%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU248+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n001.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 12:02:52 EDT 2023

% Result   : Theorem 1.02s 1.38s
% Output   : Proof 1.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU248+2 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n001.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 13:43:34 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.02/1.38  
% 1.02/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.02/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.02/1.38  %-----------------------------------------------------
% 1.02/1.38  ncf(matrix, plain, [(5055 ^ _127218) ^ [] : [-(relation(5053 ^ []))], (5057 ^ _127218) ^ [] : [subset(relation_dom(relation_rng_restriction(5052 ^ [], 5053 ^ [])), relation_dom(5053 ^ []))], (352 ^ _127218) ^ [_138355, _138357, _138359, _138361, _138363, _138365] : [-(unordered_triple(_138365, _138361, _138357) = unordered_triple(_138363, _138359, _138355)), _138365 = _138363, _138361 = _138359, _138357 = _138355], (366 ^ _127218) ^ [_138843, _138845, _138847, _138849] : [-(fiber(_138849, _138845) = fiber(_138847, _138843)), _138849 = _138847, _138845 = _138843], (376 ^ _127218) ^ [_139174, _139176] : [_139176 = _139174, -(set_meet(_139176) = set_meet(_139174))], (382 ^ _127218) ^ [_139420, _139422, _139424, _139426] : [-(relation_image(_139426, _139422) = relation_image(_139424, _139420)), _139426 = _139424, _139422 = _139420], (392 ^ _127218) ^ [_139779, _139781, _139783, _139785] : [-(relation_inverse_image(_139785, _139781) = relation_inverse_image(_139783, _139779)), _139785 = _139783, _139781 = _139779], (402 ^ _127218) ^ [_140138, _140140, _140142, _140144] : [-(relation_restriction(_140144, _140140) = relation_restriction(_140142, _140138)), _140144 = _140142, _140140 = _140138], (412 ^ _127218) ^ [_140497, _140499, _140501, _140503] : [-(cartesian_product2(_140503, _140499) = cartesian_product2(_140501, _140497)), _140503 = _140501, _140499 = _140497], (422 ^ _127218) ^ [_140828, _140830] : [_140830 = _140828, -(relation_inverse(_140830) = relation_inverse(_140828))], (428 ^ _127218) ^ [_141046, _141048] : [_141048 = _141046, -(succ(_141048) = succ(_141046))], (434 ^ _127218) ^ [_141292, _141294, _141296, _141298] : [-(union_of_subsets(_141298, _141294) = union_of_subsets(_141296, _141292)), _141298 = _141296, _141294 = _141292], (444 ^ _127218) ^ [_141651, _141653, _141655, _141657] : [-(complements_of_subsets(_141657, _141653) = complements_of_subsets(_141655, _141651)), _141657 = _141655, _141653 = _141651], (454 ^ _127218) ^ [_142038, _142040, _142042, _142044, _142046, _142048] : [-(subset_difference(_142048, _142044, _142040) = subset_difference(_142046, _142042, _142038)), _142048 = _142046, _142044 = _142042, _142040 = _142038], (468 ^ _127218) ^ [_142498, _142500] : [_142500 = _142498, -(cast_to_subset(_142500) = cast_to_subset(_142498))], (474 ^ _127218) ^ [_142744, _142746, _142748, _142750] : [-(meet_of_subsets(_142750, _142746) = meet_of_subsets(_142748, _142744)), _142750 = _142748, _142746 = _142744], (484 ^ _127218) ^ [_143103, _143105, _143107, _143109] : [-(subset_complement(_143109, _143105) = subset_complement(_143107, _143103)), _143109 = _143107, _143105 = _143103], (494 ^ _127218) ^ [_143434, _143436] : [_143436 = _143434, -(function_inverse(_143436) = function_inverse(_143434))], (500 ^ _127218) ^ [_143680, _143682, _143684, _143686] : [-(set_difference(_143686, _143682) = set_difference(_143684, _143680)), _143686 = _143684, _143682 = _143680], (510 ^ _127218) ^ [_144039, _144041, _144043, _144045] : [-(ordered_pair(_144045, _144041) = ordered_pair(_144043, _144039)), _144045 = _144043, _144041 = _144039], (520 ^ _127218) ^ [_144398, _144400, _144402, _144404] : [-(apply(_144404, _144400) = apply(_144402, _144398)), _144404 = _144402, _144400 = _144398], (530 ^ _127218) ^ [_144729, _144731] : [_144731 = _144729, -(relation_field(_144731) = relation_field(_144729))], (536 ^ _127218) ^ [_144975, _144977, _144979, _144981] : [-(set_union2(_144981, _144977) = set_union2(_144979, _144975)), _144981 = _144979, _144977 = _144975], (546 ^ _127218) ^ [_145334, _145336, _145338, _145340] : [-(set_intersection2(_145340, _145336) = set_intersection2(_145338, _145334)), _145340 = _145338, _145336 = _145334], (556 ^ _127218) ^ [_145693, _145695, _145697, _145699] : [-(relation_composition(_145699, _145695) = relation_composition(_145697, _145693)), _145699 = _145697, _145695 = _145693], (566 ^ _127218) ^ [_146024, _146026] : [_146026 = _146024, -(identity_relation(_146026) = identity_relation(_146024))], (572 ^ _127218) ^ [_146270, _146272, _146274, _146276] : [-(relation_dom_restriction(_146276, _146272) = relation_dom_restriction(_146274, _146270)), _146276 = _146274, _146272 = _146270], (582 ^ _127218) ^ [_146601, _146603] : [_146603 = _146601, -(relation_rng(_146603) = relation_rng(_146601))], (588 ^ _127218) ^ [_146819, _146821] : [_146821 = _146819, -(union(_146821) = union(_146819))], (594 ^ _127218) ^ [_147037, _147039] : [_147039 = _147037, -(powerset(_147039) = powerset(_147037))], (600 ^ _127218) ^ [_147255, _147257] : [_147257 = _147255, -(singleton(_147257) = singleton(_147255))], (606 ^ _127218) ^ [_147501, _147503, _147505, _147507] : [-(unordered_pair(_147507, _147503) = unordered_pair(_147505, _147501)), _147507 = _147505, _147503 = _147501], (626 ^ _127218) ^ [_148171, _148173] : [_148173 = _148171, -(relation_dom(_148173) = relation_dom(_148171))], (616 ^ _127218) ^ [_147860, _147862, _147864, _147866] : [-(relation_rng_restriction(_147866, _147862) = relation_rng_restriction(_147864, _147860)), _147866 = _147864, _147862 = _147860], (2 ^ _127218) ^ [_127362] : [-(_127362 = _127362)], (4 ^ _127218) ^ [_127469, _127471] : [_127471 = _127469, -(_127469 = _127471)], (10 ^ _127218) ^ [_127673, _127675, _127677] : [-(_127677 = _127673), _127677 = _127675, _127675 = _127673], (20 ^ _127218) ^ [_128014, _128016, _128018, _128020] : [-(is_antisymmetric_in(_128018, _128014)), is_antisymmetric_in(_128020, _128016), _128020 = _128018, _128016 = _128014], (34 ^ _127218) ^ [_128458, _128460, _128462, _128464] : [-(is_connected_in(_128462, _128458)), is_connected_in(_128464, _128460), _128464 = _128462, _128460 = _128458], (48 ^ _127218) ^ [_128902, _128904, _128906, _128908] : [-(is_transitive_in(_128906, _128902)), is_transitive_in(_128908, _128904), _128908 = _128906, _128904 = _128902], (62 ^ _127218) ^ [_129346, _129348, _129350, _129352] : [-(is_reflexive_in(_129350, _129346)), is_reflexive_in(_129352, _129348), _129352 = _129350, _129348 = _129346], (76 ^ _127218) ^ [_129762, _129764] : [-(reflexive(_129762)), _129764 = _129762, reflexive(_129764)], (86 ^ _127218) ^ [_130057, _130059] : [-(transitive(_130057)), _130059 = _130057, transitive(_130059)], (96 ^ _127218) ^ [_130352, _130354] : [-(antisymmetric(_130352)), _130354 = _130352, antisymmetric(_130354)], (106 ^ _127218) ^ [_130647, _130649] : [-(connected(_130647)), _130649 = _130647, connected(_130649)], (116 ^ _127218) ^ [_130942, _130944] : [-(epsilon_connected(_130942)), _130944 = _130942, epsilon_connected(_130944)], (126 ^ _127218) ^ [_131237, _131239] : [-(relation_empty_yielding(_131237)), _131239 = _131237, relation_empty_yielding(_131239)], (136 ^ _127218) ^ [_131532, _131534] : [-(epsilon_transitive(_131532)), _131534 = _131532, epsilon_transitive(_131534)], (146 ^ _127218) ^ [_131855, _131857, _131859, _131861] : [-(ordinal_subset(_131859, _131855)), ordinal_subset(_131861, _131857), _131861 = _131859, _131857 = _131855], (160 ^ _127218) ^ [_132271, _132273] : [-(ordinal(_132271)), _132273 = _132271, ordinal(_132273)], (170 ^ _127218) ^ [_132566, _132568] : [-(being_limit_ordinal(_132566)), _132568 = _132566, being_limit_ordinal(_132568)], (180 ^ _127218) ^ [_132889, _132891, _132893, _132895] : [-(element(_132893, _132889)), element(_132895, _132891), _132895 = _132893, _132891 = _132889], (194 ^ _127218) ^ [_133305, _133307] : [-(well_founded_relation(_133305)), _133307 = _133305, well_founded_relation(_133307)], (204 ^ _127218) ^ [_133628, _133630, _133632, _133634] : [-(is_well_founded_in(_133632, _133628)), is_well_founded_in(_133634, _133630), _133634 = _133632, _133630 = _133628], (218 ^ _127218) ^ [_134072, _134074, _134076, _134078] : [-(proper_subset(_134076, _134072)), proper_subset(_134078, _134074), _134078 = _134076, _134074 = _134072], (232 ^ _127218) ^ [_134488, _134490] : [-(one_to_one(_134488)), _134490 = _134488, one_to_one(_134490)], (242 ^ _127218) ^ [_134811, _134813, _134815, _134817] : [-(disjoint(_134815, _134811)), disjoint(_134817, _134813), _134817 = _134815, _134813 = _134811], (256 ^ _127218) ^ [_135227, _135229] : [-(empty(_135227)), _135229 = _135227, empty(_135229)], (266 ^ _127218) ^ [_135522, _135524] : [-(function(_135522)), _135524 = _135522, function(_135524)], (276 ^ _127218) ^ [_135845, _135847, _135849, _135851] : [-(well_orders(_135849, _135845)), well_orders(_135851, _135847), _135851 = _135849, _135847 = _135845], (290 ^ _127218) ^ [_136261, _136263] : [-(well_ordering(_136261)), _136263 = _136261, well_ordering(_136263)], (300 ^ _127218) ^ [_136584, _136586, _136588, _136590] : [-(are_equipotent(_136588, _136584)), are_equipotent(_136590, _136586), _136590 = _136588, _136586 = _136584], (314 ^ _127218) ^ [_137028, _137030, _137032, _137034] : [-(in(_137032, _137028)), in(_137034, _137030), _137034 = _137032, _137030 = _137028], (328 ^ _127218) ^ [_137444, _137446] : [-(relation(_137444)), _137446 = _137444, relation(_137446)], (338 ^ _127218) ^ [_137747, _137749, _137751, _137753] : [-(subset(_137751, _137747)), subset(_137753, _137749), _137753 = _137751, _137749 = _137747], (632 ^ _127218) ^ [_148586, _148588] : [in(_148588, _148586), in(_148586, _148588)], (638 ^ _127218) ^ [_148797, _148799] : [proper_subset(_148799, _148797), proper_subset(_148797, _148799)], (644 ^ _127218) ^ [_148994] : [empty(_148994), -(function(_148994))], (650 ^ _127218) ^ [_149180] : [ordinal(_149180), 653 ^ _127218 : [(654 ^ _127218) ^ [] : [-(epsilon_transitive(_149180))], (656 ^ _127218) ^ [] : [-(epsilon_connected(_149180))]]], (658 ^ _127218) ^ [_149437] : [empty(_149437), -(relation(_149437))], (664 ^ _127218) ^ [_149623] : [675 ^ _127218 : [(676 ^ _127218) ^ [] : [-(relation(_149623))], (678 ^ _127218) ^ [] : [-(function(_149623))], (680 ^ _127218) ^ [] : [-(one_to_one(_149623))]], relation(_149623), empty(_149623), function(_149623)], (682 ^ _127218) ^ [_150116] : [-(ordinal(_150116)), epsilon_transitive(_150116), epsilon_connected(_150116)], (692 ^ _127218) ^ [_150385] : [empty(_150385), 695 ^ _127218 : [(696 ^ _127218) ^ [] : [-(epsilon_transitive(_150385))], (698 ^ _127218) ^ [] : [-(epsilon_connected(_150385))], (700 ^ _127218) ^ [] : [-(ordinal(_150385))]]], (702 ^ _127218) ^ [_150711, _150713] : [-(unordered_pair(_150713, _150711) = unordered_pair(_150711, _150713))], (704 ^ _127218) ^ [_150811, _150813] : [-(set_union2(_150813, _150811) = set_union2(_150811, _150813))], (706 ^ _127218) ^ [_150911, _150913] : [-(set_intersection2(_150913, _150911) = set_intersection2(_150911, _150913))], (708 ^ _127218) ^ [_151026, _151028] : [ordinal(_151028), ordinal(_151026), -(ordinal_subset(_151028, _151026)), -(ordinal_subset(_151026, _151028))], (722 ^ _127218) ^ [_151413, _151415] : [relation(_151413), 725 ^ _127218 : [(748 ^ _127218) ^ [] : [-(_151413 = identity_relation(_151415)), 761 ^ _127218 : [(762 ^ _127218) ^ [] : [-(in(749 ^ [_151413, _151415], _151415))], (764 ^ _127218) ^ [] : [-(749 ^ [_151413, _151415] = 750 ^ [_151413, _151415])], (766 ^ _127218) ^ [] : [in(ordered_pair(749 ^ [_151413, _151415], 750 ^ [_151413, _151415]), _151413)]], 753 ^ _127218 : [(754 ^ _127218) ^ [] : [-(in(ordered_pair(749 ^ [_151413, _151415], 750 ^ [_151413, _151415]), _151413))], (756 ^ _127218) ^ [] : [in(749 ^ [_151413, _151415], _151415), 749 ^ [_151413, _151415] = 750 ^ [_151413, _151415]]]], (726 ^ _127218) ^ [] : [_151413 = identity_relation(_151415), 729 ^ _127218 : [(730 ^ _127218) ^ [_151723, _151725] : [in(ordered_pair(_151725, _151723), _151413), 733 ^ _127218 : [(734 ^ _127218) ^ [] : [-(in(_151725, _151415))], (736 ^ _127218) ^ [] : [-(_151725 = _151723)]]], (738 ^ _127218) ^ [_151986, _151988] : [-(in(ordered_pair(_151988, _151986), _151413)), in(_151988, _151415), _151988 = _151986]]]]], (770 ^ _127218) ^ [_153094, _153096] : [_153096 = _153094, 773 ^ _127218 : [(774 ^ _127218) ^ [] : [-(subset(_153096, _153094))], (776 ^ _127218) ^ [] : [-(subset(_153094, _153096))]]], (778 ^ _127218) ^ [_153331, _153333] : [-(_153333 = _153331), subset(_153333, _153331), subset(_153331, _153333)], (788 ^ _127218) ^ [_153618] : [relation(_153618), 791 ^ _127218 : [(792 ^ _127218) ^ [_153804, _153806] : [relation(_153804), 795 ^ _127218 : [(818 ^ _127218) ^ [] : [-(_153804 = relation_dom_restriction(_153618, _153806)), 831 ^ _127218 : [(832 ^ _127218) ^ [] : [-(in(819 ^ [_153618, _153804, _153806], _153806))], (834 ^ _127218) ^ [] : [-(in(ordered_pair(819 ^ [_153618, _153804, _153806], 820 ^ [_153618, _153804, _153806]), _153618))], (836 ^ _127218) ^ [] : [in(ordered_pair(819 ^ [_153618, _153804, _153806], 820 ^ [_153618, _153804, _153806]), _153804)]], 823 ^ _127218 : [(824 ^ _127218) ^ [] : [-(in(ordered_pair(819 ^ [_153618, _153804, _153806], 820 ^ [_153618, _153804, _153806]), _153804))], (826 ^ _127218) ^ [] : [in(819 ^ [_153618, _153804, _153806], _153806), in(ordered_pair(819 ^ [_153618, _153804, _153806], 820 ^ [_153618, _153804, _153806]), _153618)]]], (796 ^ _127218) ^ [] : [_153804 = relation_dom_restriction(_153618, _153806), 799 ^ _127218 : [(800 ^ _127218) ^ [_154129, _154131] : [in(ordered_pair(_154131, _154129), _153804), 803 ^ _127218 : [(804 ^ _127218) ^ [] : [-(in(_154131, _153806))], (806 ^ _127218) ^ [] : [-(in(ordered_pair(_154131, _154129), _153618))]]], (808 ^ _127218) ^ [_154408, _154410] : [-(in(ordered_pair(_154410, _154408), _153804)), in(_154410, _153806), in(ordered_pair(_154410, _154408), _153618)]]]]]]], (840 ^ _127218) ^ [_155563] : [relation(_155563), function(_155563), 847 ^ _127218 : [(877 ^ _127218) ^ [_156989, _156991] : [-(_156989 = relation_image(_155563, _156991)), 894 ^ _127218 : [(895 ^ _127218) ^ [] : [-(in(893 ^ [_155563, _156989, _156991], relation_dom(_155563)))], (897 ^ _127218) ^ [] : [-(in(893 ^ [_155563, _156989, _156991], _156991))], (899 ^ _127218) ^ [] : [-(878 ^ [_155563, _156989, _156991] = apply(_155563, 893 ^ [_155563, _156989, _156991]))], (901 ^ _127218) ^ [] : [in(878 ^ [_155563, _156989, _156991], _156989)]], 881 ^ _127218 : [(882 ^ _127218) ^ [] : [-(in(878 ^ [_155563, _156989, _156991], _156989))], (884 ^ _127218) ^ [_157309] : [in(_157309, relation_dom(_155563)), in(_157309, _156991), 878 ^ [_155563, _156989, _156991] = apply(_155563, _157309)]]], (848 ^ _127218) ^ [_155861, _155863] : [_155861 = relation_image(_155563, _155863), 851 ^ _127218 : [(852 ^ _127218) ^ [_156061] : [in(_156061, _155861), 856 ^ _127218 : [(857 ^ _127218) ^ [] : [-(in(855 ^ [_155563, _155861, _155863, _156061], relation_dom(_155563)))], (859 ^ _127218) ^ [] : [-(in(855 ^ [_155563, _155861, _155863, _156061], _155863))], (861 ^ _127218) ^ [] : [-(_156061 = apply(_155563, 855 ^ [_155563, _155861, _155863, _156061]))]]], (863 ^ _127218) ^ [_156516] : [-(in(_156516, _155861)), 864 ^ _127218 : [(865 ^ _127218) ^ [_156629] : [in(_156629, relation_dom(_155563)), in(_156629, _155863), _156516 = apply(_155563, _156629)]]]]]]], (905 ^ _127218) ^ [_158119, _158121] : [relation(_158119), 908 ^ _127218 : [(909 ^ _127218) ^ [_158290] : [relation(_158290), 912 ^ _127218 : [(935 ^ _127218) ^ [] : [-(_158290 = relation_rng_restriction(_158121, _158119)), 948 ^ _127218 : [(949 ^ _127218) ^ [] : [-(in(937 ^ [_158119, _158121, _158290], _158121))], (951 ^ _127218) ^ [] : [-(in(ordered_pair(936 ^ [_158119, _158121, _158290], 937 ^ [_158119, _158121, _158290]), _158119))], (953 ^ _127218) ^ [] : [in(ordered_pair(936 ^ [_158119, _158121, _158290], 937 ^ [_158119, _158121, _158290]), _158290)]], 940 ^ _127218 : [(941 ^ _127218) ^ [] : [-(in(ordered_pair(936 ^ [_158119, _158121, _158290], 937 ^ [_158119, _158121, _158290]), _158290))], (943 ^ _127218) ^ [] : [in(937 ^ [_158119, _158121, _158290], _158121), in(ordered_pair(936 ^ [_158119, _158121, _158290], 937 ^ [_158119, _158121, _158290]), _158119)]]], (913 ^ _127218) ^ [] : [_158290 = relation_rng_restriction(_158121, _158119), 916 ^ _127218 : [(917 ^ _127218) ^ [_158617, _158619] : [in(ordered_pair(_158619, _158617), _158290), 920 ^ _127218 : [(921 ^ _127218) ^ [] : [-(in(_158617, _158121))], (923 ^ _127218) ^ [] : [-(in(ordered_pair(_158619, _158617), _158119))]]], (925 ^ _127218) ^ [_158896, _158898] : [-(in(ordered_pair(_158898, _158896), _158290)), in(_158896, _158121), in(ordered_pair(_158898, _158896), _158119)]]]]]]], (957 ^ _127218) ^ [_160042] : [relation(_160042), 960 ^ _127218 : [(961 ^ _127218) ^ [] : [antisymmetric(_160042), -(is_antisymmetric_in(_160042, relation_field(_160042)))], (967 ^ _127218) ^ [] : [is_antisymmetric_in(_160042, relation_field(_160042)), -(antisymmetric(_160042))]]], (973 ^ _127218) ^ [_160473] : [relation(_160473), function(_160473), 980 ^ _127218 : [(1003 ^ _127218) ^ [_161512, _161514] : [-(_161512 = relation_inverse_image(_160473, _161514)), 1015 ^ _127218 : [(1016 ^ _127218) ^ [] : [-(in(1004 ^ [_160473, _161512, _161514], relation_dom(_160473)))], (1018 ^ _127218) ^ [] : [-(in(apply(_160473, 1004 ^ [_160473, _161512, _161514]), _161514))], (1020 ^ _127218) ^ [] : [in(1004 ^ [_160473, _161512, _161514], _161512)]], 1007 ^ _127218 : [(1008 ^ _127218) ^ [] : [-(in(1004 ^ [_160473, _161512, _161514], _161512))], (1010 ^ _127218) ^ [] : [in(1004 ^ [_160473, _161512, _161514], relation_dom(_160473)), in(apply(_160473, 1004 ^ [_160473, _161512, _161514]), _161514)]]], (981 ^ _127218) ^ [_160760, _160762] : [_160760 = relation_inverse_image(_160473, _160762), 984 ^ _127218 : [(985 ^ _127218) ^ [_160949] : [in(_160949, _160760), 988 ^ _127218 : [(989 ^ _127218) ^ [] : [-(in(_160949, relation_dom(_160473)))], (991 ^ _127218) ^ [] : [-(in(apply(_160473, _160949), _160762))]]], (993 ^ _127218) ^ [_161218] : [-(in(_161218, _160760)), in(_161218, relation_dom(_160473)), in(apply(_160473, _161218), _160762)]]]]], (1024 ^ _127218) ^ [_162280] : [relation(_162280), 1027 ^ _127218 : [(1051 ^ _127218) ^ [_163393, _163395] : [-(_163393 = relation_image(_162280, _163395)), 1064 ^ _127218 : [(1065 ^ _127218) ^ [] : [-(in(ordered_pair(1063 ^ [_162280, _163393, _163395], 1052 ^ [_162280, _163393, _163395]), _162280))], (1067 ^ _127218) ^ [] : [-(in(1063 ^ [_162280, _163393, _163395], _163395))], (1069 ^ _127218) ^ [] : [in(1052 ^ [_162280, _163393, _163395], _163393)]], 1055 ^ _127218 : [(1056 ^ _127218) ^ [] : [-(in(1052 ^ [_162280, _163393, _163395], _163393))], (1058 ^ _127218) ^ [_163697] : [in(ordered_pair(_163697, 1052 ^ [_162280, _163393, _163395]), _162280), in(_163697, _163395)]]], (1028 ^ _127218) ^ [_162487, _162489] : [_162487 = relation_image(_162280, _162489), 1031 ^ _127218 : [(1032 ^ _127218) ^ [_162679] : [in(_162679, _162487), 1036 ^ _127218 : [(1037 ^ _127218) ^ [] : [-(in(ordered_pair(1035 ^ [_162280, _162487, _162489, _162679], _162679), _162280))], (1039 ^ _127218) ^ [] : [-(in(1035 ^ [_162280, _162487, _162489, _162679], _162489))]]], (1041 ^ _127218) ^ [_163033] : [-(in(_163033, _162487)), 1042 ^ _127218 : [(1043 ^ _127218) ^ [_163138] : [in(ordered_pair(_163138, _163033), _162280), in(_163138, _162489)]]]]]]], (1073 ^ _127218) ^ [_164299] : [relation(_164299), 1076 ^ _127218 : [(1100 ^ _127218) ^ [_165412, _165414] : [-(_165412 = relation_inverse_image(_164299, _165414)), 1113 ^ _127218 : [(1114 ^ _127218) ^ [] : [-(in(ordered_pair(1101 ^ [_164299, _165412, _165414], 1112 ^ [_164299, _165412, _165414]), _164299))], (1116 ^ _127218) ^ [] : [-(in(1112 ^ [_164299, _165412, _165414], _165414))], (1118 ^ _127218) ^ [] : [in(1101 ^ [_164299, _165412, _165414], _165412)]], 1104 ^ _127218 : [(1105 ^ _127218) ^ [] : [-(in(1101 ^ [_164299, _165412, _165414], _165412))], (1107 ^ _127218) ^ [_165716] : [in(ordered_pair(1101 ^ [_164299, _165412, _165414], _165716), _164299), in(_165716, _165414)]]], (1077 ^ _127218) ^ [_164506, _164508] : [_164506 = relation_inverse_image(_164299, _164508), 1080 ^ _127218 : [(1081 ^ _127218) ^ [_164698] : [in(_164698, _164506), 1085 ^ _127218 : [(1086 ^ _127218) ^ [] : [-(in(ordered_pair(_164698, 1084 ^ [_164299, _164506, _164508, _164698]), _164299))], (1088 ^ _127218) ^ [] : [-(in(1084 ^ [_164299, _164506, _164508, _164698], _164508))]]], (1090 ^ _127218) ^ [_165052] : [-(in(_165052, _164506)), 1091 ^ _127218 : [(1092 ^ _127218) ^ [_165157] : [in(ordered_pair(_165052, _165157), _164299), in(_165157, _164508)]]]]]]], (1122 ^ _127218) ^ [_166318] : [relation(_166318), 1125 ^ _127218 : [(1126 ^ _127218) ^ [] : [connected(_166318), -(is_connected_in(_166318, relation_field(_166318)))], (1132 ^ _127218) ^ [] : [is_connected_in(_166318, relation_field(_166318)), -(connected(_166318))]]], (1138 ^ _127218) ^ [_166749] : [relation(_166749), 1141 ^ _127218 : [(1142 ^ _127218) ^ [] : [transitive(_166749), -(is_transitive_in(_166749, relation_field(_166749)))], (1148 ^ _127218) ^ [] : [is_transitive_in(_166749, relation_field(_166749)), -(transitive(_166749))]]], (1182 ^ _127218) ^ [_168215, _168217, _168219, _168221] : [-(_168215 = unordered_triple(_168221, _168219, _168217)), 1186 ^ _127218 : [(1187 ^ _127218) ^ [] : [-(in(1183 ^ [_168215, _168217, _168219, _168221], _168215))], (1189 ^ _127218) ^ [] : [1183 ^ [_168215, _168217, _168219, _168221] = _168221], (1191 ^ _127218) ^ [] : [1183 ^ [_168215, _168217, _168219, _168221] = _168219], (1193 ^ _127218) ^ [] : [1183 ^ [_168215, _168217, _168219, _168221] = _168217]], 1194 ^ _127218 : [(1205 ^ _127218) ^ [] : [in(1183 ^ [_168215, _168217, _168219, _168221], _168215)], (1195 ^ _127218) ^ [] : [-(1183 ^ [_168215, _168217, _168219, _168221] = _168221), -(1183 ^ [_168215, _168217, _168219, _168221] = _168219), -(1183 ^ [_168215, _168217, _168219, _168221] = _168217)]]], (1154 ^ _127218) ^ [_167251, _167253, _167255, _167257] : [_167251 = unordered_triple(_167257, _167255, _167253), 1157 ^ _127218 : [(1172 ^ _127218) ^ [_167853] : [1173 ^ _127218 : [(1174 ^ _127218) ^ [] : [_167853 = _167257], (1176 ^ _127218) ^ [] : [_167853 = _167255], (1178 ^ _127218) ^ [] : [_167853 = _167253]], -(in(_167853, _167251))], (1158 ^ _127218) ^ [_167453] : [in(_167453, _167251), -(_167453 = _167257), -(_167453 = _167255), -(_167453 = _167253)]]], (1209 ^ _127218) ^ [_169188] : [-(succ(_169188) = set_union2(_169188, singleton(_169188)))], (1223 ^ _127218) ^ [_169778] : [1225 ^ _127218 : [(1226 ^ _127218) ^ [] : [-(in(1224 ^ [_169778], _169778))], (1228 ^ _127218) ^ [_170015, _170017] : [1224 ^ [_169778] = ordered_pair(_170017, _170015)]], -(relation(_169778))], (1211 ^ _127218) ^ [_169317] : [relation(_169317), 1214 ^ _127218 : [(1215 ^ _127218) ^ [_169465] : [in(_169465, _169317), -(_169465 = ordered_pair(1218 ^ [_169317, _169465], 1219 ^ [_169317, _169465]))]]], (1232 ^ _127218) ^ [_170172] : [relation(_170172), 1235 ^ _127218 : [(1246 ^ _127218) ^ [_170671] : [1248 ^ _127218 : [(1249 ^ _127218) ^ [] : [-(in(1247 ^ [_170172, _170671], _170671))], (1251 ^ _127218) ^ [] : [in(ordered_pair(1247 ^ [_170172, _170671], 1247 ^ [_170172, _170671]), _170172)]], -(is_reflexive_in(_170172, _170671))], (1236 ^ _127218) ^ [_170346] : [is_reflexive_in(_170172, _170346), 1239 ^ _127218 : [(1240 ^ _127218) ^ [_170488] : [in(_170488, _170346), -(in(ordered_pair(_170488, _170488), _170172))]]]]], (1304 ^ _127218) ^ [_172778, _172780] : [_172780 = empty_set, 1307 ^ _127218 : [(1308 ^ _127218) ^ [] : [_172778 = set_meet(_172780), -(_172778 = empty_set)], (1314 ^ _127218) ^ [] : [_172778 = empty_set, -(_172778 = set_meet(_172780))]]], (1255 ^ _127218) ^ [_171071, _171073] : [-(_171073 = empty_set), 1258 ^ _127218 : [(1282 ^ _127218) ^ [] : [-(_171071 = set_meet(_171073)), 1286 ^ _127218 : [(1287 ^ _127218) ^ [] : [-(in(1283 ^ [_171071, _171073], _171071))], (1290 ^ _127218) ^ [] : [-(in(1288 ^ [_171071, _171073], _171073))], (1292 ^ _127218) ^ [] : [in(1283 ^ [_171071, _171073], 1288 ^ [_171071, _171073])]], 1293 ^ _127218 : [(1300 ^ _127218) ^ [] : [in(1283 ^ [_171071, _171073], _171071)], (1294 ^ _127218) ^ [_172473] : [in(_172473, _171073), -(in(1283 ^ [_171071, _171073], _172473))]]], (1259 ^ _127218) ^ [] : [_171071 = set_meet(_171073), 1262 ^ _127218 : [(1273 ^ _127218) ^ [_171699] : [1275 ^ _127218 : [(1276 ^ _127218) ^ [] : [-(in(1274 ^ [_171071, _171073, _171699], _171073))], (1278 ^ _127218) ^ [] : [in(_171699, 1274 ^ [_171071, _171073, _171699])]], -(in(_171699, _171071))], (1263 ^ _127218) ^ [_171369] : [in(_171369, _171071), 1266 ^ _127218 : [(1267 ^ _127218) ^ [_171514] : [in(_171514, _171073), -(in(_171369, _171514))]]]]]]], (1336 ^ _127218) ^ [_173796, _173798] : [-(_173796 = singleton(_173798)), 1340 ^ _127218 : [(1341 ^ _127218) ^ [] : [-(in(1337 ^ [_173796, _173798], _173796))], (1343 ^ _127218) ^ [] : [1337 ^ [_173796, _173798] = _173798]], 1344 ^ _127218 : [(1345 ^ _127218) ^ [] : [-(1337 ^ [_173796, _173798] = _173798)], (1347 ^ _127218) ^ [] : [in(1337 ^ [_173796, _173798], _173796)]]], (1320 ^ _127218) ^ [_173275, _173277] : [_173275 = singleton(_173277), 1323 ^ _127218 : [(1324 ^ _127218) ^ [_173445] : [in(_173445, _173275), -(_173445 = _173277)], (1330 ^ _127218) ^ [_173617] : [_173617 = _173277, -(in(_173617, _173275))]]], (1351 ^ _127218) ^ [_174347] : [_174347 = empty_set, 1354 ^ _127218 : [(1355 ^ _127218) ^ [_174460] : [in(_174460, _174347)]]], (1357 ^ _127218) ^ [_174526] : [-(in(1358 ^ [_174526], _174526)), -(_174526 = empty_set)], (1380 ^ _127218) ^ [_175338, _175340] : [-(_175338 = powerset(_175340)), 1384 ^ _127218 : [(1385 ^ _127218) ^ [] : [-(in(1381 ^ [_175338, _175340], _175338))], (1387 ^ _127218) ^ [] : [subset(1381 ^ [_175338, _175340], _175340)]], 1388 ^ _127218 : [(1389 ^ _127218) ^ [] : [-(subset(1381 ^ [_175338, _175340], _175340))], (1391 ^ _127218) ^ [] : [in(1381 ^ [_175338, _175340], _175338)]]], (1364 ^ _127218) ^ [_174817, _174819] : [_174817 = powerset(_174819), 1367 ^ _127218 : [(1368 ^ _127218) ^ [_174987] : [in(_174987, _174817), -(subset(_174987, _174819))], (1374 ^ _127218) ^ [_175159] : [subset(_175159, _174819), -(in(_175159, _174817))]]], (1405 ^ _127218) ^ [_176189] : [1407 ^ _127218 : [(1408 ^ _127218) ^ [] : [-(in(1406 ^ [_176189], _176189))], (1410 ^ _127218) ^ [] : [subset(1406 ^ [_176189], _176189)]], -(epsilon_transitive(_176189))], (1395 ^ _127218) ^ [_175889] : [epsilon_transitive(_175889), 1398 ^ _127218 : [(1399 ^ _127218) ^ [_176020] : [in(_176020, _175889), -(subset(_176020, _175889))]]], (1414 ^ _127218) ^ [_176514] : [relation(_176514), 1417 ^ _127218 : [(1418 ^ _127218) ^ [_176672] : [relation(_176672), 1421 ^ _127218 : [(1438 ^ _127218) ^ [] : [-(_176514 = _176672), 1443 ^ _127218 : [(1444 ^ _127218) ^ [] : [-(in(ordered_pair(1439 ^ [_176514, _176672], 1440 ^ [_176514, _176672]), _176514))], (1446 ^ _127218) ^ [] : [in(ordered_pair(1439 ^ [_176514, _176672], 1440 ^ [_176514, _176672]), _176672)]], 1447 ^ _127218 : [(1448 ^ _127218) ^ [] : [-(in(ordered_pair(1439 ^ [_176514, _176672], 1440 ^ [_176514, _176672]), _176672))], (1450 ^ _127218) ^ [] : [in(ordered_pair(1439 ^ [_176514, _176672], 1440 ^ [_176514, _176672]), _176514)]]], (1422 ^ _127218) ^ [] : [_176514 = _176672, 1425 ^ _127218 : [(1426 ^ _127218) ^ [_176977, _176979] : [in(ordered_pair(_176979, _176977), _176514), -(in(ordered_pair(_176979, _176977), _176672))], (1432 ^ _127218) ^ [_177167, _177169] : [in(ordered_pair(_177169, _177167), _176672), -(in(ordered_pair(_177169, _177167), _176514))]]]]]]], (1454 ^ _127218) ^ [_178004, _178006] : [-(empty(_178006)), 1457 ^ _127218 : [(1458 ^ _127218) ^ [] : [element(_178004, _178006), -(in(_178004, _178006))], (1464 ^ _127218) ^ [] : [in(_178004, _178006), -(element(_178004, _178006))]]], (1470 ^ _127218) ^ [_178417, _178419] : [empty(_178419), 1473 ^ _127218 : [(1474 ^ _127218) ^ [] : [element(_178417, _178419), -(empty(_178417))], (1480 ^ _127218) ^ [] : [empty(_178417), -(element(_178417, _178419))]]], (1508 ^ _127218) ^ [_179642, _179644, _179646] : [-(_179642 = unordered_pair(_179646, _179644)), 1512 ^ _127218 : [(1513 ^ _127218) ^ [] : [-(in(1509 ^ [_179642, _179644, _179646], _179642))], (1515 ^ _127218) ^ [] : [1509 ^ [_179642, _179644, _179646] = _179646], (1517 ^ _127218) ^ [] : [1509 ^ [_179642, _179644, _179646] = _179644]], 1518 ^ _127218 : [(1525 ^ _127218) ^ [] : [in(1509 ^ [_179642, _179644, _179646], _179642)], (1519 ^ _127218) ^ [] : [-(1509 ^ [_179642, _179644, _179646] = _179646), -(1509 ^ [_179642, _179644, _179646] = _179644)]]], (1486 ^ _127218) ^ [_178917, _178919, _178921] : [_178917 = unordered_pair(_178921, _178919), 1489 ^ _127218 : [(1500 ^ _127218) ^ [_179377] : [1501 ^ _127218 : [(1502 ^ _127218) ^ [] : [_179377 = _178921], (1504 ^ _127218) ^ [] : [_179377 = _178919]], -(in(_179377, _178917))], (1490 ^ _127218) ^ [_179099] : [in(_179099, _178917), -(_179099 = _178921), -(_179099 = _178919)]]], (1529 ^ _127218) ^ [_180379] : [relation(_180379), 1532 ^ _127218 : [(1550 ^ _127218) ^ [] : [-(well_founded_relation(_180379)), 1552 ^ _127218 : [(1553 ^ _127218) ^ [] : [-(subset(1551 ^ [_180379], relation_field(_180379)))], (1555 ^ _127218) ^ [] : [1551 ^ [_180379] = empty_set], (1557 ^ _127218) ^ [_181329] : [in(_181329, 1551 ^ [_180379]), disjoint(fiber(_180379, _181329), 1551 ^ [_180379])]]], (1533 ^ _127218) ^ [] : [well_founded_relation(_180379), 1536 ^ _127218 : [(1537 ^ _127218) ^ [_180646] : [subset(_180646, relation_field(_180379)), -(_180646 = empty_set), 1545 ^ _127218 : [(1546 ^ _127218) ^ [] : [-(in(1544 ^ [_180379, _180646], _180646))], (1548 ^ _127218) ^ [] : [-(disjoint(fiber(_180379, 1544 ^ [_180379, _180646]), _180646))]]]]]]], (1587 ^ _127218) ^ [_182393, _182395, _182397] : [-(_182393 = set_union2(_182397, _182395)), 1591 ^ _127218 : [(1592 ^ _127218) ^ [] : [-(in(1588 ^ [_182393, _182395, _182397], _182393))], (1594 ^ _127218) ^ [] : [in(1588 ^ [_182393, _182395, _182397], _182397)], (1596 ^ _127218) ^ [] : [in(1588 ^ [_182393, _182395, _182397], _182395)]], 1597 ^ _127218 : [(1604 ^ _127218) ^ [] : [in(1588 ^ [_182393, _182395, _182397], _182393)], (1598 ^ _127218) ^ [] : [-(in(1588 ^ [_182393, _182395, _182397], _182397)), -(in(1588 ^ [_182393, _182395, _182397], _182395))]]], (1565 ^ _127218) ^ [_181668, _181670, _181672] : [_181668 = set_union2(_181672, _181670), 1568 ^ _127218 : [(1579 ^ _127218) ^ [_182128] : [1580 ^ _127218 : [(1581 ^ _127218) ^ [] : [in(_182128, _181672)], (1583 ^ _127218) ^ [] : [in(_182128, _181670)]], -(in(_182128, _181668))], (1569 ^ _127218) ^ [_181850] : [in(_181850, _181668), -(in(_181850, _181672)), -(in(_181850, _181670))]]], (1638 ^ _127218) ^ [_184444, _184446, _184448] : [-(_184444 = cartesian_product2(_184448, _184446)), 1656 ^ _127218 : [(1657 ^ _127218) ^ [] : [-(in(1654 ^ [_184444, _184446, _184448], _184448))], (1659 ^ _127218) ^ [] : [-(in(1655 ^ [_184444, _184446, _184448], _184446))], (1661 ^ _127218) ^ [] : [-(1639 ^ [_184444, _184446, _184448] = ordered_pair(1654 ^ [_184444, _184446, _184448], 1655 ^ [_184444, _184446, _184448]))], (1663 ^ _127218) ^ [] : [in(1639 ^ [_184444, _184446, _184448], _184444)]], 1642 ^ _127218 : [(1643 ^ _127218) ^ [] : [-(in(1639 ^ [_184444, _184446, _184448], _184444))], (1645 ^ _127218) ^ [_184782, _184784] : [in(_184784, _184448), in(_184782, _184446), 1639 ^ [_184444, _184446, _184448] = ordered_pair(_184784, _184782)]]], (1608 ^ _127218) ^ [_183187, _183189, _183191] : [_183187 = cartesian_product2(_183191, _183189), 1611 ^ _127218 : [(1612 ^ _127218) ^ [_183388] : [in(_183388, _183187), 1617 ^ _127218 : [(1618 ^ _127218) ^ [] : [-(in(1615 ^ [_183187, _183189, _183191, _183388], _183191))], (1620 ^ _127218) ^ [] : [-(in(1616 ^ [_183187, _183189, _183191, _183388], _183189))], (1622 ^ _127218) ^ [] : [-(_183388 = ordered_pair(1615 ^ [_183187, _183189, _183191, _183388], 1616 ^ [_183187, _183189, _183191, _183388]))]]], (1624 ^ _127218) ^ [_183948] : [-(in(_183948, _183187)), 1625 ^ _127218 : [(1626 ^ _127218) ^ [_184078, _184080] : [in(_184080, _183191), in(_184078, _183189), _183948 = ordered_pair(_184080, _184078)]]]]], (1689 ^ _127218) ^ [_186345] : [1692 ^ _127218 : [(1693 ^ _127218) ^ [] : [-(in(1690 ^ [_186345], _186345))], (1695 ^ _127218) ^ [] : [-(in(1691 ^ [_186345], _186345))], (1697 ^ _127218) ^ [] : [in(1690 ^ [_186345], 1691 ^ [_186345])], (1699 ^ _127218) ^ [] : [1690 ^ [_186345] = 1691 ^ [_186345]], (1701 ^ _127218) ^ [] : [in(1691 ^ [_186345], 1690 ^ [_186345])]], -(epsilon_connected(_186345))], (1667 ^ _127218) ^ [_185707] : [epsilon_connected(_185707), 1670 ^ _127218 : [(1671 ^ _127218) ^ [_185883, _185885] : [in(_185885, _185707), in(_185883, _185707), -(in(_185885, _185883)), -(_185885 = _185883), -(in(_185883, _185885))]]], (1705 ^ _127218) ^ [_187051] : [relation(_187051), 1708 ^ _127218 : [(1709 ^ _127218) ^ [_187209] : [relation(_187209), 1712 ^ _127218 : [(1723 ^ _127218) ^ [] : [1726 ^ _127218 : [(1727 ^ _127218) ^ [] : [-(in(ordered_pair(1724 ^ [_187051, _187209], 1725 ^ [_187051, _187209]), _187051))], (1729 ^ _127218) ^ [] : [in(ordered_pair(1724 ^ [_187051, _187209], 1725 ^ [_187051, _187209]), _187209)]], -(subset(_187051, _187209))], (1713 ^ _127218) ^ [] : [subset(_187051, _187209), 1716 ^ _127218 : [(1717 ^ _127218) ^ [_187485, _187487] : [in(ordered_pair(_187487, _187485), _187051), -(in(ordered_pair(_187487, _187485), _187209))]]]]]]], (1743 ^ _127218) ^ [_188448, _188450] : [1745 ^ _127218 : [(1746 ^ _127218) ^ [] : [-(in(1744 ^ [_188448, _188450], _188450))], (1748 ^ _127218) ^ [] : [in(1744 ^ [_188448, _188450], _188448)]], -(subset(_188450, _188448))], (1733 ^ _127218) ^ [_188134, _188136] : [subset(_188136, _188134), 1736 ^ _127218 : [(1737 ^ _127218) ^ [_188271] : [in(_188271, _188136), -(in(_188271, _188134))]]], (1752 ^ _127218) ^ [_188791] : [relation(_188791), 1755 ^ _127218 : [(1773 ^ _127218) ^ [_189594] : [-(is_well_founded_in(_188791, _189594)), 1775 ^ _127218 : [(1776 ^ _127218) ^ [] : [-(subset(1774 ^ [_188791, _189594], _189594))], (1778 ^ _127218) ^ [] : [1774 ^ [_188791, _189594] = empty_set], (1780 ^ _127218) ^ [_189936] : [in(_189936, 1774 ^ [_188791, _189594]), disjoint(fiber(_188791, _189936), 1774 ^ [_188791, _189594])]]], (1756 ^ _127218) ^ [_188988] : [is_well_founded_in(_188791, _188988), 1759 ^ _127218 : [(1760 ^ _127218) ^ [_189153] : [subset(_189153, _188988), -(_189153 = empty_set), 1768 ^ _127218 : [(1769 ^ _127218) ^ [] : [-(in(1767 ^ [_188791, _188988, _189153], _189153))], (1771 ^ _127218) ^ [] : [-(disjoint(fiber(_188791, 1767 ^ [_188791, _188988, _189153]), _189153))]]]]]]], (1810 ^ _127218) ^ [_191019, _191021, _191023] : [-(_191019 = set_intersection2(_191023, _191021)), 1822 ^ _127218 : [(1823 ^ _127218) ^ [] : [-(in(1811 ^ [_191019, _191021, _191023], _191023))], (1825 ^ _127218) ^ [] : [-(in(1811 ^ [_191019, _191021, _191023], _191021))], (1827 ^ _127218) ^ [] : [in(1811 ^ [_191019, _191021, _191023], _191019)]], 1814 ^ _127218 : [(1815 ^ _127218) ^ [] : [-(in(1811 ^ [_191019, _191021, _191023], _191019))], (1817 ^ _127218) ^ [] : [in(1811 ^ [_191019, _191021, _191023], _191023), in(1811 ^ [_191019, _191021, _191023], _191021)]]], (1788 ^ _127218) ^ [_190294, _190296, _190298] : [_190294 = set_intersection2(_190298, _190296), 1791 ^ _127218 : [(1792 ^ _127218) ^ [_190476] : [in(_190476, _190294), 1795 ^ _127218 : [(1796 ^ _127218) ^ [] : [-(in(_190476, _190298))], (1798 ^ _127218) ^ [] : [-(in(_190476, _190296))]]], (1800 ^ _127218) ^ [_190735] : [-(in(_190735, _190294)), in(_190735, _190298), in(_190735, _190296)]]], (1831 ^ _127218) ^ [_191758] : [relation(_191758), function(_191758), 1838 ^ _127218 : [(1839 ^ _127218) ^ [_192050, _192052] : [in(_192052, relation_dom(_191758)), 1842 ^ _127218 : [(1843 ^ _127218) ^ [] : [_192050 = apply(_191758, _192052), -(in(ordered_pair(_192052, _192050), _191758))], (1849 ^ _127218) ^ [] : [in(ordered_pair(_192052, _192050), _191758), -(_192050 = apply(_191758, _192052))]]], (1855 ^ _127218) ^ [_192502, _192504] : [-(in(_192504, relation_dom(_191758))), 1858 ^ _127218 : [(1859 ^ _127218) ^ [] : [_192502 = apply(_191758, _192504), -(_192502 = empty_set)], (1865 ^ _127218) ^ [] : [_192502 = empty_set, -(_192502 = apply(_191758, _192504))]]]]], (1871 ^ _127218) ^ [_193020] : [ordinal(_193020), 1874 ^ _127218 : [(1875 ^ _127218) ^ [] : [-(epsilon_transitive(_193020))], (1877 ^ _127218) ^ [] : [-(epsilon_connected(_193020))]]], (1879 ^ _127218) ^ [_193243] : [-(ordinal(_193243)), epsilon_transitive(_193243), epsilon_connected(_193243)], (1889 ^ _127218) ^ [_193514] : [relation(_193514), 1892 ^ _127218 : [(1910 ^ _127218) ^ [_194326] : [-(_194326 = relation_dom(_193514)), 1914 ^ _127218 : [(1915 ^ _127218) ^ [] : [-(in(1911 ^ [_193514, _194326], _194326))], (1917 ^ _127218) ^ [_194589] : [in(ordered_pair(1911 ^ [_193514, _194326], _194589), _193514)]], 1919 ^ _127218 : [(1920 ^ _127218) ^ [] : [-(in(ordered_pair(1911 ^ [_193514, _194326], 1918 ^ [_193514, _194326]), _193514))], (1922 ^ _127218) ^ [] : [in(1911 ^ [_193514, _194326], _194326)]]], (1893 ^ _127218) ^ [_193695] : [_193695 = relation_dom(_193514), 1896 ^ _127218 : [(1897 ^ _127218) ^ [_193875] : [in(_193875, _193695), -(in(ordered_pair(_193875, 1900 ^ [_193514, _193695, _193875]), _193514))], (1904 ^ _127218) ^ [_194119] : [1905 ^ _127218 : [(1906 ^ _127218) ^ [_194198] : [in(ordered_pair(_194119, _194198), _193514)]], -(in(_194119, _193695))]]]]], (1926 ^ _127218) ^ [_194955] : [relation(_194955), 1929 ^ _127218 : [(1952 ^ _127218) ^ [_195823] : [1955 ^ _127218 : [(1956 ^ _127218) ^ [] : [-(in(1953 ^ [_194955, _195823], _195823))], (1958 ^ _127218) ^ [] : [-(in(1954 ^ [_194955, _195823], _195823))], (1960 ^ _127218) ^ [] : [-(in(ordered_pair(1953 ^ [_194955, _195823], 1954 ^ [_194955, _195823]), _194955))], (1962 ^ _127218) ^ [] : [-(in(ordered_pair(1954 ^ [_194955, _195823], 