%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU244+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n016.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 12:02:51 EDT 2023

% Result   : Theorem 42.71s 41.72s
% Output   : Proof 42.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU244+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n016.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 13:52:26 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 42.71/41.72  
% 42.71/41.72  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 42.71/41.72  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.71/41.72  %-----------------------------------------------------
% 42.71/41.72  ncf(matrix, plain, [(4970 ^ _133474) ^ [] : [-(relation(4968 ^ []))], (4972 ^ _133474) ^ [] : [4973 ^ _133474 : [(4974 ^ _133474) ^ [] : [-(well_orders(4968 ^ [], relation_field(4968 ^ [])))], (4976 ^ _133474) ^ [] : [well_ordering(4968 ^ [])]], 4977 ^ _133474 : [(4978 ^ _133474) ^ [] : [-(well_ordering(4968 ^ []))], (4980 ^ _133474) ^ [] : [well_orders(4968 ^ [], relation_field(4968 ^ []))]]], (352 ^ _133474) ^ [_144611, _144613, _144615, _144617, _144619, _144621] : [-(unordered_triple(_144621, _144617, _144613) = unordered_triple(_144619, _144615, _144611)), _144621 = _144619, _144617 = _144615, _144613 = _144611], (366 ^ _133474) ^ [_145099, _145101, _145103, _145105] : [-(fiber(_145105, _145101) = fiber(_145103, _145099)), _145105 = _145103, _145101 = _145099], (376 ^ _133474) ^ [_145430, _145432] : [_145432 = _145430, -(set_meet(_145432) = set_meet(_145430))], (382 ^ _133474) ^ [_145676, _145678, _145680, _145682] : [-(relation_rng_restriction(_145682, _145678) = relation_rng_restriction(_145680, _145676)), _145682 = _145680, _145678 = _145676], (392 ^ _133474) ^ [_146035, _146037, _146039, _146041] : [-(relation_image(_146041, _146037) = relation_image(_146039, _146035)), _146041 = _146039, _146037 = _146035], (402 ^ _133474) ^ [_146394, _146396, _146398, _146400] : [-(relation_inverse_image(_146400, _146396) = relation_inverse_image(_146398, _146394)), _146400 = _146398, _146396 = _146394], (412 ^ _133474) ^ [_146753, _146755, _146757, _146759] : [-(cartesian_product2(_146759, _146755) = cartesian_product2(_146757, _146753)), _146759 = _146757, _146755 = _146753], (422 ^ _133474) ^ [_147084, _147086] : [_147086 = _147084, -(relation_inverse(_147086) = relation_inverse(_147084))], (428 ^ _133474) ^ [_147302, _147304] : [_147304 = _147302, -(succ(_147304) = succ(_147302))], (434 ^ _133474) ^ [_147548, _147550, _147552, _147554] : [-(union_of_subsets(_147554, _147550) = union_of_subsets(_147552, _147548)), _147554 = _147552, _147550 = _147548], (444 ^ _133474) ^ [_147907, _147909, _147911, _147913] : [-(complements_of_subsets(_147913, _147909) = complements_of_subsets(_147911, _147907)), _147913 = _147911, _147909 = _147907], (454 ^ _133474) ^ [_148294, _148296, _148298, _148300, _148302, _148304] : [-(subset_difference(_148304, _148300, _148296) = subset_difference(_148302, _148298, _148294)), _148304 = _148302, _148300 = _148298, _148296 = _148294], (468 ^ _133474) ^ [_148754, _148756] : [_148756 = _148754, -(cast_to_subset(_148756) = cast_to_subset(_148754))], (474 ^ _133474) ^ [_149000, _149002, _149004, _149006] : [-(meet_of_subsets(_149006, _149002) = meet_of_subsets(_149004, _149000)), _149006 = _149004, _149002 = _149000], (484 ^ _133474) ^ [_149359, _149361, _149363, _149365] : [-(subset_complement(_149365, _149361) = subset_complement(_149363, _149359)), _149365 = _149363, _149361 = _149359], (494 ^ _133474) ^ [_149690, _149692] : [_149692 = _149690, -(function_inverse(_149692) = function_inverse(_149690))], (500 ^ _133474) ^ [_149936, _149938, _149940, _149942] : [-(set_difference(_149942, _149938) = set_difference(_149940, _149936)), _149942 = _149940, _149938 = _149936], (510 ^ _133474) ^ [_150295, _150297, _150299, _150301] : [-(ordered_pair(_150301, _150297) = ordered_pair(_150299, _150295)), _150301 = _150299, _150297 = _150295], (520 ^ _133474) ^ [_150654, _150656, _150658, _150660] : [-(apply(_150660, _150656) = apply(_150658, _150654)), _150660 = _150658, _150656 = _150654], (530 ^ _133474) ^ [_151013, _151015, _151017, _151019] : [-(set_union2(_151019, _151015) = set_union2(_151017, _151013)), _151019 = _151017, _151015 = _151013], (540 ^ _133474) ^ [_151372, _151374, _151376, _151378] : [-(set_intersection2(_151378, _151374) = set_intersection2(_151376, _151372)), _151378 = _151376, _151374 = _151372], (550 ^ _133474) ^ [_151703, _151705] : [_151705 = _151703, -(relation_dom(_151705) = relation_dom(_151703))], (556 ^ _133474) ^ [_151949, _151951, _151953, _151955] : [-(relation_composition(_151955, _151951) = relation_composition(_151953, _151949)), _151955 = _151953, _151951 = _151949], (566 ^ _133474) ^ [_152280, _152282] : [_152282 = _152280, -(identity_relation(_152282) = identity_relation(_152280))], (572 ^ _133474) ^ [_152526, _152528, _152530, _152532] : [-(relation_dom_restriction(_152532, _152528) = relation_dom_restriction(_152530, _152526)), _152532 = _152530, _152528 = _152526], (582 ^ _133474) ^ [_152857, _152859] : [_152859 = _152857, -(relation_rng(_152859) = relation_rng(_152857))], (588 ^ _133474) ^ [_153075, _153077] : [_153077 = _153075, -(union(_153077) = union(_153075))], (594 ^ _133474) ^ [_153293, _153295] : [_153295 = _153293, -(powerset(_153295) = powerset(_153293))], (600 ^ _133474) ^ [_153511, _153513] : [_153513 = _153511, -(singleton(_153513) = singleton(_153511))], (616 ^ _133474) ^ [_154068, _154070] : [_154070 = _154068, -(relation_field(_154070) = relation_field(_154068))], (606 ^ _133474) ^ [_153757, _153759, _153761, _153763] : [-(unordered_pair(_153763, _153759) = unordered_pair(_153761, _153757)), _153763 = _153761, _153759 = _153757], (2 ^ _133474) ^ [_133618] : [-(_133618 = _133618)], (4 ^ _133474) ^ [_133725, _133727] : [_133727 = _133725, -(_133725 = _133727)], (10 ^ _133474) ^ [_133929, _133931, _133933] : [-(_133933 = _133929), _133933 = _133931, _133931 = _133929], (20 ^ _133474) ^ [_134270, _134272, _134274, _134276] : [-(is_antisymmetric_in(_134274, _134270)), is_antisymmetric_in(_134276, _134272), _134276 = _134274, _134272 = _134270], (34 ^ _133474) ^ [_134714, _134716, _134718, _134720] : [-(is_connected_in(_134718, _134714)), is_connected_in(_134720, _134716), _134720 = _134718, _134716 = _134714], (48 ^ _133474) ^ [_135158, _135160, _135162, _135164] : [-(is_transitive_in(_135162, _135158)), is_transitive_in(_135164, _135160), _135164 = _135162, _135160 = _135158], (62 ^ _133474) ^ [_135602, _135604, _135606, _135608] : [-(is_reflexive_in(_135606, _135602)), is_reflexive_in(_135608, _135604), _135608 = _135606, _135604 = _135602], (76 ^ _133474) ^ [_136018, _136020] : [-(reflexive(_136018)), _136020 = _136018, reflexive(_136020)], (86 ^ _133474) ^ [_136313, _136315] : [-(transitive(_136313)), _136315 = _136313, transitive(_136315)], (96 ^ _133474) ^ [_136608, _136610] : [-(antisymmetric(_136608)), _136610 = _136608, antisymmetric(_136610)], (106 ^ _133474) ^ [_136903, _136905] : [-(connected(_136903)), _136905 = _136903, connected(_136905)], (116 ^ _133474) ^ [_137198, _137200] : [-(epsilon_connected(_137198)), _137200 = _137198, epsilon_connected(_137200)], (126 ^ _133474) ^ [_137493, _137495] : [-(relation_empty_yielding(_137493)), _137495 = _137493, relation_empty_yielding(_137495)], (136 ^ _133474) ^ [_137788, _137790] : [-(epsilon_transitive(_137788)), _137790 = _137788, epsilon_transitive(_137790)], (146 ^ _133474) ^ [_138111, _138113, _138115, _138117] : [-(ordinal_subset(_138115, _138111)), ordinal_subset(_138117, _138113), _138117 = _138115, _138113 = _138111], (160 ^ _133474) ^ [_138527, _138529] : [-(ordinal(_138527)), _138529 = _138527, ordinal(_138529)], (170 ^ _133474) ^ [_138822, _138824] : [-(being_limit_ordinal(_138822)), _138824 = _138822, being_limit_ordinal(_138824)], (180 ^ _133474) ^ [_139145, _139147, _139149, _139151] : [-(element(_139149, _139145)), element(_139151, _139147), _139151 = _139149, _139147 = _139145], (194 ^ _133474) ^ [_139561, _139563] : [-(well_founded_relation(_139561)), _139563 = _139561, well_founded_relation(_139563)], (204 ^ _133474) ^ [_139884, _139886, _139888, _139890] : [-(is_well_founded_in(_139888, _139884)), is_well_founded_in(_139890, _139886), _139890 = _139888, _139886 = _139884], (218 ^ _133474) ^ [_140328, _140330, _140332, _140334] : [-(proper_subset(_140332, _140328)), proper_subset(_140334, _140330), _140334 = _140332, _140330 = _140328], (232 ^ _133474) ^ [_140744, _140746] : [-(one_to_one(_140744)), _140746 = _140744, one_to_one(_140746)], (242 ^ _133474) ^ [_141067, _141069, _141071, _141073] : [-(disjoint(_141071, _141067)), disjoint(_141073, _141069), _141073 = _141071, _141069 = _141067], (256 ^ _133474) ^ [_141483, _141485] : [-(empty(_141483)), _141485 = _141483, empty(_141485)], (266 ^ _133474) ^ [_141778, _141780] : [-(function(_141778)), _141780 = _141778, function(_141780)], (276 ^ _133474) ^ [_142101, _142103, _142105, _142107] : [-(subset(_142105, _142101)), subset(_142107, _142103), _142107 = _142105, _142103 = _142101], (290 ^ _133474) ^ [_142545, _142547, _142549, _142551] : [-(are_equipotent(_142549, _142545)), are_equipotent(_142551, _142547), _142551 = _142549, _142547 = _142545], (304 ^ _133474) ^ [_142989, _142991, _142993, _142995] : [-(in(_142993, _142989)), in(_142995, _142991), _142995 = _142993, _142991 = _142989], (318 ^ _133474) ^ [_143405, _143407] : [-(relation(_143405)), _143407 = _143405, relation(_143407)], (342 ^ _133474) ^ [_144124, _144126] : [-(well_ordering(_144124)), _144126 = _144124, well_ordering(_144126)], (328 ^ _133474) ^ [_143728, _143730, _143732, _143734] : [-(well_orders(_143732, _143728)), well_orders(_143734, _143730), _143734 = _143732, _143730 = _143728], (622 ^ _133474) ^ [_154475, _154477] : [in(_154477, _154475), in(_154475, _154477)], (628 ^ _133474) ^ [_154686, _154688] : [proper_subset(_154688, _154686), proper_subset(_154686, _154688)], (634 ^ _133474) ^ [_154883] : [empty(_154883), -(function(_154883))], (640 ^ _133474) ^ [_155069] : [ordinal(_155069), 643 ^ _133474 : [(644 ^ _133474) ^ [] : [-(epsilon_transitive(_155069))], (646 ^ _133474) ^ [] : [-(epsilon_connected(_155069))]]], (648 ^ _133474) ^ [_155326] : [empty(_155326), -(relation(_155326))], (654 ^ _133474) ^ [_155512] : [665 ^ _133474 : [(666 ^ _133474) ^ [] : [-(relation(_155512))], (668 ^ _133474) ^ [] : [-(function(_155512))], (670 ^ _133474) ^ [] : [-(one_to_one(_155512))]], relation(_155512), empty(_155512), function(_155512)], (672 ^ _133474) ^ [_156005] : [-(ordinal(_156005)), epsilon_transitive(_156005), epsilon_connected(_156005)], (682 ^ _133474) ^ [_156274] : [empty(_156274), 685 ^ _133474 : [(686 ^ _133474) ^ [] : [-(epsilon_transitive(_156274))], (688 ^ _133474) ^ [] : [-(epsilon_connected(_156274))], (690 ^ _133474) ^ [] : [-(ordinal(_156274))]]], (692 ^ _133474) ^ [_156600, _156602] : [-(unordered_pair(_156602, _156600) = unordered_pair(_156600, _156602))], (694 ^ _133474) ^ [_156700, _156702] : [-(set_union2(_156702, _156700) = set_union2(_156700, _156702))], (696 ^ _133474) ^ [_156800, _156802] : [-(set_intersection2(_156802, _156800) = set_intersection2(_156800, _156802))], (698 ^ _133474) ^ [_156915, _156917] : [ordinal(_156917), ordinal(_156915), -(ordinal_subset(_156917, _156915)), -(ordinal_subset(_156915, _156917))], (712 ^ _133474) ^ [_157302, _157304] : [relation(_157302), 715 ^ _133474 : [(738 ^ _133474) ^ [] : [-(_157302 = identity_relation(_157304)), 751 ^ _133474 : [(752 ^ _133474) ^ [] : [-(in(739 ^ [_157302, _157304], _157304))], (754 ^ _133474) ^ [] : [-(739 ^ [_157302, _157304] = 740 ^ [_157302, _157304])], (756 ^ _133474) ^ [] : [in(ordered_pair(739 ^ [_157302, _157304], 740 ^ [_157302, _157304]), _157302)]], 743 ^ _133474 : [(744 ^ _133474) ^ [] : [-(in(ordered_pair(739 ^ [_157302, _157304], 740 ^ [_157302, _157304]), _157302))], (746 ^ _133474) ^ [] : [in(739 ^ [_157302, _157304], _157304), 739 ^ [_157302, _157304] = 740 ^ [_157302, _157304]]]], (716 ^ _133474) ^ [] : [_157302 = identity_relation(_157304), 719 ^ _133474 : [(720 ^ _133474) ^ [_157612, _157614] : [in(ordered_pair(_157614, _157612), _157302), 723 ^ _133474 : [(724 ^ _133474) ^ [] : [-(in(_157614, _157304))], (726 ^ _133474) ^ [] : [-(_157614 = _157612)]]], (728 ^ _133474) ^ [_157875, _157877] : [-(in(ordered_pair(_157877, _157875), _157302)), in(_157877, _157304), _157877 = _157875]]]]], (760 ^ _133474) ^ [_158983, _158985] : [_158985 = _158983, 763 ^ _133474 : [(764 ^ _133474) ^ [] : [-(subset(_158985, _158983))], (766 ^ _133474) ^ [] : [-(subset(_158983, _158985))]]], (768 ^ _133474) ^ [_159220, _159222] : [-(_159222 = _159220), subset(_159222, _159220), subset(_159220, _159222)], (778 ^ _133474) ^ [_159507] : [relation(_159507), 781 ^ _133474 : [(782 ^ _133474) ^ [_159693, _159695] : [relation(_159693), 785 ^ _133474 : [(808 ^ _133474) ^ [] : [-(_159693 = relation_dom_restriction(_159507, _159695)), 821 ^ _133474 : [(822 ^ _133474) ^ [] : [-(in(809 ^ [_159507, _159693, _159695], _159695))], (824 ^ _133474) ^ [] : [-(in(ordered_pair(809 ^ [_159507, _159693, _159695], 810 ^ [_159507, _159693, _159695]), _159507))], (826 ^ _133474) ^ [] : [in(ordered_pair(809 ^ [_159507, _159693, _159695], 810 ^ [_159507, _159693, _159695]), _159693)]], 