403873, _403875, _403877] : [-(_403873 = set_intersection2(_403877, _403875)), 1941 ^ _335846 : [(1946 ^ _335846) ^ [] : [in(1930 ^ [_403873, _403875, _403877], _403873)], (1944 ^ _335846) ^ [] : [-(in(1930 ^ [_403873, _403875, _403877], _403875))], (1942 ^ _335846) ^ [] : [-(in(1930 ^ [_403873, _403875, _403877], _403877))]], 1933 ^ _335846 : [(1936 ^ _335846) ^ [] : [in(1930 ^ [_403873, _403875, _403877], _403877), in(1930 ^ [_403873, _403875, _403877], _403875)], (1934 ^ _335846) ^ [] : [-(in(1930 ^ [_403873, _403875, _403877], _403873))]]], (4364 ^ _335846) ^ [_485512, _485514] : [-(_485514 = _485512), 4368 ^ _335846 : [(4371 ^ _335846) ^ [] : [in(4365 ^ [_485512, _485514], _485512)], (4369 ^ _335846) ^ [] : [-(in(4365 ^ [_485512, _485514], _485514))]], 4372 ^ _335846 : [(4375 ^ _335846) ^ [] : [in(4365 ^ [_485512, _485514], _485514)], (4373 ^ _335846) ^ [] : [-(in(4365 ^ [_485512, _485514], _485512))]]], (3054 ^ _335846) ^ [] : [-(empty(empty_set))], (5158 ^ _335846) ^ [_511610, _511612, _511614] : [-(disjoint(_511614, _511610)), subset(_511614, _511612), disjoint(_511612, _511610)], (4645 ^ _335846) ^ [_494913, _494915] : [disjoint(_494915, _494913), 4646 ^ _335846 : [(4647 ^ _335846) ^ [_495005] : [in(_495005, _494915), in(_495005, _494913)]]], (4775 ^ _335846) ^ [_499200, _499202] : [element(_499200, powerset(powerset(_499202))), -(_499200 = empty_set), complements_of_subsets(_499202, _499200) = empty_set], (3626 ^ _335846) ^ [] : [-(function(3622 ^ []))], (600 ^ _335846) ^ [_355791, _355793, _355795, _355797] : [-(set_union2(_355797, _355793) = set_union2(_355795, _355791)), _355797 = _355795, _355793 = _355791], (3007 ^ _335846) ^ [] : [true___, -(true___)], (3641 ^ _335846) ^ [] : [-(relation(3637 ^ []))], (3056 ^ _335846) ^ [] : [-(relation(empty_set))], (3092 ^ _335846) ^ [_443099] : [empty(succ(_443099))], (466 ^ _335846) ^ [_350954, _350956, _350958, _350960] : [-(fiber(_350960, _350956) = fiber(_350958, _350954)), _350960 = _350958, _350956 = _350954], (3665 ^ _335846) ^ [] : [-(ordinal(3657 ^ []))], (3345 ^ _335846) ^ [_451298, _451300] : [disjoint(singleton(_451300), _451298), in(_451300, _451298)], (2901 ^ _335846) ^ [] : [true___, -(true___)], (5134 ^ _335846) ^ [] : [-(relation_dom(empty_set) = empty_set)], (3634 ^ _335846) ^ [] : [-(epsilon_connected(3622 ^ []))], (3659 ^ _335846) ^ [] : [empty(3657 ^ [])], (1242 ^ _335846) ^ [_378910, _378912, _378914, _378916] : [-(_378910 = unordered_triple(_378916, _378914, _378912)), 1246 ^ _335846 : [(1249 ^ _335846) ^ [] : [1243 ^ [_378910, _378912, _378914, _378916] = _378916], (1251 ^ _335846) ^ [] : [1243 ^ [_378910, _378912, _378914, _378916] = _378914], (1253 ^ _335846) ^ [] : [1243 ^ [_378910, _378912, _378914, _378916] = _378912], (1247 ^ _335846) ^ [] : [-(in(1243 ^ [_378910, _378912, _378914, _378916], _378910))]], 1254 ^ _335846 : [(1255 ^ _335846) ^ [] : [-(1243 ^ [_378910, _378912, _378914, _378916] = _378916), -(1243 ^ [_378910, _378912, _378914, _378916] = _378914), -(1243 ^ [_378910, _378912, _378914, _378916] = _378912)], (1265 ^ _335846) ^ [] : [in(1243 ^ [_378910, _378912, _378914, _378916], _378910)]]], (5475 ^ _335846) ^ [_522179, _522181, _522183] : [-(in(_522179, 5471 ^ [_522183])), in(_522181, 5471 ^ [_522183]), subset(_522179, _522181)], (198 ^ _335846) ^ [_342134, _342136, _342138, _342140, _342142, _342144] : [-(relation_isomorphism(_342142, _342138, _342134)), relation_isomorphism(_342144, _342140, _342136), _342144 = _342142, _342140 = _342138, _342136 = _342134], (3661 ^ _335846) ^ [] : [-(epsilon_transitive(3657 ^ []))], (3781 ^ _335846) ^ [_466035, _466037, _466039] : [relation(_466035), 3784 ^ _335846 : [(3793 ^ _335846) ^ [] : [-(in(_466039, relation_rng(relation_rng_restriction(_466037, _466035)))), in(_466039, _466037), in(_466039, relation_rng(_466035))], (3785 ^ _335846) ^ [] : [in(_466039, relation_rng(relation_rng_restriction(_466037, _466035))), 3788 ^ _335846 : [(3791 ^ _335846) ^ [] : [-(in(_466039, relation_rng(_466035)))], (3789 ^ _335846) ^ [] : [-(in(_466039, _466037))]]]]], (642 ^ _335846) ^ [_357304, _357306, _357308, _357310] : [-(relation_dom_restriction(_357310, _357306) = relation_dom_restriction(_357308, _357304)), _357310 = _357308, _357306 = _357304], (124 ^ _335846) ^ [_339892, _339894, _339896, _339898] : [-(ordinal_subset(_339896, _339892)), ordinal_subset(_339898, _339894), _339898 = _339896, _339894 = _339892], (2949 ^ _335846) ^ [_438551, _438553] : [-(relation(relation_composition(_438553, _438551))), relation(_438553), relation(_438551)], (3561 ^ _335846) ^ [_458922, _458924, _458926] : [relation(_458922), function(_458922), 3568 ^ _335846 : [(3577 ^ _335846) ^ [] : [-(in(_458924, relation_dom(relation_dom_restriction(_458922, _458926)))), in(_458924, relation_dom(_458922)), in(_458924, _458926)], (3569 ^ _335846) ^ [] : [in(_458924, relation_dom(relation_dom_restriction(_458922, _458926))), 3572 ^ _335846 : [(3575 ^ _335846) ^ [] : [-(in(_458924, _458926))], (3573 ^ _335846) ^ [] : [-(in(_458924, relation_dom(_458922)))]]]]], (2815 ^ _335846) ^ [] : [true___, -(true___)], (2895 ^ _335846) ^ [] : [true___, -(true___)], (2361 ^ _335846) ^ [_418984] : [_418984 = union(_418984), -(being_limit_ordinal(_418984))], (3400 ^ _335846) ^ [_453301, _453303] : [in(_453303, _453301), -(subset(singleton(_453303), _453301))], (268 ^ _335846) ^ [_344314, _344316] : [-(one_to_one(_344314)), _344316 = _344314, one_to_one(_344316)], (3644 ^ _335846) ^ [_461447] : [-(element(3642 ^ [_461447], powerset(_461447)))], (3418 ^ _335846) ^ [_453932, _453934] : [element(_453932, powerset(_453934)), 3421 ^ _335846 : [(3422 ^ _335846) ^ [_454073] : [in(_454073, _453932), -(in(_454073, _453934))]]], (374 ^ _335846) ^ [_347593, _347595, _347597, _347599] : [-(subset(_347597, _347593)), subset(_347599, _347595), _347599 = _347597, _347595 = _347593], (4132 ^ _335846) ^ [_478128, _478130, _478132] : [relation(_478128), in(ordered_pair(_478132, _478130), _478128), 4139 ^ _335846 : [(4142 ^ _335846) ^ [] : [-(in(_478130, relation_rng(_478128)))], (4140 ^ _335846) ^ [] : [-(in(_478132, relation_dom(_478128)))]]], (3878 ^ _335846) ^ [_469532, _469534] : [subset(_469532, 3858 ^ [_469534]), -(are_equipotent(_469532, 3858 ^ [_469534])), -(in(_469532, 3858 ^ [_469534]))], (4755 ^ _335846) ^ [_498519, _498521] : [subset(_498521, _498519), -(_498519 = set_union2(_498521, set_difference(_498519, _498521)))], (2661 ^ _335846) ^ [_430247] : [relation(_430247), 2664 ^ _335846 : [(2665 ^ _335846) ^ [_430461] : [is_transitive_in(_430247, _430461), 2668 ^ _335846 : [(2669 ^ _335846) ^ [_430671, _430673, _430675] : [-(in(ordered_pair(_430675, _430671), _430247)), in(_430675, _430461), in(_430673, _430461), in(_430671, _430461), in(ordered_pair(_430675, _430673), _430247), in(ordered_pair(_430673, _430671), _430247)]]], (2691 ^ _335846) ^ [_431282] : [2695 ^ _335846 : [(2698 ^ _335846) ^ [] : [-(in(2693 ^ [_430247, _431282], _431282))], (2696 ^ _335846) ^ [] : [-(in(2692 ^ [_430247, _431282], _431282))], (2706 ^ _335846) ^ [] : [in(ordered_pair(2692 ^ [_430247, _431282], 2694 ^ [_430247, _431282]), _430247)], (2702 ^ _335846) ^ [] : [-(in(ordered_pair(2692 ^ [_430247, _431282], 2693 ^ [_430247, _431282]), _430247))], (2704 ^ _335846) ^ [] : [-(in(ordered_pair(2693 ^ [_430247, _431282], 2694 ^ [_430247, _431282]), _430247))], (2700 ^ _335846) ^ [] : [-(in(2694 ^ [_430247, _431282], _431282))]], -(is_transitive_in(_430247, _431282))]]], (3614 ^ _335846) ^ [] : [-(empty(3612 ^ []))], (1533 ^ _335846) ^ [_389368] : [relation(_389368), 1536 ^ _335846 : [(1537 ^ _335846) ^ [_389526] : [relation(_389526), 1540 ^ _335846 : [(1541 ^ _335846) ^ [] : [_389368 = _389526, 1544 ^ _335846 : [(1551 ^ _335846) ^ [_390021, _390023] : [in(ordered_pair(_390023, _390021), _389526), -(in(ordered_pair(_390023, _390021), _389368))], (1545 ^ _335846) ^ [_389831, _389833] : [in(ordered_pair(_389833, _389831), _389368), -(in(ordered_pair(_389833, _389831), _389526))]]], (1557 ^ _335846) ^ [] : [-(_389368 = _389526), 1562 ^ _335846 : [(1565 ^ _335846) ^ [] : [in(ordered_pair(1558 ^ [_389368, _389526], 1559 ^ [_389368, _389526]), _389526)], (1563 ^ _335846) ^ [] : [-(in(ordered_pair(1558 ^ [_389368, _389526], 1559 ^ [_389368, _389526]), _389368))]], 1566 ^ _335846 : [(1569 ^ _335846) ^ [] : [in(ordered_pair(1558 ^ [_389368, _389526], 1559 ^ [_389368, _389526]), _389368)], (1567 ^ _335846) ^ [] : [-(in(ordered_pair(1558 ^ [_389368, _389526], 1559 ^ [_389368, _389526]), _389526))]]]]]]], (4892 ^ _335846) ^ [_503213] : [relation(_503213), 4895 ^ _335846 : [(4896 ^ _335846) ^ [_503409] : [relation(_503409), 4899 ^ _335846 : [(4900 ^ _335846) ^ [_503601] : [relation(_503601), function(_503601), relation_isomorphism(_503213, _503409, _503601), 4911 ^ _335846 : [(4912 ^ _335846) ^ [] : [reflexive(_503213), -(reflexive(_503409))], (4924 ^ _335846) ^ [] : [connected(_503213), -(connected(_503409))], (4936 ^ _335846) ^ [] : [well_founded_relation(_503213), -(well_founded_relation(_503409))], (4930 ^ _335846) ^ [] : [antisymmetric(_503213), -(antisymmetric(_503409))], (4918 ^ _335846) ^ [] : [transitive(_503213), -(transitive(_503409))]]]]]]], (3278 ^ _335846) ^ [_448957, _448959] : [3285 ^ _335846 : [(3288 ^ _335846) ^ [] : [-(relation(relation_composition(_448959, _448957)))], (3286 ^ _335846) ^ [] : [-(empty(relation_composition(_448959, _448957)))]], empty(_448959), relation(_448957)], (532 ^ _335846) ^ [_353314, _353316] : [_353316 = _353314, -(cast_to_subset(_353316) = cast_to_subset(_353314))], (5378 ^ _335846) ^ [_518901, _518903] : [empty(_518903), -(_518903 = _518901), empty(_518901)], (3593 ^ _335846) ^ [] : [-(epsilon_transitive(3591 ^ []))], (1950 ^ _335846) ^ [_404612] : [relation(_404612), function(_404612), 1957 ^ _335846 : [(1974 ^ _335846) ^ [_405356, _405358] : [-(in(_405358, relation_dom(_404612))), 1977 ^ _335846 : [(1984 ^ _335846) ^ [] : [_405356 = empty_set, -(_405356 = apply(_404612, _405358))], (1978 ^ _335846) ^ [] : [_405356 = apply(_404612, _405358), -(_405356 = empty_set)]]], (1958 ^ _335846) ^ [_404904, _404906] : [in(_404906, relation_dom(_404612)), 1961 ^ _335846 : [(1968 ^ _335846) ^ [] : [in(ordered_pair(_404906, _404904), _404612), -(_404904 = apply(_404612, _404906))], (1962 ^ _335846) ^ [] : [_404904 = apply(_404612, _404906), -(in(ordered_pair(_404906, _404904), _404612))]]]]], (658 ^ _335846) ^ [_357853, _357855] : [_357855 = _357853, -(union(_357855) = union(_357853))], (4542 ^ _335846) ^ [_491441, _491443] : [subset(_491443, _491441), -(set_difference(_491443, _491441) = empty_set)], (5202 ^ _335846) ^ [_512914, _512916] : [-(in(_512914, _512916)), -(set_difference(_512916, singleton(_512914)) = _512916)], (670 ^ _335846) ^ [_358289, _358291] : [_358291 = _358289, -(singleton(_358291) = singleton(_358289))], (3872 ^ _335846) ^ [_469332, _469334] : [in(_469332, 3858 ^ [_469334]), -(in(powerset(_469332), 3858 ^ [_469334]))], (4560 ^ _335846) ^ [_492113, _492115, _492117] : [subset(unordered_pair(_492117, _492115), _492113), 4563 ^ _335846 : [(4566 ^ _335846) ^ [] : [-(in(_492115, _492113))], (4564 ^ _335846) ^ [] : [-(in(_492117, _492113))]]], (3803 ^ _335846) ^ [_466694, _466696] : [relation(_466694), -(subset(relation_rng(relation_rng_restriction(_466696, _466694)), _466696))], (5136 ^ _335846) ^ [] : [-(relation_rng(empty_set) = empty_set)], (2313 ^ _335846) ^ [_417485, _417487] : [-(ordered_pair(_417487, _417485) = unordered_pair(unordered_pair(_417487, _417485), singleton(_417487)))], (3995 ^ _335846) ^ [_473538, _473540, _473542] : [relation(_473538), 3998 ^ _335846 : [(4010 ^ _335846) ^ [] : [-(in(_473542, relation_inverse_image(_473538, _473540))), 4011 ^ _335846 : [(4012 ^ _335846) ^ [_474139] : [in(_474139, relation_rng(_473538)), in(ordered_pair(_473542, _474139), _473538), in(_474139, _473540)]]], (3999 ^ _335846) ^ [] : [in(_473542, relation_inverse_image(_473538, _473540)), 4003 ^ _335846 : [(4008 ^ _335846) ^ [] : [-(in(4002 ^ [_473538, _473540, _473542], _473540))], (4006 ^ _335846) ^ [] : [-(in(ordered_pair(_473542, 4002 ^ [_473538, _473540, _473542]), _473538))], (4004 ^ _335846) ^ [] : [-(in(4002 ^ [_473538, _473540, _473542], relation_rng(_473538)))]]]]], (4479 ^ _335846) ^ [_489305, _489307, _489309, _489311] : [ordered_pair(_489311, _489309) = ordered_pair(_489307, _489305), 4482 ^ _335846 : [(4485 ^ _335846) ^ [] : [-(_489309 = _489305)], (4483 ^ _335846) ^ [] : [-(_489311 = _489307)]]], (292 ^ _335846) ^ [_345053, _345055] : [-(empty(_345053)), _345055 = _345053, empty(_345055)], (5446 ^ _335846) ^ [_520967, _520969] : [relation(_520967), -(relation_dom(relation_dom_restriction(_520967, _520969)) = set_intersection2(relation_dom(_520967), _520969))], (3888 ^ _335846) ^ [_469886, _469888, _469890] : [relation(_469886), -(relation_dom_restriction(relation_rng_restriction(_469890, _469886), _469888) = relation_rng_restriction(_469890, relation_dom_restriction(_469886, _469888)))], (3733 ^ _335846) ^ [_464323, _464325] : [-(ordinal_subset(_464325, _464325)), ordinal(_464325), ordinal(_464323)], (3679 ^ _335846) ^ [_462538, _462540] : [element(_462538, powerset(powerset(_462540))), -(union_of_subsets(_462540, _462538) = union(_462538))], (3617 ^ _335846) ^ [] : [-(relation(3615 ^ []))], (4487 ^ _335846) ^ [_489618, _489620] : [relation(_489618), function(_489618), 4494 ^ _335846 : [(4507 ^ _335846) ^ [] : [-(_489618 = identity_relation(_489620)), relation_dom(_489618) = _489620, 4513 ^ _335846 : [(4516 ^ _335846) ^ [] : [apply(_489618, 4512 ^ [_489618, _489620]) = 4512 ^ [_489618, _489620]], (4514 ^ _335846) ^ [] : [-(in(4512 ^ [_489618, _489620], _489620))]]], (4495 ^ _335846) ^ [] : [_489618 = identity_relation(_489620), 4498 ^ _335846 : [(4501 ^ _335846) ^ [_490037] : [in(_490037, _489620), -(apply(_489618, _490037) = _490037)], (4499 ^ _335846) ^ [] : [-(relation_dom(_489618) = _489620)]]]]], (5458 ^ _335846) ^ [_521409, _521411] : [relation(_521409), -(relation_dom_restriction(_521409, _521411) = relation_composition(identity_relation(_521411), _521409))], (3122 ^ _335846) ^ [] : [-(empty(empty_set))], (4791 ^ _335846) ^ [_499723] : [relation(_499723), 4794 ^ _335846 : [(4795 ^ _335846) ^ [_499870] : [relation(_499870), subset(relation_dom(_499723), relation_rng(_499870)), -(relation_rng(relation_composition(_499870, _499723)) = relation_rng(_499723))]]], (3120 ^ _335846) ^ [] : [-(one_to_one(empty_set))], (4076 ^ _335846) ^ [_476157, _476159] : [relation(_476157), -(relation_restriction(_476157, _476159) = relation_dom_restriction(relation_rng_restriction(_476159, _476157), _476159))], (4276 ^ _335846) ^ [_482708, _482710] : [relation(_482708), connected(_482708), -(connected(relation_restriction(_482708, _482710)))], (3104 ^ _335846) ^ [_443476] : [empty(powerset(_443476))], (3357 ^ _335846) ^ [_451728, _451730] : [relation(_451728), -(subset(relation_dom(relation_rng_restriction(_451730, _451728)), relation_dom(_451728)))], (742 ^ _335846) ^ [_360811] : [-(ordinal(_360811)), epsilon_transitive(_360811), epsilon_connected(_360811)], (4655 ^ _335846) ^ [_495262] : [subset(_495262, empty_set), -(_495262 = empty_set)], (2881 ^ _335846) ^ [_436862] : [-(element(cast_to_subset(_436862), powerset(_436862)))], (3206 ^ _335846) ^ [_446728] : [ordinal(_446728), 3209 ^ _335846 : [(3214 ^ _335846) ^ [] : [-(ordinal(union(_446728)))], (3212 ^ _335846) ^ [] : [-(epsilon_connected(union(_446728)))], (3210 ^ _335846) ^ [] : [-(epsilon_transitive(union(_446728)))]]], (4614 ^ _335846) ^ [_493860, _493862, _493864] : [in(_493864, _493862), in(_493862, _493860), in(_493860, _493864)], (538 ^ _335846) ^ [_353560, _353562, _353564, _353566] : [-(meet_of_subsets(_353566, _353562) = meet_of_subsets(_353564, _353560)), _353566 = _353564, _353562 = _353560], (3013 ^ _335846) ^ [] : [true___, -(true___)], (3428 ^ _335846) ^ [_454284] : [relation(_454284), 3431 ^ _335846 : [(3432 ^ _335846) ^ [] : [antisymmetric(_454284), 3435 ^ _335846 : [(3436 ^ _335846) ^ [_454554, _454556] : [-(_454556 = _454554), in(ordered_pair(_454556, _454554), _454284), in(ordered_pair(_454554, _454556), _454284)]]], (3446 ^ _335846) ^ [] : [3449 ^ _335846 : [(3454 ^ _335846) ^ [] : [3447 ^ [_454284] = 3448 ^ [_454284]], (3452 ^ _335846) ^ [] : [-(in(ordered_pair(3448 ^ [_454284], 3447 ^ [_454284]), _454284))], (3450 ^ _335846) ^ [] : [-(in(ordered_pair(3447 ^ [_454284], 3448 ^ [_454284]), _454284))]], -(antisymmetric(_454284))]]], (3853 ^ _335846) ^ [_468583, _468585] : [subset(_468585, _468583), -(set_union2(_468585, _468583) = _468583)], (3510 ^ _335846) ^ [_457126, _457128] : [subset(_457128, singleton(_457126)), -(_457128 = empty_set), -(_457128 = singleton(_457126))], (188 ^ _335846) ^ [_341783, _341785] : [-(antisymmetric(_341783)), _341785 = _341783, antisymmetric(_341785)], (2270 ^ _335846) ^ [_415819] : [relation(_415819), 2273 ^ _335846 : [(2274 ^ _335846) ^ [_416000] : [_416000 = relation_rng(_415819), 2277 ^ _335846 : [(2285 ^ _335846) ^ [_416424] : [2286 ^ _335846 : [(2287 ^ _335846) ^ [_416503] : [in(ordered_pair(_416503, _416424), _415819)]], -(in(_416424, _416000))], (2278 ^ _335846) ^ [_416180] : [in(_416180, _416000), -(in(ordered_pair(2281 ^ [_415819, _416000, _416180], _416180), _415819))]]], (2291 ^ _335846) ^ [_416631] : [-(_416631 = relation_rng(_415819)), 2295 ^ _335846 : [(2298 ^ _335846) ^ [_416894] : [in(ordered_pair(_416894, 2292 ^ [_415819, _416631]), _415819)], (2296 ^ _335846) ^ [] : [-(in(2292 ^ [_415819, _416631], _416631))]], 2300 ^ _335846 : [(2303 ^ _335846) ^ [] : [in(2292 ^ [_415819, _416631], _416631)], (2301 ^ _335846) ^ [] : [-(in(ordered_pair(2299 ^ [_415819, _416631], 2292 ^ [_415819, _416631]), _415819))]]]]], (4661 ^ _335846) ^ [_495451, _495453] : [-(set_difference(set_union2(_495453, _495451), _495451) = set_difference(_495453, _495451))], (3262 ^ _335846) ^ [_448413] : [empty(_448413), 3265 ^ _335846 : [(3268 ^ _335846) ^ [] : [-(relation(relation_dom(_448413)))], (3266 ^ _335846) ^ [] : [-(empty(relation_dom(_448413)))]]], (34 ^ _335846) ^ [_337066, _337068, _337070, _337072] : [-(is_connected_in(_337070, _337066)), is_connected_in(_337072, _337068), _337072 = _337070, _337068 = _337066], (4340 ^ _335846) ^ [_484689, _484691, _484693] : [subset(_484693, _484691), -(subset(set_intersection2(_484693, _484689), set_intersection2(_484691, _484689)))], (4114 ^ _335846) ^ [_477528, _477530] : [in(_477530, _477528), -(element(_477530, _477528))], (3363 ^ _335846) ^ [_451936] : [relation(_451936), 3366 ^ _335846 : [(3367 ^ _335846) ^ [] : [transitive(_451936), 3370 ^ _335846 : [(3371 ^ _335846) ^ [_452228, _452230, _452232] : [-(in(ordered_pair(_452232, _452228), _451936)), in(ordered_pair(_452232, _452230), _451936), in(ordered_pair(_452230, _452228), _451936)]]], (3381 ^ _335846) ^ [] : [3385 ^ _335846 : [(3390 ^ _335846) ^ [] : [in(ordered_pair(3382 ^ [_451936], 3384 ^ [_451936]), _451936)], (3388 ^ _335846) ^ [] : [-(in(ordered_pair(3383 ^ [_451936], 3384 ^ [_451936]), _451936))], (3386 ^ _335846) ^ [] : [-(in(ordered_pair(3382 ^ [_451936], 3383 ^ [_451936]), _451936))]], -(transitive(_451936))]]], (3110 ^ _335846) ^ [_443723] : [-(relation(identity_relation(_443723)))], (1392 ^ _335846) ^ [_384415, _384417] : [_384415 = singleton(_384417), 1395 ^ _335846 : [(1402 ^ _335846) ^ [_384757] : [_384757 = _384417, -(in(_384757, _384415))], (1396 ^ _335846) ^ [_384585] : [in(_384585, _384415), -(_384585 = _384417)]]], (2603 ^ _335846) ^ [_427745] : [relation(_427745), 2606 ^ _335846 : [(2607 ^ _335846) ^ [_427930] : [relation(_427930), 2610 ^ _335846 : [(2611 ^ _335846) ^ [_428111] : [relation(_428111), 2614 ^ _335846 : [(2615 ^ _335846) ^ [] : [_428111 = relation_composition(_427745, _427930), 2618 ^ _335846 : [(2628 ^ _335846) ^ [_428831, _428833] : [-(in(ordered_pair(_428833, _428831), _428111)), 2629 ^ _335846 : [(2630 ^ _335846) ^ [_428944] : [in(ordered_pair(_428833, _428944), _427745), in(ordered_pair(_428944, _428831), _427930)]]], (2619 ^ _335846) ^ [_428446, _428448] : [in(ordered_pair(_428448, _428446), _428111), 2623 ^ _335846 : [(2626 ^ _335846) ^ [] : [-(in(ordered_pair(2622 ^ [_427745, _427930, _428111, _428446, _428448], _428446), _427930))], (2624 ^ _335846) ^ [] : [-(in(ordered_pair(_428448, 2622 ^ [_427745, _427930, _428111, _428446, _428448]), _427745))]]]]], (2638 ^ _335846) ^ [] : [-(_428111 = relation_composition(_427745, _427930)), 2652 ^ _335846 : [(2657 ^ _335846) ^ [] : [in(ordered_pair(2639 ^ [_427745, _427930, _428111], 2640 ^ [_427745, _427930, _428111]), _428111)], (2655 ^ _335846) ^ [] : [-(in(ordered_pair(2651 ^ [_427745, _427930, _428111], 2640 ^ [_427745, _427930, _428111]), _427930))], (2653 ^ _335846) ^ [] : [-(in(ordered_pair(2639 ^ [_427745, _427930, _428111], 2651 ^ [_427745, _427930, _428111]), _427745))]], 2643 ^ _335846 : [(2646 ^ _335846) ^ [_429575] : [in(ordered_pair(2639 ^ [_427745, _427930, _428111], _429575), _427745), in(ordered_pair(_429575, 2640 ^ [_427745, _427930, _428111]), _427930)], (2644 ^ _335846) ^ [] : [-(in(ordered_pair(2639 ^ [_427745, _427930, _428111], 2640 ^ [_427745, _427930, _428111]), _428111))]]]]]]]]], (4692 ^ _335846) ^ [_496427] : [ordinal(_496427), 4695 ^ _335846 : [(4705 ^ _335846) ^ [] : [being_limit_ordinal(_496427), 4706 ^ _335846 : [(4707 ^ _335846) ^ [_496898] : [ordinal(_496898), _496427 = succ(_496898)]]], (4696 ^ _335846) ^ [] : [-(being_limit_ordinal(_496427)), 4700 ^ _335846 : [(4703 ^ _335846) ^ [] : [-(_496427 = succ(4699 ^ [_496427]))], (4701 ^ _335846) ^ [] : [-(ordinal(4699 ^ [_496427]))]]]]], (1524 ^ _335846) ^ [_389043] : [1526 ^ _335846 : [(1529 ^ _335846) ^ [] : [subset(1525 ^ [_389043], _389043)], (1527 ^ _335846) ^ [] : [-(in(1525 ^ [_389043], _389043))]], -(epsilon_transitive(_389043))], (3140 ^ _335846) ^ [_444585] : [empty(singleton(_444585))], (3815 ^ _335846) ^ [_467126, _467128] : [relation(_467126), -(subset(relation_rng(relation_rng_restriction(_467128, _467126)), relation_rng(_467126)))], (3821 ^ _335846) ^ [_467362, _467364, _467366] : [subset(_467366, _467364), 3824 ^ _335846 : [(3827 ^ _335846) ^ [] : [-(subset(cartesian_product2(_467362, _467366), cartesian_product2(_467362, _467364)))], (3825 ^ _335846) ^ [] : [-(subset(cartesian_product2(_467366, _467362), cartesian_product2(_467364, _467362)))]]], (2563 ^ _335846) ^ [_426435] : [relation(_426435), function(_426435), 2570 ^ _335846 : [(2571 ^ _335846) ^ [] : [one_to_one(_426435), 2574 ^ _335846 : [(2575 ^ _335846) ^ [_426798, _426800] : [-(_426800 = _426798), in(_426800, relation_dom(_426435)), in(_426798, relation_dom(_426435)), apply(_426435, _426800) = apply(_426435, _426798)]]], (2589 ^ _335846) ^ [] : [2592 ^ _335846 : [(2595 ^ _335846) ^ [] : [-(in(2591 ^ [_426435], relation_dom(_426435)))], (2597 ^ _335846) ^ [] : [-(apply(_426435, 2590 ^ [_426435]) = apply(_426435, 2591 ^ [_426435]))], (2599 ^ _335846) ^ [] : [2590 ^ [_426435] = 2591 ^ [_426435]], (2593 ^ _335846) ^ [] : [-(in(2590 ^ [_426435], relation_dom(_426435)))]], -(one_to_one(_426435))]]], (76 ^ _335846) ^ [_338370, _338372] : [-(epsilon_connected(_338370)), _338372 = _338370, epsilon_connected(_338372)], (3314 ^ _335846) ^ [_450260] : [relation(_450260), 3317 ^ _335846 : [(3318 ^ _335846) ^ [] : [reflexive(_450260), 3321 ^ _335846 : [(3322 ^ _335846) ^ [_450504] : [in(_450504, relation_field(_450260)), -(in(ordered_pair(_450504, _450504), _450260))]]], (3328 ^ _335846) ^ [] : [3330 ^ _335846 : [(3333 ^ _335846) ^ [] : [in(ordered_pair(3329 ^ [_450260], 3329 ^ [_450260]), _450260)], (3331 ^ _335846) ^ [] : [-(in(3329 ^ [_450260], relation_field(_450260)))]], -(reflexive(_450260))]]], (4102 ^ _335846) ^ [_477132, _477134, _477136] : [-(subset(_477136, set_intersection2(_477134, _477132))), subset(_477136, _477134), subset(_477136, _477132)], (3194 ^ _335846) ^ [_446364, _446366] : [3201 ^ _335846 : [(3204 ^ _335846) ^ [] : [-(function(relation_dom_restriction(_446366, _446364)))], (3202 ^ _335846) ^ [] : [-(relation(relation_dom_restriction(_446366, _446364)))]], relation(_446366), function(_446366)], (3639 ^ _335846) ^ [] : [empty(3637 ^ [])], (456 ^ _335846) ^ [_350595, _350597, _350599, _350601] : [-(cartesian_product2(_350601, _350597) = cartesian_product2(_350599, _350595)), _350601 = _350599, _350597 = _350595], (3862 ^ _335846) ^ [_469017, _469019, _469021] : [-(in(_469017, 3858 ^ [_469021])), in(_469019, 3858 ^ [_469021]), subset(_469017, _469019)], (584 ^ _335846) ^ [_355214, _355216, _355218, _355220] : [-(apply(_355220, _355216) = apply(_355218, _355214)), _355220 = _355218, _355216 = _355214], (278 ^ _335846) ^ [_344637, _344639, _344641, _344643] : [-(disjoint(_344641, _344637)), disjoint(_344643, _344639), _344643 = _344641, _344639 = _344637], (1133 ^ _335846) ^ [_374994] : [relation(_374994), 1136 ^ _335846 : [(1137 ^ _335846) ^ [_375201, _375203] : [_375201 = relation_inverse_image(_374994, _375203), 1140 ^ _335846 : [(1150 ^ _335846) ^ [_375747] : [-(in(_375747, _375201)), 1151 ^ _335846 : [(1152 ^ _335846) ^ [_375852] : [in(ordered_pair(_375747, _375852), _374994), in(_375852, _375203)]]], (1141 ^ _335846) ^ [_375393] : [in(_375393, _375201), 1145 ^ _335846 : [(1148 ^ _335846) ^ [] : [-(in(1144 ^ [_374994, _375201, _375203, _375393], _375203))], (1146 ^ _335846) ^ [] : [-(in(ordered_pair(_375393, 1144 ^ [_374994, _375201, _375203, _375393]), _374994))]]]]], (1160 ^ _335846) ^ [_376107, _376109] : [-(_376107 = relation_inverse_image(_374994, _376109)), 1173 ^ _335846 : [(1178 ^ _335846) ^ [] : [in(1161 ^ [_374994, _376107, _376109], _376107)], (1176 ^ _335846) ^ [] : [-(in(1172 ^ [_374994, _376107, _376109], _376109))], (1174 ^ _335846) ^ [] : [-(in(ordered_pair(1161 ^ [_374994, _376107, _376109], 1172 ^ [_374994, _376107, _376109]), _374994))]], 1164 ^ _335846 : [(1167 ^ _335846) ^ [_376411] : [in(ordered_pair(1161 ^ [_374994, _376107, _376109], _376411), _374994), in(_376411, _376109)], (1165 ^ _335846) ^ [] : [-(in(1161 ^ [_374994, _376107, _376109], _376107))]]]]], (2755 ^ _335846) ^ [_433897, _433899] : [proper_subset(_433899, _433897), 2758 ^ _335846 : [(2761 ^ _335846) ^ [] : [_433899 = _433897], (2759 ^ _335846) ^ [] : [-(subset(_433899, _433897))]]], (2134 ^ _335846) ^ [_411247] : [relation(_411247), 2137 ^ _335846 : [(2152 ^ _335846) ^ [] : [-(well_ordering(_411247)), reflexive(_411247), transitive(_411247), antisymmetric(_411247), connected(_411247), well_founded_relation(_411247)], (2138 ^ _335846) ^ [] : [well_ordering(_411247), 2141 ^ _335846 : [(2142 ^ _335846) ^ [] : [-(reflexive(_411247))], (2146 ^ _335846) ^ [] : [-(antisymmetric(_411247))], (2150 ^ _335846) ^ [] : [-(well_founded_relation(_411247))], (2148 ^ _335846) ^ [] : [-(connected(_411247))], (2144 ^ _335846) ^ [] : [-(transitive(_411247))]]]]], (3656 ^ _335846) ^ [] : [-(one_to_one(3650 ^ []))], (48 ^ _335846) ^ [_337510, _337512, _337514, _337516] : [-(is_transitive_in(_337514, _337510)), is_transitive_in(_337516, _337512), _337516 = _337514, _337512 = _337510], (3148 ^ _335846) ^ [_444895] : [3159 ^ _335846 : [(3162 ^ _335846) ^ [] : [-(function(relation_inverse(_444895)))], (3160 ^ _335846) ^ [] : [-(relation(relation_inverse(_444895)))]], relation(_444895), function(_444895), one_to_one(_444895)], (3759 ^ _335846) ^ [_465244, _465246, _465248, _465250] : [-(in(ordered_pair(_465250, _465248), cartesian_product2(_465246, _465244))), in(_465250, _465246), in(_465248, _465244)], (3649 ^ _335846) ^ [] : [empty(3647 ^ [])], (848 ^ _335846) ^ [_364313] : [relation(_364313), 851 ^ _335846 : [(852 ^ _335846) ^ [_364499, _364501] : [relation(_364499), 855 ^ _335846 : [(856 ^ _335846) ^ [] : [_364499 = relation_dom_restriction(_364313, _364501), 859 ^ _335846 : [(868 ^ _335846) ^ [_365103, _365105] : [-(in(ordered_pair(_365105, _365103), _364499)), in(_365105, _364501), in(ordered_pair(_365105, _365103), _364313)], (860 ^ _335846) ^ [_364824, _364826] : [in(ordered_pair(_364826, _364824), _364499), 863 ^ _335846 : [(866 ^ _335846) ^ [] : [-(in(ordered_pair(_364826, _364824), _364313))], (864 ^ _335846) ^ [] : [-(in(_364826, _364501))]]]]], (878 ^ _335846) ^ [] : [-(_364499 = relation_dom_restriction(_364313, _364501)), 891 ^ _335846 : [(896 ^ _335846) ^ [] : [in(ordered_pair(879 ^ [_364313, _364499, _364501], 880 ^ [_364313, _364499, _364501]), _364499)], (894 ^ _335846) ^ [] : [-(in(ordered_pair(879 ^ [_364313, _364499, _364501], 880 ^ [_364313, _364499, _364501]), _364313))], (892 ^ _335846) ^ [] : [-(in(879 ^ [_364313, _364499, _364501], _364501))]], 883 ^ _335846 : [(886 ^ _335846) ^ [] : [in(879 ^ [_364313, _364499, _364501], _364501), in(ordered_pair(879 ^ [_364313, _364499, _364501], 880 ^ [_364313, _364499, _364501]), _364313)], (884 ^ _335846) ^ [] : [-(in(ordered_pair(879 ^ [_364313, _364499, _364501], 880 ^ [_364313, _364499, _364501]), _364499))]]]]]]], (2889 ^ _335846) ^ [_437092, _437094] : [relation(_437094), -(relation(relation_restriction(_437094, _437092)))], (3026 ^ _335846) ^ [_441010, _441012] : [-(relation_of2(3024 ^ [_441010, _441012], _441012, _441010))], (2373 ^ _335846) ^ [_419384] : [relation(_419384), 2376 ^ _335846 : [(2377 ^ _335846) ^ [_419592] : [is_connected_in(_419384, _419592), 2380 ^ _335846 : [(2381 ^ _335846) ^ [_419782, _419784] : [in(_419784, _419592), in(_419782, _419592), -(_419784 = _419782), -(in(ordered_pair(_419784, _419782), _419384)), -(in(ordered_pair(_419782, _419784), _419384))]]], (2399 ^ _335846) ^ [_420276] : [2402 ^ _335846 : [(2403 ^ _335846) ^ [] : [-(in(2400 ^ [_419384, _420276], _420276))], (2407 ^ _335846) ^ [] : [2400 ^ [_419384, _420276] = 2401 ^ [_419384, _420276]], (2411 ^ _335846) ^ [] : [in(ordered_pair(2401 ^ [_419384, _420276], 2400 ^ [_419384, _420276]), _419384)], (2409 ^ _335846) ^ [] : [in(ordered_pair(2400 ^ [_419384, _420276], 2401 ^ [_419384, _420276]), _419384)], (2405 ^ _335846) ^ [] : [-(in(2401 ^ [_419384, _420276], _420276))]], -(is_connected_in(_419384, _420276))]]], (346 ^ _335846) ^ [_346705, _346707, _346709, _346711] : [-(are_equipotent(_346709, _346705)), are_equipotent(_346711, _346707), _346711 = _346709, _346707 = _346705], (4735 ^ _335846) ^ [_497801] : [relation(_497801), 4738 ^ _335846 : [(4739 ^ _335846) ^ [_497938] : [relation(_497938), -(subset(relation_dom(relation_composition(_497801, _497938)), relation_dom(_497801)))]]], (5414 ^ _335846) ^ [_519953] : [relation(_519953), 5417 ^ _335846 : [(5424 ^ _335846) ^ [] : [well_ordering(_519953), -(well_orders(_519953, relation_field(_519953)))], (5418 ^ _335846) ^ [] : [well_orders(_519953, relation_field(_519953)), -(well_ordering(_519953))]]], (2931 ^ _335846) ^ [_438109] : [relation(_438109), -(relation(relation_inverse(_438109)))], (1271 ^ _335846) ^ [_380012] : [relation(_380012), 1274 ^ _335846 : [(1275 ^ _335846) ^ [_380160] : [in(_380160, _380012), -(_380160 = ordered_pair(1278 ^ [_380012, _380160], 1279 ^ [_380012, _380160]))]]], (4144 ^ _335846) ^ [_478526, _478528] : [relation(_478526), 4147 ^ _335846 : [(4150 ^ _335846) ^ [] : [-(subset(relation_field(relation_restriction(_478526, _478528)), _478528))], (4148 ^ _335846) ^ [] : [-(subset(relation_field(relation_restriction(_478526, _478528)), relation_field(_478526)))]]], (4443 ^ _335846) ^ [_488141, _488143] : [relation(_488141), well_ordering(_488141), -(well_ordering(relation_restriction(_488141, _488143)))], (254 ^ _335846) ^ [_343898, _343900, _343902, _343904] : [-(proper_subset(_343902, _343898)), proper_subset(_343904, _343900), _343904 = _343902, _343900 = _343898], (1033 ^ _335846) ^ [_371168] : [relation(_371168), function(_371168), 1040 ^ _335846 : [(1041 ^ _335846) ^ [_371455, _371457] : [_371455 = relation_inverse_image(_371168, _371457), 1044 ^ _335846 : [(1053 ^ _335846) ^ [_371913] : [-(in(_371913, _371455)), in(_371913, relation_dom(_371168)), in(apply(_371168, _371913), _371457)], (1045 ^ _335846) ^ [_371644] : [in(_371644, _371455), 1048 ^ _335846 : [(1051 ^ _335846) ^ [] : [-(in(apply(_371168, _371644), _371457))], (1049 ^ _335846) ^ [] : [-(in(_371644, relation_dom(_371168)))]]]]], (1063 ^ _335846) ^ [_372207, _372209] : [-(_372207 = relation_inverse_image(_371168, _372209)), 1075 ^ _335846 : [(1080 ^ _335846) ^ [] : [in(1064 ^ [_371168, _372207, _372209], _372207)], (1078 ^ _335846) ^ [] : [-(in(apply(_371168, 1064 ^ [_371168, _372207, _372209]), _372209))], (1076 ^ _335846) ^ [] : [-(in(1064 ^ [_371168, _372207, _372209], relation_dom(_371168)))]], 1067 ^ _335846 : [(1070 ^ _335846) ^ [] : [in(1064 ^ [_371168, _372207, _372209], relation_dom(_371168)), in(apply(_371168, 1064 ^ [_371168, _372207, _372209]), _372209)], (1068 ^ _335846) ^ [] : [-(in(1064 ^ [_371168, _372207, _372209], _372207))]]]]], (4330 ^ _335846) ^ [_484376, _484378] : [relation(_484376), antisymmetric(_484376), -(antisymmetric(relation_restriction(_484376, _484378)))], (3300 ^ _335846) ^ [_449741] : [relation(_449741), -(relation_inverse(relation_inverse(_449741)) = _449741)], (2415 ^ _335846) ^ [_421061] : [relation(_421061), 2418 ^ _335846 : [(2419 ^ _335846) ^ [_421180] : [-(relation_restriction(_421061, _421180) = set_intersection2(_421061, cartesian_product2(_421180, _421180)))]]], (1423 ^ _335846) ^ [_385458] : [relation(_385458), 1426 ^ _335846 : [(1427 ^ _335846) ^ [_385662, _385664] : [_385662 = fiber(_385458, _385664), 1430 ^ _335846 : [(1439 ^ _335846) ^ [_386117] : [-(in(_386117, _385662)), -(_386117 = _385664), in(ordered_pair(_386117, _385664), _385458)], (1431 ^ _335846) ^ [_385851] : [in(_385851, _385662), 1434 ^ _335846 : [(1437 ^ _335846) ^ [] : [-(in(ordered_pair(_385851, _385664), _385458))], (1435 ^ _335846) ^ [] : [_385851 = _385664]]]]], (1449 ^ _335846) ^ [_386410, _386412] : [-(_386410 = fiber(_385458, _386412)), 1461 ^ _335846 : [(1466 ^ _335846) ^ [] : [in(1450 ^ [_385458, _386410, _386412], _386410)], (1464 ^ _335846) ^ [] : [-(in(ordered_pair(1450 ^ [_385458, _386410, _386412], _386412), _385458))], (1462 ^ _335846) ^ [] : [1450 ^ [_385458, _386410, _386412] = _386412]], 1453 ^ _335846 : [(1456 ^ _335846) ^ [] : [-(1450 ^ [_385458, _386410, _386412] = _386412), in(ordered_pair(1450 ^ [_385458, _386410, _386412], _386412), _385458)], (1454 ^ _335846) ^ [] : [-(in(1450 ^ [_385458, _386410, _386412], _386410))]]]]], (4785 ^ _335846) ^ [_499517, _499519] : [in(_499519, _499517), -(set_union2(singleton(_499519), _499517) = _499517)], (4745 ^ _335846) ^ [_498153] : [relation(_498153), 4748 ^ _335846 : [(4749 ^ _335846) ^ [_498290] : [relation(_498290), -(subset(relation_rng(relation_composition(_498153, _498290)), relation_rng(_498290)))]]], (3670 ^ _335846) ^ [] : [-(relation_empty_yielding(3666 ^ []))], (5498 ^ _335846) ^ [_523013, _523015] : [subset(_523013, 5471 ^ [_523015]), -(are_equipotent(_523013, 5471 ^ [_523015])), -(in(_523013, 5471 ^ [_523015]))], (3961 ^ _335846) ^ [_472406, _472408] : [relation(_472406), function(_472406), subset(_472408, relation_rng(_472406)), -(relation_image(_472406, relation_inverse_image(_472406, _472408)) = _472408)], (2421 ^ _335846) ^ [_421289] : [relation(_421289), 2424 ^ _335846 : [(2425 ^ _335846) ^ [_421449] : [relation(_421449), 2428 ^ _335846 : [(2429 ^ _335846) ^ [] : [_421449 = relation_inverse(_421289), 2432 ^ _335846 : [(2439 ^ _335846) ^ [_421948, _421950] : [in(ordered_pair(_421948, _421950), _421289), -(in(ordered_pair(_421950, _421948), _421449))], (2433 ^ _335846) ^ [_421758, _421760] : [in(ordered_pair(_421760, _421758), _421449), -(in(ordered_pair(_421758, _421760), _421289))]]], (2445 ^ _335846) ^ [] : [-(_421449 = relation_inverse(_421289)), 2450 ^ _335846 : [(2453 ^ _335846) ^ [] : [in(ordered_pair(2447 ^ [_421289, _421449], 2446 ^ [_421289, _421449]), _421289)], (2451 ^ _335846) ^ [] : [-(in(ordered_pair(2446 ^ [_421289, _421449], 2447 ^ [_421289, _421449]), _421449))]], 2454 ^ _335846 : [(2457 ^ _335846) ^ [] : [in(ordered_pair(2446 ^ [_421289, _421449], 2447 ^ [_421289, _421449]), _421449)], (2455 ^ _335846) ^ [] : [-(in(ordered_pair(2447 ^ [_421289, _421449], 2446 ^ [_421289, _421449]), _421289))]]]]]]], (168 ^ _335846) ^ [_341193, _341195] : [-(transitive(_341193)), _341195 = _341193, transitive(_341195)], (4578 ^ _335846) ^ [_492681, _492683] : [relation(_492681), -(relation_field(relation_restriction(_492681, _492683)) = _492683), well_ordering(_492681), subset(_492683, relation_field(_492681))], (5485 ^ _335846) ^ [_522494, _522496] : [in(_522494, 5471 ^ [_522496]), 5489 ^ _335846 : [(5492 ^ _335846) ^ [_522806] : [subset(_522806, _522494), -(in(_522806, 5488 ^ [_522494, _522496]))], (5490 ^ _335846) ^ [] : [-(in(5488 ^ [_522494, _522496], 5471 ^ [_522496]))]]], (4554 ^ _335846) ^ [_491854, _491856] : [in(_491856, _491854), -(subset(singleton(_491856), _491854))], (5180 ^ _335846) ^ [_512258] : [relation(_512258), 5183 ^ _335846 : [(5190 ^ _335846) ^ [] : [relation_rng(_512258) = empty_set, -(relation_dom(_512258) = empty_set)], (5184 ^ _335846) ^ [] : [relation_dom(_512258) = empty_set, -(relation_rng(_512258) = empty_set)]]], (5470 ^ _335846) ^ [_521826] : [-(union(powerset(_521826)) = _521826)], (4825 ^ _335846) ^ [_500861, _500863] : [-(set_difference(_500863, set_difference(_500863, _500861)) = set_intersection2(_500863, _500861))], (3072 ^ _335846) ^ [_442577, _442579] : [3087 ^ _335846 : [(3090 ^ _335846) ^ [] : [-(function(relation_composition(_442579, _442577)))], (3088 ^ _335846) ^ [] : [-(relation(relation_composition(_442579, _442577)))]], relation(_442579), function(_442579), relation(_442577), function(_442577)], (5279 ^ _335846) ^ [_515498] : [-(relation_rng(identity_relation(_515498)) = _515498)], (426 ^ _335846) ^ [_349518, _349520, _349522, _349524] : [-(relation_image(_349524, _349520) = relation_image(_349522, _349518)), _349524 = _349522, _349520 = _349518], (4568 ^ _335846) ^ [_492364, _492366, _492368] : [-(subset(unordered_pair(_492368, _492366), _492364)), in(_492368, _492364), in(_492366, _492364)], (3809 ^ _335846) ^ [_466912, _466914] : [relation(_466912), -(subset(relation_rng_restriction(_466914, _466912), _466912))], (4381 ^ _335846) ^ [_486134, _486136, _486138] : [relation(_486134), in(ordered_pair(_486138, _486136), _486134), 4388 ^ _335846 : [(4391 ^ _335846) ^ [] : [-(in(_486136, relation_field(_486134)))], (4389 ^ _335846) ^ [] : [-(in(_486138, relation_field(_486134)))]]], (1327 ^ _335846) ^ [_382211, _382213] : [-(_382213 = empty_set), 1330 ^ _335846 : [(1331 ^ _335846) ^ [] : [_382211 = set_meet(_382213), 1334 ^ _335846 : [(1335 ^ _335846) ^ [_382509] : [in(_382509, _382211), 1338 ^ _335846 : [(1339 ^ _335846) ^ [_382654] : [in(_382654, _382213), -(in(_382509, _382654))]]], (1345 ^ _335846) ^ [_382839] : [1347 ^ _335846 : [(1350 ^ _335846) ^ [] : [in(_382839, 1346 ^ [_382211, _382213, _382839])], (1348 ^ _335846) ^ [] : [-(in(1346 ^ [_382211, _382213, _382839], _382213))]], -(in(_382839, _382211))]]], (1354 ^ _335846) ^ [] : [-(_382211 = set_meet(_382213)), 1358 ^ _335846 : [(1364 ^ _335846) ^ [] : [in(1355 ^ [_382211, _382213], 1360 ^ [_382211, _382213])], (1362 ^ _335846) ^ [] : [-(in(1360 ^ [_382211, _382213], _382213))], (1359 ^ _335846) ^ [] : [-(in(1355 ^ [_382211, _382213], _382211))]], 1365 ^ _335846 : [(1366 ^ _335846) ^ [_383613] : [in(_383613, _382213), -(in(1355 ^ [_382211, _382213], _383613))], (1372 ^ _335846) ^ [] : [in(1355 ^ [_382211, _382213], _382211)]]]]], (2919 ^ _335846) ^ [] : [true___, -(true___)], (326 ^ _335846) ^ [_346087, _346089] : [-(well_ordering(_346087)), _346089 = _346087, well_ordering(_346089)], (698 ^ _335846) ^ [_359451] : [empty(_359451), -(function(_359451))], (2989 ^ _335846) ^ [_439940, _439942] : [element(_439940, powerset(powerset(_439942))), -(element(complements_of_subsets(_439942, _439940), powerset(powerset(_439942))))], (2196 ^ _335846) ^ [_413050, _413052, _413054] : [-(_413050 = set_difference(_413054, _413052)), 2208 ^ _335846 : [(2213 ^ _335846) ^ [] : [in(2197 ^ [_413050, _413052, _413054], _413050)], (2211 ^ _335846) ^ [] : [in(2197 ^ [_413050, _413052, _413054], _413052)], (2209 ^ _335846) ^ [] : [-(in(2197 ^ [_413050, _413052, _413054], _413054))]], 2200 ^ _335846 : [(2203 ^ _335846) ^ [] : [in(2197 ^ [_413050, _413052, _413054], _413054), -(in(2197 ^ [_413050, _413052, _413054], _413052))], (2201 ^ _335846) ^ [] : [-(in(2197 ^ [_413050, _413052, _413054], _413050))]]], (2967 ^ _335846) ^ [_439157, _439159] : [element(_439157, powerset(powerset(_439159))), -(element(meet_of_subsets(_439159, _439157), powerset(_439159)))], (4942 ^ _335846) ^ [_504753] : [relation(_504753), function(_504753), one_to_one(_504753), 4953 ^ _335846 : [(4954 ^ _335846) ^ [_505140] : [relation(_505140), function(_505140), 4961 ^ _335846 : [(4962 ^ _335846) ^ [] : [_505140 = function_inverse(_504753), 4965 ^ _335846 : [(4980 ^ _335846) ^ [_506031, _506033] : [4987 ^ _335846 : [(4990 ^ _335846) ^ [] : [-(_506031 = apply(_505140, _506033))], (4988 ^ _335846) ^ [] : [-(in(_506033, relation_rng(_504753)))]], in(_506031, relation_dom(_504753)), _506033 = apply(_504753, _506031)], (4968 ^ _335846) ^ [_505657, _505659] : [4975 ^ _335846 : [(4978 ^ _335846) ^ [] : [-(_505659 = apply(_504753, _505657))], (4976 ^ _335846) ^ [] : [-(in(_505657, relation_dom(_504753)))]], in(_505659, relation_rng(_504753)), _505657 = apply(_505140, _505659)], (4966 ^ _335846) ^ [] : [-(relation_dom(_505140) = relation_rng(_504753))]]], (4992 ^ _335846) ^ [] : [-(_505140 = function_inverse(_504753)), relation_dom(_505140) = relation_rng(_504753), 