1953 ^ [_194955, _195823]), _194955))], (1964 ^ _127218) ^ [] : [1953 ^ [_194955, _195823] = 1954 ^ [_194955, _195823]]], -(is_antisymmetric_in(_194955, _195823))], (1930 ^ _127218) ^ [_195155] : [is_antisymmetric_in(_194955, _195155), 1933 ^ _127218 : [(1934 ^ _127218) ^ [_195337, _195339] : [-(_195339 = _195337), in(_195339, _195155), in(_195337, _195155), in(ordered_pair(_195339, _195337), _194955), in(ordered_pair(_195337, _195339), _194955)]]]]], (1968 ^ _127218) ^ [_196577] : [-(cast_to_subset(_196577) = _196577)], (1993 ^ _127218) ^ [_197560, _197562] : [-(_197560 = union(_197562)), 2006 ^ _127218 : [(2007 ^ _127218) ^ [] : [-(in(1994 ^ [_197560, _197562], 2005 ^ [_197560, _197562]))], (2009 ^ _127218) ^ [] : [-(in(2005 ^ [_197560, _197562], _197562))], (2011 ^ _127218) ^ [] : [in(1994 ^ [_197560, _197562], _197560)]], 1997 ^ _127218 : [(1998 ^ _127218) ^ [] : [-(in(1994 ^ [_197560, _197562], _197560))], (2000 ^ _127218) ^ [_197843] : [in(1994 ^ [_197560, _197562], _197843), in(_197843, _197562)]]], (1970 ^ _127218) ^ [_196715, _196717] : [_196715 = union(_196717), 1973 ^ _127218 : [(1974 ^ _127218) ^ [_196896] : [in(_196896, _196715), 1978 ^ _127218 : [(1979 ^ _127218) ^ [] : [-(in(_196896, 1977 ^ [_196715, _196717, _196896]))], (1981 ^ _127218) ^ [] : [-(in(1977 ^ [_196715, _196717, _196896], _196717))]]], (1983 ^ _127218) ^ [_197223] : [-(in(_197223, _196715)), 1984 ^ _127218 : [(1985 ^ _127218) ^ [_197321] : [in(_197223, _197321), in(_197321, _196717)]]]]], (2015 ^ _127218) ^ [_198393] : [relation(_198393), 2018 ^ _127218 : [(2019 ^ _127218) ^ [] : [well_ordering(_198393), 2022 ^ _127218 : [(2023 ^ _127218) ^ [] : [-(reflexive(_198393))], (2025 ^ _127218) ^ [] : [-(transitive(_198393))], (2027 ^ _127218) ^ [] : [-(antisymmetric(_198393))], (2029 ^ _127218) ^ [] : [-(connected(_198393))], (2031 ^ _127218) ^ [] : [-(well_founded_relation(_198393))]]], (2033 ^ _127218) ^ [] : [-(well_ordering(_198393)), reflexive(_198393), transitive(_198393), antisymmetric(_198393), connected(_198393), well_founded_relation(_198393)]]], (2077 ^ _127218) ^ [_200196, _200198, _200200] : [-(_200196 = set_difference(_200200, _200198)), 2089 ^ _127218 : [(2090 ^ _127218) ^ [] : [-(in(2078 ^ [_200196, _200198, _200200], _200200))], (2092 ^ _127218) ^ [] : [in(2078 ^ [_200196, _200198, _200200], _200198)], (2094 ^ _127218) ^ [] : [in(2078 ^ [_200196, _200198, _200200], _200196)]], 2081 ^ _127218 : [(2082 ^ _127218) ^ [] : [-(in(2078 ^ [_200196, _200198, _200200], _200196))], (2084 ^ _127218) ^ [] : [in(2078 ^ [_200196, _200198, _200200], _200200), -(in(2078 ^ [_200196, _200198, _200200], _200198))]]], (2055 ^ _127218) ^ [_199465, _199467, _199469] : [_199465 = set_difference(_199469, _199467), 2058 ^ _127218 : [(2059 ^ _127218) ^ [_199649] : [in(_199649, _199465), 2062 ^ _127218 : [(2063 ^ _127218) ^ [] : [-(in(_199649, _199469))], (2065 ^ _127218) ^ [] : [in(_199649, _199467)]]], (2067 ^ _127218) ^ [_199909] : [-(in(_199909, _199465)), in(_199909, _199469), -(in(_199909, _199467))]]], (2098 ^ _127218) ^ [_200939] : [relation(_200939), function(_200939), 2105 ^ _127218 : [(2129 ^ _127218) ^ [_202093] : [-(_202093 = relation_rng(_200939)), 2142 ^ _127218 : [(2143 ^ _127218) ^ [] : [-(in(2141 ^ [_200939, _202093], relation_dom(_200939)))], (2145 ^ _127218) ^ [] : [-(2130 ^ [_200939, _202093] = apply(_200939, 2141 ^ [_200939, _202093]))], (2147 ^ _127218) ^ [] : [in(2130 ^ [_200939, _202093], _202093)]], 2133 ^ _127218 : [(2134 ^ _127218) ^ [] : [-(in(2130 ^ [_200939, _202093], _202093))], (2136 ^ _127218) ^ [_202388] : [in(_202388, relation_dom(_200939)), 2130 ^ [_200939, _202093] = apply(_200939, _202388)]]], (2106 ^ _127218) ^ [_201211] : [_201211 = relation_rng(_200939), 2109 ^ _127218 : [(2110 ^ _127218) ^ [_201399] : [in(_201399, _201211), 2114 ^ _127218 : [(2115 ^ _127218) ^ [] : [-(in(2113 ^ [_200939, _201211, _201399], relation_dom(_200939)))], (2117 ^ _127218) ^ [] : [-(_201399 = apply(_200939, 2113 ^ [_200939, _201211, _201399]))]]], (2119 ^ _127218) ^ [_201741] : [-(in(_201741, _201211)), 2120 ^ _127218 : [(2121 ^ _127218) ^ [_201844] : [in(_201844, relation_dom(_200939)), _201741 = apply(_200939, _201844)]]]]]]], (2151 ^ _127218) ^ [_202965] : [relation(_202965), 2154 ^ _127218 : [(2172 ^ _127218) ^ [_203777] : [-(_203777 = relation_rng(_202965)), 2176 ^ _127218 : [(2177 ^ _127218) ^ [] : [-(in(2173 ^ [_202965, _203777], _203777))], (2179 ^ _127218) ^ [_204040] : [in(ordered_pair(_204040, 2173 ^ [_202965, _203777]), _202965)]], 2181 ^ _127218 : [(2182 ^ _127218) ^ [] : [-(in(ordered_pair(2180 ^ [_202965, _203777], 2173 ^ [_202965, _203777]), _202965))], (2184 ^ _127218) ^ [] : [in(2173 ^ [_202965, _203777], _203777)]]], (2155 ^ _127218) ^ [_203146] : [_203146 = relation_rng(_202965), 2158 ^ _127218 : [(2159 ^ _127218) ^ [_203326] : [in(_203326, _203146), -(in(ordered_pair(2162 ^ [_202965, _203146, _203326], _203326), _202965))], (2166 ^ _127218) ^ [_203570] : [2167 ^ _127218 : [(2168 ^ _127218) ^ [_203649] : [in(ordered_pair(_203649, _203570), _202965)]], -(in(_203570, _203146))]]]]], (2188 ^ _127218) ^ [_204420, _204422] : [element(_204420, powerset(_204422)), -(subset_complement(_204422, _204420) = set_difference(_204422, _204420))], (2194 ^ _127218) ^ [_204631, _204633] : [-(ordered_pair(_204633, _204631) = unordered_pair(unordered_pair(_204633, _204631), singleton(_204633)))], (2196 ^ _127218) ^ [_204737] : [relation(_204737), 2199 ^ _127218 : [(2200 ^ _127218) ^ [_204921] : [well_orders(_204737, _204921), 2203 ^ _127218 : [(2204 ^ _127218) ^ [] : [-(is_reflexive_in(_204737, _204921))], (2206 ^ _127218) ^ [] : [-(is_transitive_in(_204737, _204921))], (2208 ^ _127218) ^ [] : [-(is_antisymmetric_in(_204737, _204921))], (2210 ^ _127218) ^ [] : [-(is_connected_in(_204737, _204921))], (2212 ^ _127218) ^ [] : [-(is_well_founded_in(_204737, _204921))]]], (2214 ^ _127218) ^ [_205382] : [-(well_orders(_204737, _205382)), is_reflexive_in(_204737, _205382), is_transitive_in(_204737, _205382), is_antisymmetric_in(_204737, _205382), is_connected_in(_204737, _205382), is_well_founded_in(_204737, _205382)]]], (2236 ^ _127218) ^ [_205972] : [being_limit_ordinal(_205972), -(_205972 = union(_205972))], (2242 ^ _127218) ^ [_206130] : [_206130 = union(_206130), -(being_limit_ordinal(_206130))], (2248 ^ _127218) ^ [_206324] : [relation(_206324), -(relation_field(_206324) = set_union2(relation_dom(_206324), relation_rng(_206324)))], (2254 ^ _127218) ^ [_206530] : [relation(_206530), 2257 ^ _127218 : [(2280 ^ _127218) ^ [_207422] : [2283 ^ _127218 : [(2284 ^ _127218) ^ [] : [-(in(2281 ^ [_206530, _207422], _207422))], (2286 ^ _127218) ^ [] : [-(in(2282 ^ [_206530, _207422], _207422))], (2288 ^ _127218) ^ [] : [2281 ^ [_206530, _207422] = 2282 ^ [_206530, _207422]], (2290 ^ _127218) ^ [] : [in(ordered_pair(2281 ^ [_206530, _207422], 2282 ^ [_206530, _207422]), _206530)], (2292 ^ _127218) ^ [] : [in(ordered_pair(2282 ^ [_206530, _207422], 2281 ^ [_206530, _207422]), _206530)]], -(is_connected_in(_206530, _207422))], (2258 ^ _127218) ^ [_206738] : [is_connected_in(_206530, _206738), 2261 ^ _127218 : [(2262 ^ _127218) ^ [_206928, _206930] : [in(_206930, _206738), in(_206928, _206738), -(_206930 = _206928), -(in(ordered_pair(_206930, _206928), _206530)), -(in(ordered_pair(_206928, _206930), _206530))]]]]], (2296 ^ _127218) ^ [_208207] : [relation(_208207), 2299 ^ _127218 : [(2300 ^ _127218) ^ [_208326] : [-(relation_restriction(_208207, _208326) = set_intersection2(_208207, cartesian_product2(_208326, _208326)))]]], (2302 ^ _127218) ^ [_208435] : [relation(_208435), 2305 ^ _127218 : [(2306 ^ _127218) ^ [_208595] : [relation(_208595), 2309 ^ _127218 : [(2326 ^ _127218) ^ [] : [-(_208595 = relation_inverse(_208435)), 2331 ^ _127218 : [(2332 ^ _127218) ^ [] : [-(in(ordered_pair(2327 ^ [_208435, _208595], 2328 ^ [_208435, _208595]), _208595))], (2334 ^ _127218) ^ [] : [in(ordered_pair(2328 ^ [_208435, _208595], 2327 ^ [_208435, _208595]), _208435)]], 2335 ^ _127218 : [(2336 ^ _127218) ^ [] : [-(in(ordered_pair(2328 ^ [_208435, _208595], 2327 ^ [_208435, _208595]), _208435))], (2338 ^ _127218) ^ [] : [in(ordered_pair(2327 ^ [_208435, _208595], 2328 ^ [_208435, _208595]), _208595)]]], (2310 ^ _127218) ^ [] : [_208595 = relation_inverse(_208435), 2313 ^ _127218 : [(2314 ^ _127218) ^ [_208904, _208906] : [in(ordered_pair(_208906, _208904), _208595), -(in(ordered_pair(_208904, _208906), _208435))], (2320 ^ _127218) ^ [_209094, _209096] : [in(ordered_pair(_209094, _209096), _208435), -(in(ordered_pair(_209096, _209094), _208595))]]]]]]], (2342 ^ _127218) ^ [_209942, _209944] : [disjoint(_209944, _209942), -(set_intersection2(_209944, _209942) = empty_set)], (2348 ^ _127218) ^ [_210110, _210112] : [set_intersection2(_210112, _210110) = empty_set, -(disjoint(_210112, _210110))], (2354 ^ _127218) ^ [_210314] : [relation(_210314), function(_210314), 2361 ^ _127218 : [(2380 ^ _127218) ^ [] : [2383 ^ _127218 : [(2384 ^ _127218) ^ [] : [-(in(2381 ^ [_210314], relation_dom(_210314)))], (2386 ^ _127218) ^ [] : [-(in(2382 ^ [_210314], relation_dom(_210314)))], (2388 ^ _127218) ^ [] : [-(apply(_210314, 2381 ^ [_210314]) = apply(_210314, 2382 ^ [_210314]))], (2390 ^ _127218) ^ [] : [2381 ^ [_210314] = 2382 ^ [_210314]]], -(one_to_one(_210314))], (2362 ^ _127218) ^ [] : [one_to_one(_210314), 2365 ^ _127218 : [(2366 ^ _127218) ^ [_210677, _210679] : [-(_210679 = _210677), in(_210679, relation_dom(_210314)), in(_210677, relation_dom(_210314)), apply(_210314, _210679) = apply(_210314, _210677)]]]]], (2394 ^ _127218) ^ [_211624] : [relation(_211624), 2397 ^ _127218 : [(2398 ^ _127218) ^ [_211809] : [relation(_211809), 2401 ^ _127218 : [(2402 ^ _127218) ^ [_211990] : [relation(_211990), 2405 ^ _127218 : [(2429 ^ _127218) ^ [] : [-(_211990 = relation_composition(_211624, _211809)), 2443 ^ _127218 : [(2444 ^ _127218) ^ [] : [-(in(ordered_pair(2430 ^ [_211624, _211809, _211990], 2442 ^ [_211624, _211809, _211990]), _211624))], (2446 ^ _127218) ^ [] : [-(in(ordered_pair(2442 ^ [_211624, _211809, _211990], 2431 ^ [_211624, _211809, _211990]), _211809))], (2448 ^ _127218) ^ [] : [in(ordered_pair(2430 ^ [_211624, _211809, _211990], 2431 ^ [_211624, _211809, _211990]), _211990)]], 2434 ^ _127218 : [(2435 ^ _127218) ^ [] : [-(in(ordered_pair(2430 ^ [_211624, _211809, _211990], 2431 ^ [_211624, _211809, _211990]), _211990))], (2437 ^ _127218) ^ [_213454] : [in(ordered_pair(2430 ^ [_211624, _211809, _211990], _213454), _211624), in(ordered_pair(_213454, 2431 ^ [_211624, _211809, _211990]), _211809)]]], (2406 ^ _127218) ^ [] : [_211990 = relation_composition(_211624, _211809), 2409 ^ _127218 : [(2410 ^ _127218) ^ [_212325, _212327] : [in(ordered_pair(_212327, _212325), _211990), 2414 ^ _127218 : [(2415 ^ _127218) ^ [] : [-(in(ordered_pair(_212327, 2413 ^ [_211624, _211809, _211990, _212325, _212327]), _211624))], (2417 ^ _127218) ^ [] : [-(in(ordered_pair(2413 ^ [_211624, _211809, _211990, _212325, _212327], _212325), _211809))]]], (2419 ^ _127218) ^ [_212710, _212712] : [-(in(ordered_pair(_212712, _212710), _211990)), 2420 ^ _127218 : [(2421 ^ _127218) ^ [_212823] : [in(ordered_pair(_212712, _212823), _211624), in(ordered_pair(_212823, _212710), _211809)]]]]]]]]]]], (2452 ^ _127218) ^ [_214126] : [relation(_214126), 2455 ^ _127218 : [(2482 ^ _127218) ^ [_215161] : [2486 ^ _127218 : [(2487 ^ _127218) ^ [] : [-(in(2483 ^ [_214126, _215161], _215161))], (2489 ^ _127218) ^ [] : [-(in(2484 ^ [_214126, _215161], _215161))], (2491 ^ _127218) ^ [] : [-(in(2485 ^ [_214126, _215161], _215161))], (2493 ^ _127218) ^ [] : [-(in(ordered_pair(2483 ^ [_214126, _215161], 2484 ^ [_214126, _215161]), _214126))], (2495 ^ _127218) ^ [] : [-(in(ordered_pair(2484 ^ [_214126, _215161], 2485 ^ [_214126, _215161]), _214126))], (2497 ^ _127218) ^ [] : [in(ordered_pair(2483 ^ [_214126, _215161], 2485 ^ [_214126, _215161]), _214126)]], -(is_transitive_in(_214126, _215161))], (2456 ^ _127218) ^ [_214340] : [is_transitive_in(_214126, _214340), 2459 ^ _127218 : [(2460 ^ _127218) ^ [_214550, _214552, _214554] : [-(in(ordered_pair(_214554, _214550), _214126)), in(_214554, _214340), in(_214552, _214340), in(_214550, _214340), in(ordered_pair(_214554, _214552), _214126), in(ordered_pair(_214552, _214550), _214126)]]]]], (2501 ^ _127218) ^ [_216185, _216187] : [element(_216185, powerset(powerset(_216187))), 2504 ^ _127218 : [(2505 ^ _127218) ^ [_216365] : [element(_216365, powerset(powerset(_216187))), 2508 ^ _127218 : [(2529 ^ _127218) ^ [] : [-(_216365 = complements_of_subsets(_216187, _216185)), 2531 ^ _127218 : [(2532 ^ _127218) ^ [] : [-(element(2530 ^ [_216185, _216187, _216365], powerset(_216187)))], (2534 ^ _127218) ^ [] : [2535 ^ _127218 : [(2536 ^ _127218) ^ [] : [-(in(2530 ^ [_216185, _216187, _216365], _216365))], (2538 ^ _127218) ^ [] : [in(subset_complement(_216187, 2530 ^ [_216185, _216187, _216365]), _216185)]], 2539 ^ _127218 : [(2540 ^ _127218) ^ [] : [-(in(subset_complement(_216187, 2530 ^ [_216185, _216187, _216365]), _216185))], (2542 ^ _127218) ^ [] : [in(2530 ^ [_216185, _216187, _216365], _216365)]]]]], (2509 ^ _127218) ^ [] : [_216365 = complements_of_subsets(_216187, _216185), 2512 ^ _127218 : [(2513 ^ _127218) ^ [_216653] : [element(_216653, powerset(_216187)), 2516 ^ _127218 : [(2517 ^ _127218) ^ [] : [in(_216653, _216365), -(in(subset_complement(_216187, _216653), _216185))], (2523 ^ _127218) ^ [] : [in(subset_complement(_216187, _216653), _216185), -(in(_216653, _216365))]]]]]]]]], (2546 ^ _127218) ^ [_217776, _217778] : [proper_subset(_217778, _217776), 2549 ^ _127218 : [(2550 ^ _127218) ^ [] : [-(subset(_217778, _217776))], (2552 ^ _127218) ^ [] : [_217778 = _217776]]], (2554 ^ _127218) ^ [_218014, _218016] : [-(proper_subset(_218016, _218014)), subset(_218016, _218014), -(_218016 = _218014)], (2564 ^ _127218) ^ [_218304] : [relation(_218304), function(_218304), one_to_one(_218304), -(function_inverse(_218304) = relation_inverse(_218304))], (2578 ^ _127218) ^ [_218668] : [relation(_218668), 2581 ^ _127218 : [(2582 ^ _127218) ^ [] : [reflexive(_218668), -(is_reflexive_in(_218668, relation_field(_218668)))], (2588 ^ _127218) ^ [] : [is_reflexive_in(_218668, relation_field(_218668)), -(reflexive(_218668))]]], (2594 ^ _127218) ^ [] : [true___, -(true___)], (2600 ^ _127218) ^ [] : [true___, -(true___)], (2606 ^ _127218) ^ [] : [true___, -(true___)], (2612 ^ _127218) ^ [] : [true___, -(true___)], (2618 ^ _127218) ^ [] : [true___, -(true___)], (2624 ^ _127218) ^ [] : [true___, -(true___)], (2630 ^ _127218) ^ [] : [true___, -(true___)], (2636 ^ _127218) ^ [] : [true___, -(true___)], (2642 ^ _127218) ^ [] : [true___, -(true___)], (2648 ^ _127218) ^ [] : [true___, -(true___)], (2654 ^ _127218) ^ [_220289] : [2661 ^ _127218 : [(2662 ^ _127218) ^ [] : [-(relation(function_inverse(_220289)))], (2664 ^ _127218) ^ [] : [-(function(function_inverse(_220289)))]], relation(_220289), function(_220289)], (2666 ^ _127218) ^ [] : [true___, -(true___)], (2672 ^ _127218) ^ [_220741] : [-(element(cast_to_subset(_220741), powerset(_220741)))], (2674 ^ _127218) ^ [] : [true___, -(true___)], (2680 ^ _127218) ^ [_220971, _220973] : [relation(_220973), -(relation(relation_restriction(_220973, _220971)))], (2686 ^ _127218) ^ [] : [true___, -(true___)], (2692 ^ _127218) ^ [] : [true___, -(true___)], (2698 ^ _127218) ^ [] : [true___, -(true___)], (2704 ^ _127218) ^ [_221540, _221542] : [element(_221540, powerset(_221542)), -(element(subset_complement(_221542, _221540), powerset(_221542)))], (2710 ^ _127218) ^ [] : [true___, -(true___)], (2716 ^ _127218) ^ [] : [true___, -(true___)], (2722 ^ _127218) ^ [_221988] : [relation(_221988), -(relation(relation_inverse(_221988)))], (2728 ^ _127218) ^ [] : [true___, -(true___)], (2734 ^ _127218) ^ [] : [true___, -(true___)], (2740 ^ _127218) ^ [_222430, _222432] : [-(relation(relation_composition(_222432, _222430))), relation(_222432), relation(_222430)], (2750 ^ _127218) ^ [_222729, _222731] : [element(_222729, powerset(powerset(_222731))), -(element(union_of_subsets(_222731, _222729), powerset(_222731)))], (2756 ^ _127218) ^ [_222928] : [-(relation(identity_relation(_222928)))], (2758 ^ _127218) ^ [_223036, _223038] : [element(_223036, powerset(powerset(_223038))), -(element(meet_of_subsets(_223038, _223036), powerset(_223038)))], (2764 ^ _127218) ^ [_223278, _223280, _223282] : [-(element(subset_difference(_223282, _223280, _223278), powerset(_223282))), element(_223280, powerset(_223282)), element(_223278, powerset(_223282))], (2774 ^ _127218) ^ [_223607, _223609] : [relation(_223609), -(relation(relation_dom_restriction(_223609, _223607)))], (2780 ^ _127218) ^ [_223819, _223821] : [element(_223819, powerset(powerset(_223821))), -(element(complements_of_subsets(_223821, _223819), powerset(powerset(_223821))))], (2786 ^ _127218) ^ [_224051, _224053] : [relation(_224051), -(relation(relation_rng_restriction(_224053, _224051)))], (2792 ^ _127218) ^ [] : [true___, -(true___)], (2798 ^ _127218) ^ [] : [true___, -(true___)], (2805 ^ _127218) ^ [_224511] : [-(element(2803 ^ [_224511], _224511))], (2807 ^ _127218) ^ [_224623, _224625] : [2814 ^ _127218 : [(2815 ^ _127218) ^ [] : [-(empty(relation_composition(_224623, _224625)))], (2817 ^ _127218) ^ [] : [-(relation(relation_composition(_224623, _224625)))]], empty(_224625), relation(_224623)], (2819 ^ _127218) ^ [_224987] : [empty(_224987), 2822 ^ _127218 : [(2823 ^ _127218) ^ [] : [-(empty(relation_inverse(_224987)))], (2825 ^ _127218) ^ [] : [-(relation(relation_inverse(_224987)))]]], (2827 ^ _127218) ^ [] : [-(empty(empty_set))], (2829 ^ _127218) ^ [] : [-(relation(empty_set))], (2831 ^ _127218) ^ [] : [-(relation_empty_yielding(empty_set))], (2833 ^ _127218) ^ [_225429, _225431] : [2840 ^ _127218 : [(2841 ^ _127218) ^ [] : [-(relation(relation_dom_restriction(_225431, _225429)))], (2843 ^ _127218) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_225431, _225429)))]], relation(_225431), relation_empty_yielding(_225431)], (2845 ^ _127218) ^ [_225807, _225809] : [2860 ^ _127218 : [(2861 ^ _127218) ^ [] : [-(relation(relation_composition(_225809, _225807)))], (2863 ^ _127218) ^ [] : [-(function(relation_composition(_225809, _225807)))]], relation(_225809), function(_225809), relation(_225807), function(_225807)], (2865 ^ _127218) ^ [_226329] : [empty(succ(_226329))], (2867 ^ _127218) ^ [_226437, _226439] : [-(relation(set_intersection2(_226439, _226437))), relation(_226439), relation(_226437)], (2877 ^ _127218) ^ [_226706] : [empty(powerset(_226706))], (2879 ^ _127218) ^ [] : [-(empty(empty_set))], (2881 ^ _127218) ^ [_226851, _226853] : [empty(ordered_pair(_226853, _226851))], (2883 ^ _127218) ^ [_226953] : [-(relation(identity_relation(_226953)))], (2885 ^ _127218) ^ [_226998] : [-(function(identity_relation(_226998)))], (2887 ^ _127218) ^ [] : [-(relation(empty_set))], (2889 ^ _127218) ^ [] : [-(relation_empty_yielding(empty_set))], (2891 ^ _127218) ^ [] : [-(function(empty_set))], (2893 ^ _127218) ^ [] : [-(one_to_one(empty_set))], (2895 ^ _127218) ^ [] : [-(empty(empty_set))], (2897 ^ _127218) ^ [] : [-(epsilon_transitive(empty_set))], (2899 ^ _127218) ^ [] : [-(epsilon_connected(empty_set))], (2901 ^ _127218) ^ [] : [-(ordinal(empty_set))], (2903 ^ _127218) ^ [_227546, _227548] : [-(relation(set_union2(_227548, _227546))), relation(_227548), relation(_227546)], (2913 ^ _127218) ^ [_227815] : [empty(singleton(_227815))], (2915 ^ _127218) ^ [_227923, _227925] : [-(empty(_227925)), empty(set_union2(_227925, _227923))], (2921 ^ _127218) ^ [_228125] : [2932 ^ _127218 : [(2933 ^ _127218) ^ [] : [-(relation(relation_inverse(_228125)))], (2935 ^ _127218) ^ [] : [-(function(relation_inverse(_228125)))]], relation(_228125), function(_228125), one_to_one(_228125)], (2937 ^ _127218) ^ [_228556] : [ordinal(_228556), 2940 ^ _127218 : [(2941 ^ _127218) ^ [] : [empty(succ(_228556))], (2943 ^ _127218) ^ [] : [-(epsilon_transitive(succ(_228556)))], (2945 ^ _127218) ^ [] : [-(epsilon_connected(succ(_228556)))], (2947 ^ _127218) ^ [] : [-(ordinal(succ(_228556)))]]], (2949 ^ _127218) ^ [_228984, _228986] : [-(relation(set_difference(_228986, _228984))), relation(_228986), relation(_228984)], (2959 ^ _127218) ^ [_229267, _229269] : [empty(unordered_pair(_229269, _229267))], (2961 ^ _127218) ^ [_229378, _229380] : [-(empty(_229380)), empty(set_union2(_229378, _229380))], (2967 ^ _127218) ^ [_229594, _229596] : [2974 ^ _127218 : [(2975 ^ _127218) ^ [] : [-(relation(relation_dom_restriction(_229596, _229594)))], (2977 ^ _127218) ^ [] : [-(function(relation_dom_restriction(_229596, _229594)))]], relation(_229596), function(_229596)], (2979 ^ _127218) ^ [_229958] : [ordinal(_229958), 2982 ^ _127218 : [(2983 ^ _127218) ^ [] : [-(epsilon_transitive(union(_229958)))], (2985 ^ _127218) ^ [] : [-(epsilon_connected(union(_229958)))], (2987 ^ _127218) ^ [] : [-(ordinal(union(_229958)))]]], (2989 ^ _127218) ^ [] : [-(empty(empty_set))], (2991 ^ _127218) ^ [] : [-(relation(empty_set))], (2993 ^ _127218) ^ [_230419, _230421] : [empty(cartesian_product2(_230421, _230419)), -(empty(_230421)), -(empty(_230419))], (3003 ^ _127218) ^ [_230725, _230727] : [3010 ^ _127218 : [(3011 ^ _127218) ^ [] : [-(relation(relation_rng_restriction(_230727, _230725)))], (3013 ^ _127218) ^ [] : [-(function(relation_rng_restriction(_230727, _230725)))]], relation(_230725), function(_230725)], (3015 ^ _127218) ^ [_231089] : [empty(relation_dom(_231089)), -(empty(_231089)), relation(_231089)], (3025 ^ _127218) ^ [_231366] : [empty(relation_rng(_231366)), -(empty(_231366)), relation(_231366)], (3035 ^ _127218) ^ [_231643] : [empty(_231643), 3038 ^ _127218 : [(3039 ^ _127218) ^ [] : [-(empty(relation_dom(_231643)))], (3041 ^ _127218) ^ [] : [-(relation(relation_dom(_231643)))]]], (3043 ^ _127218) ^ [_231908] : [empty(_231908), 3046 ^ _127218 : [(3047 ^ _127218) ^ [] : [-(empty(relation_rng(_231908)))], (3049 ^ _127218) ^ [] : [-(relation(relation_rng(_231908)))]]], (3051 ^ _127218) ^ [_232187, _232189] : [3058 ^ _127218 : [(3059 ^ _127218) ^ [] : [-(empty(relation_composition(_232189, _232187)))], (3061 ^ _127218) ^ [] : [-(relation(relation_composition(_232189, _232187)))]], empty(_232189), relation(_232187)], (3063 ^ _127218) ^ [_232550, _232552] : [-(set_union2(_232552, _232552) = _232552)], (3065 ^ _127218) ^ [_232647, _232649] : [-(set_intersection2(_232649, _232649) = _232649)], (3067 ^ _127218) ^ [_232759, _232761] : [element(_232759, powerset(_232761)), -(subset_complement(_232761, subset_complement(_232761, _232759)) = _232759)], (3073 ^ _127218) ^ [_232971] : [relation(_232971), -(relation_inverse(relation_inverse(_232971)) = _232971)], (3079 ^ _127218) ^ [_233181, _233183] : [element(_233181, powerset(powerset(_233183))), -(complements_of_subsets(_233183, complements_of_subsets(_233183, _233181)) = _233181)], (3085 ^ _127218) ^ [_233395, _233397] : [proper_subset(_233397, _233397)], (3087 ^ _127218) ^ [_233490] : [relation(_233490), 3090 ^ _127218 : [(3101 ^ _127218) ^ [] : [3103 ^ _127218 : [(3104 ^ _127218) ^ [] : [-(in(3102 ^ [_233490], relation_field(_233490)))], (3106 ^ _127218) ^ [] : [in(ordered_pair(3102 ^ [_233490], 3102 ^ [_233490]), _233490)]], -(reflexive(_233490))], (3091 ^ _127218) ^ [] : [reflexive(_233490), 3094 ^ _127218 : [(3095 ^ _127218) ^ [_233734] : [in(_233734, relation_field(_233490)), -(in(ordered_pair(_233734, _233734), _233490))]]]]], (3110 ^ _127218) ^ [_234199] : [singleton(_234199) = empty_set], (3112 ^ _127218) ^ [_234308, _234310] : [in(_234310, _234308), -(set_union2(singleton(_234310), _234308) = _234308)], (3118 ^ _127218) ^ [_234528, _234530] : [disjoint(singleton(_234530), _234528), in(_234530, _234528)], (3124 ^ _127218) ^ [_234741, _234743] : [-(in(_234743, _234741)), -(disjoint(singleton(_234743), _234741))], (3130 ^ _127218) ^ [_234944] : [relation(_234944), 3133 ^ _127218 : [(3148 ^ _127218) ^ [] : [3152 ^ _127218 : [(3153 ^ _127218) ^ [] : [-(in(ordered_pair(3149 ^ [_234944], 3150 ^ [_234944]), _234944))], (3155 ^ _127218) ^ [] : [-(in(ordered_pair(3150 ^ [_234944], 3151 ^ [_234944]), _234944))], (3157 ^ _127218) ^ [] : [in(ordered_pair(3149 ^ [_234944], 3151 ^ [_234944]), _234944)]], -(transitive(_234944))], (3134 ^ _127218) ^ [] : [transitive(_234944), 3137 ^ _127218 : [(3138 ^ _127218) ^ [_235236, _235238, _235240] : [-(in(ordered_pair(_235240, _235236), _234944)), in(ordered_pair(_235240, _235238), _234944), in(ordered_pair(_235238, _235236), _234944)]]]]], (3161 ^ _127218) ^ [_236143, _236145] : [subset(singleton(_236145), _236143), -(in(_236145, _236143))], (3167 ^ _127218) ^ [_236309, _236311] : [in(_236311, _236309), -(subset(singleton(_236311), _236309))], (3173 ^ _127218) ^ [_236554, _236556] : [set_difference(_236556, _236554) = empty_set, -(subset(_236556, _236554))], (3179 ^ _127218) ^ [_236722, _236724] : [subset(_236724, _236722), -(set_difference(_236724, _236722) = empty_set)], (3185 ^ _127218) ^ [_236940, _236942] : [element(_236940, powerset(_236942)), 3188 ^ _127218 : [(3189 ^ _127218) ^ [_237081] : [in(_237081, _236940), -(in(_237081, _236942))]]], (3195 ^ _127218) ^ [_237292] : [relation(_237292), 3198 ^ _127218 : [(3213 ^ _127218) ^ [] : [3216 ^ _127218 : [(3217 ^ _127218) ^ [] : [-(in(ordered_pair(3214 ^ [_237292], 3215 ^ [_237292]), _237292))], (3219 ^ _127218) ^ [] : [-(in(ordered_pair(3215 ^ [_237292], 3214 ^ [_237292]), _237292))], (3221 ^ _127218) ^ [] : [3214 ^ [_237292] = 3215 ^ [_237292]]], -(antisymmetric(_237292))], (3199 ^ _127218) ^ [] : [antisymmetric(_237292), 3202 ^ _127218 : [(3203 ^ _127218) ^ [_237562, _237564] : [-(_237564 = _237562), in(ordered_pair(_237564, _237562), _237292), in(ordered_pair(_237562, _237564), _237292)]]]]], (3225 ^ _127218) ^ [_238342, _238344, _238346] : [subset(_238346, _238344), -(in(_238342, _238346)), -(subset(_238346, set_difference(_238344, singleton(_238342))))], (3235 ^ _127218) ^ [_238648] : [relation(_238648), 3238 ^ _127218 : [(3261 ^ _127218) ^ [] : [3264 ^ _127218 : [(3265 ^ _127218) ^ [] : [-(in(3262 ^ [_238648], relation_field(_238648)))], (3267 ^ _127218) ^ [] : [-(in(3263 ^ [_238648], relation_field(_238648)))], (3269 ^ _127218) ^ [] : [3262 ^ [_238648] = 3263 ^ [_238648]], (3271 ^ _127218) ^ [] : [in(ordered_pair(3262 ^ [_238648], 3263 ^ [_238648]), _238648)], (3273 ^ _127218) ^ [] : [in(ordered_pair(3263 ^ [_238648], 3262 ^ [_238648]), _238648)]], -(connected(_238648))], (3239 ^ _127218) ^ [] : [connected(_238648), 3242 ^ _127218 : [(3243 ^ _127218) ^ [_238942, _238944] : [in(_238944, relation_field(_238648)), in(_238942, relation_field(_238648)), -(_238944 = _238942), -(in(ordered_pair(_238944, _238942), _238648)), -(in(ordered_pair(_238942, _238944), _238648))]]]]], (3287 ^ _127218) ^ [_240394, _240396] : [3288 ^ _127218 : [(3289 ^ _127218) ^ [] : [_240396 = empty_set], (3291 ^ _127218) ^ [] : [_240396 = singleton(_240394)]], -(subset(_240396, singleton(_240394)))], (3277 ^ _127218) ^ [_240134, _240136] : [subset(_240136, singleton(_240134)), -(_240136 = empty_set), -(_240136 = singleton(_240134))], (3295 ^ _127218) ^ [_240688, _240690] : [in(_240690, _240688), -(subset(_240690, union(_240688)))], (3301 ^ _127218) ^ [_240959, _240961, _240963, _240965] : [in(ordered_pair(_240965, _240963), cartesian_product2(_240961, _240959)), 3304 ^ _127218 : [(3305 ^ _127218) ^ [] : [-(in(_240965, _240961))], (3307 ^ _127218) ^ [] : [-(in(_240963, _240959))]]], (3309 ^ _127218) ^ [_241224, _241226, _241228, _241230] : [-(in(ordered_pair(_241230, _241228), cartesian_product2(_241226, _241224))), in(_241230, _241226), in(_241228, _241224)], (3319 ^ _127218) ^ [_241557, _241559] : [3321 ^ _127218 : [(3322 ^ _127218) ^ [] : [-(in(3320 ^ [_241557, _241559], _241559))], (3324 ^ _127218) ^ [] : [in(3320 ^ [_241557, _241559], _241557)]], -(element(_241559, powerset(_241557)))], (3328 ^ _127218) ^ [_241930, _241932, _241934] : [relation(_241930), function(_241930), 3335 ^ _127218 : [(3336 ^ _127218) ^ [] : [in(_241932, relation_dom(relation_dom_restriction(_241930, _241934))), 3339 ^ _127218 : [(3340 ^ _127218) ^ [] : [-(in(_241932, relation_dom(_241930)))], (3342 ^ _127218) ^ [] : [-(in(_241932, _241934))]]], (3344 ^ _127218) ^ [] : [-(in(_241932, relation_dom(relation_dom_restriction(_241930, _241934)))), in(_241932, relation_dom(_241930)), in(_241932, _241934)]]], (3355 ^ _127218) ^ [] : [-(relation(3353 ^ []))], (3357 ^ _127218) ^ [] : [-(function(3353 ^ []))], (3360 ^ _127218) ^ [] : [-(epsilon_transitive(3358 ^ []))], (3362 ^ _127218) ^ [] : [-(epsilon_connected(3358 ^ []))], (3364 ^ _127218) ^ [] : [-(ordinal(3358 ^ []))], (3367 ^ _127218) ^ [] : [-(empty(3365 ^ []))], (3369 ^ _127218) ^ [] : [-(relation(3365 ^ []))], (3371 ^ _127218) ^ [_243175] : [-(empty(_243175)), 3375 ^ _127218 : [(3376 ^ _127218) ^ [] : [-(element(3374 ^ [_243175], powerset(_243175)))], (3378 ^ _127218) ^ [] : [empty(3374 ^ [_243175])]]], (3381 ^ _127218) ^ [] : [-(empty(3379 ^ []))], (3384 ^ _127218) ^ [] : [-(relation(3382 ^ []))], (3386 ^ _127218) ^ [] : [-(empty(3382 ^ []))], (3388 ^ _127218) ^ [] : [-(function(3382 ^ []))], (3391 ^ _127218) ^ [] : [-(relation(3389 ^ []))], (3393 ^ _127218) ^ [] : [-(function(3389 ^ []))], (3395 ^ _127218) ^ [] : [-(one_to_one(3389 ^ []))], (3397 ^ _127218) ^ [] : [-(empty(3389 ^ []))], (3399 ^ _127218) ^ [] : [-(epsilon_transitive(3389 ^ []))], (3401 ^ _127218) ^ [] : [-(epsilon_connected(3389 ^ []))], (3403 ^ _127218) ^ [] : [-(ordinal(3389 ^ []))], (3406 ^ _127218) ^ [] : [empty(3404 ^ [])], (3408 ^ _127218) ^ [] : [-(relation(3404 ^ []))], (3411 ^ _127218) ^ [_244455] : [-(element(3409 ^ [_244455], powerset(_244455)))], (3413 ^ _127218) ^ [_244506] : [-(empty(3409 ^ [_244506]))], (3416 ^ _127218) ^ [] : [empty(3414 ^ [])], (3419 ^ _127218) ^ [] : [-(relation(3417 ^ []))], (3421 ^ _127218) ^ [] : [-(function(3417 ^ []))], (3423 ^ _127218) ^ [] : [-(one_to_one(3417 ^ []))], (3426 ^ _127218) ^ [] : [empty(3424 ^ [])], (3428 ^ _127218) ^ [] : [-(epsilon_transitive(3424 ^ []))], (3430 ^ _127218) ^ [] : [-(epsilon_connected(3424 ^ []))], (3432 ^ _127218) ^ [] : [-(ordinal(3424 ^ []))], (3435 ^ _127218) ^ [] : [-(relation(3433 ^ []))], (3437 ^ _127218) ^ [] : [-(relation_empty_yielding(3433 ^ []))], (3440 ^ _127218) ^ [] : [-(relation(3438 ^ []))], (3442 ^ _127218) ^ [] : [-(relation_empty_yielding(3438 ^ []))], (3444 ^ _127218) ^ [] : [-(function(3438 ^ []))], (3446 ^ _127218) ^ [_245546, _245548] : [element(_245546, powerset(powerset(_245548))), -(union_of_subsets(_245548, _245546) = union(_245546))], (3452 ^ _127218) ^ [_245774, _245776] : [element(_245774, powerset(powerset(_245776))), -(meet_of_subsets(_245776, _245774) = set_meet(_245774))], (3458 ^ _127218) ^ [_246016, _246018, _246020] : [-(subset_difference(_246020, _246018, _246016) = set_difference(_246018, _246016)), element(_246018, powerset(_246020)), element(_246016, powerset(_246020))], (3468 ^ _127218) ^ [_246347, _246349] : [ordinal(_246349), ordinal(_246347), 3475 ^ _127218 : [(3476 ^ _127218) ^ [] : [ordinal_subset(_246349, _246347), -(subset(_246349, _246347))], (3482 ^ _127218) ^ [] : [subset(_246349, _246347), -(ordinal_subset(_246349, _246347))]]], (3488 ^ _127218) ^ [_246894, _246896] : [-(ordinal_subset(_246896, _246896)), ordinal(_246896), ordinal(_246894)], (3498 ^ _127218) ^ [_247174, _247176] : [-(subset(_247176, _247176))], (3500 ^ _127218) ^ [_247283, _247285] : [disjoint(_247285, _247283), -(disjoint(_247283, _247285))], (3506 ^ _127218) ^ [_247550, _247552, _247554, _247556] : [in(ordered_pair(_247556, _247554), cartesian_product2(_247552, _247550)), 3509 ^ _127218 : [(3510 ^ _127218) ^ [] : [-(in(_247556, _247552))], (3512 ^ _127218) ^ [] : [-(in(_247554, _247550))]]], (3514 ^ _127218) ^ [_247815, _247817, _247819, _247821] : [-(in(ordered_pair(_247821, _247819), cartesian_product2(_247817, _247815))), in(_247821, _247817), in(_247819, _247815)], (3524 ^ _127218) ^ [_248119] : [-(in(_248119, succ(_248119)))], (3526 ^ _127218) ^ [_248256, _248258, _248260, _248262] : [unordered_pair(_248262, _248260) = unordered_pair(_248258, _248256), -(_248262 = _248258), -(_248262 = _248256)], (3536 ^ _127218) ^ [_248606, _248608, _248610] : [relation(_248606), 3539 ^ _127218 : [(3540 ^ _127218) ^ [] : [in(_248610, relation_rng(relation_rng_restriction(_248608, _248606))), 3543 ^ _127218 : [(3544 ^ _127218) ^ [] : [-(in(_248610, _248608))], (3546 ^ _127218) ^ [] : [-(in(_248610, relation_rng(_248606)))]]], (3548 ^ _127218) ^ [] : [-(in(_248610, relation_rng(relation_rng_restriction(_248608, _248606)))), in(_248610, _248608), in(_248610, relation_rng(_248606))]]], (3558 ^ _127218) ^ [_249265, _249267] : [relation(_249265), -(subset(relation_rng(relation_rng_restriction(_249267, _249265)), _249267))], (3564 ^ _127218) ^ [_249483, _249485] : [relation(_249483), -(subset(relation_rng_restriction(_249485, _249483), _249483))], (3570 ^ _127218) ^ [_249697, _249699] : [relation(_249697), -(subset(relation_rng(relation_rng_restriction(_249699, _249697)), relation_rng(_249697)))], (3576 ^ _127218) ^ [_249933, _249935, _249937] : [subset(_249937, _249935), 3579 ^ _127218 : [(3580 ^ _127218) ^ [] : [-(subset(cartesian_product2(_249937, _249933), cartesian_product2(_249935, _249933)))], (3582 ^ _127218) ^ [] : [-(subset(cartesian_product2(_249933, _249937), cartesian_product2(_249933, _249935)))]]], (3584 ^ _127218) ^ [_250250, _250252] : [relation(_250250), -(relation_rng(relation_rng_restriction(_250252, _250250)) = set_intersection2(relation_rng(_250250), _250252))], (3590 ^ _127218) ^ [_250506, _250508, _250510, _250512] : [-(subset(cartesian_product2(_250512, _250508), cartesian_product2(_250510, _250506))), subset(_250512, _250510), subset(_250508, _250506)], (3600 ^ _127218) ^ [_250837, _250839] : [subset(_250839, _250837), -(set_union2(_250839, _250837) = _250837)], (3607 ^ _127218) ^ [_251159] : [-(in(_251159, 3605 ^ [_251159]))], (3609 ^ _127218) ^ [_251271, _251273, _251275] : [-(in(_251271, 3605 ^ [_251275])), in(_251273, 3605 ^ [_251275]), subset(_251271, _251273)], (3619 ^ _127218) ^ [_251586, _251588] : [in(_251586, 3605 ^ [_251588]), -(in(powerset(_251586), 3605 ^ [_251588]))], (3625 ^ _127218) ^ [_251786, _251788] : [subset(_251786, 3605 ^ [_251788]), -(are_equipotent(_251786, 3605 ^ [_251788])), -(in(_251786, 3605 ^ [_251788]))], (3635 ^ _127218) ^ [_252140, _252142, _252144] : [relation(_252140), -(relation_dom_restriction(relation_rng_restriction(_252144, _252140), _252142) = relation_rng_restriction(_252144, relation_dom_restriction(_252140, _252142)))], (3641 ^ _127218) ^ [_252392, _252394, _252396] : [relation(_252392), 3644 ^ _127218 : [(3645 ^ _127218) ^ [] : [in(_252396, relation_image(_252392, _252394)), 3649 ^ _127218 : [(3650 ^ _127218) ^ [] : [-(in(3648 ^ [_252392, _252394, _252396], relation_dom(_252392)))], (3652 ^ _127218) ^ [] : [-(in(ordered_pair(3648 ^ [_252392, _252394, _252396], _252396), _252392))], (3654 ^ _127218) ^ [] : [-(in(3648 ^ [_252392, _252394, _252396], _252394))]]], (3656 ^ _127218) ^ [] : [-(in(_252396, relation_image(_252392, _252394))), 3657 ^ _127218 : [(3658 ^ _127218) ^ [_252993] : [in(_252993, relation_dom(_252392)), in(ordered_pair(_252993, _252396), _252392), in(_252993, _252394)]]]]], (3670 ^ _127218) ^ [_253390, _253392] : [relation(_253390), -(subset(relation_image(_253390, _253392), relation_rng(_253390)))], (3676 ^ _127218) ^ [_253608, _253610] : [-(subset(relation_image(_253608, relation_inverse_image(_253608, _253610)), _253610)), relation(_253608), function(_253608)], (3686 ^ _127218) ^ [_253915, _253917] : [relation(_253915), -(relation_image(_253915, _253917) = relation_image(_253915, set_intersection2(relation_dom(_253915), _253917)))], (3692 ^ _127218) ^ [_254145, _254147] : [relation(_254145), subset(_254147, relation_dom(_254145)), -(subset(_254147, relation_inverse_image(_254145, relation_image(_254145, _254147))))], (3702 ^ _127218) ^ [_254444] : [relation(_254444), -(relation_image(_254444, relation_dom(_254444)) = relation_rng(_254444))], (3708 ^ _127218) ^ [_254660, _254662] : [relation(_254660), function(_254660), subset(_254662, relation_rng(_254660)), -(relation_image(_254660, relation_inverse_image(_254660, _254662)) = _254662)], (3722 ^ _127218) ^ [_255048] : [relation(_255048), 3725 ^ _127218 : [(3726 ^ _127218) ^ [_255188] : [relation(_255188), -(relation_rng(relation_composition(_255048, _255188)) = relation_image(_255188, relation_rng(_255048)))]]], (3732 ^ _127218) ^ [_255437, _255439, _255441] : [relation(_255437), 3735 ^ _127218 : [(3736 ^ _127218) ^ [] : [in(_255441, relation_inverse_image(_255437, _255439)), 3740 ^ _127218 : [(3741 ^ _127218) ^ [] : [-(in(3739 ^ [_255437, _255439, _255441], relation_rng(_255437)))], (3743 ^ _127218) ^ [] : [-(in(ordered_pair(_255441, 3739 ^ [_255437, _255439, _255441]), _255437))], (3745 ^ _127218) ^ [] : [-(in(3739 ^ [_255437, _255439, _255441], _255439))]]], (3747 ^ _127218) ^ [] : [-(in(_255441, relation_inverse_image(_255437, _255439))), 3748 ^ _127218 : [(3749 ^ _127218) ^ [_256038] : [in(_256038, relation_rng(_255437)), in(ordered_pair(_255441, _256038), _255437), in(_256038, _255439)]]]]], (3761 ^ _127218) ^ [_256435, _256437] : [relation(_256435), -(subset(relation_inverse_image(_256435, _256437), relation_dom(_256435)))], (3767 ^ _127218) ^ [_256667, _256669, _256671] : [relation(_256667), 3770 ^ _127218 : [(3771 ^ _127218) ^ [] : [in(_256671, relation_restriction(_256667, _256669)), 3774 ^ _127218 : [(3775 ^ _127218) ^ [] : [-(in(_256671, _256667))], (3777 ^ _127218) ^ [] : [-(in(_256671, cartesian_product2(_256669, _256669)))]]], (3779 ^ _127218) ^ [] : [-(in(_256671, relation_restriction(_256667, _256669))), in(_256671, _256667), in(_256671, cartesian_product2(_256669, _256669))]]], (3789 ^ _127218) ^ [_257323, _257325] : [relation(_257323), -(_257325 = empty_set), subset(_257325, relation_rng(_257323)), relation_inverse_image(_257323, _257325) = empty_set], (3803 ^ _127218) ^ [_257737, _257739, _257741] : [relation(_257737), subset(_257741, _257739), -(subset(relation_inverse_image(_257737, _257741), relation_inverse_image(_257737, _257739)))], (3813 ^ _127218) ^ [_258056, _258058] : [relation(_258056), -(relation_restriction(_258056, _258058) = relation_dom_restriction(relation_rng_restriction(_258058, _258056), _258058))], (3819 ^ _127218) ^ [_258267, _258269] : [-(subset(set_intersection2(_258269, _258267), _258269))], (3821 ^ _127218) ^ [_258379, _258381] : [relation(_258379), -(relation_restriction(_258379, _258381) = relation_rng_restriction(_258381, relation_dom_restriction(_258379, _258381)))], (3827 ^ _127218) ^ [_258619, _258621, _258623] : [-(subset(_258623, set_intersection2(_258621, _258619))), subset(_258623, _258621), subset(_258623, _258619)], (3837 ^ _127218) ^ [_258905] : [-(set_union2(_258905, empty_set) = _258905)], (3839 ^ _127218) ^ [_259015, _259017] : [in(_259017, _259015), -(element(_259017, _259015))], (3845 ^ _127218) ^ [_259239, _259241, _259243] : [-(subset(_259243, _259239)), subset(_259243, _259241), subset(_259241, _259239)], (3855 ^ _127218) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (3857 ^ _127218) ^ [_259615, _259617, _259619] : [relation(_259615), in(ordered_pair(_259619, _259617), _259615), 3864 ^ _127218 : [(3865 ^ _127218) ^ [] : [-(in(_259619, relation_dom(_259615)))], (3867 ^ _127218) ^ [] : [-(in(_259617, relation_rng(_259615)))]]], (3869 ^ _127218) ^ [_260013, _260015] : [relation(_260013), function(_260013), 3876 ^ _127218 : [(3877 ^ _127218) ^ [_260263] : [relation(_260263), function(_260263), 3884 ^ _127218 : [(3885 ^ _127218) ^ [] : [in(_260015, relation_dom(relation_composition(_260263, _260013))), 3888 ^ _127218 : [(3889 ^ _127218) ^ [] : [-(in(_260015, relation_dom(_260263)))], (3891 ^ _127218) ^ [] : [-(in(apply(_260263, _260015), relation_dom(_260013)))]]], (3893 ^ _127218) ^ [] : [-(in(_260015, relation_dom(relation_composition(_260263, _260013)))), in(_260015, relation_dom(_260263)), in(apply(_260263, _260015), relation_dom(_260013))]]]]], (3903 ^ _127218) ^ [_261027] : [epsilon_transitive(_261027), 3906 ^ _127218 : [(3907 ^ _127218) ^ [_261163] : [ordinal(_261163), proper_subset(_261027, _261163), -(in(_261027, _261163))]]], (3917 ^ _127218) ^ [_261453] : [relation(_261453), -(subset(_261453, cartesian_product2(relation_dom(_261453), relation_rng(_261453))))], (3923 ^ _127218) ^ [_261669, _261671] : [relation(_261669), function(_261669), 3930 ^ _127218 : [(3931 ^ _127218) ^ [_261918] : [relation(_261918), function(_261918), in(_261671, relation_dom(relation_composition(_261918, _261669))), -(apply(relation_composition(_261918, _261669), _261671) = apply(_261669, apply(_261918, _261671)))]]], (3945 ^ _127218) ^ [_262363, _262365] : [relation(_262363), function(_262363), 3952 ^ _127218 : [(3953 ^ _127218) ^ [_262609] : [relation(_262609), function(_262609), in(_262365, relation_dom(_262363)), -(apply(relation_composition(_262363, _262609), _262365) = apply(_262609, apply(_262363, _262365)))]]], (3967 ^ _127218) ^ [_263048, _263050] : [ordinal(_263048), in(_263050, _263048), -(ordinal(_263050))], (3977 ^ _127218) ^ [_263329] : [ordinal(_263329), 3980 ^ _127218 : [(3981 ^ _127218) ^ [_263479] : [ordinal(_263479), -(in(_263329, _263479)), -(_263329 = _263479), -(in(_263479, _263329))]]], (3995 ^ _127218) ^ [_263868] : [relation(_263868), 3998 ^ _127218 : [(3999 ^ _127218) ^ [_264018] : [relation(_264018), subset(_263868, _264018), 4006 ^ _127218 : [(4007 ^ _127218) ^ [] : [-(subset(relation_dom(_263868), relation_dom(_264018)))], (4009 ^ _127218) ^ [] : [-(subset(relation_rng(_263868), relation_rng(_264018)))]]]]], (4011 ^ _127218) ^ [_264427, _264429, _264431] : [subset(_264431, _264429), -(subset(set_intersection2(_264431, _264427), set_intersection2(_264429, _264427)))], (4017 ^ _127218) ^ [_264655, _264657] : [subset(_264657, _264655), -(set_intersection2(_264657, _264655) = _264657)], (4023 ^ _127218) ^ [_264842] : [-(set_intersection2(_264842, empty_set) = empty_set)], (4025 ^ _127218) ^ [_264952, _264954] : [element(_264954, _264952), -(empty(_264952)), -(in(_264954, _264952))], (4035 ^ _127218) ^ [_265250, _265252] : [-(_265252 = _265250), 4039 ^ _127218 : [(4040 ^ _127218) ^ [] : [-(in(4036 ^ [_265250, _265252], _265252))], (4042 ^ _127218) ^ [] : [in(4036 ^ [_265250, _265252], _265250)]], 4043 ^ _127218 : [(4044 ^ _127218) ^ [] : [-(in(4036 ^ [_265250, _265252], _265250))], (4046 ^ _127218) ^ [] : [in(4036 ^ [_265250, _265252], _265252)]]], (4050 ^ _127218) ^ [_265751] : [-(subset(empty_set, _265751))], (4052 ^ _127218) ^ [_265872, _265874, _265876] : [relation(_265872), in(ordered_pair(_265876, _265874), _265872), 4059 ^ _127218 : [(4060 ^ _127218) ^ [] : [-(in(_265876, relation_field(_265872)))], (4062 ^ _127218) ^ [] : [-(in(_265874, relation_field(_265872)))]]], (4064 ^ _127218) ^ [_266256] : [-(ordinal(_266256)), 4066 ^ _127218 : [(4067 ^ _127218) ^ [] : [-(in(4065 ^ [_266256], _266256))], (4069 ^ _127218) ^ [] : [ordinal(4065 ^ [_266256]), subset(4065 ^ [_266256], _266256)]]], (4077 ^ _127218) ^ [_266686, _266688] : [ordinal(_266686), subset(_266688, _266686), -(_266688 = empty_set), 4089 ^ _127218 : [(4090 ^ _127218) ^ [] : [-(ordinal(4088 ^ [_266686, _266688]))], (4092 ^ _127218) ^ [] : [-(in(4088 ^ [_266686, _266688], _266688))], (4094 ^ _127218) ^ [_267238] : [ordinal(_267238), in(_267238, _266688), -(ordinal_subset(4088 ^ [_266686, _266688], _267238))]]], (4104 ^ _127218) ^ [_267566] : [ordinal(_267566), 4107 ^ _127218 : [(4108 ^ _127218) ^ [_267704] : [ordinal(_267704), 4111 ^ _127218 : [(4112 ^ _127218) ^ [] : [in(_267566, _267704), -(ordinal_subset(succ(_267566), _267704))], (4118 ^ _127218) ^ [] : [ordinal_subset(succ(_267566), _267704), -(in(_267566, _267704))]]]]], (4124 ^ _127218) ^ [_268189, _268191, _268193] : [subset(_268193, _268191), -(subset(set_difference(_268193, _268189), set_difference(_268191, _268189)))], (4130 ^ _127218) ^ [_268445, _268447, _268449, _268451] : [ordered_pair(_268451, _268449) = ordered_pair(_268447, _268445), 4133 ^ _127218 : [(4134 ^ _127218) ^ [] : [-(_268451 = _268447)], (4136 ^ _127218) ^ [] : [-(_268449 = _268445)]]], (4138 ^ _127218) ^ [_268758, _268760] : [relation(_268758), function(_268758), 4145 ^ _127218 : [(4146 ^ _127218) ^ [] : [_268758 = identity_relation(_268760), 4149 ^ _127218 : [(4150 ^ _127218) ^ [] : [-(relation_dom(_268758) = _268760)], (4152 ^ _127218) ^ [_269177] : [in(_269177, _268760), -(apply(_268758, _269177) = _269177)]]], (4158 ^ _127218) ^ [] : [-(_268758 = identity_relation(_268760)), relation_dom(_268758) = _268760, 4164 ^ _127218 : [(4165 ^ _127218) ^ [] : [-(in(4163 ^ [_268758, _268760], _268760))], (4167 ^ _127218) ^ [] : [apply(_268758, 4163 ^ [_268758, _268760]) = 4163 ^ [_268758, _268760]]]]]], (4171 ^ _127218) ^ [_269782, _269784] : [in(_269782, _269784), -(apply(identity_relation(_269784), _269782) = _269782)], (4177 ^ _127218) ^ [_269987, _269989] : [-(subset(set_difference(_269989, _269987), _269989))], (4179 ^ _127218) ^ [_270085] : [relation(_270085), 4182 ^ _127218 : [(4183 ^ _127218) ^ [] : [-(relation_rng(_270085) = relation_dom(relation_inverse(_270085)))], (4185 ^ _127218) ^ [] : [-(relation_dom(_270085) = relation_rng(relation_inverse(_270085)))]]], (4187 ^ _127218) ^ [_270413, _270415] : [set_difference(_270415, _270413) = empty_set, -(subset(_270415, _270413))], (4193 ^ _127218) ^ [_270581, _270583] : [subset(_270583, _270581), -(set_difference(_270583, _270581) = empty_set)], (4199 ^ _127218) ^ [_270828, _270830] : [subset(singleton(_270830), _270828), -(in(_270830, _270828))], (4205 ^ _127218) ^ [_270994, _270996] : [in(_270996, _270994), -(subset(singleton(_270996), _270994))], (4211 ^ _127218) ^ [_271253, _271255, _271257] : [subset(unordered_pair(_271257, _271255), _271253), 4214 ^ _127218 : [(4215 ^ _127218) ^ [] : [-(in(_271257, _271253))], (4217 ^ _127218) ^ [] : [-(in(_271255, _271253))]]], (4219 ^ _127218) ^ [_271504, _271506, _271508] : [-(subset(unordered_pair(_271508, _271506), _271504)), in(_271508, _271504), in(_271506, _271504)], (4229 ^ _127218) ^ [_271806, _271808] : [-(set_union2(_271808, set_difference(_271806, _271808)) = set_union2(_271808, _271806))], (4241 ^ _127218) ^ [_272213, _272215] : [4242 ^ _127218 : [(4243 ^ _127218) ^ [] : [_272215 = empty_set], (4245 ^ _127218) ^ [] : [_272215 = singleton(_272213)]], -(subset(_272215, singleton(_272213)))], (4231 ^ _127218) ^ [_271953, _271955] : [subset(_271955, singleton(_271953)), -(_271955 = empty_set), -(_271955 = singleton(_271953))], (4249 ^ _127218) ^ [_272478] : [-(set_difference(_272478, empty_set) = _272478)], (4251 ^ _127218) ^ [_272602, _272604, _272606] : [in(_272606, _272604), in(_272604, _272602), in(_272602, _272606)], (4261 ^ _127218) ^ [_272939, _272941] : [element(_272941, powerset(_272939)), -(subset(_272941, _272939))], (4267 ^ _127218) ^ [_273105, _273107] : [subset(_273107, _273105), -(element(_273107, powerset(_273105)))], (4273 ^ _127218) ^ [_273341, _273343] : [-(disjoint(_273343, _273341)), 4277 ^ _127218 : [(4278 ^ _127218) ^ [] : [-(in(4276 ^ [_273341, _273343], _273343))], (4280 ^ _127218) ^ [] : [-(in(4276 ^ [_273341, _273343], _273341))]]], (4282 ^ _127218) ^ [_273655, _273657] : [disjoint(_273657, _273655), 4283 ^ _127218 : [(4284 ^ _127218) ^ [_273747] : [in(_273747, _273657), in(_273747, _273655)]]], (4292 ^ _127218) ^ [_274004] : [subset(_274004, empty_set), -(_274004 = empty_set)], (4298 ^ _127218) ^ [_274193, _274195] : [-(set_difference(set_union2(_274195, _274193), _274193) = set_difference(_274195, _274193))], (4300 ^ _127218) ^ [_274297] : [ordinal(_274297), 4303 ^ _127218 : [(4318 ^ _127218) ^ [] : [4320 ^ _127218 : [(4321 ^ _127218) ^ [] : [-(ordinal(4319 ^ [_274297]))], (4323 ^ _127218) ^ [] : [-(in(4319 ^ [_274297], _274297))], (4325 ^ _127218) ^ [] : [in(succ(4319 ^ [_274297]), _274297)]], -(being_limit_ordinal(_274297))], (4304 ^ _127218) ^ [] : [being_limit_ordinal(_274297), 4307 ^ _127218 : [(4308 ^ _127218) ^ [_274543] : [ordinal(_274543), in(_274543, _274297), -(in(succ(_274543), _274297))]]]]], (4329 ^ _127218) ^ [_275169] : [ordinal(_275169), 4332 ^ _127218 : [(4333 ^ _127218) ^ [] : [-(being_limit_ordinal(_275169)), 4337 ^ _127218 : [(4338 ^ _127218) ^ [] : [-(ordinal(4336 ^ [_275169]))], (4340 ^ _127218) ^ [] : [-(_275169 = succ(4336 ^ [_275169]))]]], (4342 ^ _127218) ^ [] : [being_limit_ordinal(_275169), 4343 ^ _127218 : [(4344 ^ _127218) ^ [_275640] : [ordinal(_275640), _275169 = succ(_275640)]]]]], (4352 ^ _127218) ^ [_275907, _275909] : [element(_275907, powerset(_275909)), 4355 ^ _127218 : [(4356 ^ _127218) ^ [_276059] : [element(_276059, powerset(_275909)), 4359 ^ _127218 : [(4360 ^ _127218) ^ [] : [disjoint(_275907, _276059), -(subset(_275907, subset_complement(_275909, _276059)))], (4366 ^ _127218) ^ [] : [subset(_275907, subset_complement(_275909, _276059)), -(disjoint(_275907, _276059))]]]]], (4372 ^ _127218) ^ [_276543] : [relation(_276543), 4375 ^ _127218 : [(4376 ^ _127218) ^ [_276680] : [relation(_276680), -(subset(relation_dom(relation_composition(_276543, _276680)), relation_dom(_276543)))]]], (4382 ^ _127218) ^ [_276895] : [relation(_276895), 4385 ^ _127218 : [(4386 ^ _127218) ^ [_277032] : [relation(_277032), -(subset(relation_rng(relation_composition(_276895, _277032)), relation_rng(_277032)))]]], (4392 ^ _127218) ^ [_277261, _277263] : [subset(_277263, _277261), -(_277261 = set_union2(_277263, set_difference(_277261, _277263)))], (4398 ^ _127218) ^ [_277469] : [relation(_277469), 4401 ^ _127218 : [(4402 ^ _127218) ^ [_277616] : [relation(_277616), subset(relation_rng(_277469), relation_dom(_277616)), -(relation_dom(relation_composition(_277469, _277616)) = relation_dom(_277469))]]], (4412 ^ _127218) ^ [_277942, _277944] : [element(_277942, powerset(powerset(_277944))), -(_277942 = empty_set), complements_of_subsets(_277944, _277942) = empty_set], (4422 ^ _127218) ^ [_278259, _278261] : [in(_278261, _278259), -(set_union2(singleton(_278261), _278259) = _278259)], (4428 ^ _127218) ^ [_278465] : [relation(_278465), 4431 ^ _127218 : [(4432 ^ _127218) ^ [_278612] : [relation(_278612), subset(relation_dom(_278465), relation_rng(_278612)), -(relation_rng(relation_composition(_278612, _278465)) = relation_rng(_278465))]]], (4442 ^ _127218) ^ [_278938, _278940] : [element(_278938, powerset(powerset(_278940))), -(_278938 = empty_set), -(subset_difference(_278940, cast_to_subset(_278940), union_of_subsets(_278940, _278938)) = meet_of_subsets(_278940, complements_of_subsets(_278940, _278938)))], (4452 ^ _127218) ^ [_279278, _279280] : [element(_279278, powerset(powerset(_279280))), -(_279278 = empty_set), -(union_of_subsets(_279280, complements_of_subsets(_279280, _279278)) = subset_difference(_279280, cast_to_subset(_279280), meet_of_subsets(_279280, _279278)))], (4462 ^ _127218) ^ [_279603, _279605] : [-(set_difference(_279605, set_difference(_279605, _279603)) = set_intersection2(_279605, _279603))], (4464 ^ _127218) ^ [_279692] : [-(set_difference(empty_set, _279692) = empty_set)], (4466 ^ _127218) ^ [_279816, _279818, _279820] : [-(element(_279820, _279816)), in(_279820, _279818), element(_279818, powerset(_279816))], (4476 ^ _127218) ^ [_280149, _280151] : [-(disjoint(_280151, _280149)), -(in(4479 ^ [_280149, _280151], set_intersection2(_280151, _280149)))], (4483 ^ _127218) ^ [_280384, _280386] : [4484 ^ _127218 : [(4485 ^ _127218) ^ [_280457] : [in(_280457, set_intersection2(_280386, _280384))]], disjoint(_280386, _280384)], (4489 ^ _127218) ^ [_280609] : [-(_280609 = empty_set), 4492 ^ _127218 : [(4493 ^ _127218) ^ [_280769] : [element(_280769, powerset(_280609)), 4496 ^ _127218 : [(4497 ^ _127218) ^ [_280923] : [element(_280923, _280609), -(in(_280923, _280769)), -(in(_280923, subset_complement(_280609, _280769)))]]]]], (4507 ^ _127218) ^ [_281241] : [relation(_281241), function(_281241), one_to_one(_281241), 4518 ^ _127218 : [(4519 ^ _127218) ^ [_281628] : [relation(_281628), function(_281628), 4526 ^ _127218 : [(4557 ^ _127218) ^ [] : [-(_281628 = function_inverse(_281241)), relation_dom(_281628) = relation_rng(_281241), 4566 ^ _127218 : [(4567 ^ _127218) ^ [] : [-(in(4562 ^ [_281241, _281628], relation_rng(_281241)))], (4569 ^ _127218) ^ [] : [-(4563 ^ [_281241, _281628] = apply(_281628, 4562 ^ [_281241, _281628]))], (4571 ^ _127218) ^ [] : [in(4563 ^ [_281241, _281628], relation_dom(_281241)), 4562 ^ [_281241, _281628] = apply(_281241, 4563 ^ [_281241, _281628])]], 4576 ^ _127218 : [(4577 ^ _127218) ^ [] : [-(in(4563 ^ [_281241, _281628], relation_dom(_281241)))], (4579 ^ _127218) ^ [] : [-(4562 ^ [_281241, _281628] = apply(_281241, 4563 ^ [_281241, _281628]))], (4581 ^ _127218) ^ [] : [in(4562 ^ [_281241, _281628], relation_rng(_281241)), 4563 ^ [_281241, _281628] = apply(_281628, 4562 ^ [_281241, _281628])]]], (4527 ^ _127218) ^ [] : [_281628 = function_inverse(_281241), 4530 ^ _127218 : [(4531 ^ _127218) ^ [] : [-(relation_dom(_281628) = relation_rng(_281241))], (4533 ^ _127218) ^ [_282145, _282147] : [4540 ^ _127218 : [(4541 ^ _127218) ^ [] : [-(in(_282145, relation_dom(_281241)))], (4543 ^ _127218) ^ [] : [-(_282147 = apply(_281241, _282145))]], in(_282147, relation_rng(_281241)), _282145 = apply(_281628, _282147)], (4545 ^ _127218) ^ [_282519, _282521] : [4552 ^ _127218 : [(4553 ^ _127218) ^ [] : [-(in(_282521, relation_rng(_281241)))], (4555 ^ _127218) ^ [] : [-(_282519 = apply(_281628, _282521))]], in(_282519, relation_dom(_281241)), _282521 = apply(_281241, _282519)]]]]]]], (4589 ^ _127218) ^ [_284094, _284096, _284098] : [element(_284094, powerset(_284098)), in(_284096, subset_complement(_284098, _284094)), in(_284096, _284094)], (4599 ^ _127218) ^ [_284400] : [relation(_284400), function(_284400), one_to_one(_284400), 4610 ^ _127218 : [(4611 ^ _127218) ^ [] : [-(relation_rng(_284400) = relation_dom(function_inverse(_284400)))], (4613 ^ _127218) ^ [] : [-(relation_dom(_284400) = relation_rng(function_inverse(_284400)))]]], (4615 ^ _127218) ^ [_284853] : [relation(_284853), -(in(ordered_pair(4620 ^ [_284853], 4621 ^ [_284853]), _284853)), -(_284853 = empty_set)], (4627 ^ _127218) ^ [_285271, _285273] : [relation(_285271), function(_285271), 4642 ^ _127218 : [(4643 ^ _127218) ^ [] : [-(_285273 = apply(_285271, apply(function_inverse(_285271), _285273)))], (4645 ^ _127218) ^ [] : [-(_285273 = apply(relation_composition(function_inverse(_285271), _285271), _285273))]], one_to_one(_285271), in(_285273, relation_rng(_285271))], (4647 ^ _127218) ^ [_285869, _285871, _285873] : [in(_285873, _285871), element(_285871, powerset(_285869)), empty(_285869)], (4657 ^ _127218) ^ [_286165] : [relation(_286165), 4660 ^ _127218 : [(4661 ^ _127218) ^ [] : [well_founded_relation(_286165), -(is_well_founded_in(_286165, relation_field(_286165)))], (4667 ^ _127218) ^ [] : [is_well_founded_in(_286165, relation_field(_286165)), -(well_founded_relation(_286165))]]], (4673 ^ _127218) ^ [] : [-(relation_dom(empty_set) = empty_set)], (4675 ^ _127218) ^ [] : [-(relation_rng(empty_set) = empty_set)], (4677 ^ _127218) ^ [_286718, _286720] : [subset(_286720, _286718), proper_subset(_286718, _286720)], (4683 ^ _127218) ^ [_286913] : [relation(_286913), function(_286913), one_to_one(_286913), -(one_to_one(function_inverse(_286913)))], (4697 ^ _127218) ^ [_287299, _287301, _287303] : [-(disjoint(_287303, _287299)), subset(_287303, _287301), disjoint(_287301, _287299)], (4707 ^ _127218) ^ [_287594] : [relation(_287594), 4712 ^ _127218 : [(4713 ^ _127218) ^ [] : [relation_dom(_287594) = empty_set], (4715 ^ _127218) ^ [] : [relation_rng(_287594) = empty_set]], -(_287594 = empty_set)], (4719 ^ _127218) ^ [_287947] : [relation(_287947), 4722 ^ _127218 : [(4723 ^ _127218) ^ [] : [relation_dom(_287947) = empty_set, -(relation_rng(_287947) = empty_set)], (4729 ^ _127218) ^ [] : [relation_rng(_287947) = empty_set, -(relation_dom(_287947) = empty_set)]]], (4735 ^ _127218) ^ [_288430, _288432] : [set_difference(_288432, singleton(_288430)) = _288432, in(_288430, _288432)], (4741 ^ _127218) ^ [_288603, _288605] : [-(in(_288603, _288605)), -(set_difference(_288605, singleton(_288603)) = _288605)], (4747 ^ _127218) ^ [_288828, _288830] : [relation(_288828), function(_288828), 4754 ^ _127218 : [(4755 ^ _127218) ^ [_289095] : [relation(_289095), function(_289095), 4762 ^ _127218 : [(4763 ^ _127218) ^ [] : [_288828 = relation_dom_restriction(_289095, _288830), 4766 ^ _127218 : [(4767 ^ _127218) ^ [] : [-(relation_dom(_288828) = set_intersection2(relation_dom(_289095), _288830))], (4769 ^ _127218) ^ [_289549] : [in(_289549, relation_dom(_288828)), -(apply(_288828, _289549) = apply(_289095, _289549))]]], (4775 ^ _127218) ^ [] : [-(_288828 = relation_dom_restriction(_289095, _288830)), relation_dom(_288828) = set_intersection2(relation_dom(_289095), _288830), 4781 ^ _127218 : [(4782 ^ _127218) ^ [] : [-(in(4780 ^ [_288828, _288830, _289095], relation_dom(_288828)))], (4784 ^ _127218) ^ [] : [apply(_288828, 4780 ^ [_288828, _288830, _289095]) = apply(_289095, 4780 ^ [_288828, _288830, _289095])]]]]]]], (4788 ^ _127218) ^ [_290188] : [-(unordered_pair(_290188, _290188) = singleton(_290188))], (4790 ^ _127218) ^ [_290286] : [empty(_290286), -(_290286 = empty_set)], (4796 ^ _127218) ^ [_290488, _290490] : [subset(singleton(_290490), singleton(_290488)), -(_290490 = _290488)], (4802 ^ _127218) ^ [_290720, _290722, _290724] : [relation(_290720), function(_290720), in(_290722, relation_dom(relation_dom_restriction(_290720, _290724))), -(apply(relation_dom_restriction(_290720, _290724), _290722) = apply(_290720, _290722))], (4816 ^ _127218) ^ [_291139] : [-(relation_dom(identity_relation(_291139)) = _291139)], (4818 ^ _127218) ^ [_291187] : [-(relation_rng(identity_relation(_291187)) = _291187)], (4820 ^ _127218) ^ [_291314, _291316, _291318] : [relation(_291314), function(_291314), in(_291316, _291318), -(apply(relation_dom_restriction(_291314, _291318), _291316) = apply(_291314, _291316))], (4834 ^ _127218) ^ [_291760, _291762, _291764, _291766] : [relation(_291760), 4837 ^ _127218 : [(4838 ^ _127218) ^ [] : [in(ordered_pair(_291766, _291764), relation_composition(identity_relation(_291762), _291760)), 4841 ^ _127218 : [(4842 ^ _127218) ^ [] : [-(in(_291766, _291762))], (4844 ^ _127218) ^ [] : [-(in(ordered_pair(_291766, _291764), _291760))]]], (4846 ^ _127218) ^ [] : [-(in(ordered_pair(_291766, _291764), relation_composition(identity_relation(_291762), _291760))), in(_291766, _291762), in(ordered_pair(_291766, _291764), _291760)]]], (4856 ^ _127218) ^ [_292453, _292455] : [in(_292455, _292453), empty(_292453)], (4862 ^ _127218) ^ [_292660, _292662] : [in(_292662, _292660), 4866 ^ _127218 : [(4867 ^ _127218) ^ [] : [-(in(4865 ^ [_292660, _292662], _292660))], (4869 ^ _127218) ^ [_292951] : [in(_292951, _292660), in(_292951, 4865 ^ [_292660, _292662])]]], (4875 ^ _127218) ^ [_293176, _293178] : [-(subset(_293178, set_union2(_293178, _293176)))], (4877 ^ _127218) ^ [_293317, _293319] : [disjoint(_293319, _293317), -(set_difference(_293319, _293317) = _293319)], (4883 ^ _127218) ^ [_293485, _293487] : [set_difference(_293487, _293485) = _293487, -(disjoint(_293487, _293485))], (4889 ^ _127218) ^ [_293717, _293719, _293721] : [relation(_293717), 4892 ^ _127218 : [(4893 ^ _127218) ^ [] : [in(_293721, relation_dom(relation_dom_restriction(_293717, _293719))), 4896 ^ _127218 : [(4897 ^ _127218) ^ [] : [-(in(_293721, _293719))], (4899 ^ _127218) ^ [] : [-(in(_293721, relation_dom(_293717)))]]], (4901 ^ _127218) ^ [] : [-(in(_293721, relation_dom(relation_dom_restriction(_293717, _293719)))), in(_293721, _293719), in(_293721, relation_dom(_293717))]]], (4911 ^ _127218) ^ [_294376, _294378] : [relation(_294376), -(subset(relation_dom_restriction(_294376, _294378), _294376))], (4917 ^ _127218) ^ [_294590, _294592] : [empty(_294592), -(_294592 = _294590), empty(_294590)], (4927 ^ _127218) ^ [_294901, _294903, _294905] : [relation(_294901), function(_294901), 4934 ^ _127218 : [(4935 ^ _127218) ^ [] : [in(ordered_pair(_294905, _294903), _294901), 4938 ^ _127218 : [(4939 ^ _127218) ^ [] : [-(in(_294905, relation_dom(_294901)))], (4941 ^ _127218) ^ [] : [-(_294903 = apply(_294901, _294905))]]], (4943 ^ _127218) ^ [] : [-(in(ordered_pair(_294905, _294903), _294901)), in(_294905, relation_dom(_294901)), _294903 = apply(_294901, _294905)]]], (4953 ^ _127218) ^ [_295642] : [relation(_295642), 4956 ^ _127218 : [(4957 ^ _127218) ^ [] : [well_orders(_295642, relation_field(_295642)), -(well_ordering(_295642))], (4963 ^ _127218) ^ [] : [well_ordering(_295642), -(well_orders(_295642, relation_field(_295642)))]]], (4969 ^ _127218) ^ [_296101, _296103, _296105] : [-(subset(set_union2(_296105, _296101), _296103)), subset(_296105, _296103), subset(_296101, _296103)], (4979 ^ _127218) ^ [_296430, _296432, _296434] : [singleton(_296434) = unordered_pair(_296432, _296430), -(_296434 = _296432)], (4985 ^ _127218) ^ [_296656, _296658] : [relation(_296656), -(relation_dom(relation_dom_restriction(_296656, _296658)) = set_intersection2(relation_dom(_296656), _296658))], (4991 ^ _127218) ^ [_296884, _296886] : [in(_296886, _296884), -(subset(_296886, union(_296884)))], (4997 ^ _127218) ^ [_297098, _297100] : [relation(_297098), -(relation_dom_restriction(_297098, _297100) = relation_composition(identity_relation(_297100), _297098))], (5003 ^ _127218) ^ [_297322, _297324] : [relation(_297322), -(subset(relation_rng(relation_dom_restriction(_297322, _297324)), relation_rng(_297322)))], (5009 ^ _127218) ^ [_297515] : [-(union(powerset(_297515)) = _297515)], (5047 ^ _127218) ^ [_299036, _299038, _299040] : [singleton(_299040) = unordered_pair(_299038, _299036), -(_299038 = _299036)], (5012 ^ _127218) ^ [_297756] : [-(in(_297756, 5010 ^ [_297756]))], (5014 ^ _127218) ^ [_297868, _297870, _297872] : [-(in(_297868, 5010 ^ [_297872])), in(_297870, 5010 ^ [_297872]), subset(_297868, _297870)], (5024 ^ _127218) ^ [_298183, _298185] : [in(_298183, 5010 ^ [_298185]), 5028 ^ _127218 : [(5029 ^ _127218) ^ [] : [-(in(5027 ^ [_298183, _298185], 5010 ^ [_298185]))], (5031 ^ _127218) ^ [_298495] : [subset(_298495, _298183), -(in(_298495, 5027 ^ [_298183, _298185]))]]], (5037 ^ _127218) ^ [_298702, _298704] : [subset(_298702, 5010 ^ [_298704]), -(are_equipotent(_298702, 5010 ^ [_298704])), -(in(_298702, 5010 ^ [_298704]))]], input).
% 1.02/1.38  ncf('1',plain,[subset(relation_dom(relation_rng_restriction(5052 ^ [], 5053 ^ [])), relation_dom(5053 ^ []))],start(5057 ^ 0)).
% 1.02/1.38  ncf('1.1',plain,[-(subset(relation_dom(relation_rng_restriction(5052 ^ [], 5053 ^ [])), relation_dom(5053 ^ []))), 3999 : relation(5053 ^ []), 3999 : subset(relation_rng_restriction(5052 ^ [], 5053 ^ []), 5053 ^ []), 3999 : relation(relation_rng_restriction(5052 ^ [], 5053 ^ []))],extension(3995 ^ 1,bind([[_263868, _264018], [relation_rng_restriction(5052 ^ [], 5053 ^ []), 5053 ^ []]]))).
% 1.02/1.38  ncf('1.1.1',plain,[-(relation(5053 ^ []))],extension(5055 ^ 4)).
% 1.02/1.38  ncf('1.1.2',plain,[-(subset(relation_rng_restriction(5052 ^ [], 5053 ^ []), 5053 ^ [])), relation(5053 ^ [])],extension(3564 ^ 4,bind([[_249483, _249485], [5053 ^ [], 5052 ^ []]]))).
% 1.02/1.38  ncf('1.1.2.1',plain,[-(relation(5053 ^ []))],lemmata('[1].x')).
% 1.02/1.38  ncf('1.1.3',plain,[-(relation(relation_rng_restriction(5052 ^ [], 5053 ^ []))), relation(5053 ^ [])],extension(2786 ^ 2,bind([[_224051, _224053], [5053 ^ [], 5052 ^ []]]))).
% 1.02/1.38  ncf('1.1.3.1',plain,[-(relation(5053 ^ []))],extension(5055 ^ 3)).
% 1.02/1.38  %-----------------------------------------------------
% 1.02/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------