813 ^ _133474 : [(814 ^ _133474) ^ [] : [-(in(ordered_pair(809 ^ [_159507, _159693, _159695], 810 ^ [_159507, _159693, _159695]), _159693))], (816 ^ _133474) ^ [] : [in(809 ^ [_159507, _159693, _159695], _159695), in(ordered_pair(809 ^ [_159507, _159693, _159695], 810 ^ [_159507, _159693, _159695]), _159507)]]], (786 ^ _133474) ^ [] : [_159693 = relation_dom_restriction(_159507, _159695), 789 ^ _133474 : [(790 ^ _133474) ^ [_160018, _160020] : [in(ordered_pair(_160020, _160018), _159693), 793 ^ _133474 : [(794 ^ _133474) ^ [] : [-(in(_160020, _159695))], (796 ^ _133474) ^ [] : [-(in(ordered_pair(_160020, _160018), _159507))]]], (798 ^ _133474) ^ [_160297, _160299] : [-(in(ordered_pair(_160299, _160297), _159693)), in(_160299, _159695), in(ordered_pair(_160299, _160297), _159507)]]]]]]], (830 ^ _133474) ^ [_161452] : [relation(_161452), function(_161452), 837 ^ _133474 : [(867 ^ _133474) ^ [_162878, _162880] : [-(_162878 = relation_image(_161452, _162880)), 884 ^ _133474 : [(885 ^ _133474) ^ [] : [-(in(883 ^ [_161452, _162878, _162880], relation_dom(_161452)))], (887 ^ _133474) ^ [] : [-(in(883 ^ [_161452, _162878, _162880], _162880))], (889 ^ _133474) ^ [] : [-(868 ^ [_161452, _162878, _162880] = apply(_161452, 883 ^ [_161452, _162878, _162880]))], (891 ^ _133474) ^ [] : [in(868 ^ [_161452, _162878, _162880], _162878)]], 871 ^ _133474 : [(872 ^ _133474) ^ [] : [-(in(868 ^ [_161452, _162878, _162880], _162878))], (874 ^ _133474) ^ [_163198] : [in(_163198, relation_dom(_161452)), in(_163198, _162880), 868 ^ [_161452, _162878, _162880] = apply(_161452, _163198)]]], (838 ^ _133474) ^ [_161750, _161752] : [_161750 = relation_image(_161452, _161752), 841 ^ _133474 : [(842 ^ _133474) ^ [_161950] : [in(_161950, _161750), 846 ^ _133474 : [(847 ^ _133474) ^ [] : [-(in(845 ^ [_161452, _161750, _161752, _161950], relation_dom(_161452)))], (849 ^ _133474) ^ [] : [-(in(845 ^ [_161452, _161750, _161752, _161950], _161752))], (851 ^ _133474) ^ [] : [-(_161950 = apply(_161452, 845 ^ [_161452, _161750, _161752, _161950]))]]], (853 ^ _133474) ^ [_162405] : [-(in(_162405, _161750)), 854 ^ _133474 : [(855 ^ _133474) ^ [_162518] : [in(_162518, relation_dom(_161452)), in(_162518, _161752), _162405 = apply(_161452, _162518)]]]]]]], (895 ^ _133474) ^ [_164008, _164010] : [relation(_164008), 898 ^ _133474 : [(899 ^ _133474) ^ [_164179] : [relation(_164179), 902 ^ _133474 : [(925 ^ _133474) ^ [] : [-(_164179 = relation_rng_restriction(_164010, _164008)), 938 ^ _133474 : [(939 ^ _133474) ^ [] : [-(in(927 ^ [_164008, _164010, _164179], _164010))], (941 ^ _133474) ^ [] : [-(in(ordered_pair(926 ^ [_164008, _164010, _164179], 927 ^ [_164008, _164010, _164179]), _164008))], (943 ^ _133474) ^ [] : [in(ordered_pair(926 ^ [_164008, _164010, _164179], 927 ^ [_164008, _164010, _164179]), _164179)]], 930 ^ _133474 : [(931 ^ _133474) ^ [] : [-(in(ordered_pair(926 ^ [_164008, _164010, _164179], 927 ^ [_164008, _164010, _164179]), _164179))], (933 ^ _133474) ^ [] : [in(927 ^ [_164008, _164010, _164179], _164010), in(ordered_pair(926 ^ [_164008, _164010, _164179], 927 ^ [_164008, _164010, _164179]), _164008)]]], (903 ^ _133474) ^ [] : [_164179 = relation_rng_restriction(_164010, _164008), 906 ^ _133474 : [(907 ^ _133474) ^ [_164506, _164508] : [in(ordered_pair(_164508, _164506), _164179), 910 ^ _133474 : [(911 ^ _133474) ^ [] : [-(in(_164506, _164010))], (913 ^ _133474) ^ [] : [-(in(ordered_pair(_164508, _164506), _164008))]]], (915 ^ _133474) ^ [_164785, _164787] : [-(in(ordered_pair(_164787, _164785), _164179)), in(_164785, _164010), in(ordered_pair(_164787, _164785), _164008)]]]]]]], (947 ^ _133474) ^ [_165931] : [relation(_165931), 950 ^ _133474 : [(951 ^ _133474) ^ [] : [antisymmetric(_165931), -(is_antisymmetric_in(_165931, relation_field(_165931)))], (957 ^ _133474) ^ [] : [is_antisymmetric_in(_165931, relation_field(_165931)), -(antisymmetric(_165931))]]], (963 ^ _133474) ^ [_166362] : [relation(_166362), function(_166362), 970 ^ _133474 : [(993 ^ _133474) ^ [_167401, _167403] : [-(_167401 = relation_inverse_image(_166362, _167403)), 1005 ^ _133474 : [(1006 ^ _133474) ^ [] : [-(in(994 ^ [_166362, _167401, _167403], relation_dom(_166362)))], (1008 ^ _133474) ^ [] : [-(in(apply(_166362, 994 ^ [_166362, _167401, _167403]), _167403))], (1010 ^ _133474) ^ [] : [in(994 ^ [_166362, _167401, _167403], _167401)]], 997 ^ _133474 : [(998 ^ _133474) ^ [] : [-(in(994 ^ [_166362, _167401, _167403], _167401))], (1000 ^ _133474) ^ [] : [in(994 ^ [_166362, _167401, _167403], relation_dom(_166362)), in(apply(_166362, 994 ^ [_166362, _167401, _167403]), _167403)]]], (971 ^ _133474) ^ [_166649, _166651] : [_166649 = relation_inverse_image(_166362, _166651), 974 ^ _133474 : [(975 ^ _133474) ^ [_166838] : [in(_166838, _166649), 978 ^ _133474 : [(979 ^ _133474) ^ [] : [-(in(_166838, relation_dom(_166362)))], (981 ^ _133474) ^ [] : [-(in(apply(_166362, _166838), _166651))]]], (983 ^ _133474) ^ [_167107] : [-(in(_167107, _166649)), in(_167107, relation_dom(_166362)), in(apply(_166362, _167107), _166651)]]]]], (1014 ^ _133474) ^ [_168169] : [relation(_168169), 1017 ^ _133474 : [(1041 ^ _133474) ^ [_169282, _169284] : [-(_169282 = relation_image(_168169, _169284)), 1054 ^ _133474 : [(1055 ^ _133474) ^ [] : [-(in(ordered_pair(1053 ^ [_168169, _169282, _169284], 1042 ^ [_168169, _169282, _169284]), _168169))], (1057 ^ _133474) ^ [] : [-(in(1053 ^ [_168169, _169282, _169284], _169284))], (1059 ^ _133474) ^ [] : [in(1042 ^ [_168169, _169282, _169284], _169282)]], 1045 ^ _133474 : [(1046 ^ _133474) ^ [] : [-(in(1042 ^ [_168169, _169282, _169284], _169282))], (1048 ^ _133474) ^ [_169586] : [in(ordered_pair(_169586, 1042 ^ [_168169, _169282, _169284]), _168169), in(_169586, _169284)]]], (1018 ^ _133474) ^ [_168376, _168378] : [_168376 = relation_image(_168169, _168378), 1021 ^ _133474 : [(1022 ^ _133474) ^ [_168568] : [in(_168568, _168376), 1026 ^ _133474 : [(1027 ^ _133474) ^ [] : [-(in(ordered_pair(1025 ^ [_168169, _168376, _168378, _168568], _168568), _168169))], (1029 ^ _133474) ^ [] : [-(in(1025 ^ [_168169, _168376, _168378, _168568], _168378))]]], (1031 ^ _133474) ^ [_168922] : [-(in(_168922, _168376)), 1032 ^ _133474 : [(1033 ^ _133474) ^ [_169027] : [in(ordered_pair(_169027, _168922), _168169), in(_169027, _168378)]]]]]]], (1063 ^ _133474) ^ [_170188] : [relation(_170188), 1066 ^ _133474 : [(1090 ^ _133474) ^ [_171301, _171303] : [-(_171301 = relation_inverse_image(_170188, _171303)), 1103 ^ _133474 : [(1104 ^ _133474) ^ [] : [-(in(ordered_pair(1091 ^ [_170188, _171301, _171303], 1102 ^ [_170188, _171301, _171303]), _170188))], (1106 ^ _133474) ^ [] : [-(in(1102 ^ [_170188, _171301, _171303], _171303))], (1108 ^ _133474) ^ [] : [in(1091 ^ [_170188, _171301, _171303], _171301)]], 1094 ^ _133474 : [(1095 ^ _133474) ^ [] : [-(in(1091 ^ [_170188, _171301, _171303], _171301))], (1097 ^ _133474) ^ [_171605] : [in(ordered_pair(1091 ^ [_170188, _171301, _171303], _171605), _170188), in(_171605, _171303)]]], (1067 ^ _133474) ^ [_170395, _170397] : [_170395 = relation_inverse_image(_170188, _170397), 1070 ^ _133474 : [(1071 ^ _133474) ^ [_170587] : [in(_170587, _170395), 1075 ^ _133474 : [(1076 ^ _133474) ^ [] : [-(in(ordered_pair(_170587, 1074 ^ [_170188, _170395, _170397, _170587]), _170188))], (1078 ^ _133474) ^ [] : [-(in(1074 ^ [_170188, _170395, _170397, _170587], _170397))]]], (1080 ^ _133474) ^ [_170941] : [-(in(_170941, _170395)), 1081 ^ _133474 : [(1082 ^ _133474) ^ [_171046] : [in(ordered_pair(_170941, _171046), _170188), in(_171046, _170397)]]]]]]], (1112 ^ _133474) ^ [_172207] : [relation(_172207), 1115 ^ _133474 : [(1116 ^ _133474) ^ [] : [connected(_172207), -(is_connected_in(_172207, relation_field(_172207)))], (1122 ^ _133474) ^ [] : [is_connected_in(_172207, relation_field(_172207)), -(connected(_172207))]]], (1128 ^ _133474) ^ [_172638] : [relation(_172638), 1131 ^ _133474 : [(1132 ^ _133474) ^ [] : [transitive(_172638), -(is_transitive_in(_172638, relation_field(_172638)))], (1138 ^ _133474) ^ [] : [is_transitive_in(_172638, relation_field(_172638)), -(transitive(_172638))]]], (1172 ^ _133474) ^ [_174104, _174106, _174108, _174110] : [-(_174104 = unordered_triple(_174110, _174108, _174106)), 1176 ^ _133474 : [(1177 ^ _133474) ^ [] : [-(in(1173 ^ [_174104, _174106, _174108, _174110], _174104))], (1179 ^ _133474) ^ [] : [1173 ^ [_174104, _174106, _174108, _174110] = _174110], (1181 ^ _133474) ^ [] : [1173 ^ [_174104, _174106, _174108, _174110] = _174108], (1183 ^ _133474) ^ [] : [1173 ^ [_174104, _174106, _174108, _174110] = _174106]], 1184 ^ _133474 : [(1195 ^ _133474) ^ [] : [in(1173 ^ [_174104, _174106, _174108, _174110], _174104)], (1185 ^ _133474) ^ [] : [-(1173 ^ [_174104, _174106, _174108, _174110] = _174110), -(1173 ^ [_174104, _174106, _174108, _174110] = _174108), -(1173 ^ [_174104, _174106, _174108, _174110] = _174106)]]], (1144 ^ _133474) ^ [_173140, _173142, _173144, _173146] : [_173140 = unordered_triple(_173146, _173144, _173142), 1147 ^ _133474 : [(1162 ^ _133474) ^ [_173742] : [1163 ^ _133474 : [(1164 ^ _133474) ^ [] : [_173742 = _173146], (1166 ^ _133474) ^ [] : [_173742 = _173144], (1168 ^ _133474) ^ [] : [_173742 = _173142]], -(in(_173742, _173140))], (1148 ^ _133474) ^ [_173342] : [in(_173342, _173140), -(_173342 = _173146), -(_173342 = _173144), -(_173342 = _173142)]]], (1199 ^ _133474) ^ [_175077] : [-(succ(_175077) = set_union2(_175077, singleton(_175077)))], (1213 ^ _133474) ^ [_175667] : [1215 ^ _133474 : [(1216 ^ _133474) ^ [] : [-(in(1214 ^ [_175667], _175667))], (1218 ^ _133474) ^ [_175904, _175906] : [1214 ^ [_175667] = ordered_pair(_175906, _175904)]], -(relation(_175667))], (1201 ^ _133474) ^ [_175206] : [relation(_175206), 1204 ^ _133474 : [(1205 ^ _133474) ^ [_175354] : [in(_175354, _175206), -(_175354 = ordered_pair(1208 ^ [_175206, _175354], 1209 ^ [_175206, _175354]))]]], (1222 ^ _133474) ^ [_176061] : [relation(_176061), 1225 ^ _133474 : [(1236 ^ _133474) ^ [_176560] : [1238 ^ _133474 : [(1239 ^ _133474) ^ [] : [-(in(1237 ^ [_176061, _176560], _176560))], (1241 ^ _133474) ^ [] : [in(ordered_pair(1237 ^ [_176061, _176560], 1237 ^ [_176061, _176560]), _176061)]], -(is_reflexive_in(_176061, _176560))], (1226 ^ _133474) ^ [_176235] : [is_reflexive_in(_176061, _176235), 1229 ^ _133474 : [(1230 ^ _133474) ^ [_176377] : [in(_176377, _176235), -(in(ordered_pair(_176377, _176377), _176061))]]]]], (1294 ^ _133474) ^ [_178667, _178669] : [_178669 = empty_set, 1297 ^ _133474 : [(1298 ^ _133474) ^ [] : [_178667 = set_meet(_178669), -(_178667 = empty_set)], (1304 ^ _133474) ^ [] : [_178667 = empty_set, -(_178667 = set_meet(_178669))]]], (1245 ^ _133474) ^ [_176960, _176962] : [-(_176962 = empty_set), 1248 ^ _133474 : [(1272 ^ _133474) ^ [] : [-(_176960 = set_meet(_176962)), 1276 ^ _133474 : [(1277 ^ _133474) ^ [] : [-(in(1273 ^ [_176960, _176962], _176960))], (1280 ^ _133474) ^ [] : [-(in(1278 ^ [_176960, _176962], _176962))], (1282 ^ _133474) ^ [] : [in(1273 ^ [_176960, _176962], 1278 ^ [_176960, _176962])]], 1283 ^ _133474 : [(1290 ^ _133474) ^ [] : [in(1273 ^ [_176960, _176962], _176960)], (1284 ^ _133474) ^ [_178362] : [in(_178362, _176962), -(in(1273 ^ [_176960, _176962], _178362))]]], (1249 ^ _133474) ^ [] : [_176960 = set_meet(_176962), 1252 ^ _133474 : [(1263 ^ _133474) ^ [_177588] : [1265 ^ _133474 : [(1266 ^ _133474) ^ [] : [-(in(1264 ^ [_176960, _176962, _177588], _176962))], (1268 ^ _133474) ^ [] : [in(_177588, 1264 ^ [_176960, _176962, _177588])]], -(in(_177588, _176960))], (1253 ^ _133474) ^ [_177258] : [in(_177258, _176960), 1256 ^ _133474 : [(1257 ^ _133474) ^ [_177403] : [in(_177403, _176962), -(in(_177258, _177403))]]]]]]], (1326 ^ _133474) ^ [_179685, _179687] : [-(_179685 = singleton(_179687)), 1330 ^ _133474 : [(1331 ^ _133474) ^ [] : [-(in(1327 ^ [_179685, _179687], _179685))], (1333 ^ _133474) ^ [] : [1327 ^ [_179685, _179687] = _179687]], 1334 ^ _133474 : [(1335 ^ _133474) ^ [] : [-(1327 ^ [_179685, _179687] = _179687)], (1337 ^ _133474) ^ [] : [in(1327 ^ [_179685, _179687], _179685)]]], (1310 ^ _133474) ^ [_179164, _179166] : [_179164 = singleton(_179166), 1313 ^ _133474 : [(1314 ^ _133474) ^ [_179334] : [in(_179334, _179164), -(_179334 = _179166)], (1320 ^ _133474) ^ [_179506] : [_179506 = _179166, -(in(_179506, _179164))]]], (1341 ^ _133474) ^ [_180236] : [_180236 = empty_set, 1344 ^ _133474 : [(1345 ^ _133474) ^ [_180349] : [in(_180349, _180236)]]], (1347 ^ _133474) ^ [_180415] : [-(in(1348 ^ [_180415], _180415)), -(_180415 = empty_set)], (1370 ^ _133474) ^ [_181227, _181229] : [-(_181227 = powerset(_181229)), 1374 ^ _133474 : [(1375 ^ _133474) ^ [] : [-(in(1371 ^ [_181227, _181229], _181227))], (1377 ^ _133474) ^ [] : [subset(1371 ^ [_181227, _181229], _181229)]], 1378 ^ _133474 : [(1379 ^ _133474) ^ [] : [-(subset(1371 ^ [_181227, _181229], _181229))], (1381 ^ _133474) ^ [] : [in(1371 ^ [_181227, _181229], _181227)]]], (1354 ^ _133474) ^ [_180706, _180708] : [_180706 = powerset(_180708), 1357 ^ _133474 : [(1358 ^ _133474) ^ [_180876] : [in(_180876, _180706), -(subset(_180876, _180708))], (1364 ^ _133474) ^ [_181048] : [subset(_181048, _180708), -(in(_181048, _180706))]]], (1395 ^ _133474) ^ [_182078] : [1397 ^ _133474 : [(1398 ^ _133474) ^ [] : [-(in(1396 ^ [_182078], _182078))], (1400 ^ _133474) ^ [] : [subset(1396 ^ [_182078], _182078)]], -(epsilon_transitive(_182078))], (1385 ^ _133474) ^ [_181778] : [epsilon_transitive(_181778), 1388 ^ _133474 : [(1389 ^ _133474) ^ [_181909] : [in(_181909, _181778), -(subset(_181909, _181778))]]], (1404 ^ _133474) ^ [_182403] : [relation(_182403), 1407 ^ _133474 : [(1408 ^ _133474) ^ [_182561] : [relation(_182561), 1411 ^ _133474 : [(1428 ^ _133474) ^ [] : [-(_182403 = _182561), 1433 ^ _133474 : [(1434 ^ _133474) ^ [] : [-(in(ordered_pair(1429 ^ [_182403, _182561], 1430 ^ [_182403, _182561]), _182403))], (1436 ^ _133474) ^ [] : [in(ordered_pair(1429 ^ [_182403, _182561], 1430 ^ [_182403, _182561]), _182561)]], 1437 ^ _133474 : [(1438 ^ _133474) ^ [] : [-(in(ordered_pair(1429 ^ [_182403, _182561], 1430 ^ [_182403, _182561]), _182561))], (1440 ^ _133474) ^ [] : [in(ordered_pair(1429 ^ [_182403, _182561], 1430 ^ [_182403, _182561]), _182403)]]], (1412 ^ _133474) ^ [] : [_182403 = _182561, 1415 ^ _133474 : [(1416 ^ _133474) ^ [_182866, _182868] : [in(ordered_pair(_182868, _182866), _182403), -(in(ordered_pair(_182868, _182866), _182561))], (1422 ^ _133474) ^ [_183056, _183058] : [in(ordered_pair(_183058, _183056), _182561), -(in(ordered_pair(_183058, _183056), _182403))]]]]]]], (1444 ^ _133474) ^ [_183893, _183895] : [-(empty(_183895)), 1447 ^ _133474 : [(1448 ^ _133474) ^ [] : [element(_183893, _183895), -(in(_183893, _183895))], (1454 ^ _133474) ^ [] : [in(_183893, _183895), -(element(_183893, _183895))]]], (1460 ^ _133474) ^ [_184306, _184308] : [empty(_184308), 1463 ^ _133474 : [(1464 ^ _133474) ^ [] : [element(_184306, _184308), -(empty(_184306))], (1470 ^ _133474) ^ [] : [empty(_184306), -(element(_184306, _184308))]]], (1498 ^ _133474) ^ [_185531, _185533, _185535] : [-(_185531 = unordered_pair(_185535, _185533)), 1502 ^ _133474 : [(1503 ^ _133474) ^ [] : [-(in(1499 ^ [_185531, _185533, _185535], _185531))], (1505 ^ _133474) ^ [] : [1499 ^ [_185531, _185533, _185535] = _185535], (1507 ^ _133474) ^ [] : [1499 ^ [_185531, _185533, _185535] = _185533]], 1508 ^ _133474 : [(1515 ^ _133474) ^ [] : [in(1499 ^ [_185531, _185533, _185535], _185531)], (1509 ^ _133474) ^ [] : [-(1499 ^ [_185531, _185533, _185535] = _185535), -(1499 ^ [_185531, _185533, _185535] = _185533)]]], (1476 ^ _133474) ^ [_184806, _184808, _184810] : [_184806 = unordered_pair(_184810, _184808), 1479 ^ _133474 : [(1490 ^ _133474) ^ [_185266] : [1491 ^ _133474 : [(1492 ^ _133474) ^ [] : [_185266 = _184810], (1494 ^ _133474) ^ [] : [_185266 = _184808]], -(in(_185266, _184806))], (1480 ^ _133474) ^ [_184988] : [in(_184988, _184806), -(_184988 = _184810), -(_184988 = _184808)]]], (1519 ^ _133474) ^ [_186268] : [relation(_186268), 1522 ^ _133474 : [(1540 ^ _133474) ^ [] : [-(well_founded_relation(_186268)), 1542 ^ _133474 : [(1543 ^ _133474) ^ [] : [-(subset(1541 ^ [_186268], relation_field(_186268)))], (1545 ^ _133474) ^ [] : [1541 ^ [_186268] = empty_set], (1547 ^ _133474) ^ [_187218] : [in(_187218, 1541 ^ [_186268]), disjoint(fiber(_186268, _187218), 1541 ^ [_186268])]]], (1523 ^ _133474) ^ [] : [well_founded_relation(_186268), 1526 ^ _133474 : [(1527 ^ _133474) ^ [_186535] : [subset(_186535, relation_field(_186268)), -(_186535 = empty_set), 1535 ^ _133474 : [(1536 ^ _133474) ^ [] : [-(in(1534 ^ [_186268, _186535], _186535))], (1538 ^ _133474) ^ [] : [-(disjoint(fiber(_186268, 1534 ^ [_186268, _186535]), _186535))]]]]]]], (1577 ^ _133474) ^ [_188282, _188284, _188286] : [-(_188282 = set_union2(_188286, _188284)), 1581 ^ _133474 : [(1582 ^ _133474) ^ [] : [-(in(1578 ^ [_188282, _188284, _188286], _188282))], (1584 ^ _133474) ^ [] : [in(1578 ^ [_188282, _188284, _188286], _188286)], (1586 ^ _133474) ^ [] : [in(1578 ^ [_188282, _188284, _188286], _188284)]], 1587 ^ _133474 : [(1594 ^ _133474) ^ [] : [in(1578 ^ [_188282, _188284, _188286], _188282)], (1588 ^ _133474) ^ [] : [-(in(1578 ^ [_188282, _188284, _188286], _188286)), -(in(1578 ^ [_188282, _188284, _188286], _188284))]]], (1555 ^ _133474) ^ [_187557, _187559, _187561] : [_187557 = set_union2(_187561, _187559), 1558 ^ _133474 : [(1569 ^ _133474) ^ [_188017] : [1570 ^ _133474 : [(1571 ^ _133474) ^ [] : [in(_188017, _187561)], (1573 ^ _133474) ^ [] : [in(_188017, _187559)]], -(in(_188017, _187557))], (1559 ^ _133474) ^ [_187739] : [in(_187739, _187557), -(in(_187739, _187561)), -(in(_187739, _187559))]]], (1628 ^ _133474) ^ [_190333, _190335, _190337] : [-(_190333 = cartesian_product2(_190337, _190335)), 1646 ^ _133474 : [(1647 ^ _133474) ^ [] : [-(in(1644 ^ [_190333, _190335, _190337], _190337))], (1649 ^ _133474) ^ [] : [-(in(1645 ^ [_190333, _190335, _190337], _190335))], (1651 ^ _133474) ^ [] : [-(1629 ^ [_190333, _190335, _190337] = ordered_pair(1644 ^ [_190333, _190335, _190337], 1645 ^ [_190333, _190335, _190337]))], (1653 ^ _133474) ^ [] : [in(1629 ^ [_190333, _190335, _190337], _190333)]], 1632 ^ _133474 : [(1633 ^ _133474) ^ [] : [-(in(1629 ^ [_190333, _190335, _190337], _190333))], (1635 ^ _133474) ^ [_190671, _190673] : [in(_190673, _190337), in(_190671, _190335), 1629 ^ [_190333, _190335, _190337] = ordered_pair(_190673, _190671)]]], (1598 ^ _133474) ^ [_189076, _189078, _189080] : [_189076 = cartesian_product2(_189080, _189078), 1601 ^ _133474 : [(1602 ^ _133474) ^ [_189277] : [in(_189277, _189076), 1607 ^ _133474 : [(1608 ^ _133474) ^ [] : [-(in(1605 ^ [_189076, _189078, _189080, _189277], _189080))], (1610 ^ _133474) ^ [] : [-(in(1606 ^ [_189076, _189078, _189080, _189277], _189078))], (1612 ^ _133474) ^ [] : [-(_189277 = ordered_pair(1605 ^ [_189076, _189078, _189080, _189277], 1606 ^ [_189076, _189078, _189080, _189277]))]]], (1614 ^ _133474) ^ [_189837] : [-(in(_189837, _189076)), 1615 ^ _133474 : [(1616 ^ _133474) ^ [_189967, _189969] : [in(_189969, _189080), in(_189967, _189078), _189837 = ordered_pair(_189969, _189967)]]]]], (1679 ^ _133474) ^ [_192234] : [1682 ^ _133474 : [(1683 ^ _133474) ^ [] : [-(in(1680 ^ [_192234], _192234))], (1685 ^ _133474) ^ [] : [-(in(1681 ^ [_192234], _192234))], (1687 ^ _133474) ^ [] : [in(1680 ^ [_192234], 1681 ^ [_192234])], (1689 ^ _133474) ^ [] : [1680 ^ [_192234] = 1681 ^ [_192234]], (1691 ^ _133474) ^ [] : [in(1681 ^ [_192234], 1680 ^ [_192234])]], -(epsilon_connected(_192234))], (1657 ^ _133474) ^ [_191596] : [epsilon_connected(_191596), 1660 ^ _133474 : [(1661 ^ _133474) ^ [_191772, _191774] : [in(_191774, _191596), in(_191772, _191596), -(in(_191774, _191772)), -(_191774 = _191772), -(in(_191772, _191774))]]], (1695 ^ _133474) ^ [_192940] : [relation(_192940), 1698 ^ _133474 : [(1699 ^ _133474) ^ [_193098] : [relation(_193098), 1702 ^ _133474 : [(1713 ^ _133474) ^ [] : [1716 ^ _133474 : [(1717 ^ _133474) ^ [] : [-(in(ordered_pair(1714 ^ [_192940, _193098], 1715 ^ [_192940, _193098]), _192940))], (1719 ^ _133474) ^ [] : [in(ordered_pair(1714 ^ [_192940, _193098], 1715 ^ [_192940, _193098]), _193098)]], -(subset(_192940, _193098))], (1703 ^ _133474) ^ [] : [subset(_192940, _193098), 1706 ^ _133474 : [(1707 ^ _133474) ^ [_193374, _193376] : [in(ordered_pair(_193376, _193374), _192940), -(in(ordered_pair(_193376, _193374), _193098))]]]]]]], (1733 ^ _133474) ^ [_194337, _194339] : [1735 ^ _133474 : [(1736 ^ _133474) ^ [] : [-(in(1734 ^ [_194337, _194339], _194339))], (1738 ^ _133474) ^ [] : [in(1734 ^ [_194337, _194339], _194337)]], -(subset(_194339, _194337))], (1723 ^ _133474) ^ [_194023, _194025] : [subset(_194025, _194023), 1726 ^ _133474 : [(1727 ^ _133474) ^ [_194160] : [in(_194160, _194025), -(in(_194160, _194023))]]], (1742 ^ _133474) ^ [_194680] : [relation(_194680), 1745 ^ _133474 : [(1763 ^ _133474) ^ [_195483] : [-(is_well_founded_in(_194680, _195483)), 1765 ^ _133474 : [(1766 ^ _133474) ^ [] : [-(subset(1764 ^ [_194680, _195483], _195483))], (1768 ^ _133474) ^ [] : [1764 ^ [_194680, _195483] = empty_set], (1770 ^ _133474) ^ [_195825] : [in(_195825, 1764 ^ [_194680, _195483]), disjoint(fiber(_194680, _195825), 1764 ^ [_194680, _195483])]]], (1746 ^ _133474) ^ [_194877] : [is_well_founded_in(_194680, _194877), 1749 ^ _133474 : [(1750 ^ _133474) ^ [_195042] : [subset(_195042, _194877), -(_195042 = empty_set), 1758 ^ _133474 : [(1759 ^ _133474) ^ [] : [-(in(1757 ^ [_194680, _194877, _195042], _195042))], (1761 ^ _133474) ^ [] : [-(disjoint(fiber(_194680, 1757 ^ [_194680, _194877, _195042]), _195042))]]]]]]], (1800 ^ _133474) ^ [_196908, _196910, _196912] : [-(_196908 = set_intersection2(_196912, _196910)), 1812 ^ _133474 : [(1813 ^ _133474) ^ [] : [-(in(1801 ^ [_196908, _196910, _196912], _196912))], (1815 ^ _133474) ^ [] : [-(in(1801 ^ [_196908, _196910, _196912], _196910))], (1817 ^ _133474) ^ [] : [in(1801 ^ [_196908, _196910, _196912], _196908)]], 1804 ^ _133474 : [(1805 ^ _133474) ^ [] : [-(in(1801 ^ [_196908, _196910, _196912], _196908))], (1807 ^ _133474) ^ [] : [in(1801 ^ [_196908, _196910, _196912], _196912), in(1801 ^ [_196908, _196910, _196912], _196910)]]], (1778 ^ _133474) ^ [_196183, _196185, _196187] : [_196183 = set_intersection2(_196187, _196185), 1781 ^ _133474 : [(1782 ^ _133474) ^ [_196365] : [in(_196365, _196183), 1785 ^ _133474 : [(1786 ^ _133474) ^ [] : [-(in(_196365, _196187))], (1788 ^ _133474) ^ [] : [-(in(_196365, _196185))]]], (1790 ^ _133474) ^ [_196624] : [-(in(_196624, _196183)), in(_196624, _196187), in(_196624, _196185)]]], (1821 ^ _133474) ^ [_197647] : [relation(_197647), function(_197647), 1828 ^ _133474 : [(1829 ^ _133474) ^ [_197939, _197941] : [in(_197941, relation_dom(_197647)), 1832 ^ _133474 : [(1833 ^ _133474) ^ [] : [_197939 = apply(_197647, _197941), -(in(ordered_pair(_197941, _197939), _197647))], (1839 ^ _133474) ^ [] : [in(ordered_pair(_197941, _197939), _197647), -(_197939 = apply(_197647, _197941))]]], (1845 ^ _133474) ^ [_198391, _198393] : [-(in(_198393, relation_dom(_197647))), 1848 ^ _133474 : [(1849 ^ _133474) ^ [] : [_198391 = apply(_197647, _198393), -(_198391 = empty_set)], (1855 ^ _133474) ^ [] : [_198391 = empty_set, -(_198391 = apply(_197647, _198393))]]]]], (1861 ^ _133474) ^ [_198909] : [ordinal(_198909), 1864 ^ _133474 : [(1865 ^ _133474) ^ [] : [-(epsilon_transitive(_198909))], (1867 ^ _133474) ^ [] : [-(epsilon_connected(_198909))]]], (1869 ^ _133474) ^ [_199132] : [-(ordinal(_199132)), epsilon_transitive(_199132), epsilon_connected(_199132)], (1879 ^ _133474) ^ [_199403] : [relation(_199403), 1882 ^ _133474 : [(1900 ^ _133474) ^ [_200215] : [-(_200215 = relation_dom(_199403)), 1904 ^ _133474 : [(1905 ^ _133474) ^ [] : [-(in(1901 ^ [_199403, _200215], _200215))], (1907 ^ _133474) ^ [_200478] : [in(ordered_pair(1901 ^ [_199403, _200215], _200478), _199403)]], 1909 ^ _133474 : [(1910 ^ _133474) ^ [] : [-(in(ordered_pair(1901 ^ [_199403, _200215], 1908 ^ [_199403, _200215]), _199403))], (1912 ^ _133474) ^ [] : [in(1901 ^ [_199403, _200215], _200215)]]], (1883 ^ _133474) ^ [_199584] : [_199584 = relation_dom(_199403), 1886 ^ _133474 : [(1887 ^ _133474) ^ [_199764] : [in(_199764, _199584), -(in(ordered_pair(_199764, 1890 ^ [_199403, _199584, _199764]), _199403))], (1894 ^ _133474) ^ [_200008] : [1895 ^ _133474 : [(1896 ^ _133474) ^ [_200087] : [in(ordered_pair(_200008, _200087), _199403)]], -(in(_200008, _199584))]]]]], (1916 ^ _133474) ^ [_200844] : [relation(_200844), 1919 ^ _133474 : [(1942 ^ _133474) ^ [_201712] : [1945 ^ _133474 : [(1946 ^ _133474) ^ [] : [-(in(1943 ^ [_200844, _201712], _201712))], (1948 ^ _133474) ^ [] : [-(in(1944 ^ [_200844, _201712], _201712))], (1950 ^ _133474) ^ [] : [-(in(ordered_pair(1943 ^ [_200844, _201712], 1944 ^ [_200844, _201712]), _200844))], (1952 ^ _133474) ^ [] : [-(in(ordered_pair(1944 ^ [_200844, _201712], 1943 ^ [_200844, _201712]), _200844))], (1954 ^ _133474) ^ [] : [1943 ^ [_200844, _201712] = 1944 ^ [_200844, _201712]]], -(is_antisymmetric_in(_200844, _201712))], (1920 ^ _133474) ^ [_201044] : [is_antisymmetric_in(_200844, _201044), 1923 ^ _133474 : [(1924 ^ _133474) ^ [_201226, _201228] : [-(_201228 = _201226), in(_201228, _201044), in(_201226, _201044), in(ordered_pair(_201228, _201226), _200844), in(ordered_pair(_201226, _201228), _200844)]]]]], (1958 ^ _133474) ^ [_202466] : [-(cast_to_subset(_202466) = _202466)], (1983 ^ _133474) ^ [_203449, _203451] : [-(_203449 = union(_203451)), 1996 ^ _133474 : [(1997 ^ _133474) ^ [] : [-(in(1984 ^ [_203449, _203451], 1995 ^ [_203449, _203451]))], (1999 ^ _133474) ^ [] : [-(in(1995 ^ [_203449, _203451], _203451))], (2001 ^ _133474) ^ [] : [in(1984 ^ [_203449, _203451], _203449)]], 1987 ^ _133474 : [(1988 ^ _133474) ^ [] : [-(in(1984 ^ [_203449, _203451], _203449))], (1990 ^ _133474) ^ [_203732] : [in(1984 ^ [_203449, _203451], _203732), in(_203732, _203451)]]], (1960 ^ _133474) ^ [_202604, _202606] : [_202604 = union(_202606), 1963 ^ _133474 : [(1964 ^ _133474) ^ [_202785] : [in(_202785, _202604), 1968 ^ _133474 : [(1969 ^ _133474) ^ [] : [-(in(_202785, 1967 ^ [_202604, _202606, _202785]))], (1971 ^ _133474) ^ [] : [-(in(1967 ^ [_202604, _202606, _202785], _202606))]]], (1973 ^ _133474) ^ [_203112] : [-(in(_203112, _202604)), 1974 ^ _133474 : [(1975 ^ _133474) ^ [_203210] : [in(_203112, _203210), in(_203210, _202606)]]]]], (2005 ^ _133474) ^ [_204282] : [relation(_204282), 2008 ^ _133474 : [(2009 ^ _133474) ^ [] : [well_ordering(_204282), 2012 ^ _133474 : [(2013 ^ _133474) ^ [] : [-(reflexive(_204282))], (2015 ^ _133474) ^ [] : [-(transitive(_204282))], (2017 ^ _133474) ^ [] : [-(antisymmetric(_204282))], (2019 ^ _133474) ^ [] : [-(connected(_204282))], (2021 ^ _133474) ^ [] : [-(well_founded_relation(_204282))]]], (2023 ^ _133474) ^ [] : [-(well_ordering(_204282)), reflexive(_204282), transitive(_204282), antisymmetric(_204282), connected(_204282), well_founded_relation(_204282)]]], (2067 ^ _133474) ^ [_206085, _206087, _206089] : [-(_206085 = set_difference(_206089, _206087)), 2079 ^ _133474 : [(2080 ^ _133474) ^ [] : [-(in(2068 ^ [_206085, _206087, _206089], _206089))], (2082 ^ _133474) ^ [] : [in(2068 ^ [_206085, _206087, _206089], _206087)], (2084 ^ _133474) ^ [] : [in(2068 ^ [_206085, _206087, _206089], _206085)]], 2071 ^ _133474 : [(2072 ^ _133474) ^ [] : [-(in(2068 ^ [_206085, _206087, _206089], _206085))], (2074 ^ _133474) ^ [] : [in(2068 ^ [_206085, _206087, _206089], _206089), -(in(2068 ^ [_206085, _206087, _206089], _206087))]]], (2045 ^ _133474) ^ [_205354, _205356, _205358] : [_205354 = set_difference(_205358, _205356), 2048 ^ _133474 : [(2049 ^ _133474) ^ [_205538] : [in(_205538, _205354), 2052 ^ _133474 : [(2053 ^ _133474) ^ [] : [-(in(_205538, _205358))], (2055 ^ _133474) ^ [] : [in(_205538, _205356)]]], (2057 ^ _133474) ^ [_205798] : [-(in(_205798, _205354)), in(_205798, _205358), -(in(_205798, _205356))]]], (2088 ^ _133474) ^ [_206828] : [relation(_206828), function(_206828), 2095 ^ _133474 : [(2119 ^ _133474) ^ [_207982] : [-(_207982 = relation_rng(_206828)), 2132 ^ _133474 : [(2133 ^ _133474) ^ [] : [-(in(2131 ^ [_206828, _207982], relation_dom(_206828)))], (2135 ^ _133474) ^ [] : [-(2120 ^ [_206828, _207982] = apply(_206828, 2131 ^ [_206828, _207982]))], (2137 ^ _133474) ^ [] : [in(2120 ^ [_206828, _207982], _207982)]], 2123 ^ _133474 : [(2124 ^ _133474) ^ [] : [-(in(2120 ^ [_206828, _207982], _207982))], (2126 ^ _133474) ^ [_208277] : [in(_208277, relation_dom(_206828)), 2120 ^ [_206828, _207982] = apply(_206828, _208277)]]], (2096 ^ _133474) ^ [_207100] : [_207100 = relation_rng(_206828), 2099 ^ _133474 : [(2100 ^ _133474) ^ [_207288] : [in(_207288, _207100), 2104 ^ _133474 : [(2105 ^ _133474) ^ [] : [-(in(2103 ^ [_206828, _207100, _207288], relation_dom(_206828)))], (2107 ^ _133474) ^ [] : [-(_207288 = apply(_206828, 2103 ^ [_206828, _207100, _207288]))]]], (2109 ^ _133474) ^ [_207630] : [-(in(_207630, _207100)), 2110 ^ _133474 : [(2111 ^ _133474) ^ [_207733] : [in(_207733, relation_dom(_206828)), _207630 = apply(_206828, _207733)]]]]]]], (2141 ^ _133474) ^ [_208854] : [relation(_208854), 2144 ^ _133474 : [(2162 ^ _133474) ^ [_209666] : [-(_209666 = relation_rng(_208854)), 2166 ^ _133474 : [(2167 ^ _133474) ^ [] : [-(in(2163 ^ [_208854, _209666], _209666))], (2169 ^ _133474) ^ [_209929] : [in(ordered_pair(_209929, 2163 ^ [_208854, _209666]), _208854)]], 2171 ^ _133474 : [(2172 ^ _133474) ^ [] : [-(in(ordered_pair(2170 ^ [_208854, _209666], 2163 ^ [_208854, _209666]), _208854))], (2174 ^ _133474) ^ [] : [in(2163 ^ [_208854, _209666], _209666)]]], (2145 ^ _133474) ^ [_209035] : [_209035 = relation_rng(_208854), 2148 ^ _133474 : [(2149 ^ _133474) ^ [_209215] : [in(_209215, _209035), -(in(ordered_pair(2152 ^ [_208854, _209035, _209215], _209215), _208854))], (2156 ^ _133474) ^ [_209459] : [2157 ^ _133474 : [(2158 ^ _133474) ^ [_209538] : [in(ordered_pair(_209538, _209459), _208854)]], -(in(_209459, _209035))]]]]], (2178 ^ _133474) ^ [_210309, _210311] : [element(_210309, powerset(_210311)), -(subset_complement(_210311, _210309) = set_difference(_210311, _210309))], (2184 ^ _133474) ^ [_210520, _210522] : [-(ordered_pair(_210522, _210520) = unordered_pair(unordered_pair(_210522, _210520), singleton(_210522)))], (2186 ^ _133474) ^ [_210626] : [relation(_210626), 2189 ^ _133474 : [(2190 ^ _133474) ^ [_210810] : [well_orders(_210626, _210810), 2193 ^ _133474 : [(2194 ^ _133474) ^ [] : [-(is_reflexive_in(_210626, _210810))], (2196 ^ _133474) ^ [] : [-(is_transitive_in(_210626, _210810))], (2198 ^ _133474) ^ [] : [-(is_antisymmetric_in(_210626, _210810))], (2200 ^ _133474) ^ [] : [-(is_connected_in(_210626, _210810))], (2202 ^ _133474) ^ [] : [-(is_well_founded_in(_210626, _210810))]]], (2204 ^ _133474) ^ [_211271] : [-(well_orders(_210626, _211271)), is_reflexive_in(_210626, _211271), is_transitive_in(_210626, _211271), is_antisymmetric_in(_210626, _211271), is_connected_in(_210626, _211271), is_well_founded_in(_210626, _211271)]]], (2226 ^ _133474) ^ [_211861] : [being_limit_ordinal(_211861), -(_211861 = union(_211861))], (2232 ^ _133474) ^ [_212019] : [_212019 = union(_212019), -(being_limit_ordinal(_212019))], (2238 ^ _133474) ^ [_212213] : [relation(_212213), -(relation_field(_212213) = set_union2(relation_dom(_212213), relation_rng(_212213)))], (2244 ^ _133474) ^ [_212419] : [relation(_212419), 2247 ^ _133474 : [(2270 ^ _133474) ^ [_213311] : [2273 ^ _133474 : [(2274 ^ _133474) ^ [] : [-(in(2271 ^ [_212419, _213311], _213311))], (2276 ^ _133474) ^ [] : [-(in(2272 ^ [_212419, _213311], _213311))], (2278 ^ _133474) ^ [] : [2271 ^ [_212419, _213311] = 2272 ^ [_212419, _213311]], (2280 ^ _133474) ^ [] : [in(ordered_pair(2271 ^ [_212419, _213311], 2272 ^ [_212419, _213311]), _212419)], (2282 ^ _133474) ^ [] : [in(ordered_pair(2272 ^ [_212419, _213311], 2271 ^ [_212419, _213311]), _212419)]], -(is_connected_in(_212419, _213311))], (2248 ^ _133474) ^ [_212627] : [is_connected_in(_212419, _212627), 2251 ^ _133474 : [(2252 ^ _133474) ^ [_212817, _212819] : [in(_212819, _212627), in(_212817, _212627), -(_212819 = _212817), -(in(ordered_pair(_212819, _212817), _212419)), -(in(ordered_pair(_212817, _212819), _212419))]]]]], (2286 ^ _133474) ^ [_214096] : [relation(_214096), 2289 ^ _133474 : [(2290 ^ _133474) ^ [_214256] : [relation(_214256), 2293 ^ _133474 : [(2310 ^ _133474) ^ [] : [-(_214256 = relation_inverse(_214096)), 2315 ^ _133474 : [(2316 ^ _133474) ^ [] : [-(in(ordered_pair(2311 ^ [_214096, _214256], 2312 ^ [_214096, _214256]), _214256))], (2318 ^ _133474) ^ [] : [in(ordered_pair(2312 ^ [_214096, _214256], 2311 ^ [_214096, _214256]), _214096)]], 2319 ^ _133474 : [(2320 ^ _133474) ^ [] : [-(in(ordered_pair(2312 ^ [_214096, _214256], 2311 ^ [_214096, _214256]), _214096))], (2322 ^ _133474) ^ [] : [in(ordered_pair(2311 ^ [_214096, _214256], 2312 ^ [_214096, _214256]), _214256)]]], (2294 ^ _133474) ^ [] : [_214256 = relation_inverse(_214096), 2297 ^ _133474 : [(2298 ^ _133474) ^ [_214565, _214567] : [in(ordered_pair(_214567, _214565), _214256), -(in(ordered_pair(_214565, _214567), _214096))], (2304 ^ _133474) ^ [_214755, _214757] : [in(ordered_pair(_214755, _214757), _214096), -(in(ordered_pair(_214757, _214755), _214256))]]]]]]], (2326 ^ _133474) ^ [_215603, _215605] : [disjoint(_215605, _215603), -(set_intersection2(_215605, _215603) = empty_set)], (2332 ^ _133474) ^ [_215771, _215773] : [set_intersection2(_215773, _215771) = empty_set, -(disjoint(_215773, _215771))], (2338 ^ _133474) ^ [_215975] : [relation(_215975), function(_215975), 2345 ^ _133474 : [(2364 ^ _133474) ^ [] : [2367 ^ _133474 : [(2368 ^ _133474) ^ [] : [-(in(2365 ^ [_215975], relation_dom(_215975)))], (2370 ^ _133474) ^ [] : [-(in(2366 ^ [_215975], relation_dom(_215975)))], (2372 ^ _133474) ^ [] : [-(apply(_215975, 2365 ^ [_215975]) = apply(_215975, 2366 ^ [_215975]))], (2374 ^ _133474) ^ [] : [2365 ^ [_215975] = 2366 ^ [_215975]]], -(one_to_one(_215975))], (2346 ^ _133474) ^ [] : [one_to_one(_215975), 2349 ^ _133474 : [(2350 ^ _133474) ^ [_216338, _216340] : [-(_216340 = _216338), in(_216340, relation_dom(_215975)), in(_216338, relation_dom(_215975)), apply(_215975, _216340) = apply(_215975, _216338)]]]]], (2378 ^ _133474) ^ [_217285] : [relation(_217285), 2381 ^ _133474 : [(2382 ^ _133474) ^ [_217470] : [relation(_217470), 2385 ^ _133474 : [(2386 ^ _133474) ^ [_217651] : [relation(_217651), 2389 ^ _133474 : [(2413 ^ _133474) ^ [] : [-(_217651 = relation_composition(_217285, _217470)), 2427 ^ _133474 : [(2428 ^ _133474) ^ [] : [-(in(ordered_pair(2414 ^ [_217285, _217470, _217651], 2426 ^ [_217285, _217470, _217651]), _217285))], (2430 ^ _133474) ^ [] : [-(in(ordered_pair(2426 ^ [_217285, _217470, _217651], 2415 ^ [_217285, _217470, _217651]), _217470))], (2432 ^ _133474) ^ [] : [in(ordered_pair(2414 ^ [_217285, _217470, _217651], 2415 ^ [_217285, _217470, _217651]), _217651)]], 2418 ^ _133474 : [(2419 ^ _133474) ^ [] : [-(in(ordered_pair(2414 ^ [_217285, _217470, _217651], 2415 ^ [_217285, _217470, _217651]), _217651))], (2421 ^ _133474) ^ [_219115] : [in(ordered_pair(2414 ^ [_217285, _217470, _217651], _219115), _217285), in(ordered_pair(_219115, 2415 ^ [_217285, _217470, _217651]), _217470)]]], (2390 ^ _133474) ^ [] : [_217651 = relation_composition(_217285, _217470), 2393 ^ _133474 : [(2394 ^ _133474) ^ [_217986, _217988] : [in(ordered_pair(_217988, _217986), _217651), 2398 ^ _133474 : [(2399 ^ _133474) ^ [] : [-(in(ordered_pair(_217988, 2397 ^ [_217285, _217470, _217651, _217986, _217988]), _217285))], (2401 ^ _133474) ^ [] : [-(in(ordered_pair(2397 ^ [_217285, _217470, _217651, _217986, _217988], _217986), _217470))]]], (2403 ^ _133474) ^ [_218371, _218373] : [-(in(ordered_pair(_218373, _218371), _217651)), 2404 ^ _133474 : [(2405 ^ _133474) ^ [_218484] : [in(ordered_pair(_218373, _218484), _217285), in(ordered_pair(_218484, _218371), _217470)]]]]]]]]]]], (2436 ^ _133474) ^ [_219787] : [relation(_219787), 2439 ^ _133474 : [(2466 ^ _133474) ^ [_220822] : [2470 ^ _133474 : [(2471 ^ _133474) ^ [] : [-(in(2467 ^ [_219787, _220822], _220822))], (2473 ^ _133474) ^ [] : [-(in(2468 ^ [_219787, _220822], _220822))], (2475 ^ _133474) ^ [] : [-(in(2469 ^ [_219787, _220822], _220822))], (2477 ^ _133474) ^ [] : [-(in(ordered_pair(2467 ^ [_219787, _220822], 2468 ^ [_219787, _220822]), _219787))], (2479 ^ _133474) ^ [] : [-(in(ordered_pair(2468 ^ [_219787, _220822], 2469 ^ [_219787, _220822]), _219787))], (2481 ^ _133474) ^ [] : [in(ordered_pair(2467 ^ [_219787, _220822], 2469 ^ [_219787, _220822]), _219787)]], -(is_transitive_in(_219787, _220822))], (2440 ^ _133474) ^ [_220001] : [is_transitive_in(_219787, _220001), 2443 ^ _133474 : [(2444 ^ _133474) ^ [_220211, _220213, _220215] : [-(in(ordered_pair(_220215, _220211), _219787)), in(_220215, _220001), in(_220213, _220001), in(_220211, _220001), in(ordered_pair(_220215, _220213), _219787), in(ordered_pair(_220213, _220211), _219787)]]]]], (2485 ^ _133474) ^ [_221846, _221848] : [element(_221846, powerset(powerset(_221848))), 2488 ^ _133474 : [(2489 ^ _133474) ^ [_222026] : [element(_222026, powerset(powerset(_221848))), 2492 ^ _133474 : [(2513 ^ _133474) ^ [] : [-(_222026 = complements_of_subsets(_221848, _221846)), 2515 ^ _133474 : [(2516 ^ _133474) ^ [] : [-(element(2514 ^ [_221846, _221848, _222026], powerset(_221848)))], (2518 ^ _133474) ^ [] : [2519 ^ _133474 : [(2520 ^ _133474) ^ [] : [-(in(2514 ^ [_221846, _221848, _222026], _222026))], (2522 ^ _133474) ^ [] : [in(subset_complement(_221848, 2514 ^ [_221846, _221848, _222026]), _221846)]], 2523 ^ _133474 : [(2524 ^ _133474) ^ [] : [-(in(subset_complement(_221848, 2514 ^ [_221846, _221848, _222026]), _221846))], (2526 ^ _133474) ^ [] : [in(2514 ^ [_221846, _221848, _222026], _222026)]]]]], (2493 ^ _133474) ^ [] : [_222026 = complements_of_subsets(_221848, _221846), 2496 ^ _133474 : [(2497 ^ _133474) ^ [_222314] : [element(_222314, powerset(_221848)), 2500 ^ _133474 : [(2501 ^ _133474) ^ [] : [in(_222314, _222026), -(in(subset_complement(_221848, _222314), _221846))], (2507 ^ _133474) ^ [] : [in(subset_complement(_221848, _222314), _221846), -(in(_222314, _222026))]]]]]]]]], (2530 ^ _133474) ^ [_223437, _223439] : [proper_subset(_223439, _223437), 2533 ^ _133474 : [(2534 ^ _133474) ^ [] : [-(subset(_223439, _223437))], (2536 ^ _133474) ^ [] : [_223439 = _223437]]], (2538 ^ _133474) ^ [_223675, _223677] : [-(proper_subset(_223677, _223675)), subset(_223677, _223675), -(_223677 = _223675)], (2548 ^ _133474) ^ [_223965] : [relation(_223965), function(_223965), one_to_one(_223965), -(function_inverse(_223965) = relation_inverse(_223965))], (2562 ^ _133474) ^ [_224329] : [relation(_224329), 2565 ^ _133474 : [(2566 ^ _133474) ^ [] : [reflexive(_224329), -(is_reflexive_in(_224329, relation_field(_224329)))], (2572 ^ _133474) ^ [] : [is_reflexive_in(_224329, relation_field(_224329)), -(reflexive(_224329))]]], (2578 ^ _133474) ^ [] : [true___, -(true___)], (2584 ^ _133474) ^ [] : [true___, -(true___)], (2590 ^ _133474) ^ [] : [true___, -(true___)], (2596 ^ _133474) ^ [] : [true___, -(true___)], (2602 ^ _133474) ^ [] : [true___, -(true___)], (2608 ^ _133474) ^ [] : [true___, -(true___)], (2614 ^ _133474) ^ [] : [true___, -(true___)], (2620 ^ _133474) ^ [] : [true___, -(true___)], (2626 ^ _133474) ^ [] : [true___, -(true___)], (2632 ^ _133474) ^ [] : [true___, -(true___)], (2638 ^ _133474) ^ [_225950] : [2645 ^ _133474 : [(2646 ^ _133474) ^ [] : [-(relation(function_inverse(_225950)))], (2648 ^ _133474) ^ [] : [-(function(function_inverse(_225950)))]], relation(_225950), function(_225950)], (2650 ^ _133474) ^ [] : [true___, -(true___)], (2656 ^ _133474) ^ [_226402] : [-(element(cast_to_subset(_226402), powerset(_226402)))], (2658 ^ _133474) ^ [] : [true___, -(true___)], (2664 ^ _133474) ^ [] : [true___, -(true___)], (2670 ^ _133474) ^ [] : [true___, -(true___)], (2676 ^ _133474) ^ [] : [true___, -(true___)], (2682 ^ _133474) ^ [_226989, _226991] : [element(_226989, powerset(_226991)), -(element(subset_complement(_226991, _226989), powerset(_226991)))], (2688 ^ _133474) ^ [] : [true___, -(true___)], (2694 ^ _133474) ^ [] : [true___, -(true___)], (2700 ^ _133474) ^ [_227437] : [relation(_227437), -(relation(relation_inverse(_227437)))], (2706 ^ _133474) ^ [] : [true___, -(true___)], (2712 ^ _133474) ^ [] : [true___, -(true___)], (2718 ^ _133474) ^ [_227879, _227881] : [-(relation(relation_composition(_227881, _227879))), relation(_227881), relation(_227879)], (2728 ^ _133474) ^ [_228178, _228180] : [element(_228178, powerset(powerset(_228180))), -(element(union_of_subsets(_228180, _228178), powerset(_228180)))], (2734 ^ _133474) ^ [_228377] : [-(relation(identity_relation(_228377)))], (2736 ^ _133474) ^ [_228485, _228487] : [element(_228485, powerset(powerset(_228487))), -(element(meet_of_subsets(_228487, _228485), powerset(_228487)))], (2742 ^ _133474) ^ [_228727, _228729, _228731] : [-(element(subset_difference(_228731, _228729, _228727), powerset(_228731))), element(_228729, powerset(_228731)), element(_228727, powerset(_228731))], (2752 ^ _133474) ^ [_229056, _229058] : [relation(_229058), -(relation(relation_dom_restriction(_229058, _229056)))], (2758 ^ _133474) ^ [_229268, _229270] : [element(_229268, powerset(powerset(_229270))), -(element(complements_of_subsets(_229270, _229268), powerset(powerset(_229270))))], (2764 ^ _133474) ^ [_229500, _229502] : [relation(_229500), -(relation(relation_rng_restriction(_229502, _229500)))], (2770 ^ _133474) ^ [] : [true___, -(true___)], (2776 ^ _133474) ^ [] : [true___, -(true___)], (2783 ^ _133474) ^ [_229960] : [-(element(2781 ^ [_229960], _229960))], (2785 ^ _133474) ^ [_230072, _230074] : [2792 ^ _133474 : [(2793 ^ _133474) ^ [] : [-(empty(relation_composition(_230072, _230074)))], (2795 ^ _133474) ^ [] : [-(relation(relation_composition(_230072, _230074)))]], empty(_230074), relation(_230072)], (2797 ^ _133474) ^ [_230436] : [empty(_230436), 2800 ^ _133474 : [(2801 ^ _133474) ^ [] : [-(empty(relation_inverse(_230436)))], (2803 ^ _133474) ^ [] : [-(relation(relation_inverse(_230436)))]]], (2805 ^ _133474) ^ [] : [-(empty(empty_set))], (2807 ^ _133474) ^ [] : [-(relation(empty_set))], (2809 ^ _133474) ^ [] : [-(relation_empty_yielding(empty_set))], (2811 ^ _133474) ^ [_230878, _230880] : [2818 ^ _133474 : [(2819 ^ _133474) ^ [] : [-(relation(relation_dom_restriction(_230880, _230878)))], (2821 ^ _133474) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_230880, _230878)))]], relation(_230880), relation_empty_yielding(_230880)], (2823 ^ _133474) ^ [_231256, _231258] : [2838 ^ _133474 : [(2839 ^ _133474) ^ [] : [-(relation(relation_composition(_231258, _231256)))], (2841 ^ _133474) ^ [] : [-(function(relation_composition(_231258, _231256)))]], relation(_231258), function(_231258), relation(_231256), function(_231256)], (2843 ^ _133474) ^ [_231778] : [empty(succ(_231778))], (2845 ^ _133474) ^ [_231886, _231888] : [-(relation(set_intersection2(_231888, _231886))), relation(_231888), relation(_231886)], (2855 ^ _133474) ^ [_232155] : [empty(powerset(_232155))], (2857 ^ _133474) ^ [] : [-(empty(empty_set))], (2859 ^ _133474) ^ [_232300, _232302] : [empty(ordered_pair(_232302, _232300))], (2861 ^ _133474) ^ [_232402] : [-(relation(identity_relation(_232402)))], (2863 ^ _133474) ^ [_232447] : [-(function(identity_relation(_232447)))], (2865 ^ _133474) ^ [] : [-(relation(empty_set))], (2867 ^ _133474) ^ [] : [-(relation_empty_yielding(empty_set))], (2869 ^ _133474) ^ [] : [-(function(empty_set))], (2871 ^ _133474) ^ [] : [-(one_to_one(empty_set))], (2873 ^ _133474) ^ [] : [-(empty(empty_set))], (2875 ^ _133474) ^ [] : [-(epsilon_transitive(empty_set))], (2877 ^ _133474) ^ [] : [-(epsilon_connected(empty_set))], (2879 ^ _133474) ^ [] : [-(ordinal(empty_set))], (2881 ^ _133474) ^ [_232995, _232997] : [-(relation(set_union2(_232997, _232995))), relation(_232997), relation(_232995)], (2891 ^ _133474) ^ [_233264] : [empty(singleton(_233264))], (2893 ^ _133474) ^ [_233372, _233374] : [-(empty(_233374)), empty(set_union2(_233374, _233372))], (2899 ^ _133474) ^ [_233574] : [2910 ^ _133474 : [(2911 ^ _133474) ^ [] : [-(relation(relation_inverse(_233574)))], (2913 ^ _133474) ^ [] : [-(function(relation_inverse(_233574)))]], relation(_233574), function(_233574), one_to_one(_233574)], (2915 ^ _133474) ^ [_234005] : [ordinal(_234005), 2918 ^ _133474 : [(2919 ^ _133474) ^ [] : [empty(succ(_234005))], (2921 ^ _133474) ^ [] : [-(epsilon_transitive(succ(_234005)))], (2923 ^ _133474) ^ [] : [-(epsilon_connected(succ(_234005)))], (2925 ^ _133474) ^ [] : [-(ordinal(succ(_234005)))]]], (2927 ^ _133474) ^ [_234433, _234435] : [-(relation(set_difference(_234435, _234433))), relation(_234435), relation(_234433)], (2937 ^ _133474) ^ [_234716, _234718] : [empty(unordered_pair(_234718, _234716))], (2939 ^ _133474) ^ [_234827, _234829] : [-(empty(_234829)), empty(set_union2(_234827, _234829))], (2945 ^ _133474) ^ [_235043, _235045] : [2952 ^ _133474 : [(2953 ^ _133474) ^ [] : [-(relation(relation_dom_restriction(_235045, _235043)))], (2955 ^ _133474) ^ [] : [-(function(relation_dom_restriction(_235045, _235043)))]], relation(_235045), function(_235045)], (2957 ^ _133474) ^ [_235407] : [ordinal(_235407), 2960 ^ _133474 : [(2961 ^ _133474) ^ [] : [-(epsilon_transitive(union(_235407)))], (2963 ^ _133474) ^ [] : [-(epsilon_connected(union(_235407)))], (2965 ^ _133474) ^ [] : [-(ordinal(union(_235407)))]]], (2967 ^ _133474) ^ [] : [-(empty(empty_set))], (2969 ^ _133474) ^ [] : [-(relation(empty_set))], (2971 ^ _133474) ^ [_235868, _235870] : [empty(cartesian_product2(_235870, _235868)), -(empty(_235870)), -(empty(_235868))], (2981 ^ _133474) ^ [_236160] : [empty(relation_dom(_236160)), -(empty(_236160)), relation(_236160)], (2991 ^ _133474) ^ [_236437] : [empty(relation_rng(_236437)), -(empty(_236437)), relation(_236437)], (3001 ^ _133474) ^ [_236714] : [empty(_236714), 3004 ^ _133474 : [(3005 ^ _133474) ^ [] : [-(empty(relation_dom(_236714)))], (3007 ^ _133474) ^ [] : [-(relation(relation_dom(_236714)))]]], (3009 ^ _133474) ^ [_236979] : [empty(_236979), 3012 ^ _133474 : [(3013 ^ _133474) ^ [] : [-(empty(relation_rng(_236979)))], (3015 ^ _133474) ^ [] : [-(relation(relation_rng(_236979)))]]], (3017 ^ _133474) ^ [_237258, _237260] : [3024 ^ _133474 : [(3025 ^ _133474) ^ [] : [-(empty(relation_composition(_237260, _237258)))], (3027 ^ _133474) ^ [] : [-(relation(relation_composition(_237260, _237258)))]], empty(_237260), relation(_237258)], (3029 ^ _133474) ^ [_237621, _237623] : [-(set_union2(_237623, _237623) = _237623)], (3031 ^ _133474) ^ [_237718, _237720] : [-(set_intersection2(_237720, _237720) = _237720)], (3033 ^ _133474) ^ [_237830, _237832] : [element(_237830, powerset(_237832)), -(subset_complement(_237832, subset_complement(_237832, _237830)) = _237830)], (3039 ^ _133474) ^ [_238042] : [relation(_238042), -(relation_inverse(relation_inverse(_238042)) = _238042)], (3045 ^ _133474) ^ [_238252, _238254] : [element(_238252, powerset(powerset(_238254))), -(complements_of_subsets(_238254, complements_of_subsets(_238254, _238252)) = _238252)], (3051 ^ _133474) ^ [_238466, _238468] : [proper_subset(_238468, _238468)], (3053 ^ _133474) ^ [_238561] : [relation(_238561), 3056 ^ _133474 : [(3067 ^ _133474) ^ [] : [3069 ^ _133474 : [(3070 ^ _133474) ^ [] : [-(in(3068 ^ [_238561], relation_field(_238561)))], (3072 ^ _133474) ^ [] : [in(ordered_pair(3068 ^ [_238561], 3068 ^ [_238561]), _238561)]], -(reflexive(_238561))], (3057 ^ _133474) ^ [] : [reflexive(_238561), 3060 ^ _133474 : [(3061 ^ _133474) ^ [_238805] : [in(_238805, relation_field(_238561)), -(in(ordered_pair(_238805, _238805), _238561))]]]]], (3076 ^ _133474) ^ [_239270] : [singleton(_239270) = empty_set], (3078 ^ _133474) ^ [_239379, _239381] : [in(_239381, _239379), -(set_union2(singleton(_239381), _239379) = _239379)], (3084 ^ _133474) ^ [_239599, _239601] : [disjoint(singleton(_239601), _239599), in(_239601, _239599)], (3090 ^ _133474) ^ [_239812, _239814] : [-(in(_239814, _239812)), -(disjoint(singleton(_239814), _239812))], (3096 ^ _133474) ^ [_240015] : [relation(_240015), 3099 ^ _133474 : [(3114 ^ _133474) ^ [] : [3118 ^ _133474 : [(3119 ^ _133474) ^ [] : [-(in(ordered_pair(3115 ^ [_240015], 3116 ^ [_240015]), _240015))], (3121 ^ _133474) ^ [] : [-(in(ordered_pair(3116 ^ [_240015], 3117 ^ [_240015]), _240015))], (3123 ^ _133474) ^ [] : [in(ordered_pair(3115 ^ [_240015], 3117 ^ [_240015]), _240015)]], -(transitive(_240015))], (3100 ^ _133474) ^ [] : [transitive(_240015), 3103 ^ _133474 : [(3104 ^ _133474) ^ [_240307, _240309, _240311] : [-(in(ordered_pair(_240311, _240307), _240015)), in(ordered_pair(_240311, _240309), _240015), in(ordered_pair(_240309, _240307), _240015)]]]]], (3127 ^ _133474) ^ [_241214, _241216] : [subset(singleton(_241216), _241214), -(in(_241216, _241214))], (3133 ^ _133474) ^ [_241380, _241382] : [in(_241382, _241380), -(subset(singleton(_241382), _241380))], (3139 ^ _133474) ^ [_241625, _241627] : [set_difference(_241627, _241625) = empty_set, -(subset(_241627, _241625))], (3145 ^ _133474) ^ [_241793, _241795] : [subset(_241795, _241793), -(set_difference(_241795, _241793) = empty_set)], (3151 ^ _133474) ^ [_242011, _242013] : [element(_242011, powerset(_242013)), 3154 ^ _133474 : [(3155 ^ _133474) ^ [_242152] : [in(_242152, _242011), -(in(_242152, _242013))]]], (3161 ^ _133474) ^ [_242363] : [relation(_242363), 3164 ^ _133474 : [(3179 ^ _133474) ^ [] : [3182 ^ _133474 : [(3183 ^ _133474) ^ [] : [-(in(ordered_pair(3180 ^ [_242363], 3181 ^ [_242363]), _242363))], (3185 ^ _133474) ^ [] : [-(in(ordered_pair(3181 ^ [_242363], 3180 ^ [_242363]), _242363))], (3187 ^ _133474) ^ [] : [3180 ^ [_242363] = 3181 ^ [_242363]]], -(antisymmetric(_242363))], (3165 ^ _133474) ^ [] : [antisymmetric(_242363), 3168 ^ _133474 : [(3169 ^ _133474) ^ [_242633, _242635] : [-(_242635 = _242633), in(ordered_pair(_242635, _242633), _242363), in(ordered_pair(_242633, _242635), _242363)]]]]], (3191 ^ _133474) ^ [_243413, _243415, _243417] : [subset(_243417, _243415), -(in(_243413, _243417)), -(subset(_243417, set_difference(_243415, singleton(_243413))))], (3201 ^ _133474) ^ [_243719] : [relation(_243719), 3204 ^ _133474 : [(3227 ^ _133474) ^ [] : [3230 ^ _133474 : [(3231 ^ _133474) ^ [] : [-(in(3228 ^ [_243719], relation_field(_243719)))], (3233 ^ _133474) ^ [] : [-(in(3229 ^ [_243719], relation_field(_243719)))], (3235 ^ _133474) ^ [] : [3228 ^ [_243719] = 3229 ^ [_243719]], (3237 ^ _133474) ^ [] : [in(ordered_pair(3228 ^ [_243719], 3229 ^ [_243719]), _243719)], (3239 ^ _133474) ^ [] : [in(ordered_pair(3229 ^ [_243719], 3228 ^ [_243719]), _243719)]], -(connected(_243719))], (3205 ^ _133474) ^ [] : [connected(_243719), 3208 ^ _133474 : [(3209 ^ _133474) ^ [_244013, _244015] : [in(_244015, relation_field(_243719)), in(_244013, relation_field(_243719)), -(_244015 = _244013), -(in(ordered_pair(_244015, _244013), _243719)), -(in(ordered_pair(_244013, _244015), _243719))]]]]], (3253 ^ _133474) ^ [_245465, _245467] : [3254 ^ _133474 : [(3255 ^ _133474) ^ [] : [_245467 = empty_set], (3257 ^ _133474) ^ [] : [_245467 = singleton(_245465)]], -(subset(_245467, singleton(_245465)))], (3243 ^ _133474) ^ [_245205, _245207] : [subset(_245207, singleton(_245205)), -(_245207 = empty_set), -(_245207 = singleton(_245205))], (3261 ^ _133474) ^ [_245759, _245761] : [in(_245761, _245759), -(subset(_245761, union(_245759)))], (3267 ^ _133474) ^ [_246030, _246032, _246034, _246036] : [in(ordered_pair(_246036, _246034), cartesian_product2(_246032, _246030)), 3270 ^ _133474 : [(3271 ^ _133474) ^ [] : [-(in(_246036, _246032))], (3273 ^ _133474) ^ [] : [-(in(_246034, _246030))]]], (3275 ^ _133474) ^ [_246295, _246297, _246299, _246301] : [-(in(ordered_pair(_246301, _246299), cartesian_product2(_246297, _246295))), in(_246301, _246297), in(_246299, _246295)], (3285 ^ _133474) ^ [_246628, _246630] : [3287 ^ _133474 : [(3288 ^ _133474) ^ [] : [-(in(3286 ^ [_246628, _246630], _246630))], (3290 ^ _133474) ^ [] : [in(3286 ^ [_246628, _246630], _246628)]], -(element(_246630, powerset(_246628)))], (3294 ^ _133474) ^ [_247001, _247003, _247005] : [relation(_247001), function(_247001), 3301 ^ _133474 : [(3302 ^ _133474) ^ [] : [in(_247003, relation_dom(relation_dom_restriction(_247001, _247005))), 3305 ^ _133474 : [(3306 ^ _133474) ^ [] : [-(in(_247003, relation_dom(_247001)))], (3308 ^ _133474) ^ [] : [-(in(_247003, _247005))]]], (3310 ^ _133474) ^ [] : [-(in(_247003, relation_dom(relation_dom_restriction(_247001, _247005)))), in(_247003, relation_dom(_247001)), in(_247003, _247005)]]], (3321 ^ _133474) ^ [] : [-(relation(3319 ^ []))], (3323 ^ _133474) ^ [] : [-(function(3319 ^ []))], (3326 ^ _133474) ^ [] : [-(epsilon_transitive(3324 ^ []))], (3328 ^ _133474) ^ [] : [-(epsilon_connected(3324 ^ []))], (3330 ^ _133474) ^ [] : [-(ordinal(3324 ^ []))], (3333 ^ _133474) ^ [] : [-(empty(3331 ^ []))], (3335 ^ _133474) ^ [] : [-(relation(3331 ^ []))], (3337 ^ _133474) ^ [_248246] : [-(empty(_248246)), 3341 ^ _133474 : [(3342 ^ _133474) ^ [] : [-(element(3340 ^ [_248246], powerset(_248246)))], (3344 ^ _133474) ^ [] : [empty(3340 ^ [_248246])]]], (3347 ^ _133474) ^ [] : [-(empty(3345 ^ []))], (3350 ^ _133474) ^ [] : [-(relation(3348 ^ []))], (3352 ^ _133474) ^ [] : [-(empty(3348 ^ []))], (3354 ^ _133474) ^ [] : [-(function(3348 ^ []))], (3357 ^ _133474) ^ [] : [-(relation(3355 ^ []))], (3359 ^ _133474) ^ [] : [-(function(3355 ^ []))], (3361 ^ _133474) ^ [] : [-(one_to_one(3355 ^ []))], (3363 ^ _133474) ^ [] : [-(empty(3355 ^ []))], (3365 ^ _133474) ^ [] : [-(epsilon_transitive(3355 ^ []))], (3367 ^ _133474) ^ [] : [-(epsilon_connected(3355 ^ []))], (3369 ^ _133474) ^ [] : [-(ordinal(3355 ^ []))], (3372 ^ _133474) ^ [] : [empty(3370 ^ [])], (3374 ^ _133474) ^ [] : [-(relation(3370 ^ []))], (3377 ^ _133474) ^ [_249526] : [-(element(3375 ^ [_249526], powerset(_249526)))], (3379 ^ _133474) ^ [_249577] : [-(empty(3375 ^ [_249577]))], (3382 ^ _133474) ^ [] : [empty(3380 ^ [])], (3385 ^ _133474) ^ [] : [-(relation(3383 ^ []))], (3387 ^ _133474) ^ [] : [-(function(3383 ^ []))], (3389 ^ _133474) ^ [] : [-(one_to_one(3383 ^ []))], (3392 ^ _133474) ^ [] : [empty(3390 ^ [])], (3394 ^ _133474) ^ [] : [-(epsilon_transitive(3390 ^ []))], (3396 ^ _133474) ^ [] : [-(epsilon_connected(3390 ^ []))], (3398 ^ _133474) ^ [] : [-(ordinal(3390 ^ []))], (3401 ^ _133474) ^ [] : [-(relation(3399 ^ []))], (3403 ^ _133474) ^ [] : [-(relation_empty_yielding(3399 ^ []))], (3406 ^ _133474) ^ [] : [-(relation(3404 ^ []))], (3408 ^ _133474) ^ [] : [-(relation_empty_yielding(3404 ^ []))], (3410 ^ _133474) ^ [] : [-(function(3404 ^ []))], (3412 ^ _133474) ^ [_250617, _250619] : [element(_250617, powerset(powerset(_250619))), -(union_of_subsets(_250619, _250617) = union(_250617))], (3418 ^ _133474) ^ [_250845, _250847] : [element(_250845, powerset(powerset(_250847))), -(meet_of_subsets(_250847, _250845) = set_meet(_250845))], (3424 ^ _133474) ^ [_251087, _251089, _251091] : [-(subset_difference(_251091, _251089, _251087) = set_difference(_251089, _251087)), element(_251089, powerset(_251091)), element(_251087, powerset(_251091))], (3434 ^ _133474) ^ [_251418, _251420] : [ordinal(_251420), ordinal(_251418), 3441 ^ _133474 : [(3442 ^ _133474) ^ [] : [ordinal_subset(_251420, _251418), -(subset(_251420, _251418))], (3448 ^ _133474) ^ [] : [subset(_251420, _251418), -(ordinal_subset(_251420, _251418))]]], (3454 ^ _133474) ^ [_251965, _251967] : [-(ordinal_subset(_251967, _251967)), ordinal(_251967), ordinal(_251965)], (3464 ^ _133474) ^ [_252245, _252247] : [-(subset(_252247, _252247))], (3466 ^ _133474) ^ [_252354, _252356] : [disjoint(_252356, _252354), -(disjoint(_252354, _252356))], (3472 ^ _133474) ^ [_252621, _252623, _252625, _252627] : [in(ordered_pair(_252627, _252625), cartesian_product2(_252623, _252621)), 3475 ^ _133474 : [(3476 ^ _133474) ^ [] : [-(in(_252627, _252623))], (3478 ^ _133474) ^ [] : [-(in(_252625, _252621))]]], (3480 ^ _133474) ^ [_252886, _252888, _252890, _252892] : [-(in(ordered_pair(_252892, _252890), cartesian_product2(_252888, _252886))), in(_252892, _252888), in(_252890, _252886)], (3490 ^ _133474) ^ [_253190] : [-(in(_253190, succ(_253190)))], (3492 ^ _133474) ^ [_253327, _253329, _253331, _253333] : [unordered_pair(_253333, _253331) = unordered_pair(_253329, _253327), -(_253333 = _253329), -(_253333 = _253327)], (3502 ^ _133474) ^ [_253677, _253679, _253681] : [relation(_253677), 3505 ^ _133474 : [(3506 ^ _133474) ^ [] : [in(_253681, relation_rng(relation_rng_restriction(_253679, _253677))), 3509 ^ _133474 : [(3510 ^ _133474) ^ [] : [-(in(_253681, _253679))], (3512 ^ _133474) ^ [] : [-(in(_253681, relation_rng(_253677)))]]], (3514 ^ _133474) ^ [] : [-(in(_253681, relation_rng(relation_rng_restriction(_253679, _253677)))), in(_253681, _253679), in(_253681, relation_rng(_253677))]]], (3524 ^ _133474) ^ [_254336, _254338] : [relation(_254336), -(subset(relation_rng(relation_rng_restriction(_254338, _254336)), _254338))], (3530 ^ _133474) ^ [_254554, _254556] : [relation(_254554), -(subset(relation_rng_restriction(_254556, _254554), _254554))], (3536 ^ _133474) ^ [_254768, _254770] : [relation(_254768), -(subset(relation_rng(relation_rng_restriction(_254770, _254768)), relation_rng(_254768)))], (3542 ^ _133474) ^ [_255004, _255006, _255008] : [subset(_255008, _255006), 3545 ^ _133474 : [(3546 ^ _133474) ^ [] : [-(subset(cartesian_product2(_255008, _255004), cartesian_product2(_255006, _255004)))], (3548 ^ _133474) ^ [] : [-(subset(cartesian_product2(_255004, _255008), cartesian_product2(_255004, _255006)))]]], (3550 ^ _133474) ^ [_255321, _255323] : [relation(_255321), -(relation_rng(relation_rng_restriction(_255323, _255321)) = set_intersection2(relation_rng(_255321), _255323))], (3556 ^ _133474) ^ [_255577, _255579, _255581, _255583] : [-(subset(cartesian_product2(_255583, _255579), cartesian_product2(_255581, _255577))), subset(_255583, _255581), subset(_255579, _255577)], (3566 ^ _133474) ^ [_255908, _255910] : [subset(_255910, _255908), -(set_union2(_255910, _255908) = _255908)], (3573 ^ _133474) ^ [_256230] : [-(in(_256230, 3571 ^ [_256230]))], (3575 ^ _133474) ^ [_256342, _256344, _256346] : [-(in(_256342, 3571 ^ [_256346])), in(_256344, 3571 ^ [_256346]), subset(_256342, _256344)], (3585 ^ _133474) ^ [_256657, _256659] : [in(_256657, 3571 ^ [_256659]), -(in(powerset(_256657), 3571 ^ [_256659]))], (3591 ^ _133474) ^ [_256857, _256859] : [subset(_256857, 3571 ^ [_256859]), -(are_equipotent(_256857, 3571 ^ [_256859])), -(in(_256857, 3571 ^ [_256859]))], (3601 ^ _133474) ^ [_257211, _257213, _257215] : [relation(_257211), -(relation_dom_restriction(relation_rng_restriction(_257215, _257211), _257213) = relation_rng_restriction(_257215, relation_dom_restriction(_257211, _257213)))], (3607 ^ _133474) ^ [_257463, _257465, _257467] : [relation(_257463), 3610 ^ _133474 : [(3611 ^ _133474) ^ [] : [in(_257467, relation_image(_257463, _257465)), 3615 ^ _133474 : [(3616 ^ _133474) ^ [] : [-(in(3614 ^ [_257463, _257465, _257467], relation_dom(_257463)))], (3618 ^ _133474) ^ [] : [-(in(ordered_pair(3614 ^ [_257463, _257465, _257467], _257467), _257463))], (3620 ^ _133474) ^ [] : [-(in(3614 ^ [_257463, _257465, _257467], _257465))]]], (3622 ^ _133474) ^ [] : [-(in(_257467, relation_image(_257463, _257465))), 3623 ^ _133474 : [(3624 ^ _133474) ^ [_258064] : [in(_258064, relation_dom(_257463)), in(ordered_pair(_258064, _257467), _257463), in(_258064, _257465)]]]]], (3636 ^ _133474) ^ [_258461, _258463] : [relation(_258461), -(subset(relation_image(_258461, _258463), relation_rng(_258461)))], (3642 ^ _133474) ^ [_258679, _258681] : [-(subset(relation_image(_258679, relation_inverse_image(_258679, _258681)), _258681)), relation(_258679), function(_258679)], (3652 ^ _133474) ^ [_258986, _258988] : [relation(_258986), -(relation_image(_258986, _258988) = relation_image(_258986, set_intersection2(relation_dom(_258986), _258988)))], (3658 ^ _133474) ^ [_259216, _259218] : [relation(_259216), subset(_259218, relation_dom(_259216)), -(subset(_259218, relation_inverse_image(_259216, relation_image(_259216, _259218))))], (3668 ^ _133474) ^ [_259515] : [relation(_259515), -(relation_image(_259515, relation_dom(_259515)) = relation_rng(_259515))], (3674 ^ _133474) ^ [_259731, _259733] : [relation(_259731), function(_259731), subset(_259733, relation_rng(_259731)), -(relation_image(_259731, relation_inverse_image(_259731, _259733)) = _259733)], (3688 ^ _133474) ^ [_260119] : [relation(_260119), 3691 ^ _133474 : [(3692 ^ _133474) ^ [_260259] : [relation(_260259), -(relation_rng(relation_composition(_260119, _260259)) = relation_image(_260259, relation_rng(_260119)))]]], (3698 ^ _133474) ^ [_260508, _260510, _260512] : [relation(_260508), 3701 ^ _133474 : [(3702 ^ _133474) ^ [] : [in(_260512, relation_inverse_image(_260508, _260510)), 3706 ^ _133474 : [(3707 ^ _133474) ^ [] : [-(in(3705 ^ [_260508, _260510, _260512], relation_rng(_260508)))], (3709 ^ _133474) ^ [] : [-(in(ordered_pair(_260512, 3705 ^ [_260508, _260510, _260512]), _260508))], (3711 ^ _133474) ^ [] : [-(in(3705 ^ [_260508, _260510, _260512], _260510))]]], (3713 ^ _133474) ^ [] : [-(in(_260512, relation_inverse_image(_260508, _260510))), 3714 ^ _133474 : [(3715 ^ _133474) ^ [_261109] : [in(_261109, relation_rng(_260508)), in(ordered_pair(_260512, _261109), _260508), in(_261109, _260510)]]]]], (3727 ^ _133474) ^ [_261506, _261508] : [relation(_261506), -(subset(relation_inverse_image(_261506, _261508), relation_dom(_261506)))], (3733 ^ _133474) ^ [_261724, _261726] : [relation(_261724), -(_261726 = empty_set), subset(_261726, relation_rng(_261724)), relation_inverse_image(_261724, _261726) = empty_set], (3747 ^ _133474) ^ [_262138, _262140, _262142] : [relation(_262138), subset(_262142, _262140), -(subset(relation_inverse_image(_262138, _262142), relation_inverse_image(_262138, _262140)))], (3757 ^ _133474) ^ [_262442, _262444] : [-(subset(set_intersection2(_262444, _262442), _262444))], (3759 ^ _133474) ^ [_262568, _262570, _262572] : [-(subset(_262572, set_intersection2(_262570, _262568))), subset(_262572, _262570), subset(_262572, _262568)], (3769 ^ _133474) ^ [_262854] : [-(set_union2(_262854, empty_set) = _262854)], (3771 ^ _133474) ^ [_262964, _262966] : [in(_262966, _262964), -(element(_262966, _262964))], (3777 ^ _133474) ^ [_263188, _263190, _263192] : [-(subset(_263192, _263188)), subset(_263192, _263190), subset(_263190, _263188)], (3787 ^ _133474) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (3789 ^ _133474) ^ [_263564, _263566, _263568] : [relation(_263564), in(ordered_pair(_263568, _263566), _263564), 3796 ^ _133474 : [(3797 ^ _133474) ^ [] : [-(in(_263568, relation_dom(_263564)))], (3799 ^ _133474) ^ [] : [-(in(_263566, relation_rng(_263564)))]]], (3801 ^ _133474) ^ [_263962, _263964] : [relation(_263962), function(_263962), 3808 ^ _133474 : [(3809 ^ _133474) ^ [_264212] : [relation(_264212), function(_264212), 3816 ^ _133474 : [(3817 ^ _133474) ^ [] : [in(_263964, relation_dom(relation_composition(_264212, _263962))), 3820 ^ _133474 : [(3821 ^ _133474) ^ [] : [-(in(_263964, relation_dom(_264212)))], (3823 ^ _133474) ^ [] : [-(in(apply(_264212, _263964), relation_dom(_263962)))]]], (3825 ^ _133474) ^ [] : [-(in(_263964, relation_dom(relation_composition(_264212, _263962)))), in(_263964, relation_dom(_264212)), in(apply(_264212, _263964), relation_dom(_263962))]]]]], (3835 ^ _133474) ^ [_264976] : [epsilon_transitive(_264976), 3838 ^ _133474 : [(3839 ^ _133474) ^ [_265112] : [ordinal(_265112), proper_subset(_264976, _265112), -(in(_264976, _265112))]]], (3849 ^ _133474) ^ [_265402] : [relation(_265402), -(subset(_265402, cartesian_product2(relation_dom(_265402), relation_rng(_265402))))], (3855 ^ _133474) ^ [_265618, _265620] : [relation(_265618), function(_265618), 3862 ^ _133474 : [(3863 ^ _133474) ^ [_265867] : [relation(_265867), function(_265867), in(_265620, relation_dom(relation_composition(_265867, _265618))), -(apply(relation_composition(_265867, _265618), _265620) = apply(_265618, apply(_265867, _265620)))]]], (3877 ^ _133474) ^ [_266312, _266314] : [relation(_266312), function(_266312), 3884 ^ _133474 : [(3885 ^ _133474) ^ [_266558] : [relation(_266558), function(_266558), in(_266314, relation_dom(_266312)), -(apply(relation_composition(_266312, _266558), _266314) = apply(_266558, apply(_266312, _266314)))]]], (3899 ^ _133474) ^ [_266997, _266999] : [ordinal(_266997), in(_266999, _266997), -(ordinal(_266999))], (3909 ^ _133474) ^ [_267278] : [ordinal(_267278), 3912 ^ _133474 : [(3913 ^ _133474) ^ [_267428] : [ordinal(_267428), -(in(_267278, _267428)), -(_267278 = _267428), -(in(_267428, _267278))]]], (3927 ^ _133474) ^ [_267817] : [relation(_267817), 3930 ^ _133474 : [(3931 ^ _133474) ^ [_267967] : [relation(_267967), subset(_267817, _267967), 3938 ^ _133474 : [(3939 ^ _133474) ^ [] : [-(subset(relation_dom(_267817), relation_dom(_267967)))], (3941 ^ _133474) ^ [] : [-(subset(relation_rng(_267817), relation_rng(_267967)))]]]]], (3943 ^ _133474) ^ [_268376, _268378, _268380] : [subset(_268380, _268378), -(subset(set_intersection2(_268380, _268376), set_intersection2(_268378, _268376)))], (3949 ^ _133474) ^ [_268604, _268606] : [subset(_268606, _268604), -(set_intersection2(_268606, _268604) = _268606)], (3955 ^ _133474) ^ [_268791] : [-(set_intersection2(_268791, empty_set) = empty_set)], (3957 ^ _133474) ^ [_268901, _268903] : [element(_268903, _268901), -(empty(_268901)), -(in(_268903, _268901))], (3967 ^ _133474) ^ [_269199, _269201] : [-(_269201 = _269199), 3971 ^ _133474 : [(3972 ^ _133474) ^ [] : [-(in(3968 ^ [_269199, _269201], _269201))], (3974 ^ _133474) ^ [] : [in(3968 ^ [_269199, _269201], _269199)]], 3975 ^ _133474 : [(3976 ^ _133474) ^ [] : [-(in(3968 ^ [_269199, _269201], _269199))], (3978 ^ _133474) ^ [] : [in(3968 ^ [_269199, _269201], _269201)]]], (3982 ^ _133474) ^ [_269700] : [-(subset(empty_set, _269700))], (3984 ^ _133474) ^ [_269821, _269823, _269825] : [relation(_269821), in(ordered_pair(_269825, _269823), _269821), 3991 ^ _133474 : [(3992 ^ _133474) ^ [] : [-(in(_269825, relation_field(_269821)))], (3994 ^ _133474) ^ [] : [-(in(_269823, relation_field(_269821)))]]], (3996 ^ _133474) ^ [_270205] : [-(ordinal(_270205)), 3998 ^ _133474 : [(3999 ^ _133474) ^ [] : [-(in(3997 ^ [_270205], _270205))], (4001 ^ _133474) ^ [] : [ordinal(3997 ^ [_270205]), subset(3997 ^ [_270205], _270205)]]], (4009 ^ _133474) ^ [_270635, _270637] : [ordinal(_270635), subset(_270637, _270635), -(_270637 = empty_set), 4021 ^ _133474 : [(4022 ^ _133474) ^ [] : [-(ordinal(4020 ^ [_270635, _270637]))], (4024 ^ _133474) ^ [] : [-(in(4020 ^ [_270635, _270637], _270637))], (4026 ^ _133474) ^ [_271187] : [ordinal(_271187), in(_271187, _270637), -(ordinal_subset(4020 ^ [_270635, _270637], _271187))]]], (4036 ^ _133474) ^ [_271515] : [ordinal(_271515), 4039 ^ _133474 : [(4040 ^ _133474) ^ [_271653] : [ordinal(_271653), 4043 ^ _133474 : [(4044 ^ _133474) ^ [] : [in(_271515, _271653), -(ordinal_subset(succ(_271515), _271653))], (4050 ^ _133474) ^ [] : [ordinal_subset(succ(_271515), _271653), -(in(_271515, _271653))]]]]], (4056 ^ _133474) ^ [_272138, _272140, _272142] : [subset(_272142, _272140), -(subset(set_difference(_272142, _272138), set_difference(_272140, _272138)))], (4062 ^ _133474) ^ [_272394, _272396, _272398, _272400] : [ordered_pair(_272400, _272398) = ordered_pair(_272396, _272394), 4065 ^ _133474 : [(4066 ^ _133474) ^ [] : [-(_272400 = _272396)], (4068 ^ _133474) ^ [] : [-(_272398 = _272394)]]], (4070 ^ _133474) ^ [_272707, _272709] : [relation(_272707), function(_272707), 4077 ^ _133474 : [(4078 ^ _133474) ^ [] : [_272707 = identity_relation(_272709), 4081 ^ _133474 : [(4082 ^ _133474) ^ [] : [-(relation_dom(_272707) = _272709)], (4084 ^ _133474) ^ [_273126] : [in(_273126, _272709), -(apply(_272707, _273126) = _273126)]]], (4090 ^ _133474) ^ [] : [-(_272707 = identity_relation(_272709)), relation_dom(_272707) = _272709, 4096 ^ _133474 : [(4097 ^ _133474) ^ [] : [-(in(4095 ^ [_272707, _272709], _272709))], (4099 ^ _133474) ^ [] : [apply(_272707, 4095 ^ [_272707, _272709]) = 4095 ^ [_272707, _272709]]]]]], (4103 ^ _133474) ^ [_273731, _273733] : [in(_273731, _273733), -(apply(identity_relation(_273733), _273731) = _273731)], (4109 ^ _133474) ^ [_273936, _273938] : [-(subset(set_difference(_273938, _273936), _273938))], (4111 ^ _133474) ^ [_274034] : [relation(_274034), 4114 ^ _133474 : [(4115 ^ _133474) ^ [] : [-(relation_rng(_274034) = relation_dom(relation_inverse(_274034)))], (4117 ^ _133474) ^ [] : [-(relation_dom(_274034) = relation_rng(relation_inverse(_274034)))]]], (4119 ^ _133474) ^ [_274362, _274364] : [set_difference(_274364, _274362) = empty_set, -(subset(_274364, _274362))], (4125 ^ _133474) ^ [_274530, _274532] : [subset(_274532, _274530), -(set_difference(_274532, _274530) = empty_set)], (4131 ^ _133474) ^ [_274777, _274779] : [subset(singleton(_274779), _274777), -(in(_274779, _274777))], (4137 ^ _133474) ^ [_274943, _274945] : [in(_274945, _274943), -(subset(singleton(_274945), _274943))], (4143 ^ _133474) ^ [_275202, _275204, _275206] : [subset(unordered_pair(_275206, _275204), _275202), 4146 ^ _133474 : [(4147 ^ _133474) ^ [] : [-(in(_275206, _275202))], (4149 ^ _133474) ^ [] : [-(in(_275204, _275202))]]], (4151 ^ _133474) ^ [_275453, _275455, _275457] : [-(subset(unordered_pair(_275457, _275455), _275453)), in(_275457, _275453), in(_275455, _275453)], (4161 ^ _133474) ^ [_275755, _275757] : [-(set_union2(_275757, set_difference(_275755, _275757)) = set_union2(_275757, _275755))], (4173 ^ _133474) ^ [_276162, _276164] : [4174 ^ _133474 : [(4175 ^ _133474) ^ [] : [_276164 = empty_set], (4177 ^ _133474) ^ [] : [_276164 = singleton(_276162)]], -(subset(_276164, singleton(_276162)))], (4163 ^ _133474) ^ [_275902, _275904] : [subset(_275904, singleton(_275902)), -(_275904 = empty_set), -(_275904 = singleton(_275902))], (4181 ^ _133474) ^ [_276427] : [-(set_difference(_276427, empty_set) = _276427)], (4183 ^ _133474) ^ [_276551, _276553, _276555] : [in(_276555, _276553), in(_276553, _276551), in(_276551, _276555)], (4193 ^ _133474) ^ [_276888, _276890] : [element(_276890, powerset(_276888)), -(subset(_276890, _276888))], (4199 ^ _133474) ^ [_277054, _277056] : [subset(_277056, _277054), -(element(_277056, powerset(_277054)))], (4205 ^ _133474) ^ [_277290, _277292] : [-(disjoint(_277292, _277290)), 4209 ^ _133474 : [(4210 ^ _133474) ^ [] : [-(in(4208 ^ [_277290, _277292], _277292))], (4212 ^ _133474) ^ [] : [-(in(4208 ^ [_277290, _277292], _277290))]]], (4214 ^ _133474) ^ [_277604, _277606] : [disjoint(_277606, _277604), 4215 ^ _133474 : [(4216 ^ _133474) ^ [_277696] : [in(_277696, _277606), in(_277696, _277604)]]], (4224 ^ _133474) ^ [_277953] : [subset(_277953, empty_set), -(_277953 = empty_set)], (4230 ^ _133474) ^ [_278142, _278144] : [-(set_difference(set_union2(_278144, _278142), _278142) = set_difference(_278144, _278142))], (4232 ^ _133474) ^ [_278246] : [ordinal(_278246), 4235 ^ _133474 : [(4250 ^ _133474) ^ [] : [4252 ^ _133474 : [(4253 ^ _133474) ^ [] : [-(ordinal(4251 ^ [_278246]))], (4255 ^ _133474) ^ [] : [-(in(4251 ^ [_278246], _278246))], (4257 ^ _133474) ^ [] : [in(succ(4251 ^ [_278246]), _278246)]], -(being_limit_ordinal(_278246))], (4236 ^ _133474) ^ [] : [being_limit_ordinal(_278246), 4239 ^ _133474 : [(4240 ^ _133474) ^ [_278492] : [ordinal(_278492), in(_278492, _278246), -(in(succ(_278492), _278246))]]]]], (4261 ^ _133474) ^ [_279118] : [ordinal(_279118), 4264 ^ _133474 : [(4265 ^ _133474) ^ [] : [-(being_limit_ordinal(_279118)), 4269 ^ _133474 : [(4270 ^ _133474) ^ [] : [-(ordinal(4268 ^ [_279118]))], (4272 ^ _133474) ^ [] : [-(_279118 = succ(4268 ^ [_279118]))]]], (4274 ^ _133474) ^ [] : [being_limit_ordinal(_279118), 4275 ^ _133474 : [(4276 ^ _133474) ^ [_279589] : [ordinal(_279589), _279118 = succ(_279589)]]]]], (4284 ^ _133474) ^ [_279856, _279858] : [element(_279856, powerset(_279858)), 4287 ^ _133474 : [(4288 ^ _133474) ^ [_280008] : [element(_280008, powerset(_279858)), 4291 ^ _133474 : [(4292 ^ _133474) ^ [] : [disjoint(_279856, _280008), -(subset(_279856, subset_complement(_279858, _280008)))], (4298 ^ _133474) ^ [] : [subset(_279856, subset_complement(_279858, _280008)), -(disjoint(_279856, _280008))]]]]], (4304 ^ _133474) ^ [_280492] : [relation(_280492), 4307 ^ _133474 : [(4308 ^ _133474) ^ [_280629] : [relation(_280629), -(subset(relation_dom(relation_composition(_280492, _280629)), relation_dom(_280492)))]]], (4314 ^ _133474) ^ [_280844] : [relation(_280844), 4317 ^ _133474 : [(4318 ^ _133474) ^ [_280981] : [relation(_280981), -(subset(relation_rng(relation_composition(_280844, _280981)), relation_rng(_280981)))]]], (4324 ^ _133474) ^ [_281210, _281212] : [subset(_281212, _281210), -(_281210 = set_union2(_281212, set_difference(_281210, _281212)))], (4330 ^ _133474) ^ [_281418] : [relation(_281418), 4333 ^ _133474 : [(4334 ^ _133474) ^ [_281565] : [relation(_281565), subset(relation_rng(_281418), relation_dom(_281565)), -(relation_dom(relation_composition(_281418, _281565)) = relation_dom(_281418))]]], (4344 ^ _133474) ^ [_281891, _281893] : [element(_281891, powerset(powerset(_281893))), -(_281891 = empty_set), complements_of_subsets(_281893, _281891) = empty_set], (4354 ^ _133474) ^ [_282208, _282210] : [in(_282210, _282208), -(set_union2(singleton(_282210), _282208) = _282208)], (4360 ^ _133474) ^ [_282414] : [relation(_282414), 4363 ^ _133474 : [(4364 ^ _133474) ^ [_282561] : [relation(_282561), subset(relation_dom(_282414), relation_rng(_282561)), -(relation_rng(relation_composition(_282561, _282414)) = relation_rng(_282414))]]], (4374 ^ _133474) ^ [_282887, _282889] : [element(_282887, powerset(powerset(_282889))), -(_282887 = empty_set), -(subset_difference(_282889, cast_to_subset(_282889), union_of_subsets(_282889, _282887)) = meet_of_subsets(_282889, complements_of_subsets(_282889, _282887)))], (4384 ^ _133474) ^ [_283227, _283229] : [element(_283227, powerset(powerset(_283229))), -(_283227 = empty_set), -(union_of_subsets(_283229, complements_of_subsets(_283229, _283227)) = subset_difference(_283229, cast_to_subset(_283229), meet_of_subsets(_283229, _283227)))], (4394 ^ _133474) ^ [_283552, _283554] : [-(set_difference(_283554, set_difference(_283554, _283552)) = set_intersection2(_283554, _283552))], (4396 ^ _133474) ^ [_283641] : [-(set_difference(empty_set, _283641) = empty_set)], (4398 ^ _133474) ^ [_283765, _283767, _283769] : [-(element(_283769, _283765)), in(_283769, _283767), element(_283767, powerset(_283765))], (4408 ^ _133474) ^ [_284098, _284100] : [-(disjoint(_284100, _284098)), -(in(4411 ^ [_284098, _284100], set_intersection2(_284100, _284098)))], (4415 ^ _133474) ^ [_284333, _284335] : [4416 ^ _133474 : [(4417 ^ _133474) ^ [_284406] : [in(_284406, set_intersection2(_284335, _284333))]], disjoint(_284335, _284333)], (4421 ^ _133474) ^ [_284558] : [-(_284558 = empty_set), 4424 ^ _133474 : [(4425 ^ _133474) ^ [_284718] : [element(_284718, powerset(_284558)), 4428 ^ _133474 : [(4429 ^ _133474) ^ [_284872] : [element(_284872, _284558), -(in(_284872, _284718)), -(in(_284872, subset_complement(_284558, _284718)))]]]]], (4439 ^ _133474) ^ [_285190] : [relation(_285190), function(_285190), one_to_one(_285190), 4450 ^ _133474 : [(4451 ^ _133474) ^ [_285577] : [relation(_285577), function(_285577), 4458 ^ _133474 : [(4489 ^ _133474) ^ [] : [-(_285577 = function_inverse(_285190)), relation_dom(_285577) = relation_rng(_285190), 4498 ^ _133474 : [(4499 ^ _133474) ^ [] : [-(in(4494 ^ [_285190, _285577], relation_rng(_285190)))], (4501 ^ _133474) ^ [] : [-(4495 ^ [_285190, _285577] = apply(_285577, 4494 ^ [_285190, _285577]))], (4503 ^ _133474) ^ [] : [in(4495 ^ [_285190, _285577], relation_dom(_285190)), 4494 ^ [_285190, _285577] = apply(_285190, 4495 ^ [_285190, _285577])]], 4508 ^ _133474 : [(4509 ^ _133474) ^ [] : [-(in(4495 ^ [_285190, _285577], relation_dom(_285190)))], (4511 ^ _133474) ^ [] : [-(4494 ^ [_285190, _285577] = apply(_285190, 4495 ^ [_285190, _285577]))], (4513 ^ _133474) ^ [] : [in(4494 ^ [_285190, _285577], relation_rng(_285190)), 4495 ^ [_285190, _285577] = apply(_285577, 4494 ^ [_285190, _285577])]]], (4459 ^ _133474) ^ [] : [_285577 = function_inverse(_285190), 4462 ^ _133474 : [(4463 ^ _133474) ^ [] : [-(relation_dom(_285577) = relation_rng(_285190))], (4465 ^ _133474) ^ [_286094, _286096] : [4472 ^ _133474 : [(4473 ^ _133474) ^ [] : [-(in(_286094, relation_dom(_285190)))], (4475 ^ _133474) ^ [] : [-(_286096 = apply(_285190, _286094))]], in(_286096, relation_rng(_285190)), _286094 = apply(_285577, _286096)], (4477 ^ _133474) ^ [_286468, _286470] : [4484 ^ _133474 : [(4485 ^ _133474) ^ [] : [-(in(_286470, relation_rng(_285190)))], (4487 ^ _133474) ^ [] : [-(_286468 = apply(_285577, _286470))]], in(_286468, relation_dom(_285190)), _286470 = apply(_285190, _286468)]]]]]]], (4521 ^ _133474) ^ [_288043, _288045, _288047] : [element(_288043, powerset(_288047)), in(_288045, subset_complement(_288047, _288043)), in(_288045, _288043)], (4531 ^ _133474) ^ [_288349] : [relation(_288349), function(_288349), one_to_one(_288349), 4542 ^ _133474 : [(4543 ^ _133474) ^ [] : [-(relation_rng(_288349) = relation_dom(function_inverse(_288349)))], (4545 ^ _133474) ^ [] : [-(relation_dom(_288349) = relation_rng(function_inverse(_288349)))]]], (4547 ^ _133474) ^ [_288802] : [relation(_288802), -(in(ordered_pair(4552 ^ [_288802], 4553 ^ [_288802]), _288802)), -(_288802 = empty_set)], (4559 ^ _133474) ^ [_289220, _289222] : [relation(_289220), function(_289220), 4574 ^ _133474 : [(4575 ^ _133474) ^ [] : [-(_289222 = apply(_289220, apply(function_inverse(_289220), _289222)))], (4577 ^ _133474) ^ [] : [-(_289222 = apply(relation_composition(function_inverse(_289220), _289220), _289222))]], one_to_one(_289220), in(_289222, relation_rng(_289220))], (4579 ^ _133474) ^ [_289818, _289820, _289822] : [in(_289822, _289820), element(_289820, powerset(_289818)), empty(_289818)], (4589 ^ _133474) ^ [_290114] : [relation(_290114), 4592 ^ _133474 : [(4593 ^ _133474) ^ [] : [well_founded_relation(_290114), -(is_well_founded_in(_290114, relation_field(_290114)))], (4599 ^ _133474) ^ [] : [is_well_founded_in(_290114, relation_field(_290114)), -(well_founded_relation(_290114))]]], (4605 ^ _133474) ^ [] : [-(relation_dom(empty_set) = empty_set)], (4607 ^ _133474) ^ [] : [-(relation_rng(empty_set) = empty_set)], (4609 ^ _133474) ^ [_290667, _290669] : [subset(_290669, _290667), proper_subset(_290667, _290669)], (4615 ^ _133474) ^ [_290862] : [relation(_290862), function(_290862), one_to_one(_290862), -(one_to_one(function_inverse(_290862)))], (4629 ^ _133474) ^ [_291248, _291250, _291252] : [-(disjoint(_291252, _291248)), subset(_291252, _291250), disjoint(_291250, _291248)], (4639 ^ _133474) ^ [_291543] : [relation(_291543), 4644 ^ _133474 : [(4645 ^ _133474) ^ [] : [relation_dom(_291543) = empty_set], (4647 ^ _133474) ^ [] : [relation_rng(_291543) = empty_set]], -(_291543 = empty_set)], (4651 ^ _133474) ^ [_291896] : [relation(_291896), 4654 ^ _133474 : [(4655 ^ _133474) ^ [] : [relation_dom(_291896) = empty_set, -(relation_rng(_291896) = empty_set)], (4661 ^ _133474) ^ [] : [relation_rng(_291896) = empty_set, -(relation_dom(_291896) = empty_set)]]], (4667 ^ _133474) ^ [_292379, _292381] : [set_difference(_292381, singleton(_292379)) = _292381, in(_292379, _292381)], (4673 ^ _133474) ^ [_292552, _292554] : [-(in(_292552, _292554)), -(set_difference(_292554, singleton(_292552)) = _292554)], (4679 ^ _133474) ^ [_292777, _292779] : [relation(_292777), function(_292777), 4686 ^ _133474 : [(4687 ^ _133474) ^ [_293044] : [relation(_293044), function(_293044), 4694 ^ _133474 : [(4695 ^ _133474) ^ [] : [_292777 = relation_dom_restriction(_293044, _292779), 4698 ^ _133474 : [(4699 ^ _133474) ^ [] : [-(relation_dom(_292777) = set_intersection2(relation_dom(_293044), _292779))], (4701 ^ _133474) ^ [_293498] : [in(_293498, relation_dom(_292777)), -(apply(_292777, _293498) = apply(_293044, _293498))]]], (4707 ^ _133474) ^ [] : [-(_292777 = relation_dom_restriction(_293044, _292779)), relation_dom(_292777) = set_intersection2(relation_dom(_293044), _292779), 4713 ^ _133474 : [(4714 ^ _133474) ^ [] : [-(in(4712 ^ [_292777, _292779, _293044], relation_dom(_292777)))], (4716 ^ _133474) ^ [] : [apply(_292777, 4712 ^ [_292777, _292779, _293044]) = apply(_293044, 4712 ^ [_292777, _292779, _293044])]]]]]]], (4720 ^ _133474) ^ [_294137] : [-(unordered_pair(_294137, _294137) = singleton(_294137))], (4722 ^ _133474) ^ [_294235] : [empty(_294235), -(_294235 = empty_set)], (4728 ^ _133474) ^ [_294437, _294439] : [subset(singleton(_294439), singleton(_294437)), -(_294439 = _294437)], (4734 ^ _133474) ^ [_294669, _294671, _294673] : [relation(_294669), function(_294669), in(_294671, relation_dom(relation_dom_restriction(_294669, _294673))), -(apply(relation_dom_restriction(_294669, _294673), _294671) = apply(_294669, _294671))], (4748 ^ _133474) ^ [_295088] : [-(relation_dom(identity_relation(_295088)) = _295088)], (4750 ^ _133474) ^ [_295136] : [-(relation_rng(identity_relation(_295136)) = _295136)], (4752 ^ _133474) ^ [_295263, _295265, _295267] : [relation(_295263), function(_295263), in(_295265, _295267), -(apply(relation_dom_restriction(_295263, _295267), _295265) = apply(_295263, _295265))], (4766 ^ _133474) ^ [_295709, _295711, _295713, _295715] : [relation(_295709), 4769 ^ _133474 : [(4770 ^ _133474) ^ [] : [in(ordered_pair(_295715, _295713), relation_composition(identity_relation(_295711), _295709)), 4773 ^ _133474 : [(4774 ^ _133474) ^ [] : [-(in(_295715, _295711))], (4776 ^ _133474) ^ [] : [-(in(ordered_pair(_295715, _295713), _295709))]]], (4778 ^ _133474) ^ [] : [-(in(ordered_pair(_295715, _295713), relation_composition(identity_relation(_295711), _295709))), in(_295715, _295711), in(ordered_pair(_295715, _295713), _295709)]]], (4788 ^ _133474) ^ [_296402, _296404] : [in(_296404, _296402), empty(_296402)], (4794 ^ _133474) ^ [_296609, _296611] : [in(_296611, _296609), 4798 ^ _133474 : [(4799 ^ _133474) ^ [] : [-(in(4797 ^ [_296609, _296611], _296609))], (4801 ^ _133474) ^ [_296900] : [in(_296900, _296609), in(_296900, 4797 ^ [_296609, _296611])]]], (4807 ^ _133474) ^ [_297125, _297127] : [-(subset(_297127, set_union2(_297127, _297125)))], (4809 ^ _133474) ^ [_297266, _297268] : [disjoint(_297268, _297266), -(set_difference(_297268, _297266) = _297268)], (4815 ^ _133474) ^ [_297434, _297436] : [set_difference(_297436, _297434) = _297436, -(disjoint(_297436, _297434))], (4821 ^ _133474) ^ [_297666, _297668, _297670] : [relation(_297666), 4824 ^ _133474 : [(4825 ^ _133474) ^ [] : [in(_297670, relation_dom(relation_dom_restriction(_297666, _297668))), 4828 ^ _133474 : [(4829 ^ _133474) ^ [] : [-(in(_297670, _297668))], (4831 ^ _133474) ^ [] : [-(in(_297670, relation_dom(_297666)))]]], (4833 ^ _133474) ^ [] : [-(in(_297670, relation_dom(relation_dom_restriction(_297666, _297668)))), in(_297670, _297668), in(_297670, relation_dom(_297666))]]], (4843 ^ _133474) ^ [_298325, _298327] : [relation(_298325), -(subset(relation_dom_restriction(_298325, _298327), _298325))], (4849 ^ _133474) ^ [_298539, _298541] : [empty(_298541), -(_298541 = _298539), empty(_298539)], (4859 ^ _133474) ^ [_298850, _298852, _298854] : [relation(_298850), function(_298850), 4866 ^ _133474 : [(4867 ^ _133474) ^ [] : [in(ordered_pair(_298854, _298852), _298850), 4870 ^ _133474 : [(4871 ^ _133474) ^ [] : [-(in(_298854, relation_dom(_298850)))], (4873 ^ _133474) ^ [] : [-(_298852 = apply(_298850, _298854))]]], (4875 ^ _133474) ^ [] : [-(in(ordered_pair(_298854, _298852), _298850)), in(_298854, relation_dom(_298850)), _298852 = apply(_298850, _298854)]]], (4885 ^ _133474) ^ [_299619, _299621, _299623] : [-(subset(set_union2(_299623, _299619), _299621)), subset(_299623, _299621), subset(_299619, _299621)], (4895 ^ _133474) ^ [_299948, _299950, _299952] : [singleton(_299952) = unordered_pair(_299950, _299948), -(_299952 = _299950)], (4901 ^ _133474) ^ [_300174, _300176] : [relation(_300174), -(relation_dom(relation_dom_restriction(_300174, _300176)) = set_intersection2(relation_dom(_300174), _300176))], (4907 ^ _133474) ^ [_300402, _300404] : [in(_300404, _300402), -(subset(_300404, union(_300402)))], (4913 ^ _133474) ^ [_300616, _300618] : [relation(_300616), -(relation_dom_restriction(_300616, _300618) = relation_composition(identity_relation(_300618), _300616))], (4919 ^ _133474) ^ [_300840, _300842] : [relation(_300840), -(subset(relation_rng(relation_dom_restriction(_300840, _300842)), relation_rng(_300840)))], (4925 ^ _133474) ^ [_301033] : [-(union(powerset(_301033)) = _301033)], (4963 ^ _133474) ^ [_302554, _302556, _302558] : [singleton(_302558) = unordered_pair(_302556, _302554), -(_302556 = _302554)], (4928 ^ _133474) ^ [_301274] : [-(in(_301274, 4926 ^ [_301274]))], (4930 ^ _133474) ^ [_301386, _301388, _301390] : [-(in(_301386, 4926 ^ [_301390])), in(_301388, 4926 ^ [_301390]), subset(_301386, _301388)], (4940 ^ _133474) ^ [_301701, _301703] : [in(_301701, 4926 ^ [_301703]), 4944 ^ _133474 : [(4945 ^ _133474) ^ [] : [-(in(4943 ^ [_301701, _301703], 4926 ^ [_301703]))], (4947 ^ _133474) ^ [_302013] : [subset(_302013, _301701), -(in(_302013, 4943 ^ [_301701, _301703]))]]], (4953 ^ _133474) ^ [_302220, _302222] : [subset(_302220, 4926 ^ [_302222]), -(are_equipotent(_302220, 4926 ^ [_302222])), -(in(_302220, 4926 ^ [_302222]))]], input).
% 42.71/41.72  ncf('1',plain,[4976 : well_ordering(4968 ^ []), 4980 : well_orders(4968 ^ [], relation_field(4968 ^ []))],start(4972 ^ 0)).
% 42.71/41.72  ncf('1.1',plain,[-(well_ordering(4968 ^ [])), 2023 : reflexive(4968 ^ []), 2023 : transitive(4968 ^ []), 2023 : antisymmetric(4968 ^ []), 2023 : connected(4968 ^ []), 2023 : well_founded_relation(4968 ^ []), 2023 : relation(4968 ^ [])],extension(2005 ^ 3,bind([[_204282], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.1.1',plain,[-(reflexive(4968 ^ [])), 2572 : is_reflexive_in(4968 ^ [], relation_field(4968 ^ [])), 2572 : relation(4968 ^ [])],extension(2562 ^ 6,bind([[_224329], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.1.1.1',plain,[-(is_reflexive_in(4968 ^ [], relation_field(4968 ^ []))), 2190 : well_orders(4968 ^ [], relation_field(4968 ^ [])), 2190 : relation(4968 ^ [])],extension(2186 ^ 9,bind([[_210626, _210810], [4968 ^ [], relation_field(4968 ^ [])]]))).
% 42.71/41.72  ncf('1.1.1.1.1',plain,[-(well_orders(4968 ^ [], relation_field(4968 ^ [])))],extension(4974 ^ 12)).
% 42.71/41.72  ncf('1.1.1.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.1.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.1.2',plain,[-(transitive(4968 ^ [])), 1138 : is_transitive_in(4968 ^ [], relation_field(4968 ^ [])), 1138 : relation(4968 ^ [])],extension(1128 ^ 6,bind([[_172638], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.1.2.1',plain,[-(is_transitive_in(4968 ^ [], relation_field(4968 ^ []))), 2190 : well_orders(4968 ^ [], relation_field(4968 ^ [])), 2190 : relation(4968 ^ [])],extension(2186 ^ 9,bind([[_210626, _210810], [4968 ^ [], relation_field(4968 ^ [])]]))).
% 42.71/41.72  ncf('1.1.2.1.1',plain,[-(well_orders(4968 ^ [], relation_field(4968 ^ [])))],extension(4974 ^ 12)).
% 42.71/41.72  ncf('1.1.2.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.1.2.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.1.3',plain,[-(antisymmetric(4968 ^ [])), 957 : is_antisymmetric_in(4968 ^ [], relation_field(4968 ^ [])), 957 : relation(4968 ^ [])],extension(947 ^ 6,bind([[_165931], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.1.3.1',plain,[-(is_antisymmetric_in(4968 ^ [], relation_field(4968 ^ []))), 2190 : well_orders(4968 ^ [], relation_field(4968 ^ [])), 2190 : relation(4968 ^ [])],extension(2186 ^ 9,bind([[_210626, _210810], [4968 ^ [], relation_field(4968 ^ [])]]))).
% 42.71/41.72  ncf('1.1.3.1.1',plain,[-(well_orders(4968 ^ [], relation_field(4968 ^ [])))],extension(4974 ^ 12)).
% 42.71/41.72  ncf('1.1.3.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.1.3.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.1.4',plain,[-(connected(4968 ^ [])), 1122 : is_connected_in(4968 ^ [], relation_field(4968 ^ [])), 1122 : relation(4968 ^ [])],extension(1112 ^ 6,bind([[_172207], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.1.4.1',plain,[-(is_connected_in(4968 ^ [], relation_field(4968 ^ []))), 2190 : well_orders(4968 ^ [], relation_field(4968 ^ [])), 2190 : relation(4968 ^ [])],extension(2186 ^ 9,bind([[_210626, _210810], [4968 ^ [], relation_field(4968 ^ [])]]))).
% 42.71/41.72  ncf('1.1.4.1.1',plain,[-(well_orders(4968 ^ [], relation_field(4968 ^ [])))],extension(4974 ^ 12)).
% 42.71/41.72  ncf('1.1.4.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.1.4.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.1.5',plain,[-(well_founded_relation(4968 ^ [])), 4599 : is_well_founded_in(4968 ^ [], relation_field(4968 ^ [])), 4599 : relation(4968 ^ [])],extension(4589 ^ 6,bind([[_290114], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.1.5.1',plain,[-(is_well_founded_in(4968 ^ [], relation_field(4968 ^ []))), 2190 : well_orders(4968 ^ [], relation_field(4968 ^ [])), 2190 : relation(4968 ^ [])],extension(2186 ^ 9,bind([[_210626, _210810], [4968 ^ [], relation_field(4968 ^ [])]]))).
% 42.71/41.72  ncf('1.1.5.1.1',plain,[-(well_orders(4968 ^ [], relation_field(4968 ^ [])))],extension(4974 ^ 12)).
% 42.71/41.72  ncf('1.1.5.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.1.5.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.1.6',plain,[-(relation(4968 ^ []))],extension(4970 ^ 4)).
% 42.71/41.72  ncf('1.2',plain,[-(well_orders(4968 ^ [], relation_field(4968 ^ []))), 2204 : is_reflexive_in(4968 ^ [], relation_field(4968 ^ [])), 2204 : is_transitive_in(4968 ^ [], relation_field(4968 ^ [])), 2204 : is_antisymmetric_in(4968 ^ [], relation_field(4968 ^ [])), 2204 : is_connected_in(4968 ^ [], relation_field(4968 ^ [])), 2204 : is_well_founded_in(4968 ^ [], relation_field(4968 ^ [])), 2204 : relation(4968 ^ [])],extension(2186 ^ 3,bind([[_210626, _211271], [4968 ^ [], relation_field(4968 ^ [])]]))).
% 42.71/41.72  ncf('1.2.1',plain,[-(is_reflexive_in(4968 ^ [], relation_field(4968 ^ []))), 2566 : reflexive(4968 ^ []), 2566 : relation(4968 ^ [])],extension(2562 ^ 6,bind([[_224329], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.1.1',plain,[-(reflexive(4968 ^ [])), 2009 : well_ordering(4968 ^ []), 2009 : relation(4968 ^ [])],extension(2005 ^ 9,bind([[_204282], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.1.1.1',plain,[-(well_ordering(4968 ^ []))],extension(4978 ^ 12)).
% 42.71/41.72  ncf('1.2.1.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.2.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.2.2',plain,[-(is_transitive_in(4968 ^ [], relation_field(4968 ^ []))), 1132 : transitive(4968 ^ []), 1132 : relation(4968 ^ [])],extension(1128 ^ 6,bind([[_172638], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.2.1',plain,[-(transitive(4968 ^ [])), 2009 : well_ordering(4968 ^ []), 2009 : relation(4968 ^ [])],extension(2005 ^ 9,bind([[_204282], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.2.1.1',plain,[-(well_ordering(4968 ^ []))],extension(4978 ^ 12)).
% 42.71/41.72  ncf('1.2.2.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.2.2.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.2.3',plain,[-(is_antisymmetric_in(4968 ^ [], relation_field(4968 ^ []))), 951 : antisymmetric(4968 ^ []), 951 : relation(4968 ^ [])],extension(947 ^ 6,bind([[_165931], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.3.1',plain,[-(antisymmetric(4968 ^ [])), 2009 : well_ordering(4968 ^ []), 2009 : relation(4968 ^ [])],extension(2005 ^ 9,bind([[_204282], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.3.1.1',plain,[-(well_ordering(4968 ^ []))],extension(4978 ^ 12)).
% 42.71/41.72  ncf('1.2.3.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.2.3.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.2.4',plain,[-(is_connected_in(4968 ^ [], relation_field(4968 ^ []))), 1116 : connected(4968 ^ []), 1116 : relation(4968 ^ [])],extension(1112 ^ 6,bind([[_172207], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.4.1',plain,[-(connected(4968 ^ [])), 2009 : well_ordering(4968 ^ []), 2009 : relation(4968 ^ [])],extension(2005 ^ 9,bind([[_204282], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.4.1.1',plain,[-(well_ordering(4968 ^ []))],extension(4978 ^ 12)).
% 42.71/41.72  ncf('1.2.4.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.2.4.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.2.5',plain,[-(is_well_founded_in(4968 ^ [], relation_field(4968 ^ []))), 4593 : well_founded_relation(4968 ^ []), 4593 : relation(4968 ^ [])],extension(4589 ^ 6,bind([[_290114], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.5.1',plain,[-(well_founded_relation(4968 ^ [])), 2009 : well_ordering(4968 ^ []), 2009 : relation(4968 ^ [])],extension(2005 ^ 9,bind([[_204282], [4968 ^ []]]))).
% 42.71/41.72  ncf('1.2.5.1.1',plain,[-(well_ordering(4968 ^ []))],extension(4978 ^ 12)).
% 42.71/41.72  ncf('1.2.5.1.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 10)).
% 42.71/41.72  ncf('1.2.5.2',plain,[-(relation(4968 ^ []))],extension(4970 ^ 7)).
% 42.71/41.72  ncf('1.2.6',plain,[-(relation(4968 ^ []))],extension(4970 ^ 4)).
% 42.71/41.72  %-----------------------------------------------------
% 42.71/41.72  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------