5001 ^ _335846 : [(5006 ^ _335846) ^ [] : [in(4998 ^ [_504753, _505140], relation_dom(_504753)), 4997 ^ [_504753, _505140] = apply(_504753, 4998 ^ [_504753, _505140])], (5004 ^ _335846) ^ [] : [-(4998 ^ [_504753, _505140] = apply(_505140, 4997 ^ [_504753, _505140]))], (5002 ^ _335846) ^ [] : [-(in(4997 ^ [_504753, _505140], relation_rng(_504753)))]], 5011 ^ _335846 : [(5016 ^ _335846) ^ [] : [in(4997 ^ [_504753, _505140], relation_rng(_504753)), 4998 ^ [_504753, _505140] = apply(_505140, 4997 ^ [_504753, _505140])], (5014 ^ _335846) ^ [] : [-(4997 ^ [_504753, _505140] = apply(_504753, 4998 ^ [_504753, _505140]))], (5012 ^ _335846) ^ [] : [-(in(4998 ^ [_504753, _505140], relation_dom(_504753)))]]]]]]], (178 ^ _335846) ^ [_341488, _341490] : [-(connected(_341488)), _341490 = _341488, connected(_341490)], (20 ^ _335846) ^ [_336622, _336624, _336626, _336628] : [-(is_antisymmetric_in(_336626, _336622)), is_antisymmetric_in(_336628, _336624), _336628 = _336626, _336624 = _336622], (3034 ^ _335846) ^ [_441393, _441395] : [3041 ^ _335846 : [(3044 ^ _335846) ^ [] : [-(relation(relation_composition(_441393, _441395)))], (3042 ^ _335846) ^ [] : [-(empty(relation_composition(_441393, _441395)))]], empty(_441395), relation(_441393)], (1706 ^ _335846) ^ [_395247, _395249, _395251] : [-(_395247 = set_union2(_395251, _395249)), 1710 ^ _335846 : [(1715 ^ _335846) ^ [] : [in(1707 ^ [_395247, _395249, _395251], _395249)], (1713 ^ _335846) ^ [] : [in(1707 ^ [_395247, _395249, _395251], _395251)], (1711 ^ _335846) ^ [] : [-(in(1707 ^ [_395247, _395249, _395251], _395247))]], 1716 ^ _335846 : [(1717 ^ _335846) ^ [] : [-(in(1707 ^ [_395247, _395249, _395251], _395251)), -(in(1707 ^ [_395247, _395249, _395251], _395249))], (1723 ^ _335846) ^ [] : [in(1707 ^ [_395247, _395249, _395251], _395247)]]], (5464 ^ _335846) ^ [_521633, _521635] : [relation(_521633), -(subset(relation_rng(relation_dom_restriction(_521633, _521635)), relation_rng(_521633)))], (4874 ^ _335846) ^ [_502581] : [-(_502581 = empty_set), 4877 ^ _335846 : [(4878 ^ _335846) ^ [_502741] : [element(_502741, powerset(_502581)), 4881 ^ _335846 : [(4882 ^ _335846) ^ [_502895] : [element(_502895, _502581), -(in(_502895, _502741)), -(in(_502895, subset_complement(_502581, _502741)))]]]]], (724 ^ _335846) ^ [_360318] : [735 ^ _335846 : [(740 ^ _335846) ^ [] : [-(one_to_one(_360318))], (738 ^ _335846) ^ [] : [-(function(_360318))], (736 ^ _335846) ^ [] : [-(relation(_360318))]], relation(_360318), empty(_360318), function(_360318)], (3604 ^ _335846) ^ [_460167] : [-(empty(_460167)), 3608 ^ _335846 : [(3611 ^ _335846) ^ [] : [empty(3607 ^ [_460167])], (3609 ^ _335846) ^ [] : [-(element(3607 ^ [_460167], powerset(_460167)))]]], (652 ^ _335846) ^ [_357635, _357637] : [_357637 = _357635, -(relation_rng(_357637) = relation_rng(_357635))], (114 ^ _335846) ^ [_339569, _339571] : [-(epsilon_transitive(_339569)), _339571 = _339569, epsilon_transitive(_339571)], (2315 ^ _335846) ^ [_417591] : [relation(_417591), 2318 ^ _335846 : [(2333 ^ _335846) ^ [_418236] : [-(well_orders(_417591, _418236)), is_reflexive_in(_417591, _418236), is_transitive_in(_417591, _418236), is_antisymmetric_in(_417591, _418236), is_connected_in(_417591, _418236), is_well_founded_in(_417591, _418236)], (2319 ^ _335846) ^ [_417775] : [well_orders(_417591, _417775), 2322 ^ _335846 : [(2323 ^ _335846) ^ [] : [-(is_reflexive_in(_417591, _417775))], (2327 ^ _335846) ^ [] : [-(is_antisymmetric_in(_417591, _417775))], (2331 ^ _335846) ^ [] : [-(is_well_founded_in(_417591, _417775))], (2329 ^ _335846) ^ [] : [-(is_connected_in(_417591, _417775))], (2325 ^ _335846) ^ [] : [-(is_transitive_in(_417591, _417775))]]]]], (4024 ^ _335846) ^ [_474536, _474538] : [relation(_474536), -(subset(relation_inverse_image(_474536, _474538), relation_dom(_474536)))], (4536 ^ _335846) ^ [_491273, _491275] : [set_difference(_491275, _491273) = empty_set, -(subset(_491275, _491273))], (4120 ^ _335846) ^ [_477752, _477754, _477756] : [-(subset(_477756, _477752)), subset(_477756, _477754), subset(_477754, _477752)], (3029 ^ _335846) ^ [_441137] : [-(element(3027 ^ [_441137], _441137))], (4851 ^ _335846) ^ [_501788, _501790, _501792] : [-(element(_501792, _501788)), in(_501792, _501790), element(_501790, powerset(_501788))], (5430 ^ _335846) ^ [_520412, _520414, _520416] : [-(subset(set_union2(_520416, _520412), _520414)), subset(_520416, _520414), subset(_520412, _520414)]], input).
% 43.90/42.80  ncf('1',plain,[-(subset(5513 ^ [], 5514 ^ []))],start(5520 ^ 0)).
% 43.90/42.80  ncf('1.1',plain,[subset(5513 ^ [], 5514 ^ []), -(subset(relation_rng(5516 ^ []), 5514 ^ [])), subset(relation_rng(5516 ^ []), 5513 ^ [])],extension(4120 ^ 1,bind([[_477752, _477754, _477756], [5514 ^ [], 5513 ^ [], relation_rng(5516 ^ [])]]))).
% 43.90/42.80  ncf('1.1.1',plain,[subset(relation_rng(5516 ^ []), 5514 ^ []), relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5513 ^ []), -(relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5514 ^ []))],extension(3975 ^ 2,bind([[_472836, _472838, _472840, _472842], [5516 ^ [], 5515 ^ [], 5514 ^ [], 5513 ^ []]]))).
% 43.90/42.80  ncf('1.1.1.1',plain,[-(relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5513 ^ []))],extension(5518 ^ 3)).
% 43.90/42.80  ncf('1.1.1.2',plain,[relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5514 ^ [])],extension(5522 ^ 3)).
% 43.90/42.80  ncf('1.1.2',plain,[-(subset(relation_rng(5516 ^ []), 5513 ^ [])), relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5513 ^ [])],extension(3845 ^ 2,bind([[_468280, _468282, _468284], [5516 ^ [], 5513 ^ [], 5515 ^ []]]))).
% 43.90/42.80  ncf('1.1.2.1',plain,[-(relation_of2_as_subset(5516 ^ [], 5515 ^ [], 5513 ^ []))],extension(5518 ^ 3)).
% 43.90/42.80  %-----------------------------------------------------
% 43.90/42.80  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------