%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n002.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 12:02:56 EDT 2023

% Result   : Theorem 1.66s 2.42s
% Output   : Proof 1.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n002.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 13:32:04 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 1.66/2.42  
% 1.66/2.42  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.66/2.42  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.66/2.42  %-----------------------------------------------------
% 1.66/2.42  ncf(matrix, plain, [(5698 ^ _310321) ^ [] : [pair_first(ordered_pair(5695 ^ [], 5696 ^ [])) = 5695 ^ [], pair_second(ordered_pair(5695 ^ [], 5696 ^ [])) = 5696 ^ []], (406 ^ _310321) ^ [_323307, _323309, _323311, _323313, _323315, _323317] : [-(unordered_triple(_323317, _323313, _323309) = unordered_triple(_323315, _323311, _323307)), _323317 = _323315, _323313 = _323311, _323309 = _323307], (420 ^ _310321) ^ [_323767, _323769] : [_323769 = _323767, -(set_meet(_323769) = set_meet(_323767))], (426 ^ _310321) ^ [_324013, _324015, _324017, _324019] : [-(relation_image(_324019, _324015) = relation_image(_324017, _324013)), _324019 = _324017, _324015 = _324013], (436 ^ _310321) ^ [_324372, _324374, _324376, _324378] : [-(relation_inverse_image(_324378, _324374) = relation_inverse_image(_324376, _324372)), _324378 = _324376, _324374 = _324372], (446 ^ _310321) ^ [_324731, _324733, _324735, _324737] : [-(relation_rng_restriction(_324737, _324733) = relation_rng_restriction(_324735, _324731)), _324737 = _324735, _324733 = _324731], (456 ^ _310321) ^ [_325090, _325092, _325094, _325096] : [-(cartesian_product2(_325096, _325092) = cartesian_product2(_325094, _325090)), _325096 = _325094, _325092 = _325090], (466 ^ _310321) ^ [_325449, _325451, _325453, _325455] : [-(fiber(_325455, _325451) = fiber(_325453, _325449)), _325455 = _325453, _325451 = _325449], (476 ^ _310321) ^ [_325836, _325838, _325840, _325842, _325844, _325846] : [-(relation_dom_as_subset(_325846, _325842, _325838) = relation_dom_as_subset(_325844, _325840, _325836)), _325846 = _325844, _325842 = _325840, _325838 = _325836], (490 ^ _310321) ^ [_326352, _326354, _326356, _326358, _326360, _326362] : [-(relation_rng_as_subset(_326362, _326358, _326354) = relation_rng_as_subset(_326360, _326356, _326352)), _326362 = _326360, _326358 = _326356, _326354 = _326352], (504 ^ _310321) ^ [_326812, _326814] : [_326814 = _326812, -(relation_inverse(_326814) = relation_inverse(_326812))], (510 ^ _310321) ^ [_327058, _327060, _327062, _327064] : [-(relation_restriction(_327064, _327060) = relation_restriction(_327062, _327058)), _327064 = _327062, _327060 = _327058], (520 ^ _310321) ^ [_327389, _327391] : [_327391 = _327389, -(succ(_327391) = succ(_327389))], (526 ^ _310321) ^ [_327635, _327637, _327639, _327641] : [-(union_of_subsets(_327641, _327637) = union_of_subsets(_327639, _327635)), _327641 = _327639, _327637 = _327635], (536 ^ _310321) ^ [_327994, _327996, _327998, _328000] : [-(complements_of_subsets(_328000, _327996) = complements_of_subsets(_327998, _327994)), _328000 = _327998, _327996 = _327994], (546 ^ _310321) ^ [_328381, _328383, _328385, _328387, _328389, _328391] : [-(subset_difference(_328391, _328387, _328383) = subset_difference(_328389, _328385, _328381)), _328391 = _328389, _328387 = _328385, _328383 = _328381], (560 ^ _310321) ^ [_328841, _328843] : [_328843 = _328841, -(cast_to_subset(_328843) = cast_to_subset(_328841))], (566 ^ _310321) ^ [_329087, _329089, _329091, _329093] : [-(meet_of_subsets(_329093, _329089) = meet_of_subsets(_329091, _329087)), _329093 = _329091, _329089 = _329087], (576 ^ _310321) ^ [_329446, _329448, _329450, _329452] : [-(subset_complement(_329452, _329448) = subset_complement(_329450, _329446)), _329452 = _329450, _329448 = _329446], (586 ^ _310321) ^ [_329777, _329779] : [_329779 = _329777, -(function_inverse(_329779) = function_inverse(_329777))], (592 ^ _310321) ^ [_330023, _330025, _330027, _330029] : [-(set_difference(_330029, _330025) = set_difference(_330027, _330023)), _330029 = _330027, _330025 = _330023], (602 ^ _310321) ^ [_330382, _330384, _330386, _330388] : [-(apply(_330388, _330384) = apply(_330386, _330382)), _330388 = _330386, _330384 = _330382], (612 ^ _310321) ^ [_330713, _330715] : [_330715 = _330713, -(relation_field(_330715) = relation_field(_330713))], (618 ^ _310321) ^ [_330959, _330961, _330963, _330965] : [-(set_union2(_330965, _330961) = set_union2(_330963, _330959)), _330965 = _330963, _330961 = _330959], (628 ^ _310321) ^ [_331318, _331320, _331322, _331324] : [-(set_intersection2(_331324, _331320) = set_intersection2(_331322, _331318)), _331324 = _331322, _331320 = _331318], (638 ^ _310321) ^ [_331649, _331651] : [_331651 = _331649, -(relation_dom(_331651) = relation_dom(_331649))], (644 ^ _310321) ^ [_331895, _331897, _331899, _331901] : [-(relation_composition(_331901, _331897) = relation_composition(_331899, _331895)), _331901 = _331899, _331897 = _331895], (654 ^ _310321) ^ [_332226, _332228] : [_332228 = _332226, -(identity_relation(_332228) = identity_relation(_332226))], (660 ^ _310321) ^ [_332472, _332474, _332476, _332478] : [-(relation_dom_restriction(_332478, _332474) = relation_dom_restriction(_332476, _332472)), _332478 = _332476, _332474 = _332472], (670 ^ _310321) ^ [_332803, _332805] : [_332805 = _332803, -(relation_rng(_332805) = relation_rng(_332803))], (676 ^ _310321) ^ [_333021, _333023] : [_333023 = _333021, -(union(_333023) = union(_333021))], (682 ^ _310321) ^ [_333239, _333241] : [_333241 = _333239, -(powerset(_333241) = powerset(_333239))], (688 ^ _310321) ^ [_333457, _333459] : [_333459 = _333457, -(singleton(_333459) = singleton(_333457))], (694 ^ _310321) ^ [_333703, _333705, _333707, _333709] : [-(unordered_pair(_333709, _333705) = unordered_pair(_333707, _333703)), _333709 = _333707, _333705 = _333703], (704 ^ _310321) ^ [_334034, _334036] : [_334036 = _334034, -(pair_first(_334036) = pair_first(_334034))], (710 ^ _310321) ^ [_334252, _334254] : [_334254 = _334252, -(pair_second(_334254) = pair_second(_334252))], (716 ^ _310321) ^ [_334478, _334480, _334482, _334484] : [-(ordered_pair(_334484, _334480) = ordered_pair(_334482, _334478)), _334484 = _334482, _334480 = _334478], (2 ^ _310321) ^ [_310465] : [-(_310465 = _310465)], (4 ^ _310321) ^ [_310572, _310574] : [_310574 = _310572, -(_310572 = _310574)], (10 ^ _310321) ^ [_310776, _310778, _310780] : [-(_310780 = _310776), _310780 = _310778, _310778 = _310776], (20 ^ _310321) ^ [_311117, _311119, _311121, _311123] : [-(is_antisymmetric_in(_311121, _311117)), is_antisymmetric_in(_311123, _311119), _311123 = _311121, _311119 = _311117], (34 ^ _310321) ^ [_311561, _311563, _311565, _311567] : [-(is_connected_in(_311565, _311561)), is_connected_in(_311567, _311563), _311567 = _311565, _311563 = _311561], (48 ^ _310321) ^ [_312005, _312007, _312009, _312011] : [-(is_transitive_in(_312009, _312005)), is_transitive_in(_312011, _312007), _312011 = _312009, _312007 = _312005], (62 ^ _310321) ^ [_312449, _312451, _312453, _312455] : [-(is_reflexive_in(_312453, _312449)), is_reflexive_in(_312455, _312451), _312455 = _312453, _312451 = _312449], (76 ^ _310321) ^ [_312865, _312867] : [-(epsilon_connected(_312865)), _312867 = _312865, epsilon_connected(_312867)], (86 ^ _310321) ^ [_313160, _313162] : [-(relation_empty_yielding(_313160)), _313162 = _313160, relation_empty_yielding(_313162)], (96 ^ _310321) ^ [_313511, _313513, _313515, _313517, _313519, _313521] : [-(relation_of2(_313519, _313515, _313511)), relation_of2(_313521, _313517, _313513), _313521 = _313519, _313517 = _313515, _313513 = _313511], (114 ^ _310321) ^ [_314064, _314066] : [-(epsilon_transitive(_314064)), _314066 = _314064, epsilon_transitive(_314066)], (124 ^ _310321) ^ [_314415, _314417, _314419, _314421, _314423, _314425] : [-(relation_of2_as_subset(_314423, _314419, _314415)), relation_of2_as_subset(_314425, _314421, _314417), _314425 = _314423, _314421 = _314419, _314417 = _314415], (142 ^ _310321) ^ [_314996, _314998, _315000, _315002] : [-(ordinal_subset(_315000, _314996)), ordinal_subset(_315002, _314998), _315002 = _315000, _314998 = _314996], (156 ^ _310321) ^ [_315412, _315414] : [-(ordinal(_315412)), _315414 = _315412, ordinal(_315414)], (166 ^ _310321) ^ [_315707, _315709] : [-(being_limit_ordinal(_315707)), _315709 = _315707, being_limit_ordinal(_315709)], (176 ^ _310321) ^ [_316002, _316004] : [-(reflexive(_316002)), _316004 = _316002, reflexive(_316004)], (186 ^ _310321) ^ [_316297, _316299] : [-(transitive(_316297)), _316299 = _316297, transitive(_316299)], (196 ^ _310321) ^ [_316592, _316594] : [-(connected(_316592)), _316594 = _316592, connected(_316594)], (206 ^ _310321) ^ [_316887, _316889] : [-(antisymmetric(_316887)), _316889 = _316887, antisymmetric(_316889)], (216 ^ _310321) ^ [_317238, _317240, _317242, _317244, _317246, _317248] : [-(relation_isomorphism(_317246, _317242, _317238)), relation_isomorphism(_317248, _317244, _317240), _317248 = _317246, _317244 = _317242, _317240 = _317238], (234 ^ _310321) ^ [_317819, _317821, _317823, _317825] : [-(element(_317823, _317819)), element(_317825, _317821), _317825 = _317823, _317821 = _317819], (248 ^ _310321) ^ [_318235, _318237] : [-(well_founded_relation(_318235)), _318237 = _318235, well_founded_relation(_318237)], (258 ^ _310321) ^ [_318558, _318560, _318562, _318564] : [-(is_well_founded_in(_318562, _318558)), is_well_founded_in(_318564, _318560), _318564 = _318562, _318560 = _318558], (272 ^ _310321) ^ [_319002, _319004, _319006, _319008] : [-(proper_subset(_319006, _319002)), proper_subset(_319008, _319004), _319008 = _319006, _319004 = _319002], (286 ^ _310321) ^ [_319418, _319420] : [-(one_to_one(_319418)), _319420 = _319418, one_to_one(_319420)], (296 ^ _310321) ^ [_319741, _319743, _319745, _319747] : [-(disjoint(_319745, _319741)), disjoint(_319747, _319743), _319747 = _319745, _319743 = _319741], (310 ^ _310321) ^ [_320157, _320159] : [-(empty(_320157)), _320159 = _320157, empty(_320159)], (320 ^ _310321) ^ [_320452, _320454] : [-(function(_320452)), _320454 = _320452, function(_320454)], (330 ^ _310321) ^ [_320775, _320777, _320779, _320781] : [-(well_orders(_320779, _320775)), well_orders(_320781, _320777), _320781 = _320779, _320777 = _320775], (344 ^ _310321) ^ [_321191, _321193] : [-(well_ordering(_321191)), _321193 = _321191, well_ordering(_321193)], (354 ^ _310321) ^ [_321486, _321488] : [-(relation(_321486)), _321488 = _321486, relation(_321488)], (364 ^ _310321) ^ [_321809, _321811, _321813, _321815] : [-(subset(_321813, _321809)), subset(_321815, _321811), _321815 = _321813, _321811 = _321809], (378 ^ _310321) ^ [_322253, _322255, _322257, _322259] : [-(are_equipotent(_322257, _322253)), are_equipotent(_322259, _322255), _322259 = _322257, _322255 = _322253], (392 ^ _310321) ^ [_322677, _322679, _322681, _322683] : [-(in(_322681, _322677)), in(_322683, _322679), _322683 = _322681, _322679 = _322677], (726 ^ _310321) ^ [_335034, _335036] : [in(_335036, _335034), in(_335034, _335036)], (732 ^ _310321) ^ [_335245, _335247] : [proper_subset(_335247, _335245), proper_subset(_335245, _335247)], (738 ^ _310321) ^ [_335442] : [empty(_335442), -(function(_335442))], (744 ^ _310321) ^ [_335628] : [ordinal(_335628), 747 ^ _310321 : [(748 ^ _310321) ^ [] : [-(epsilon_transitive(_335628))], (750 ^ _310321) ^ [] : [-(epsilon_connected(_335628))]]], (752 ^ _310321) ^ [_335885] : [empty(_335885), -(relation(_335885))], (758 ^ _310321) ^ [_336099, _336101, _336103] : [element(_336099, powerset(cartesian_product2(_336103, _336101))), -(relation(_336099))], (764 ^ _310321) ^ [_336309] : [775 ^ _310321 : [(776 ^ _310321) ^ [] : [-(relation(_336309))], (778 ^ _310321) ^ [] : [-(function(_336309))], (780 ^ _310321) ^ [] : [-(one_to_one(_336309))]], relation(_336309), empty(_336309), function(_336309)], (782 ^ _310321) ^ [_336802] : [-(ordinal(_336802)), epsilon_transitive(_336802), epsilon_connected(_336802)], (792 ^ _310321) ^ [_337071] : [empty(_337071), 795 ^ _310321 : [(796 ^ _310321) ^ [] : [-(epsilon_transitive(_337071))], (798 ^ _310321) ^ [] : [-(epsilon_connected(_337071))], (800 ^ _310321) ^ [] : [-(ordinal(_337071))]]], (802 ^ _310321) ^ [_337397, _337399] : [-(unordered_pair(_337399, _337397) = unordered_pair(_337397, _337399))], (804 ^ _310321) ^ [_337497, _337499] : [-(set_union2(_337499, _337497) = set_union2(_337497, _337499))], (806 ^ _310321) ^ [_337597, _337599] : [-(set_intersection2(_337599, _337597) = set_intersection2(_337597, _337599))], (808 ^ _310321) ^ [_337712, _337714] : [ordinal(_337714), ordinal(_337712), -(ordinal_subset(_337714, _337712)), -(ordinal_subset(_337712, _337714))], (822 ^ _310321) ^ [_338099, _338101] : [relation(_338099), 825 ^ _310321 : [(848 ^ _310321) ^ [] : [-(_338099 = identity_relation(_338101)), 861 ^ _310321 : [(862 ^ _310321) ^ [] : [-(in(849 ^ [_338099, _338101], _338101))], (864 ^ _310321) ^ [] : [-(849 ^ [_338099, _338101] = 850 ^ [_338099, _338101])], (866 ^ _310321) ^ [] : [in(ordered_pair(849 ^ [_338099, _338101], 850 ^ [_338099, _338101]), _338099)]], 853 ^ _310321 : [(854 ^ _310321) ^ [] : [-(in(ordered_pair(849 ^ [_338099, _338101], 850 ^ [_338099, _338101]), _338099))], (856 ^ _310321) ^ [] : [in(849 ^ [_338099, _338101], _338101), 849 ^ [_338099, _338101] = 850 ^ [_338099, _338101]]]], (826 ^ _310321) ^ [] : [_338099 = identity_relation(_338101), 829 ^ _310321 : [(830 ^ _310321) ^ [_338409, _338411] : [in(ordered_pair(_338411, _338409), _338099), 833 ^ _310321 : [(834 ^ _310321) ^ [] : [-(in(_338411, _338101))], (836 ^ _310321) ^ [] : [-(_338411 = _338409)]]], (838 ^ _310321) ^ [_338672, _338674] : [-(in(ordered_pair(_338674, _338672), _338099)), in(_338674, _338101), _338674 = _338672]]]]], (870 ^ _310321) ^ [_339780, _339782] : [_339782 = _339780, 873 ^ _310321 : [(874 ^ _310321) ^ [] : [-(subset(_339782, _339780))], (876 ^ _310321) ^ [] : [-(subset(_339780, _339782))]]], (878 ^ _310321) ^ [_340017, _340019] : [-(_340019 = _340017), subset(_340019, _340017), subset(_340017, _340019)], (888 ^ _310321) ^ [_340304] : [relation(_340304), 891 ^ _310321 : [(892 ^ _310321) ^ [_340490, _340492] : [relation(_340490), 895 ^ _310321 : [(918 ^ _310321) ^ [] : [-(_340490 = relation_dom_restriction(_340304, _340492)), 931 ^ _310321 : [(932 ^ _310321) ^ [] : [-(in(919 ^ [_340304, _340490, _340492], _340492))], (934 ^ _310321) ^ [] : [-(in(ordered_pair(919 ^ [_340304, _340490, _340492], 920 ^ [_340304, _340490, _340492]), _340304))], (936 ^ _310321) ^ [] : [in(ordered_pair(919 ^ [_340304, _340490, _340492], 920 ^ [_340304, _340490, _340492]), _340490)]], 923 ^ _310321 : [(924 ^ _310321) ^ [] : [-(in(ordered_pair(919 ^ [_340304, _340490, _340492], 920 ^ [_340304, _340490, _340492]), _340490))], (926 ^ _310321) ^ [] : [in(919 ^ [_340304, _340490, _340492], _340492), in(ordered_pair(919 ^ [_340304, _340490, _340492], 920 ^ [_340304, _340490, _340492]), _340304)]]], (896 ^ _310321) ^ [] : [_340490 = relation_dom_restriction(_340304, _340492), 899 ^ _310321 : [(900 ^ _310321) ^ [_340815, _340817] : [in(ordered_pair(_340817, _340815), _340490), 903 ^ _310321 : [(904 ^ _310321) ^ [] : [-(in(_340817, _340492))], (906 ^ _310321) ^ [] : [-(in(ordered_pair(_340817, _340815), _340304))]]], (908 ^ _310321) ^ [_341094, _341096] : [-(in(ordered_pair(_341096, _341094), _340490)), in(_341096, _340492), in(ordered_pair(_341096, _341094), _340304)]]]]]]], (940 ^ _310321) ^ [_342249] : [relation(_342249), function(_342249), 947 ^ _310321 : [(977 ^ _310321) ^ [_343675, _343677] : [-(_343675 = relation_image(_342249, _343677)), 994 ^ _310321 : [(995 ^ _310321) ^ [] : [-(in(993 ^ [_342249, _343675, _343677], relation_dom(_342249)))], (997 ^ _310321) ^ [] : [-(in(993 ^ [_342249, _343675, _343677], _343677))], (999 ^ _310321) ^ [] : [-(978 ^ [_342249, _343675, _343677] = apply(_342249, 993 ^ [_342249, _343675, _343677]))], (1001 ^ _310321) ^ [] : [in(978 ^ [_342249, _343675, _343677], _343675)]], 981 ^ _310321 : [(982 ^ _310321) ^ [] : [-(in(978 ^ [_342249, _343675, _343677], _343675))], (984 ^ _310321) ^ [_343995] : [in(_343995, relation_dom(_342249)), in(_343995, _343677), 978 ^ [_342249, _343675, _343677] = apply(_342249, _343995)]]], (948 ^ _310321) ^ [_342547, _342549] : [_342547 = relation_image(_342249, _342549), 951 ^ _310321 : [(952 ^ _310321) ^ [_342747] : [in(_342747, _342547), 956 ^ _310321 : [(957 ^ _310321) ^ [] : [-(in(955 ^ [_342249, _342547, _342549, _342747], relation_dom(_342249)))], (959 ^ _310321) ^ [] : [-(in(955 ^ [_342249, _342547, _342549, _342747], _342549))], (961 ^ _310321) ^ [] : [-(_342747 = apply(_342249, 955 ^ [_342249, _342547, _342549, _342747]))]]], (963 ^ _310321) ^ [_343202] : [-(in(_343202, _342547)), 964 ^ _310321 : [(965 ^ _310321) ^ [_343315] : [in(_343315, relation_dom(_342249)), in(_343315, _342549), _343202 = apply(_342249, _343315)]]]]]]], (1005 ^ _310321) ^ [_344805, _344807] : [relation(_344805), 1008 ^ _310321 : [(1009 ^ _310321) ^ [_344976] : [relation(_344976), 1012 ^ _310321 : [(1035 ^ _310321) ^ [] : [-(_344976 = relation_rng_restriction(_344807, _344805)), 1048 ^ _310321 : [(1049 ^ _310321) ^ [] : [-(in(1037 ^ [_344805, _344807, _344976], _344807))], (1051 ^ _310321) ^ [] : [-(in(ordered_pair(1036 ^ [_344805, _344807, _344976], 1037 ^ [_344805, _344807, _344976]), _344805))], (1053 ^ _310321) ^ [] : [in(ordered_pair(1036 ^ [_344805, _344807, _344976], 1037 ^ [_344805, _344807, _344976]), _344976)]], 1040 ^ _310321 : [(1041 ^ _310321) ^ [] : [-(in(ordered_pair(1036 ^ [_344805, _344807, _344976], 1037 ^ [_344805, _344807, _344976]), _344976))], (1043 ^ _310321) ^ [] : [in(1037 ^ [_344805, _344807, _344976], _344807), in(ordered_pair(1036 ^ [_344805, _344807, _344976], 1037 ^ [_344805, _344807, _344976]), _344805)]]], (1013 ^ _310321) ^ [] : [_344976 = relation_rng_restriction(_344807, _344805), 1016 ^ _310321 : [(1017 ^ _310321) ^ [_345303, _345305] : [in(ordered_pair(_345305, _345303), _344976), 1020 ^ _310321 : [(1021 ^ _310321) ^ [] : [-(in(_345303, _344807))], (1023 ^ _310321) ^ [] : [-(in(ordered_pair(_345305, _345303), _344805))]]], (1025 ^ _310321) ^ [_345582, _345584] : [-(in(ordered_pair(_345584, _345582), _344976)), in(_345582, _344807), in(ordered_pair(_345584, _345582), _344805)]]]]]]], (1057 ^ _310321) ^ [_346728] : [relation(_346728), 1060 ^ _310321 : [(1061 ^ _310321) ^ [] : [antisymmetric(_346728), -(is_antisymmetric_in(_346728, relation_field(_346728)))], (1067 ^ _310321) ^ [] : [is_antisymmetric_in(_346728, relation_field(_346728)), -(antisymmetric(_346728))]]], (1073 ^ _310321) ^ [_347159] : [relation(_347159), function(_347159), 1080 ^ _310321 : [(1103 ^ _310321) ^ [_348198, _348200] : [-(_348198 = relation_inverse_image(_347159, _348200)), 1115 ^ _310321 : [(1116 ^ _310321) ^ [] : [-(in(1104 ^ [_347159, _348198, _348200], relation_dom(_347159)))], (1118 ^ _310321) ^ [] : [-(in(apply(_347159, 1104 ^ [_347159, _348198, _348200]), _348200))], (1120 ^ _310321) ^ [] : [in(1104 ^ [_347159, _348198, _348200], _348198)]], 1107 ^ _310321 : [(1108 ^ _310321) ^ [] : [-(in(1104 ^ [_347159, _348198, _348200], _348198))], (1110 ^ _310321) ^ [] : [in(1104 ^ [_347159, _348198, _348200], relation_dom(_347159)), in(apply(_347159, 1104 ^ [_347159, _348198, _348200]), _348200)]]], (1081 ^ _310321) ^ [_347446, _347448] : [_347446 = relation_inverse_image(_347159, _347448), 1084 ^ _310321 : [(1085 ^ _310321) ^ [_347635] : [in(_347635, _347446), 1088 ^ _310321 : [(1089 ^ _310321) ^ [] : [-(in(_347635, relation_dom(_347159)))], (1091 ^ _310321) ^ [] : [-(in(apply(_347159, _347635), _347448))]]], (1093 ^ _310321) ^ [_347904] : [-(in(_347904, _347446)), in(_347904, relation_dom(_347159)), in(apply(_347159, _347904), _347448)]]]]], (1124 ^ _310321) ^ [_348966] : [relation(_348966), 1127 ^ _310321 : [(1151 ^ _310321) ^ [_350079, _350081] : [-(_350079 = relation_image(_348966, _350081)), 1164 ^ _310321 : [(1165 ^ _310321) ^ [] : [-(in(ordered_pair(1163 ^ [_348966, _350079, _350081], 1152 ^ [_348966, _350079, _350081]), _348966))], (1167 ^ _310321) ^ [] : [-(in(1163 ^ [_348966, _350079, _350081], _350081))], (1169 ^ _310321) ^ [] : [in(1152 ^ [_348966, _350079, _350081], _350079)]], 1155 ^ _310321 : [(1156 ^ _310321) ^ [] : [-(in(1152 ^ [_348966, _350079, _350081], _350079))], (1158 ^ _310321) ^ [_350383] : [in(ordered_pair(_350383, 1152 ^ [_348966, _350079, _350081]), _348966), in(_350383, _350081)]]], (1128 ^ _310321) ^ [_349173, _349175] : [_349173 = relation_image(_348966, _349175), 1131 ^ _310321 : [(1132 ^ _310321) ^ [_349365] : [in(_349365, _349173), 1136 ^ _310321 : [(1137 ^ _310321) ^ [] : [-(in(ordered_pair(1135 ^ [_348966, _349173, _349175, _349365], _349365), _348966))], (1139 ^ _310321) ^ [] : [-(in(1135 ^ [_348966, _349173, _349175, _349365], _349175))]]], (1141 ^ _310321) ^ [_349719] : [-(in(_349719, _349173)), 1142 ^ _310321 : [(1143 ^ _310321) ^ [_349824] : [in(ordered_pair(_349824, _349719), _348966), in(_349824, _349175)]]]]]]], (1173 ^ _310321) ^ [_350985] : [relation(_350985), 1176 ^ _310321 : [(1200 ^ _310321) ^ [_352098, _352100] : [-(_352098 = relation_inverse_image(_350985, _352100)), 1213 ^ _310321 : [(1214 ^ _310321) ^ [] : [-(in(ordered_pair(1201 ^ [_350985, _352098, _352100], 1212 ^ [_350985, _352098, _352100]), _350985))], (1216 ^ _310321) ^ [] : [-(in(1212 ^ [_350985, _352098, _352100], _352100))], (1218 ^ _310321) ^ [] : [in(1201 ^ [_350985, _352098, _352100], _352098)]], 1204 ^ _310321 : [(1205 ^ _310321) ^ [] : [-(in(1201 ^ [_350985, _352098, _352100], _352098))], (1207 ^ _310321) ^ [_352402] : [in(ordered_pair(1201 ^ [_350985, _352098, _352100], _352402), _350985), in(_352402, _352100)]]], (1177 ^ _310321) ^ [_351192, _351194] : [_351192 = relation_inverse_image(_350985, _351194), 1180 ^ _310321 : [(1181 ^ _310321) ^ [_351384] : [in(_351384, _351192), 1185 ^ _310321 : [(1186 ^ _310321) ^ [] : [-(in(ordered_pair(_351384, 1184 ^ [_350985, _351192, _351194, _351384]), _350985))], (1188 ^ _310321) ^ [] : [-(in(1184 ^ [_350985, _351192, _351194, _351384], _351194))]]], (1190 ^ _310321) ^ [_351738] : [-(in(_351738, _351192)), 1191 ^ _310321 : [(1192 ^ _310321) ^ [_351843] : [in(ordered_pair(_351738, _351843), _350985), in(_351843, _351194)]]]]]]], (1222 ^ _310321) ^ [_353004] : [relation(_353004), 1225 ^ _310321 : [(1226 ^ _310321) ^ [] : [connected(_353004), -(is_connected_in(_353004, relation_field(_353004)))], (1232 ^ _310321) ^ [] : [is_connected_in(_353004, relation_field(_353004)), -(connected(_353004))]]], (1238 ^ _310321) ^ [_353435] : [relation(_353435), 1241 ^ _310321 : [(1242 ^ _310321) ^ [] : [transitive(_353435), -(is_transitive_in(_353435, relation_field(_353435)))], (1248 ^ _310321) ^ [] : [is_transitive_in(_353435, relation_field(_353435)), -(transitive(_353435))]]], (1282 ^ _310321) ^ [_354901, _354903, _354905, _354907] : [-(_354901 = unordered_triple(_354907, _354905, _354903)), 1286 ^ _310321 : [(1287 ^ _310321) ^ [] : [-(in(1283 ^ [_354901, _354903, _354905, _354907], _354901))], (1289 ^ _310321) ^ [] : [1283 ^ [_354901, _354903, _354905, _354907] = _354907], (1291 ^ _310321) ^ [] : [1283 ^ [_354901, _354903, _354905, _354907] = _354905], (1293 ^ _310321) ^ [] : [1283 ^ [_354901, _354903, _354905, _354907] = _354903]], 1294 ^ _310321 : [(1305 ^ _310321) ^ [] : [in(1283 ^ [_354901, _354903, _354905, _354907], _354901)], (1295 ^ _310321) ^ [] : [-(1283 ^ [_354901, _354903, _354905, _354907] = _354907), -(1283 ^ [_354901, _354903, _354905, _354907] = _354905), -(1283 ^ [_354901, _354903, _354905, _354907] = _354903)]]], (1254 ^ _310321) ^ [_353937, _353939, _353941, _353943] : [_353937 = unordered_triple(_353943, _353941, _353939), 1257 ^ _310321 : [(1272 ^ _310321) ^ [_354539] : [1273 ^ _310321 : [(1274 ^ _310321) ^ [] : [_354539 = _353943], (1276 ^ _310321) ^ [] : [_354539 = _353941], (1278 ^ _310321) ^ [] : [_354539 = _353939]], -(in(_354539, _353937))], (1258 ^ _310321) ^ [_354139] : [in(_354139, _353937), -(_354139 = _353943), -(_354139 = _353941), -(_354139 = _353939)]]], (1309 ^ _310321) ^ [_355889] : [1310 ^ _310321 : [(1311 ^ _310321) ^ [_356011, _356013] : [_355889 = ordered_pair(_356013, _356011)]], 1312 ^ _310321 : [(1323 ^ _310321) ^ [_356474] : [1326 ^ _310321 : [(1327 ^ _310321) ^ [] : [-(_355889 = ordered_pair(1324 ^ [_355889, _356474], 1325 ^ [_355889, _356474]))], (1329 ^ _310321) ^ [] : [_356474 = 1324 ^ [_355889, _356474]]], -(_356474 = pair_first(_355889))], (1313 ^ _310321) ^ [_356120] : [_356120 = pair_first(_355889), 1316 ^ _310321 : [(1317 ^ _310321) ^ [_356285, _356287] : [_355889 = ordered_pair(_356287, _356285), -(_356120 = _356287)]]]]], (1333 ^ _310321) ^ [_356908] : [-(succ(_356908) = set_union2(_356908, singleton(_356908)))], (1347 ^ _310321) ^ [_357498] : [1349 ^ _310321 : [(1350 ^ _310321) ^ [] : [-(in(1348 ^ [_357498], _357498))], (1352 ^ _310321) ^ [_357735, _357737] : [1348 ^ [_357498] = ordered_pair(_357737, _357735)]], -(relation(_357498))], (1335 ^ _310321) ^ [_357037] : [relation(_357037), 1338 ^ _310321 : [(1339 ^ _310321) ^ [_357185] : [in(_357185, _357037), -(_357185 = ordered_pair(1342 ^ [_357037, _357185], 1343 ^ [_357037, _357185]))]]], (1356 ^ _310321) ^ [_357892] : [relation(_357892), 1359 ^ _310321 : [(1370 ^ _310321) ^ [_358391] : [1372 ^ _310321 : [(1373 ^ _310321) ^ [] : [-(in(1371 ^ [_357892, _358391], _358391))], (1375 ^ _310321) ^ [] : [in(ordered_pair(1371 ^ [_357892, _358391], 1371 ^ [_357892, _358391]), _357892)]], -(is_reflexive_in(_357892, _358391))], (1360 ^ _310321) ^ [_358066] : [is_reflexive_in(_357892, _358066), 1363 ^ _310321 : [(1364 ^ _310321) ^ [_358208] : [in(_358208, _358066), -(in(ordered_pair(_358208, _358208), _357892))]]]]], (1379 ^ _310321) ^ [_358814, _358816, _358818] : [relation_of2(_358814, _358818, _358816), -(subset(_358814, cartesian_product2(_358818, _358816)))], (1385 ^ _310321) ^ [_358990, _358992, _358994] : [subset(_358990, cartesian_product2(_358994, _358992)), -(relation_of2(_358990, _358994, _358992))], (1440 ^ _310321) ^ [_360943, _360945] : [_360945 = empty_set, 1443 ^ _310321 : [(1444 ^ _310321) ^ [] : [_360943 = set_meet(_360945), -(_360943 = empty_set)], (1450 ^ _310321) ^ [] : [_360943 = empty_set, -(_360943 = set_meet(_360945))]]], (1391 ^ _310321) ^ [_359236, _359238] : [-(_359238 = empty_set), 1394 ^ _310321 : [(1418 ^ _310321) ^ [] : [-(_359236 = set_meet(_359238)), 1422 ^ _310321 : [(1423 ^ _310321) ^ [] : [-(in(1419 ^ [_359236, _359238], _359236))], (1426 ^ _310321) ^ [] : [-(in(1424 ^ [_359236, _359238], _359238))], (1428 ^ _310321) ^ [] : [in(1419 ^ [_359236, _359238], 1424 ^ [_359236, _359238])]], 1429 ^ _310321 : [(1436 ^ _310321) ^ [] : [in(1419 ^ [_359236, _359238], _359236)], (1430 ^ _310321) ^ [_360638] : [in(_360638, _359238), -(in(1419 ^ [_359236, _359238], _360638))]]], (1395 ^ _310321) ^ [] : [_359236 = set_meet(_359238), 1398 ^ _310321 : [(1409 ^ _310321) ^ [_359864] : [1411 ^ _310321 : [(1412 ^ _310321) ^ [] : [-(in(1410 ^ [_359236, _359238, _359864], _359238))], (1414 ^ _310321) ^ [] : [in(_359864, 1410 ^ [_359236, _359238, _359864])]], -(in(_359864, _359236))], (1399 ^ _310321) ^ [_359534] : [in(_359534, _359236), 1402 ^ _310321 : [(1403 ^ _310321) ^ [_359679] : [in(_359679, _359238), -(in(_359534, _359679))]]]]]]], (1472 ^ _310321) ^ [_361961, _361963] : [-(_361961 = singleton(_361963)), 1476 ^ _310321 : [(1477 ^ _310321) ^ [] : [-(in(1473 ^ [_361961, _361963], _361961))], (1479 ^ _310321) ^ [] : [1473 ^ [_361961, _361963] = _361963]], 1480 ^ _310321 : [(1481 ^ _310321) ^ [] : [-(1473 ^ [_361961, _361963] = _361963)], (1483 ^ _310321) ^ [] : [in(1473 ^ [_361961, _361963], _361961)]]], (1456 ^ _310321) ^ [_361440, _361442] : [_361440 = singleton(_361442), 1459 ^ _310321 : [(1460 ^ _310321) ^ [_361610] : [in(_361610, _361440), -(_361610 = _361442)], (1466 ^ _310321) ^ [_361782] : [_361782 = _361442, -(in(_361782, _361440))]]], (1487 ^ _310321) ^ [_362483] : [relation(_362483), 1490 ^ _310321 : [(1513 ^ _310321) ^ [_363435, _363437] : [-(_363435 = fiber(_362483, _363437)), 1525 ^ _310321 : [(1526 ^ _310321) ^ [] : [1514 ^ [_362483, _363435, _363437] = _363437], (1528 ^ _310321) ^ [] : [-(in(ordered_pair(1514 ^ [_362483, _363435, _363437], _363437), _362483))], (1530 ^ _310321) ^ [] : [in(1514 ^ [_362483, _363435, _363437], _363435)]], 1517 ^ _310321 : [(1518 ^ _310321) ^ [] : [-(in(1514 ^ [_362483, _363435, _363437], _363435))], (1520 ^ _310321) ^ [] : [-(1514 ^ [_362483, _363435, _363437] = _363437), in(ordered_pair(1514 ^ [_362483, _363435, _363437], _363437), _362483)]]], (1491 ^ _310321) ^ [_362687, _362689] : [_362687 = fiber(_362483, _362689), 1494 ^ _310321 : [(1495 ^ _310321) ^ [_362876] : [in(_362876, _362687), 1498 ^ _310321 : [(1499 ^ _310321) ^ [] : [_362876 = _362689], (1501 ^ _310321) ^ [] : [-(in(ordered_pair(_362876, _362689), _362483))]]], (1503 ^ _310321) ^ [_363142] : [-(in(_363142, _362687)), -(_363142 = _362689), in(ordered_pair(_363142, _362689), _362483)]]]]], (1534 ^ _310321) ^ [_364226] : [_364226 = empty_set, 1537 ^ _310321 : [(1538 ^ _310321) ^ [_364339] : [in(_364339, _364226)]]], (1540 ^ _310321) ^ [_364405] : [-(in(1541 ^ [_364405], _364405)), -(_364405 = empty_set)], (1563 ^ _310321) ^ [_365217, _365219] : [-(_365217 = powerset(_365219)), 1567 ^ _310321 : [(1568 ^ _310321) ^ [] : [-(in(1564 ^ [_365217, _365219], _365217))], (1570 ^ _310321) ^ [] : [subset(1564 ^ [_365217, _365219], _365219)]], 1571 ^ _310321 : [(1572 ^ _310321) ^ [] : [-(subset(1564 ^ [_365217, _365219], _365219))], (1574 ^ _310321) ^ [] : [in(1564 ^ [_365217, _365219], _365217)]]], (1547 ^ _310321) ^ [_364696, _364698] : [_364696 = powerset(_364698), 1550 ^ _310321 : [(1551 ^ _310321) ^ [_364866] : [in(_364866, _364696), -(subset(_364866, _364698))], (1557 ^ _310321) ^ [_365038] : [subset(_365038, _364698), -(in(_365038, _364696))]]], (1578 ^ _310321) ^ [_365739] : [1579 ^ _310321 : [(1580 ^ _310321) ^ [_365861, _365863] : [_365739 = ordered_pair(_365863, _365861)]], 1581 ^ _310321 : [(1592 ^ _310321) ^ [_366324] : [1595 ^ _310321 : [(1596 ^ _310321) ^ [] : [-(_365739 = ordered_pair(1593 ^ [_365739, _366324], 1594 ^ [_365739, _366324]))], (1598 ^ _310321) ^ [] : [_366324 = 1594 ^ [_365739, _366324]]], -(_366324 = pair_second(_365739))], (1582 ^ _310321) ^ [_365970] : [_365970 = pair_second(_365739), 1585 ^ _310321 : [(1586 ^ _310321) ^ [_366135, _366137] : [_365739 = ordered_pair(_366137, _366135), -(_365970 = _366135)]]]]], (1612 ^ _310321) ^ [_367095] : [1614 ^ _310321 : [(1615 ^ _310321) ^ [] : [-(in(1613 ^ [_367095], _367095))], (1617 ^ _310321) ^ [] : [subset(1613 ^ [_367095], _367095)]], -(epsilon_transitive(_367095))], (1602 ^ _310321) ^ [_366795] : [epsilon_transitive(_366795), 1605 ^ _310321 : [(1606 ^ _310321) ^ [_366926] : [in(_366926, _366795), -(subset(_366926, _366795))]]], (1621 ^ _310321) ^ [_367420] : [relation(_367420), 1624 ^ _310321 : [(1625 ^ _310321) ^ [_367578] : [relation(_367578), 1628 ^ _310321 : [(1645 ^ _310321) ^ [] : [-(_367420 = _367578), 1650 ^ _310321 : [(1651 ^ _310321) ^ [] : [-(in(ordered_pair(1646 ^ [_367420, _367578], 1647 ^ [_367420, _367578]), _367420))], (1653 ^ _310321) ^ [] : [in(ordered_pair(1646 ^ [_367420, _367578], 1647 ^ [_367420, _367578]), _367578)]], 1654 ^ _310321 : [(1655 ^ _310321) ^ [] : [-(in(ordered_pair(1646 ^ [_367420, _367578], 1647 ^ [_367420, _367578]), _367578))], (1657 ^ _310321) ^ [] : [in(ordered_pair(1646 ^ [_367420, _367578], 1647 ^ [_367420, _367578]), _367420)]]], (1629 ^ _310321) ^ [] : [_367420 = _367578, 1632 ^ _310321 : [(1633 ^ _310321) ^ [_367883, _367885] : [in(ordered_pair(_367885, _367883), _367420), -(in(ordered_pair(_367885, _367883), _367578))], (1639 ^ _310321) ^ [_368073, _368075] : [in(ordered_pair(_368075, _368073), _367578), -(in(ordered_pair(_368075, _368073), _367420))]]]]]]], (1661 ^ _310321) ^ [_368910, _368912] : [-(empty(_368912)), 1664 ^ _310321 : [(1665 ^ _310321) ^ [] : [element(_368910, _368912), -(in(_368910, _368912))], (1671 ^ _310321) ^ [] : [in(_368910, _368912), -(element(_368910, _368912))]]], (1677 ^ _310321) ^ [_369323, _369325] : [empty(_369325), 1680 ^ _310321 : [(1681 ^ _310321) ^ [] : [element(_369323, _369325), -(empty(_369323))], (1687 ^ _310321) ^ [] : [empty(_369323), -(element(_369323, _369325))]]], (1715 ^ _310321) ^ [_370548, _370550, _370552] : [-(_370548 = unordered_pair(_370552, _370550)), 1719 ^ _310321 : [(1720 ^ _310321) ^ [] : [-(in(1716 ^ [_370548, _370550, _370552], _370548))], (1722 ^ _310321) ^ [] : [1716 ^ [_370548, _370550, _370552] = _370552], (1724 ^ _310321) ^ [] : [1716 ^ [_370548, _370550, _370552] = _370550]], 1725 ^ _310321 : [(1732 ^ _310321) ^ [] : [in(1716 ^ [_370548, _370550, _370552], _370548)], (1726 ^ _310321) ^ [] : [-(1716 ^ [_370548, _370550, _370552] = _370552), -(1716 ^ [_370548, _370550, _370552] = _370550)]]], (1693 ^ _310321) ^ [_369823, _369825, _369827] : [_369823 = unordered_pair(_369827, _369825), 1696 ^ _310321 : [(1707 ^ _310321) ^ [_370283] : [1708 ^ _310321 : [(1709 ^ _310321) ^ [] : [_370283 = _369827], (1711 ^ _310321) ^ [] : [_370283 = _369825]], -(in(_370283, _369823))], (1697 ^ _310321) ^ [_370005] : [in(_370005, _369823), -(_370005 = _369827), -(_370005 = _369825)]]], (1736 ^ _310321) ^ [_371285] : [relation(_371285), 1739 ^ _310321 : [(1757 ^ _310321) ^ [] : [-(well_founded_relation(_371285)), 1759 ^ _310321 : [(1760 ^ _310321) ^ [] : [-(subset(1758 ^ [_371285], relation_field(_371285)))], (1762 ^ _310321) ^ [] : [1758 ^ [_371285] = empty_set], (1764 ^ _310321) ^ [_372235] : [in(_372235, 1758 ^ [_371285]), disjoint(fiber(_371285, _372235), 1758 ^ [_371285])]]], (1740 ^ _310321) ^ [] : [well_founded_relation(_371285), 1743 ^ _310321 : [(1744 ^ _310321) ^ [_371552] : [subset(_371552, relation_field(_371285)), -(_371552 = empty_set), 1752 ^ _310321 : [(1753 ^ _310321) ^ [] : [-(in(1751 ^ [_371285, _371552], _371552))], (1755 ^ _310321) ^ [] : [-(disjoint(fiber(_371285, 1751 ^ [_371285, _371552]), _371552))]]]]]]], (1794 ^ _310321) ^ [_373299, _373301, _373303] : [-(_373299 = set_union2(_373303, _373301)), 1798 ^ _310321 : [(1799 ^ _310321) ^ [] : [-(in(1795 ^ [_373299, _373301, _373303], _373299))], (1801 ^ _310321) ^ [] : [in(1795 ^ [_373299, _373301, _373303], _373303)], (1803 ^ _310321) ^ [] : [in(1795 ^ [_373299, _373301, _373303], _373301)]], 1804 ^ _310321 : [(1811 ^ _310321) ^ [] : [in(1795 ^ [_373299, _373301, _373303], _373299)], (1805 ^ _310321) ^ [] : [-(in(1795 ^ [_373299, _373301, _373303], _373303)), -(in(1795 ^ [_373299, _373301, _373303], _373301))]]], (1772 ^ _310321) ^ [_372574, _372576, _372578] : [_372574 = set_union2(_372578, _372576), 1775 ^ _310321 : [(1786 ^ _310321) ^ [_373034] : [1787 ^ _310321 : [(1788 ^ _310321) ^ [] : [in(_373034, _372578)], (1790 ^ _310321) ^ [] : [in(_373034, _372576)]], -(in(_373034, _372574))], (1776 ^ _310321) ^ [_372756] : [in(_372756, _372574), -(in(_372756, _372578)), -(in(_372756, _372576))]]], (1845 ^ _310321) ^ [_375350, _375352, _375354] : [-(_375350 = cartesian_product2(_375354, _375352)), 1863 ^ _310321 : [(1864 ^ _310321) ^ [] : [-(in(1861 ^ [_375350, _375352, _375354], _375354))], (1866 ^ _310321) ^ [] : [-(in(1862 ^ [_375350, _375352, _375354], _375352))], (1868 ^ _310321) ^ [] : [-(1846 ^ [_375350, _375352, _375354] = ordered_pair(1861 ^ [_375350, _375352, _375354], 1862 ^ [_375350, _375352, _375354]))], (1870 ^ _310321) ^ [] : [in(1846 ^ [_375350, _375352, _375354], _375350)]], 1849 ^ _310321 : [(1850 ^ _310321) ^ [] : [-(in(1846 ^ [_375350, _375352, _375354], _375350))], (1852 ^ _310321) ^ [_375688, _375690] : [in(_375690, _375354), in(_375688, _375352), 1846 ^ [_375350, _375352, _375354] = ordered_pair(_375690, _375688)]]], (1815 ^ _310321) ^ [_374093, _374095, _374097] : [_374093 = cartesian_product2(_374097, _374095), 1818 ^ _310321 : [(1819 ^ _310321) ^ [_374294] : [in(_374294, _374093), 1824 ^ _310321 : [(1825 ^ _310321) ^ [] : [-(in(1822 ^ [_374093, _374095, _374097, _374294], _374097))], (1827 ^ _310321) ^ [] : [-(in(1823 ^ [_374093, _374095, _374097, _374294], _374095))], (1829 ^ _310321) ^ [] : [-(_374294 = ordered_pair(1822 ^ [_374093, _374095, _374097, _374294], 1823 ^ [_374093, _374095, _374097, _374294]))]]], (1831 ^ _310321) ^ [_374854] : [-(in(_374854, _374093)), 1832 ^ _310321 : [(1833 ^ _310321) ^ [_374984, _374986] : [in(_374986, _374097), in(_374984, _374095), _374854 = ordered_pair(_374986, _374984)]]]]], (1896 ^ _310321) ^ [_377251] : [1899 ^ _310321 : [(1900 ^ _310321) ^ [] : [-(in(1897 ^ [_377251], _377251))], (1902 ^ _310321) ^ [] : [-(in(1898 ^ [_377251], _377251))], (1904 ^ _310321) ^ [] : [in(1897 ^ [_377251], 1898 ^ [_377251])], (1906 ^ _310321) ^ [] : [1897 ^ [_377251] = 1898 ^ [_377251]], (1908 ^ _310321) ^ [] : [in(1898 ^ [_377251], 1897 ^ [_377251])]], -(epsilon_connected(_377251))], (1874 ^ _310321) ^ [_376613] : [epsilon_connected(_376613), 1877 ^ _310321 : [(1878 ^ _310321) ^ [_376789, _376791] : [in(_376791, _376613), in(_376789, _376613), -(in(_376791, _376789)), -(_376791 = _376789), -(in(_376789, _376791))]]], (1912 ^ _310321) ^ [_377957] : [relation(_377957), 1915 ^ _310321 : [(1916 ^ _310321) ^ [_378115] : [relation(_378115), 1919 ^ _310321 : [(1930 ^ _310321) ^ [] : [1933 ^ _310321 : [(1934 ^ _310321) ^ [] : [-(in(ordered_pair(1931 ^ [_377957, _378115], 1932 ^ [_377957, _378115]), _377957))], (1936 ^ _310321) ^ [] : [in(ordered_pair(1931 ^ [_377957, _378115], 1932 ^ [_377957, _378115]), _378115)]], -(subset(_377957, _378115))], (1920 ^ _310321) ^ [] : [subset(_377957, _378115), 1923 ^ _310321 : [(1924 ^ _310321) ^ [_378391, _378393] : [in(ordered_pair(_378393, _378391), _377957), -(in(ordered_pair(_378393, _378391), _378115))]]]]]]], (1950 ^ _310321) ^ [_379354, _379356] : [1952 ^ _310321 : [(1953 ^ _310321) ^ [] : [-(in(1951 ^ [_379354, _379356], _379356))], (1955 ^ _310321) ^ [] : [in(1951 ^ [_379354, _379356], _379354)]], -(subset(_379356, _379354))], (1940 ^ _310321) ^ [_379040, _379042] : [subset(_379042, _379040), 1943 ^ _310321 : [(1944 ^ _310321) ^ [_379177] : [in(_379177, _379042), -(in(_379177, _379040))]]], (1959 ^ _310321) ^ [_379697] : [relation(_379697), 1962 ^ _310321 : [(1980 ^ _310321) ^ [_380500] : [-(is_well_founded_in(_379697, _380500)), 1982 ^ _310321 : [(1983 ^ _310321) ^ [] : [-(subset(1981 ^ [_379697, _380500], _380500))], (1985 ^ _310321) ^ [] : [1981 ^ [_379697, _380500] = empty_set], (1987 ^ _310321) ^ [_380842] : [in(_380842, 1981 ^ [_379697, _380500]), disjoint(fiber(_379697, _380842), 1981 ^ [_379697, _380500])]]], (1963 ^ _310321) ^ [_379894] : [is_well_founded_in(_379697, _379894), 1966 ^ _310321 : [(1967 ^ _310321) ^ [_380059] : [subset(_380059, _379894), -(_380059 = empty_set), 1975 ^ _310321 : [(1976 ^ _310321) ^ [] : [-(in(1974 ^ [_379697, _379894, _380059], _380059))], (1978 ^ _310321) ^ [] : [-(disjoint(fiber(_379697, 1974 ^ [_379697, _379894, _380059]), _380059))]]]]]]], (2017 ^ _310321) ^ [_381925, _381927, _381929] : [-(_381925 = set_intersection2(_381929, _381927)), 2029 ^ _310321 : [(2030 ^ _310321) ^ [] : [-(in(2018 ^ [_381925, _381927, _381929], _381929))], (2032 ^ _310321) ^ [] : [-(in(2018 ^ [_381925, _381927, _381929], _381927))], (2034 ^ _310321) ^ [] : [in(2018 ^ [_381925, _381927, _381929], _381925)]], 2021 ^ _310321 : [(2022 ^ _310321) ^ [] : [-(in(2018 ^ [_381925, _381927, _381929], _381925))], (2024 ^ _310321) ^ [] : [in(2018 ^ [_381925, _381927, _381929], _381929), in(2018 ^ [_381925, _381927, _381929], _381927)]]], (1995 ^ _310321) ^ [_381200, _381202, _381204] : [_381200 = set_intersection2(_381204, _381202), 1998 ^ _310321 : [(1999 ^ _310321) ^ [_381382] : [in(_381382, _381200), 2002 ^ _310321 : [(2003 ^ _310321) ^ [] : [-(in(_381382, _381204))], (2005 ^ _310321) ^ [] : [-(in(_381382, _381202))]]], (2007 ^ _310321) ^ [_381641] : [-(in(_381641, _381200)), in(_381641, _381204), in(_381641, _381202)]]], (2038 ^ _310321) ^ [_382664] : [relation(_382664), function(_382664), 2045 ^ _310321 : [(2046 ^ _310321) ^ [_382956, _382958] : [in(_382958, relation_dom(_382664)), 2049 ^ _310321 : [(2050 ^ _310321) ^ [] : [_382956 = apply(_382664, _382958), -(in(ordered_pair(_382958, _382956), _382664))], (2056 ^ _310321) ^ [] : [in(ordered_pair(_382958, _382956), _382664), -(_382956 = apply(_382664, _382958))]]], (2062 ^ _310321) ^ [_383408, _383410] : [-(in(_383410, relation_dom(_382664))), 2065 ^ _310321 : [(2066 ^ _310321) ^ [] : [_383408 = apply(_382664, _383410), -(_383408 = empty_set)], (2072 ^ _310321) ^ [] : [_383408 = empty_set, -(_383408 = apply(_382664, _383410))]]]]], (2078 ^ _310321) ^ [_383926] : [ordinal(_383926), 2081 ^ _310321 : [(2082 ^ _310321) ^ [] : [-(epsilon_transitive(_383926))], (2084 ^ _310321) ^ [] : [-(epsilon_connected(_383926))]]], (2086 ^ _310321) ^ [_384149] : [-(ordinal(_384149)), epsilon_transitive(_384149), epsilon_connected(_384149)], (2096 ^ _310321) ^ [_384420] : [relation(_384420), 2099 ^ _310321 : [(2117 ^ _310321) ^ [_385232] : [-(_385232 = relation_dom(_384420)), 2121 ^ _310321 : [(2122 ^ _310321) ^ [] : [-(in(2118 ^ [_384420, _385232], _385232))], (2124 ^ _310321) ^ [_385495] : [in(ordered_pair(2118 ^ [_384420, _385232], _385495), _384420)]], 2126 ^ _310321 : [(2127 ^ _310321) ^ [] : [-(in(ordered_pair(2118 ^ [_384420, _385232], 2125 ^ [_384420, _385232]), _384420))], (2129 ^ _310321) ^ [] : [in(2118 ^ [_384420, _385232], _385232)]]], (2100 ^ _310321) ^ [_384601] : [_384601 = relation_dom(_384420), 2103 ^ _310321 : [(2104 ^ _310321) ^ [_384781] : [in(_384781, _384601), -(in(ordered_pair(_384781, 2107 ^ [_384420, _384601, _384781]), _384420))], (2111 ^ _310321) ^ [_385025] : [2112 ^ _310321 : [(2113 ^ _310321) ^ [_385104] : [in(ordered_pair(_385025, _385104), _384420)]], -(in(_385025, _384601))]]]]], (2133 ^ _310321) ^ [_385861] : [relation(_385861), 2136 ^ _310321 : [(2159 ^ _310321) ^ [_386729] : [2162 ^ _310321 : [(2163 ^ _310321) ^ [] : [-(in(2160 ^ [_385861, _386729], _386729))], (2165 ^ _310321) ^ [] : [-(in(2161 ^ [_385861, _386729], _386729))], (2167 ^ _310321) ^ [] : [-(in(ordered_pair(2160 ^ [_385861, _386729], 2161 ^ [_385861, _386729]), _385861))], (2169 ^ _310321) ^ [] : [-(in(ordered_pair(2161 ^ [_385861, _386729], 2160 ^ [_385861, _386729]), _385861))], (2171 ^ _310321) ^ [] : [2160 ^ [_385861, _386729] = 2161 ^ [_385861, _386729]]], -(is_antisymmetric_in(_385861, _386729))], (2137 ^ _310321) ^ [_386061] : [is_antisymmetric_in(_385861, _386061), 2140 ^ _310321 : [(2141 ^ _310321) ^ [_386243, _386245] : [-(_386245 = _386243), in(_386245, _386061), in(_386243, _386061), in(ordered_pair(_386245, _386243), _385861), in(ordered_pair(_386243, _386245), _385861)]]]]], (2175 ^ _310321) ^ [_387483] : [-(cast_to_subset(_387483) = _387483)], (2200 ^ _310321) ^ [_388466, _388468] : [-(_388466 = union(_388468)), 2213 ^ _310321 : [(2214 ^ _310321) ^ [] : [-(in(2201 ^ [_388466, _388468], 2212 ^ [_388466, _388468]))], (2216 ^ _310321) ^ [] : [-(in(2212 ^ [_388466, _388468], _388468))], (2218 ^ _310321) ^ [] : [in(2201 ^ [_388466, _388468], _388466)]], 2204 ^ _310321 : [(2205 ^ _310321) ^ [] : [-(in(2201 ^ [_388466, _388468], _388466))], (2207 ^ _310321) ^ [_388749] : [in(2201 ^ [_388466, _388468], _388749), in(_388749, _388468)]]], (2177 ^ _310321) ^ [_387621, _387623] : [_387621 = union(_387623), 2180 ^ _310321 : [(2181 ^ _310321) ^ [_387802] : [in(_387802, _387621), 2185 ^ _310321 : [(2186 ^ _310321) ^ [] : [-(in(_387802, 2184 ^ [_387621, _387623, _387802]))], (2188 ^ _310321) ^ [] : [-(in(2184 ^ [_387621, _387623, _387802], _387623))]]], (2190 ^ _310321) ^ [_388129] : [-(in(_388129, _387621)), 2191 ^ _310321 : [(2192 ^ _310321) ^ [_388227] : [in(_388129, _388227), in(_388227, _387623)]]]]], (2222 ^ _310321) ^ [_389299] : [relation(_389299), 2225 ^ _310321 : [(2226 ^ _310321) ^ [] : [well_ordering(_389299), 2229 ^ _310321 : [(2230 ^ _310321) ^ [] : [-(reflexive(_389299))], (2232 ^ _310321) ^ [] : [-(transitive(_389299))], (2234 ^ _310321) ^ [] : [-(antisymmetric(_389299))], (2236 ^ _310321) ^ [] : [-(connected(_389299))], (2238 ^ _310321) ^ [] : [-(well_founded_relation(_389299))]]], (2240 ^ _310321) ^ [] : [-(well_ordering(_389299)), reflexive(_389299), transitive(_389299), antisymmetric(_389299), connected(_389299), well_founded_relation(_389299)]]], (2284 ^ _310321) ^ [_391102, _391104, _391106] : [-(_391102 = set_difference(_391106, _391104)), 2296 ^ _310321 : [(2297 ^ _310321) ^ [] : [-(in(2285 ^ [_391102, _391104, _391106], _391106))], (2299 ^ _310321) ^ [] : [in(2285 ^ [_391102, _391104, _391106], _391104)], (2301 ^ _310321) ^ [] : [in(2285 ^ [_391102, _391104, _391106], _391102)]], 2288 ^ _310321 : [(2289 ^ _310321) ^ [] : [-(in(2285 ^ [_391102, _391104, _391106], _391102))], (2291 ^ _310321) ^ [] : [in(2285 ^ [_391102, _391104, _391106], _391106), -(in(2285 ^ [_391102, _391104, _391106], _391104))]]], (2262 ^ _310321) ^ [_390371, _390373, _390375] : [_390371 = set_difference(_390375, _390373), 2265 ^ _310321 : [(2266 ^ _310321) ^ [_390555] : [in(_390555, _390371), 2269 ^ _310321 : [(2270 ^ _310321) ^ [] : [-(in(_390555, _390375))], (2272 ^ _310321) ^ [] : [in(_390555, _390373)]]], (2274 ^ _310321) ^ [_390815] : [-(in(_390815, _390371)), in(_390815, _390375), -(in(_390815, _390373))]]], (2305 ^ _310321) ^ [_391845] : [relation(_391845), function(_391845), 2312 ^ _310321 : [(2336 ^ _310321) ^ [_392999] : [-(_392999 = relation_rng(_391845)), 2349 ^ _310321 : [(2350 ^ _310321) ^ [] : [-(in(2348 ^ [_391845, _392999], relation_dom(_391845)))], (2352 ^ _310321) ^ [] : [-(2337 ^ [_391845, _392999] = apply(_391845, 2348 ^ [_391845, _392999]))], (2354 ^ _310321) ^ [] : [in(2337 ^ [_391845, _392999], _392999)]], 2340 ^ _310321 : [(2341 ^ _310321) ^ [] : [-(in(2337 ^ [_391845, _392999], _392999))], (2343 ^ _310321) ^ [_393294] : [in(_393294, relation_dom(_391845)), 2337 ^ [_391845, _392999] = apply(_391845, _393294)]]], (2313 ^ _310321) ^ [_392117] : [_392117 = relation_rng(_391845), 2316 ^ _310321 : [(2317 ^ _310321) ^ [_392305] : [in(_392305, _392117), 2321 ^ _310321 : [(2322 ^ _310321) ^ [] : [-(in(2320 ^ [_391845, _392117, _392305], relation_dom(_391845)))], (2324 ^ _310321) ^ [] : [-(_392305 = apply(_391845, 2320 ^ [_391845, _392117, _392305]))]]], (2326 ^ _310321) ^ [_392647] : [-(in(_392647, _392117)), 2327 ^ _310321 : [(2328 ^ _310321) ^ [_392750] : [in(_392750, relation_dom(_391845)), _392647 = apply(_391845, _392750)]]]]]]], (2358 ^ _310321) ^ [_393871] : [relation(_393871), 2361 ^ _310321 : [(2379 ^ _310321) ^ [_394683] : [-(_394683 = relation_rng(_393871)), 2383 ^ _310321 : [(2384 ^ _310321) ^ [] : [-(in(2380 ^ [_393871, _394683], _394683))], (2386 ^ _310321) ^ [_394946] : [in(ordered_pair(_394946, 2380 ^ [_393871, _394683]), _393871)]], 2388 ^ _310321 : [(2389 ^ _310321) ^ [] : [-(in(ordered_pair(2387 ^ [_393871, _394683], 2380 ^ [_393871, _394683]), _393871))], (2391 ^ _310321) ^ [] : [in(2380 ^ [_393871, _394683], _394683)]]], (2362 ^ _310321) ^ [_394052] : [_394052 = relation_rng(_393871), 2365 ^ _310321 : [(2366 ^ _310321) ^ [_394232] : [in(_394232, _394052), -(in(ordered_pair(2369 ^ [_393871, _394052, _394232], _394232), _393871))], (2373 ^ _310321) ^ [_394476] : [2374 ^ _310321 : [(2375 ^ _310321) ^ [_394555] : [in(ordered_pair(_394555, _394476), _393871)]], -(in(_394476, _394052))]]]]], (2395 ^ _310321) ^ [_395326, _395328] : [element(_395326, powerset(_395328)), -(subset_complement(_395328, _395326) = set_difference(_395328, _395326))], (2401 ^ _310321) ^ [_395537, _395539] : [-(ordered_pair(_395539, _395537) = unordered_pair(unordered_pair(_395539, _395537), singleton(_395539)))], (2403 ^ _310321) ^ [_395643] : [relation(_395643), 2406 ^ _310321 : [(2407 ^ _310321) ^ [_395827] : [well_orders(_395643, _395827), 2410 ^ _310321 : [(2411 ^ _310321) ^ [] : [-(is_reflexive_in(_395643, _395827))], (2413 ^ _310321) ^ [] : [-(is_transitive_in(_395643, _395827))], (2415 ^ _310321) ^ [] : [-(is_antisymmetric_in(_395643, _395827))], (2417 ^ _310321) ^ [] : [-(is_connected_in(_395643, _395827))], (2419 ^ _310321) ^ [] : [-(is_well_founded_in(_395643, _395827))]]], (2421 ^ _310321) ^ [_396288] : [-(well_orders(_395643, _396288)), is_reflexive_in(_395643, _396288), is_transitive_in(_395643, _396288), is_antisymmetric_in(_395643, _396288), is_connected_in(_395643, _396288), is_well_founded_in(_395643, _396288)]]], (2443 ^ _310321) ^ [_396878] : [being_limit_ordinal(_396878), -(_396878 = union(_396878))], (2449 ^ _310321) ^ [_397036] : [_397036 = union(_397036), -(being_limit_ordinal(_397036))], (2455 ^ _310321) ^ [_397230] : [relation(_397230), -(relation_field(_397230) = set_union2(relation_dom(_397230), relation_rng(_397230)))], (2461 ^ _310321) ^ [_397436] : [relation(_397436), 2464 ^ _310321 : [(2487 ^ _310321) ^ [_398328] : [2490 ^ _310321 : [(2491 ^ _310321) ^ [] : [-(in(2488 ^ [_397436, _398328], _398328))], (2493 ^ _310321) ^ [] : [-(in(2489 ^ [_397436, _398328], _398328))], (2495 ^ _310321) ^ [] : [2488 ^ [_397436, _398328] = 2489 ^ [_397436, _398328]], (2497 ^ _310321) ^ [] : [in(ordered_pair(2488 ^ [_397436, _398328], 2489 ^ [_397436, _398328]), _397436)], (2499 ^ _310321) ^ [] : [in(ordered_pair(2489 ^ [_397436, _398328], 2488 ^ [_397436, _398328]), _397436)]], -(is_connected_in(_397436, _398328))], (2465 ^ _310321) ^ [_397644] : [is_connected_in(_397436, _397644), 2468 ^ _310321 : [(2469 ^ _310321) ^ [_397834, _397836] : [in(_397836, _397644), in(_397834, _397644), -(_397836 = _397834), -(in(ordered_pair(_397836, _397834), _397436)), -(in(ordered_pair(_397834, _397836), _397436))]]]]], (2503 ^ _310321) ^ [_399113] : [relation(_399113), 2506 ^ _310321 : [(2507 ^ _310321) ^ [_399232] : [-(relation_restriction(_399113, _399232) = set_intersection2(_399113, cartesian_product2(_399232, _399232)))]]], (2509 ^ _310321) ^ [_399341] : [relation(_399341), 2512 ^ _310321 : [(2513 ^ _310321) ^ [_399501] : [relation(_399501), 2516 ^ _310321 : [(2533 ^ _310321) ^ [] : [-(_399501 = relation_inverse(_399341)), 2538 ^ _310321 : [(2539 ^ _310321) ^ [] : [-(in(ordered_pair(2534 ^ [_399341, _399501], 2535 ^ [_399341, _399501]), _399501))], (2541 ^ _310321) ^ [] : [in(ordered_pair(2535 ^ [_399341, _399501], 2534 ^ [_399341, _399501]), _399341)]], 2542 ^ _310321 : [(2543 ^ _310321) ^ [] : [-(in(ordered_pair(2535 ^ [_399341, _399501], 2534 ^ [_399341, _399501]), _399341))], (2545 ^ _310321) ^ [] : [in(ordered_pair(2534 ^ [_399341, _399501], 2535 ^ [_399341, _399501]), _399501)]]], (2517 ^ _310321) ^ [] : [_399501 = relation_inverse(_399341), 2520 ^ _310321 : [(2521 ^ _310321) ^ [_399810, _399812] : [in(ordered_pair(_399812, _399810), _399501), -(in(ordered_pair(_399810, _399812), _399341))], (2527 ^ _310321) ^ [_400000, _400002] : [in(ordered_pair(_400000, _400002), _399341), -(in(ordered_pair(_400002, _400000), _399501))]]]]]]], (2549 ^ _310321) ^ [_400805] : [relation(_400805), 2552 ^ _310321 : [(2553 ^ _310321) ^ [_401026] : [relation(_401026), 2556 ^ _310321 : [(2557 ^ _310321) ^ [_401243] : [relation(_401243), function(_401243), 2564 ^ _310321 : [(2599 ^ _310321) ^ [] : [-(relation_isomorphism(_400805, _401026, _401243)), relation_dom(_401243) = relation_field(_400805), relation_rng(_401243) = relation_field(_401026), one_to_one(_401243), 2628 ^ _310321 : [(2629 ^ _310321) ^ [] : [-(in(2612 ^ [_400805, _401026, _401243], relation_field(_400805)))], (2631 ^ _310321) ^ [] : [-(in(2613 ^ [_400805, _401026, _401243], relation_field(_400805)))], (2633 ^ _310321) ^ [] : [-(in(ordered_pair(apply(_401243, 2612 ^ [_400805, _401026, _401243]), apply(_401243, 2613 ^ [_400805, _401026, _401243])), _401026))], (2635 ^ _310321) ^ [] : [in(ordered_pair(2612 ^ [_400805, _401026, _401243], 2613 ^ [_400805, _401026, _401243]), _400805)]], 2616 ^ _310321 : [(2617 ^ _310321) ^ [] : [-(in(ordered_pair(2612 ^ [_400805, _401026, _401243], 2613 ^ [_400805, _401026, _401243]), _400805))], (2619 ^ _310321) ^ [] : [in(2612 ^ [_400805, _401026, _401243], relation_field(_400805)), in(2613 ^ [_400805, _401026, _401243], relation_field(_400805)), in(ordered_pair(apply(_401243, 2612 ^ [_400805, _401026, _401243]), apply(_401243, 2613 ^ [_400805, _401026, _401243])), _401026)]]], (2565 ^ _310321) ^ [] : [relation_isomorphism(_400805, _401026, _401243), 2568 ^ _310321 : [(2569 ^ _310321) ^ [] : [-(relation_dom(_401243) = relation_field(_400805))], (2571 ^ _310321) ^ [] : [-(relation_rng(_401243) = relation_field(_401026))], (2573 ^ _310321) ^ [] : [-(one_to_one(_401243))], (2575 ^ _310321) ^ [_401909, _401911] : [in(ordered_pair(_401911, _401909), _400805), 2578 ^ _310321 : [(2579 ^ _310321) ^ [] : [-(in(_401911, relation_field(_400805)))], (2581 ^ _310321) ^ [] : [-(in(_401909, relation_field(_400805)))], (2583 ^ _310321) ^ [] : [-(in(ordered_pair(apply(_401243, _401911), apply(_401243, _401909)), _401026))]]], (2585 ^ _310321) ^ [_402288, _402290] : [-(in(ordered_pair(_402290, _402288), _400805)), in(_402290, relation_field(_400805)), in(_402288, relation_field(_400805)), in(ordered_pair(apply(_401243, _402290), apply(_401243, _402288)), _401026)]]]]]]]]], (2639 ^ _310321) ^ [_404115, _404117] : [disjoint(_404117, _404115), -(set_intersection2(_404117, _404115) = empty_set)], (2645 ^ _310321) ^ [_404283, _404285] : [set_intersection2(_404285, _404283) = empty_set, -(disjoint(_404285, _404283))], (2651 ^ _310321) ^ [_404487] : [relation(_404487), function(_404487), 2658 ^ _310321 : [(2677 ^ _310321) ^ [] : [2680 ^ _310321 : [(2681 ^ _310321) ^ [] : [-(in(2678 ^ [_404487], relation_dom(_404487)))], (2683 ^ _310321) ^ [] : [-(in(2679 ^ [_404487], relation_dom(_404487)))], (2685 ^ _310321) ^ [] : [-(apply(_404487, 2678 ^ [_404487]) = apply(_404487, 2679 ^ [_404487]))], (2687 ^ _310321) ^ [] : [2678 ^ [_404487] = 2679 ^ [_404487]]], -(one_to_one(_404487))], (2659 ^ _310321) ^ [] : [one_to_one(_404487), 2662 ^ _310321 : [(2663 ^ _310321) ^ [_404850, _404852] : [-(_404852 = _404850), in(_404852, relation_dom(_404487)), in(_404850, relation_dom(_404487)), apply(_404487, _404852) = apply(_404487, _404850)]]]]], (2691 ^ _310321) ^ [_405797] : [relation(_405797), 2694 ^ _310321 : [(2695 ^ _310321) ^ [_405982] : [relation(_405982), 2698 ^ _310321 : [(2699 ^ _310321) ^ [_406163] : [relation(_406163), 2702 ^ _310321 : [(2726 ^ _310321) ^ [] : [-(_406163 = relation_composition(_405797, _405982)), 2740 ^ _310321 : [(2741 ^ _310321) ^ [] : [-(in(ordered_pair(2727 ^ [_405797, _405982, _406163], 2739 ^ [_405797, _405982, _406163]), _405797))], (2743 ^ _310321) ^ [] : [-(in(ordered_pair(2739 ^ [_405797, _405982, _406163], 2728 ^ [_405797, _405982, _406163]), _405982))], (2745 ^ _310321) ^ [] : [in(ordered_pair(2727 ^ [_405797, _405982, _406163], 2728 ^ [_405797, _405982, _406163]), _406163)]], 2731 ^ _310321 : [(2732 ^ _310321) ^ [] : [-(in(ordered_pair(2727 ^ [_405797, _405982, _406163], 2728 ^ [_405797, _405982, _406163]), _406163))], (2734 ^ _310321) ^ [_407627] : [in(ordered_pair(2727 ^ [_405797, _405982, _406163], _407627), _405797), in(ordered_pair(_407627, 2728 ^ [_405797, _405982, _406163]), _405982)]]], (2703 ^ _310321) ^ [] : [_406163 = relation_composition(_405797, _405982), 2706 ^ _310321 : [(2707 ^ _310321) ^ [_406498, _406500] : [in(ordered_pair(_406500, _406498), _406163), 2711 ^ _310321 : [(2712 ^ _310321) ^ [] : [-(in(ordered_pair(_406500, 2710 ^ [_405797, _405982, _406163, _406498, _406500]), _405797))], (2714 ^ _310321) ^ [] : [-(in(ordered_pair(2710 ^ [_405797, _405982, _406163, _406498, _406500], _406498), _405982))]]], (2716 ^ _310321) ^ [_406883, _406885] : [-(in(ordered_pair(_406885, _406883), _406163)), 2717 ^ _310321 : [(2718 ^ _310321) ^ [_406996] : [in(ordered_pair(_406885, _406996), _405797), in(ordered_pair(_406996, _406883), _405982)]]]]]]]]]]], (2749 ^ _310321) ^ [_408299] : [relation(_408299), 2752 ^ _310321 : [(2779 ^ _310321) ^ [_409334] : [2783 ^ _310321 : [(2784 ^ _310321) ^ [] : [-(in(2780 ^ [_408299, _409334], _409334))], (2786 ^ _310321) ^ [] : [-(in(2781 ^ [_408299, _409334], _409334))], (2788 ^ _310321) ^ [] : [-(in(2782 ^ [_408299, _409334], _409334))], (2790 ^ _310321) ^ [] : [-(in(ordered_pair(2780 ^ [_408299, _409334], 2781 ^ [_408299, _409334]), _408299))], (2792 ^ _310321) ^ [] : [-(in(ordered_pair(2781 ^ [_408299, _409334], 2782 ^ [_408299, _409334]), _408299))], (2794 ^ _310321) ^ [] : [in(ordered_pair(2780 ^ [_408299, _409334], 2782 ^ [_408299, _409334]), _408299)]], -(is_transitive_in(_408299, _409334))], (2753 ^ _310321) ^ [_408513] : [is_transitive_in(_408299, _408513), 2756 ^ _310321 : [(2757 ^ _310321) ^ [_408723, _408725, _408727] : [-(in(ordered_pair(_408727, _408723), _408299)), in(_408727, _408513), in(_408725, _408513), in(_408723, _408513), in(ordered_pair(_408727, _408725), _408299), in(ordered_pair(_408725, _408723), _408299)]]]]], (2798 ^ _310321) ^ [_410358, _410360] : [element(_410358, powerset(powerset(_410360))), 2801 ^ _310321 : [(2802 ^ _310321) ^ [_410538] : [element(_410538, powerset(powerset(_410360))), 2805 ^ _310321 : [(2826 ^ _310321) ^ [] : [-(_410538 = complements_of_subsets(_410360, _410358)), 2828 ^ _310321 : [(2829 ^ _310321) ^ [] : [-(element(2827 ^ [_410358, _410360, _410538], powerset(_410360)))], (2831 ^ _310321) ^ [] : [2832 ^ _310321 : [(2833 ^ _310321) ^ [] : [-(in(2827 ^ [_410358, _410360, _410538], _410538))], (2835 ^ _310321) ^ [] : [in(subset_complement(_410360, 2827 ^ [_410358, _410360, _410538]), _410358)]], 2836 ^ _310321 : [(2837 ^ _310321) ^ [] : [-(in(subset_complement(_410360, 2827 ^ [_410358, _410360, _410538]), _410358))], (2839 ^ _310321) ^ [] : [in(2827 ^ [_410358, _410360, _410538], _410538)]]]]], (2806 ^ _310321) ^ [] : [_410538 = complements_of_subsets(_410360, _410358), 2809 ^ _310321 : [(2810 ^ _310321) ^ [_410826] : [element(_410826, powerset(_410360)), 2813 ^ _310321 : [(2814 ^ _310321) ^ [] : [in(_410826, _410538), -(in(subset_complement(_410360, _410826), _410358))], (2820 ^ _310321) ^ [] : [in(subset_complement(_410360, _410826), _410358), -(in(_410826, _410538))]]]]]]]]], (2843 ^ _310321) ^ [_411949, _411951] : [proper_subset(_411951, _411949), 2846 ^ _310321 : [(2847 ^ _310321) ^ [] : [-(subset(_411951, _411949))], (2849 ^ _310321) ^ [] : [_411951 = _411949]]], (2851 ^ _310321) ^ [_412187, _412189] : [-(proper_subset(_412189, _412187)), subset(_412189, _412187), -(_412189 = _412187)], (2861 ^ _310321) ^ [_412477] : [relation(_412477), function(_412477), one_to_one(_412477), -(function_inverse(_412477) = relation_inverse(_412477))], (2875 ^ _310321) ^ [_412841] : [relation(_412841), 2878 ^ _310321 : [(2879 ^ _310321) ^ [] : [reflexive(_412841), -(is_reflexive_in(_412841, relation_field(_412841)))], (2885 ^ _310321) ^ [] : [is_reflexive_in(_412841, relation_field(_412841)), -(reflexive(_412841))]]], (2891 ^ _310321) ^ [] : [true___, -(true___)], (2897 ^ _310321) ^ [] : [true___, -(true___)], (2903 ^ _310321) ^ [] : [true___, -(true___)], (2909 ^ _310321) ^ [] : [true___, -(true___)], (2915 ^ _310321) ^ [] : [true___, -(true___)], (2921 ^ _310321) ^ [] : [true___, -(true___)], (2927 ^ _310321) ^ [] : [true___, -(true___)], (2933 ^ _310321) ^ [] : [true___, -(true___)], (2939 ^ _310321) ^ [] : [true___, -(true___)], (2945 ^ _310321) ^ [] : [true___, -(true___)], (2951 ^ _310321) ^ [] : [true___, -(true___)], (2957 ^ _310321) ^ [_414581] : [2964 ^ _310321 : [(2965 ^ _310321) ^ [] : [-(relation(function_inverse(_414581)))], (2967 ^ _310321) ^ [] : [-(function(function_inverse(_414581)))]], relation(_414581), function(_414581)], (2969 ^ _310321) ^ [] : [true___, -(true___)], (2975 ^ _310321) ^ [] : [true___, -(true___)], (2981 ^ _310321) ^ [_415152] : [-(element(cast_to_subset(_415152), powerset(_415152)))], (2983 ^ _310321) ^ [] : [true___, -(true___)], (2989 ^ _310321) ^ [_415382, _415384] : [relation(_415384), -(relation(relation_restriction(_415384, _415382)))], (2995 ^ _310321) ^ [] : [true___, -(true___)], (3001 ^ _310321) ^ [] : [true___, -(true___)], (3007 ^ _310321) ^ [] : [true___, -(true___)], (3013 ^ _310321) ^ [_415951, _415953] : [element(_415951, powerset(_415953)), -(element(subset_complement(_415953, _415951), powerset(_415953)))], (3019 ^ _310321) ^ [] : [true___, -(true___)], (3025 ^ _310321) ^ [] : [true___, -(true___)], (3031 ^ _310321) ^ [_416399] : [relation(_416399), -(relation(relation_inverse(_416399)))], (3037 ^ _310321) ^ [_416617, _416619, _416621] : [relation_of2(_416617, _416621, _416619), -(element(relation_dom_as_subset(_416621, _416619, _416617), powerset(_416621)))], (3043 ^ _310321) ^ [] : [true___, -(true___)], (3049 ^ _310321) ^ [] : [true___, -(true___)], (3055 ^ _310321) ^ [_417085, _417087] : [-(relation(relation_composition(_417087, _417085))), relation(_417087), relation(_417085)], (3065 ^ _310321) ^ [_417398, _417400, _417402] : [relation_of2(_417398, _417402, _417400), -(element(relation_rng_as_subset(_417402, _417400, _417398), powerset(_417400)))], (3071 ^ _310321) ^ [_417628, _417630] : [element(_417628, powerset(powerset(_417630))), -(element(union_of_subsets(_417630, _417628), powerset(_417630)))], (3077 ^ _310321) ^ [_417827] : [-(relation(identity_relation(_417827)))], (3079 ^ _310321) ^ [_417935, _417937] : [element(_417935, powerset(powerset(_417937))), -(element(meet_of_subsets(_417937, _417935), powerset(_417937)))], (3085 ^ _310321) ^ [_418177, _418179, _418181] : [-(element(subset_difference(_418181, _418179, _418177), powerset(_418181))), element(_418179, powerset(_418181)), element(_418177, powerset(_418181))], (3095 ^ _310321) ^ [_418506, _418508] : [relation(_418508), -(relation(relation_dom_restriction(_418508, _418506)))], (3101 ^ _310321) ^ [_418718, _418720] : [element(_418718, powerset(powerset(_418720))), -(element(complements_of_subsets(_418720, _418718), powerset(powerset(_418720))))], (3107 ^ _310321) ^ [_418950, _418952] : [relation(_418950), -(relation(relation_rng_restriction(_418952, _418950)))], (3113 ^ _310321) ^ [] : [true___, -(true___)], (3119 ^ _310321) ^ [] : [true___, -(true___)], (3125 ^ _310321) ^ [] : [true___, -(true___)], (3131 ^ _310321) ^ [_419533, _419535, _419537] : [relation_of2_as_subset(_419533, _419537, _419535), -(element(_419533, powerset(cartesian_product2(_419537, _419535))))], (3138 ^ _310321) ^ [_419788, _419790] : [-(relation_of2(3136 ^ [_419788, _419790], _419790, _419788))], (3141 ^ _310321) ^ [_419915] : [-(element(3139 ^ [_419915], _419915))], (3144 ^ _310321) ^ [_420054, _420056] : [-(relation_of2_as_subset(3142 ^ [_420054, _420056], _420056, _420054))], (3146 ^ _310321) ^ [_420171, _420173] : [3153 ^ _310321 : [(3154 ^ _310321) ^ [] : [-(empty(relation_composition(_420171, _420173)))], (3156 ^ _310321) ^ [] : [-(relation(relation_composition(_420171, _420173)))]], empty(_420173), relation(_420171)], (3158 ^ _310321) ^ [_420535] : [empty(_420535), 3161 ^ _310321 : [(3162 ^ _310321) ^ [] : [-(empty(relation_inverse(_420535)))], (3164 ^ _310321) ^ [] : [-(relation(relation_inverse(_420535)))]]], (3166 ^ _310321) ^ [] : [-(empty(empty_set))], (3168 ^ _310321) ^ [] : [-(relation(empty_set))], (3170 ^ _310321) ^ [] : [-(relation_empty_yielding(empty_set))], (3172 ^ _310321) ^ [_420977, _420979] : [3179 ^ _310321 : [(3180 ^ _310321) ^ [] : [-(relation(relation_dom_restriction(_420979, _420977)))], (3182 ^ _310321) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_420979, _420977)))]], relation(_420979), relation_empty_yielding(_420979)], (3184 ^ _310321) ^ [_421355, _421357] : [3199 ^ _310321 : [(3200 ^ _310321) ^ [] : [-(relation(relation_composition(_421357, _421355)))], (3202 ^ _310321) ^ [] : [-(function(relation_composition(_421357, _421355)))]], relation(_421357), function(_421357), relation(_421355), function(_421355)], (3204 ^ _310321) ^ [_421877] : [empty(succ(_421877))], (3206 ^ _310321) ^ [_421985, _421987] : [-(relation(set_intersection2(_421987, _421985))), relation(_421987), relation(_421985)], (3216 ^ _310321) ^ [_422254] : [empty(powerset(_422254))], (3218 ^ _310321) ^ [] : [-(empty(empty_set))], (3220 ^ _310321) ^ [_422399, _422401] : [empty(ordered_pair(_422401, _422399))], (3222 ^ _310321) ^ [_422501] : [-(relation(identity_relation(_422501)))], (3224 ^ _310321) ^ [_422546] : [-(function(identity_relation(_422546)))], (3226 ^ _310321) ^ [] : [-(relation(empty_set))], (3228 ^ _310321) ^ [] : [-(relation_empty_yielding(empty_set))], (3230 ^ _310321) ^ [] : [-(function(empty_set))], (3232 ^ _310321) ^ [] : [-(one_to_one(empty_set))], (3234 ^ _310321) ^ [] : [-(empty(empty_set))], (3236 ^ _310321) ^ [] : [-(epsilon_transitive(empty_set))], (3238 ^ _310321) ^ [] : [-(epsilon_connected(empty_set))], (3240 ^ _310321) ^ [] : [-(ordinal(empty_set))], (3242 ^ _310321) ^ [_423094, _423096] : [-(relation(set_union2(_423096, _423094))), relation(_423096), relation(_423094)], (3252 ^ _310321) ^ [_423363] : [empty(singleton(_423363))], (3254 ^ _310321) ^ [_423471, _423473] : [-(empty(_423473)), empty(set_union2(_423473, _423471))], (3260 ^ _310321) ^ [_423673] : [3271 ^ _310321 : [(3272 ^ _310321) ^ [] : [-(relation(relation_inverse(_423673)))], (3274 ^ _310321) ^ [] : [-(function(relation_inverse(_423673)))]], relation(_423673), function(_423673), one_to_one(_423673)], (3276 ^ _310321) ^ [_424104] : [ordinal(_424104), 3279 ^ _310321 : [(3280 ^ _310321) ^ [] : [empty(succ(_424104))], (3282 ^ _310321) ^ [] : [-(epsilon_transitive(succ(_424104)))], (3284 ^ _310321) ^ [] : [-(epsilon_connected(succ(_424104)))], (3286 ^ _310321) ^ [] : [-(ordinal(succ(_424104)))]]], (3288 ^ _310321) ^ [_424532, _424534] : [-(relation(set_difference(_424534, _424532))), relation(_424534), relation(_424532)], (3298 ^ _310321) ^ [_424815, _424817] : [empty(unordered_pair(_424817, _424815))], (3300 ^ _310321) ^ [_424926, _424928] : [-(empty(_424928)), empty(set_union2(_424926, _424928))], (3306 ^ _310321) ^ [_425142, _425144] : [3313 ^ _310321 : [(3314 ^ _310321) ^ [] : [-(relation(relation_dom_restriction(_425144, _425142)))], (3316 ^ _310321) ^ [] : [-(function(relation_dom_restriction(_425144, _425142)))]], relation(_425144), function(_425144)], (3318 ^ _310321) ^ [_425506] : [ordinal(_425506), 3321 ^ _310321 : [(3322 ^ _310321) ^ [] : [-(epsilon_transitive(union(_425506)))], (3324 ^ _310321) ^ [] : [-(epsilon_connected(union(_425506)))], (3326 ^ _310321) ^ [] : [-(ordinal(union(_425506)))]]], (3328 ^ _310321) ^ [] : [-(empty(empty_set))], (3330 ^ _310321) ^ [] : [-(relation(empty_set))], (3332 ^ _310321) ^ [_425967, _425969] : [empty(cartesian_product2(_425969, _425967)), -(empty(_425969)), -(empty(_425967))], (3342 ^ _310321) ^ [_426273, _426275] : [3349 ^ _310321 : [(3350 ^ _310321) ^ [] : [-(relation(relation_rng_restriction(_426275, _426273)))], (3352 ^ _310321) ^ [] : [-(function(relation_rng_restriction(_426275, _426273)))]], relation(_426273), function(_426273)], (3354 ^ _310321) ^ [_426637] : [empty(relation_dom(_426637)), -(empty(_426637)), relation(_426637)], (3364 ^ _310321) ^ [_426914] : [empty(relation_rng(_426914)), -(empty(_426914)), relation(_426914)], (3374 ^ _310321) ^ [_427191] : [empty(_427191), 3377 ^ _310321 : [(3378 ^ _310321) ^ [] : [-(empty(relation_dom(_427191)))], (3380 ^ _310321) ^ [] : [-(relation(relation_dom(_427191)))]]], (3382 ^ _310321) ^ [_427456] : [empty(_427456), 3385 ^ _310321 : [(3386 ^ _310321) ^ [] : [-(empty(relation_rng(_427456)))], (3388 ^ _310321) ^ [] : [-(relation(relation_rng(_427456)))]]], (3390 ^ _310321) ^ [_427735, _427737] : [3397 ^ _310321 : [(3398 ^ _310321) ^ [] : [-(empty(relation_composition(_427737, _427735)))], (3400 ^ _310321) ^ [] : [-(relation(relation_composition(_427737, _427735)))]], empty(_427737), relation(_427735)], (3402 ^ _310321) ^ [_428098, _428100] : [-(set_union2(_428100, _428100) = _428100)], (3404 ^ _310321) ^ [_428195, _428197] : [-(set_intersection2(_428197, _428197) = _428197)], (3406 ^ _310321) ^ [_428307, _428309] : [element(_428307, powerset(_428309)), -(subset_complement(_428309, subset_complement(_428309, _428307)) = _428307)], (3412 ^ _310321) ^ [_428519] : [relation(_428519), -(relation_inverse(relation_inverse(_428519)) = _428519)], (3418 ^ _310321) ^ [_428729, _428731] : [element(_428729, powerset(powerset(_428731))), -(complements_of_subsets(_428731, complements_of_subsets(_428731, _428729)) = _428729)], (3424 ^ _310321) ^ [_428943, _428945] : [proper_subset(_428945, _428945)], (3426 ^ _310321) ^ [_429038] : [relation(_429038), 3429 ^ _310321 : [(3440 ^ _310321) ^ [] : [3442 ^ _310321 : [(3443 ^ _310321) ^ [] : [-(in(3441 ^ [_429038], relation_field(_429038)))], (3445 ^ _310321) ^ [] : [in(ordered_pair(3441 ^ [_429038], 3441 ^ [_429038]), _429038)]], -(reflexive(_429038))], (3430 ^ _310321) ^ [] : [reflexive(_429038), 3433 ^ _310321 : [(3434 ^ _310321) ^ [_429282] : [in(_429282, relation_field(_429038)), -(in(ordered_pair(_429282, _429282), _429038))]]]]], (3449 ^ _310321) ^ [_429747] : [singleton(_429747) = empty_set], (3451 ^ _310321) ^ [_429856, _429858] : [in(_429858, _429856), -(set_union2(singleton(_429858), _429856) = _429856)], (3457 ^ _310321) ^ [_430076, _430078] : [disjoint(singleton(_430078), _430076), in(_430078, _430076)], (3463 ^ _310321) ^ [_430289, _430291] : [-(in(_430291, _430289)), -(disjoint(singleton(_430291), _430289))], (3469 ^ _310321) ^ [_430506, _430508] : [relation(_430506), -(subset(relation_dom(relation_rng_restriction(_430508, _430506)), relation_dom(_430506)))], (3475 ^ _310321) ^ [_430714] : [relation(_430714), 3478 ^ _310321 : [(3493 ^ _310321) ^ [] : [3497 ^ _310321 : [(3498 ^ _310321) ^ [] : [-(in(ordered_pair(3494 ^ [_430714], 3495 ^ [_430714]), _430714))], (3500 ^ _310321) ^ [] : [-(in(ordered_pair(3495 ^ [_430714], 3496 ^ [_430714]), _430714))], (3502 ^ _310321) ^ [] : [in(ordered_pair(3494 ^ [_430714], 3496 ^ [_430714]), _430714)]], -(transitive(_430714))], (3479 ^ _310321) ^ [] : [transitive(_430714), 3482 ^ _310321 : [(3483 ^ _310321) ^ [_431006, _431008, _431010] : [-(in(ordered_pair(_431010, _431006), _430714)), in(ordered_pair(_431010, _431008), _430714), in(ordered_pair(_431008, _431006), _430714)]]]]], (3506 ^ _310321) ^ [_431913, _431915] : [subset(singleton(_431915), _431913), -(in(_431915, _431913))], (3512 ^ _310321) ^ [_432079, _432081] : [in(_432081, _432079), -(subset(singleton(_432081), _432079))], (3518 ^ _310321) ^ [_432324, _432326] : [set_difference(_432326, _432324) = empty_set, -(subset(_432326, _432324))], (3524 ^ _310321) ^ [_432492, _432494] : [subset(_432494, _432492), -(set_difference(_432494, _432492) = empty_set)], (3530 ^ _310321) ^ [_432710, _432712] : [element(_432710, powerset(_432712)), 3533 ^ _310321 : [(3534 ^ _310321) ^ [_432851] : [in(_432851, _432710), -(in(_432851, _432712))]]], (3540 ^ _310321) ^ [_433062] : [relation(_433062), 3543 ^ _310321 : [(3558 ^ _310321) ^ [] : [3561 ^ _310321 : [(3562 ^ _310321) ^ [] : [-(in(ordered_pair(3559 ^ [_433062], 3560 ^ [_433062]), _433062))], (3564 ^ _310321) ^ [] : [-(in(ordered_pair(3560 ^ [_433062], 3559 ^ [_433062]), _433062))], (3566 ^ _310321) ^ [] : [3559 ^ [_433062] = 3560 ^ [_433062]]], -(antisymmetric(_433062))], (3544 ^ _310321) ^ [] : [antisymmetric(_433062), 3547 ^ _310321 : [(3548 ^ _310321) ^ [_433332, _433334] : [-(_433334 = _433332), in(ordered_pair(_433334, _433332), _433062), in(ordered_pair(_433332, _433334), _433062)]]]]], (3570 ^ _310321) ^ [_434112, _434114, _434116] : [subset(_434116, _434114), -(in(_434112, _434116)), -(subset(_434116, set_difference(_434114, singleton(_434112))))], (3580 ^ _310321) ^ [_434418] : [relation(_434418), 3583 ^ _310321 : [(3606 ^ _310321) ^ [] : [3609 ^ _310321 : [(3610 ^ _310321) ^ [] : [-(in(3607 ^ [_434418], relation_field(_434418)))], (3612 ^ _310321) ^ [] : [-(in(3608 ^ [_434418], relation_field(_434418)))], (3614 ^ _310321) ^ [] : [3607 ^ [_434418] = 3608 ^ [_434418]], (3616 ^ _310321) ^ [] : [in(ordered_pair(3607 ^ [_434418], 3608 ^ [_434418]), _434418)], (3618 ^ _310321) ^ [] : [in(ordered_pair(3608 ^ [_434418], 3607 ^ [_434418]), _434418)]], -(connected(_434418))], (3584 ^ _310321) ^ [] : [connected(_434418), 3587 ^ _310321 : [(3588 ^ _310321) ^ [_434712, _434714] : [in(_434714, relation_field(_434418)), in(_434712, relation_field(_434418)), -(_434714 = _434712), -(in(ordered_pair(_434714, _434712), _434418)), -(in(ordered_pair(_434712, _434714), _434418))]]]]], (3632 ^ _310321) ^ [_436164, _436166] : [3633 ^ _310321 : [(3634 ^ _310321) ^ [] : [_436166 = empty_set], (3636 ^ _310321) ^ [] : [_436166 = singleton(_436164)]], -(subset(_436166, singleton(_436164)))], (3622 ^ _310321) ^ [_435904, _435906] : [subset(_435906, singleton(_435904)), -(_435906 = empty_set), -(_435906 = singleton(_435904))], (3640 ^ _310321) ^ [_436458, _436460] : [in(_436460, _436458), -(subset(_436460, union(_436458)))], (3646 ^ _310321) ^ [_436729, _436731, _436733, _436735] : [in(ordered_pair(_436735, _436733), cartesian_product2(_436731, _436729)), 3649 ^ _310321 : [(3650 ^ _310321) ^ [] : [-(in(_436735, _436731))], (3652 ^ _310321) ^ [] : [-(in(_436733, _436729))]]], (3654 ^ _310321) ^ [_436994, _436996, _436998, _437000] : [-(in(ordered_pair(_437000, _436998), cartesian_product2(_436996, _436994))), in(_437000, _436996), in(_436998, _436994)], (3664 ^ _310321) ^ [_437327, _437329] : [3666 ^ _310321 : [(3667 ^ _310321) ^ [] : [-(in(3665 ^ [_437327, _437329], _437329))], (3669 ^ _310321) ^ [] : [in(3665 ^ [_437327, _437329], _437327)]], -(element(_437329, powerset(_437327)))], (3673 ^ _310321) ^ [_437700, _437702, _437704] : [relation(_437700), function(_437700), 3680 ^ _310321 : [(3681 ^ _310321) ^ [] : [in(_437702, relation_dom(relation_dom_restriction(_437700, _437704))), 3684 ^ _310321 : [(3685 ^ _310321) ^ [] : [-(in(_437702, relation_dom(_437700)))], (3687 ^ _310321) ^ [] : [-(in(_437702, _437704))]]], (3689 ^ _310321) ^ [] : [-(in(_437702, relation_dom(relation_dom_restriction(_437700, _437704)))), in(_437702, relation_dom(_437700)), in(_437702, _437704)]]], (3700 ^ _310321) ^ [] : [-(relation(3698 ^ []))], (3702 ^ _310321) ^ [] : [-(function(3698 ^ []))], (3705 ^ _310321) ^ [] : [-(epsilon_transitive(3703 ^ []))], (3707 ^ _310321) ^ [] : [-(epsilon_connected(3703 ^ []))], (3709 ^ _310321) ^ [] : [-(ordinal(3703 ^ []))], (3712 ^ _310321) ^ [] : [-(empty(3710 ^ []))], (3714 ^ _310321) ^ [] : [-(relation(3710 ^ []))], (3716 ^ _310321) ^ [_438945] : [-(empty(_438945)), 3720 ^ _310321 : [(3721 ^ _310321) ^ [] : [-(element(3719 ^ [_438945], powerset(_438945)))], (3723 ^ _310321) ^ [] : [empty(3719 ^ [_438945])]]], (3726 ^ _310321) ^ [] : [-(empty(3724 ^ []))], (3729 ^ _310321) ^ [] : [-(relation(3727 ^ []))], (3731 ^ _310321) ^ [] : [-(empty(3727 ^ []))], (3733 ^ _310321) ^ [] : [-(function(3727 ^ []))], (3736 ^ _310321) ^ [] : [-(relation(3734 ^ []))], (3738 ^ _310321) ^ [] : [-(function(3734 ^ []))], (3740 ^ _310321) ^ [] : [-(one_to_one(3734 ^ []))], (3742 ^ _310321) ^ [] : [-(empty(3734 ^ []))], (3744 ^ _310321) ^ [] : [-(epsilon_transitive(3734 ^ []))], (3746 ^ _310321) ^ [] : [-(epsilon_connected(3734 ^ []))], (3748 ^ _310321) ^ [] : [-(ordinal(3734 ^ []))], (3751 ^ _310321) ^ [] : [empty(3749 ^ [])], (3753 ^ _310321) ^ [] : [-(relation(3749 ^ []))], (3756 ^ _310321) ^ [_440225] : [-(element(3754 ^ [_440225], powerset(_440225)))], (3758 ^ _310321) ^ [_440276] : [-(empty(3754 ^ [_440276]))], (3761 ^ _310321) ^ [] : [empty(3759 ^ [])], (3764 ^ _310321) ^ [] : [-(relation(3762 ^ []))], (3766 ^ _310321) ^ [] : [-(function(3762 ^ []))], (3768 ^ _310321) ^ [] : [-(one_to_one(3762 ^ []))], (3771 ^ _310321) ^ [] : [empty(3769 ^ [])], (3773 ^ _310321) ^ [] : [-(epsilon_transitive(3769 ^ []))], (3775 ^ _310321) ^ [] : [-(epsilon_connected(3769 ^ []))], (3777 ^ _310321) ^ [] : [-(ordinal(3769 ^ []))], (3780 ^ _310321) ^ [] : [-(relation(3778 ^ []))], (3782 ^ _310321) ^ [] : [-(relation_empty_yielding(3778 ^ []))], (3785 ^ _310321) ^ [] : [-(relation(3783 ^ []))], (3787 ^ _310321) ^ [] : [-(relation_empty_yielding(3783 ^ []))], (3789 ^ _310321) ^ [] : [-(function(3783 ^ []))], (3791 ^ _310321) ^ [_441330, _441332, _441334] : [relation_of2(_441330, _441334, _441332), -(relation_dom_as_subset(_441334, _441332, _441330) = relation_dom(_441330))], (3797 ^ _310321) ^ [_441574, _441576, _441578] : [relation_of2(_441574, _441578, _441576), -(relation_rng_as_subset(_441578, _441576, _441574) = relation_rng(_441574))], (3803 ^ _310321) ^ [_441804, _441806] : [element(_441804, powerset(powerset(_441806))), -(union_of_subsets(_441806, _441804) = union(_441804))], (3809 ^ _310321) ^ [_442032, _442034] : [element(_442032, powerset(powerset(_442034))), -(meet_of_subsets(_442034, _442032) = set_meet(_442032))], (3815 ^ _310321) ^ [_442274, _442276, _442278] : [-(subset_difference(_442278, _442276, _442274) = set_difference(_442276, _442274)), element(_442276, powerset(_442278)), element(_442274, powerset(_442278))], (3825 ^ _310321) ^ [_442648, _442650, _442652] : [relation_of2_as_subset(_442648, _442652, _442650), -(relation_of2(_442648, _442652, _442650))], (3831 ^ _310321) ^ [_442820, _442822, _442824] : [relation_of2(_442820, _442824, _442822), -(relation_of2_as_subset(_442820, _442824, _442822))], (3837 ^ _310321) ^ [_443042, _443044] : [ordinal(_443044), ordinal(_443042), 3844 ^ _310321 : [(3845 ^ _310321) ^ [] : [ordinal_subset(_443044, _443042), -(subset(_443044, _443042))], (3851 ^ _310321) ^ [] : [subset(_443044, _443042), -(ordinal_subset(_443044, _443042))]]], (3857 ^ _310321) ^ [_443589, _443591] : [-(ordinal_subset(_443591, _443591)), ordinal(_443591), ordinal(_443589)], (3867 ^ _310321) ^ [_443869, _443871] : [-(subset(_443871, _443871))], (3869 ^ _310321) ^ [_443978, _443980] : [disjoint(_443980, _443978), -(disjoint(_443978, _443980))], (3875 ^ _310321) ^ [_444245, _444247, _444249, _444251] : [in(ordered_pair(_444251, _444249), cartesian_product2(_444247, _444245)), 3878 ^ _310321 : [(3879 ^ _310321) ^ [] : [-(in(_444251, _444247))], (3881 ^ _310321) ^ [] : [-(in(_444249, _444245))]]], (3883 ^ _310321) ^ [_444510, _444512, _444514, _444516] : [-(in(ordered_pair(_444516, _444514), cartesian_product2(_444512, _444510))), in(_444516, _444512), in(_444514, _444510)], (3893 ^ _310321) ^ [_444814] : [-(in(_444814, succ(_444814)))], (3895 ^ _310321) ^ [_444951, _444953, _444955, _444957] : [unordered_pair(_444957, _444955) = unordered_pair(_444953, _444951), -(_444957 = _444953), -(_444957 = _444951)], (3905 ^ _310321) ^ [_445301, _445303, _445305] : [relation(_445301), 3908 ^ _310321 : [(3909 ^ _310321) ^ [] : [in(_445305, relation_rng(relation_rng_restriction(_445303, _445301))), 3912 ^ _310321 : [(3913 ^ _310321) ^ [] : [-(in(_445305, _445303))], (3915 ^ _310321) ^ [] : [-(in(_445305, relation_rng(_445301)))]]], (3917 ^ _310321) ^ [] : [-(in(_445305, relation_rng(relation_rng_restriction(_445303, _445301)))), in(_445305, _445303), in(_445305, relation_rng(_445301))]]], (3927 ^ _310321) ^ [_445960, _445962] : [relation(_445960), -(subset(relation_rng(relation_rng_restriction(_445962, _445960)), _445962))], (3933 ^ _310321) ^ [_446178, _446180] : [relation(_446178), -(subset(relation_rng_restriction(_446180, _446178), _446178))], (3939 ^ _310321) ^ [_446392, _446394] : [relation(_446392), -(subset(relation_rng(relation_rng_restriction(_446394, _446392)), relation_rng(_446392)))], (3945 ^ _310321) ^ [_446628, _446630, _446632] : [subset(_446632, _446630), 3948 ^ _310321 : [(3949 ^ _310321) ^ [] : [-(subset(cartesian_product2(_446632, _446628), cartesian_product2(_446630, _446628)))], (3951 ^ _310321) ^ [] : [-(subset(cartesian_product2(_446628, _446632), cartesian_product2(_446628, _446630)))]]], (3953 ^ _310321) ^ [_446945, _446947] : [relation(_446945), -(relation_rng(relation_rng_restriction(_446947, _446945)) = set_intersection2(relation_rng(_446945), _446947))], (3959 ^ _310321) ^ [_447201, _447203, _447205, _447207] : [-(subset(cartesian_product2(_447207, _447203), cartesian_product2(_447205, _447201))), subset(_447207, _447205), subset(_447203, _447201)], (3969 ^ _310321) ^ [_447546, _447548, _447550] : [relation_of2_as_subset(_447546, _447550, _447548), 3972 ^ _310321 : [(3973 ^ _310321) ^ [] : [-(subset(relation_dom(_447546), _447550))], (3975 ^ _310321) ^ [] : [-(subset(relation_rng(_447546), _447548))]]], (3977 ^ _310321) ^ [_447849, _447851] : [subset(_447851, _447849), -(set_union2(_447851, _447849) = _447849)], (3984 ^ _310321) ^ [_448171] : [-(in(_448171, 3982 ^ [_448171]))], (3986 ^ _310321) ^ [_448283, _448285, _448287] : [-(in(_448283, 3982 ^ [_448287])), in(_448285, 3982 ^ [_448287]), subset(_448283, _448285)], (3996 ^ _310321) ^ [_448598, _448600] : [in(_448598, 3982 ^ [_448600]), -(in(powerset(_448598), 3982 ^ [_448600]))], (4002 ^ _310321) ^ [_448798, _448800] : [subset(_448798, 3982 ^ [_448800]), -(are_equipotent(_448798, 3982 ^ [_448800])), -(in(_448798, 3982 ^ [_448800]))], (4012 ^ _310321) ^ [_449152, _449154, _449156] : [relation(_449152), -(relation_dom_restriction(relation_rng_restriction(_449156, _449152), _449154) = relation_rng_restriction(_449156, relation_dom_restriction(_449152, _449154)))], (4018 ^ _310321) ^ [_449404, _449406, _449408] : [relation(_449404), 4021 ^ _310321 : [(4022 ^ _310321) ^ [] : [in(_449408, relation_image(_449404, _449406)), 4026 ^ _310321 : [(4027 ^ _310321) ^ [] : [-(in(4025 ^ [_449404, _449406, _449408], relation_dom(_449404)))], (4029 ^ _310321) ^ [] : [-(in(ordered_pair(4025 ^ [_449404, _449406, _449408], _449408), _449404))], (4031 ^ _310321) ^ [] : [-(in(4025 ^ [_449404, _449406, _449408], _449406))]]], (4033 ^ _310321) ^ [] : [-(in(_449408, relation_image(_449404, _449406))), 4034 ^ _310321 : [(4035 ^ _310321) ^ [_450005] : [in(_450005, relation_dom(_449404)), in(ordered_pair(_450005, _449408), _449404), in(_450005, _449406)]]]]], (4047 ^ _310321) ^ [_450402, _450404] : [relation(_450402), -(subset(relation_image(_450402, _450404), relation_rng(_450402)))], (4053 ^ _310321) ^ [_450620, _450622] : [-(subset(relation_image(_450620, relation_inverse_image(_450620, _450622)), _450622)), relation(_450620), function(_450620)], (4063 ^ _310321) ^ [_450927, _450929] : [relation(_450927), -(relation_image(_450927, _450929) = relation_image(_450927, set_intersection2(relation_dom(_450927), _450929)))], (4069 ^ _310321) ^ [_451157, _451159] : [relation(_451157), subset(_451159, relation_dom(_451157)), -(subset(_451159, relation_inverse_image(_451157, relation_image(_451157, _451159))))], (4079 ^ _310321) ^ [_451456] : [relation(_451456), -(relation_image(_451456, relation_dom(_451456)) = relation_rng(_451456))], (4085 ^ _310321) ^ [_451672, _451674] : [relation(_451672), function(_451672), subset(_451674, relation_rng(_451672)), -(relation_image(_451672, relation_inverse_image(_451672, _451674)) = _451674)], (4099 ^ _310321) ^ [_452102, _452104, _452106, _452108] : [relation_of2_as_subset(_452102, _452104, _452108), subset(relation_rng(_452102), _452106), -(relation_of2_as_subset(_452102, _452104, _452106))], (4109 ^ _310321) ^ [_452415] : [relation(_452415), 4112 ^ _310321 : [(4113 ^ _310321) ^ [_452555] : [relation(_452555), -(relation_rng(relation_composition(_452415, _452555)) = relation_image(_452555, relation_rng(_452415)))]]], (4119 ^ _310321) ^ [_452804, _452806, _452808] : [relation(_452804), 4122 ^ _310321 : [(4123 ^ _310321) ^ [] : [in(_452808, relation_inverse_image(_452804, _452806)), 4127 ^ _310321 : [(4128 ^ _310321) ^ [] : [-(in(4126 ^ [_452804, _452806, _452808], relation_rng(_452804)))], (4130 ^ _310321) ^ [] : [-(in(ordered_pair(_452808, 4126 ^ [_452804, _452806, _452808]), _452804))], (4132 ^ _310321) ^ [] : [-(in(4126 ^ [_452804, _452806, _452808], _452806))]]], (4134 ^ _310321) ^ [] : [-(in(_452808, relation_inverse_image(_452804, _452806))), 4135 ^ _310321 : [(4136 ^ _310321) ^ [_453405] : [in(_453405, relation_rng(_452804)), in(ordered_pair(_452808, _453405), _452804), in(_453405, _452806)]]]]], (4148 ^ _310321) ^ [_453802, _453804] : [relation(_453802), -(subset(relation_inverse_image(_453802, _453804), relation_dom(_453802)))], (4154 ^ _310321) ^ [_454048, _454050, _454052, _454054] : [relation_of2_as_subset(_454048, _454050, _454054), subset(_454054, _454052), -(relation_of2_as_subset(_454048, _454050, _454052))], (4164 ^ _310321) ^ [_454385, _454387, _454389] : [relation(_454385), 4167 ^ _310321 : [(4168 ^ _310321) ^ [] : [in(_454389, relation_restriction(_454385, _454387)), 4171 ^ _310321 : [(4172 ^ _310321) ^ [] : [-(in(_454389, _454385))], (4174 ^ _310321) ^ [] : [-(in(_454389, cartesian_product2(_454387, _454387)))]]], (4176 ^ _310321) ^ [] : [-(in(_454389, relation_restriction(_454385, _454387))), in(_454389, _454385), in(_454389, cartesian_product2(_454387, _454387))]]], (4186 ^ _310321) ^ [_455041, _455043] : [relation(_455041), -(_455043 = empty_set), subset(_455043, relation_rng(_455041)), relation_inverse_image(_455041, _455043) = empty_set], (4200 ^ _310321) ^ [_455455, _455457, _455459] : [relation(_455455), subset(_455459, _455457), -(subset(relation_inverse_image(_455455, _455459), relation_inverse_image(_455455, _455457)))], (4210 ^ _310321) ^ [_455774, _455776] : [relation(_455774), -(relation_restriction(_455774, _455776) = relation_dom_restriction(relation_rng_restriction(_455776, _455774), _455776))], (4216 ^ _310321) ^ [_455985, _455987] : [-(subset(set_intersection2(_455987, _455985), _455987))], (4218 ^ _310321) ^ [_456097, _456099] : [relation(_456097), -(relation_restriction(_456097, _456099) = relation_rng_restriction(_456099, relation_dom_restriction(_456097, _456099)))], (4224 ^ _310321) ^ [_456337, _456339, _456341] : [relation(_456337), in(_456341, relation_field(relation_restriction(_456337, _456339))), 4231 ^ _310321 : [(4232 ^ _310321) ^ [] : [-(in(_456341, relation_field(_456337)))], (4234 ^ _310321) ^ [] : [-(in(_456341, _456339))]]], (4236 ^ _310321) ^ [_456749, _456751, _456753] : [-(subset(_456753, set_intersection2(_456751, _456749))), subset(_456753, _456751), subset(_456753, _456749)], (4246 ^ _310321) ^ [_457035] : [-(set_union2(_457035, empty_set) = _457035)], (4248 ^ _310321) ^ [_457145, _457147] : [in(_457147, _457145), -(element(_457147, _457145))], (4254 ^ _310321) ^ [_457369, _457371, _457373] : [-(subset(_457373, _457369)), subset(_457373, _457371), subset(_457371, _457369)], (4264 ^ _310321) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (4266 ^ _310321) ^ [_457745, _457747, _457749] : [relation(_457745), in(ordered_pair(_457749, _457747), _457745), 4273 ^ _310321 : [(4274 ^ _310321) ^ [] : [-(in(_457749, relation_dom(_457745)))], (4276 ^ _310321) ^ [] : [-(in(_457747, relation_rng(_457745)))]]], (4278 ^ _310321) ^ [_458143, _458145] : [relation(_458143), 4281 ^ _310321 : [(4282 ^ _310321) ^ [] : [-(subset(relation_field(relation_restriction(_458143, _458145)), relation_field(_458143)))], (4284 ^ _310321) ^ [] : [-(subset(relation_field(relation_restriction(_458143, _458145)), _458145))]]], (4286 ^ _310321) ^ [_458450, _458452] : [relation(_458450), function(_458450), 4293 ^ _310321 : [(4294 ^ _310321) ^ [_458700] : [relation(_458700), function(_458700), 4301 ^ _310321 : [(4302 ^ _310321) ^ [] : [in(_458452, relation_dom(relation_composition(_458700, _458450))), 4305 ^ _310321 : [(4306 ^ _310321) ^ [] : [-(in(_458452, relation_dom(_458700)))], (4308 ^ _310321) ^ [] : [-(in(apply(_458700, _458452), relation_dom(_458450)))]]], (4310 ^ _310321) ^ [] : [-(in(_458452, relation_dom(relation_composition(_458700, _458450)))), in(_458452, relation_dom(_458700)), in(apply(_458700, _458452), relation_dom(_458450))]]]]], (4320 ^ _310321) ^ [_459464] : [epsilon_transitive(_459464), 4323 ^ _310321 : [(4324 ^ _310321) ^ [_459600] : [ordinal(_459600), proper_subset(_459464, _459600), -(in(_459464, _459600))]]], (4334 ^ _310321) ^ [_459890] : [relation(_459890), -(subset(_459890, cartesian_product2(relation_dom(_459890), relation_rng(_459890))))], (4340 ^ _310321) ^ [_460120, _460122, _460124] : [relation(_460120), -(subset(fiber(relation_restriction(_460120, _460124), _460122), fiber(_460120, _460122)))], (4346 ^ _310321) ^ [_460352, _460354] : [relation(_460352), function(_460352), 4353 ^ _310321 : [(4354 ^ _310321) ^ [_460601] : [relation(_460601), function(_460601), in(_460354, relation_dom(relation_composition(_460601, _460352))), -(apply(relation_composition(_460601, _460352), _460354) = apply(_460352, apply(_460601, _460354)))]]], (4368 ^ _310321) ^ [_461060, _461062, _461064] : [relation_of2_as_subset(_461060, _461062, _461064), 4371 ^ _310321 : [(4372 ^ _310321) ^ [] : [4374 ^ _310321 : [(4375 ^ _310321) ^ [] : [-(in(4373 ^ [_461060, _461062, _461064], _461062))], (4377 ^ _310321) ^ [_461418] : [in(ordered_pair(4373 ^ [_461060, _461062, _461064], _461418), _461060)]], -(relation_dom_as_subset(_461062, _461064, _461060) = _461062)], (4381 ^ _310321) ^ [] : [relation_dom_as_subset(_461062, _461064, _461060) = _461062, 4384 ^ _310321 : [(4385 ^ _310321) ^ [_461655] : [in(_461655, _461062), -(in(ordered_pair(_461655, 4388 ^ [_461060, _461062, _461064, _461655]), _461060))]]]]], (4392 ^ _310321) ^ [_461977, _461979] : [relation(_461977), reflexive(_461977), -(reflexive(relation_restriction(_461977, _461979)))], (4402 ^ _310321) ^ [_462276, _462278] : [relation(_462276), function(_462276), 4409 ^ _310321 : [(4410 ^ _310321) ^ [_462522] : [relation(_462522), function(_462522), in(_462278, relation_dom(_462276)), -(apply(relation_composition(_462276, _462522), _462278) = apply(_462522, apply(_462276, _462278)))]]], (4424 ^ _310321) ^ [_462961, _462963] : [ordinal(_462961), in(_462963, _462961), -(ordinal(_462963))], (4434 ^ _310321) ^ [_463270, _463272, _463274] : [relation_of2_as_subset(_463270, _463274, _463272), 4437 ^ _310321 : [(4438 ^ _310321) ^ [] : [4440 ^ _310321 : [(4441 ^ _310321) ^ [] : [-(in(4439 ^ [_463270, _463272, _463274], _463272))], (4443 ^ _310321) ^ [_463628] : [in(ordered_pair(_463628, 4439 ^ [_463270, _463272, _463274]), _463270)]], -(relation_rng_as_subset(_463274, _463272, _463270) = _463272)], (4447 ^ _310321) ^ [] : [relation_rng_as_subset(_463274, _463272, _463270) = _463272, 4450 ^ _310321 : [(4451 ^ _310321) ^ [_463865] : [in(_463865, _463272), -(in(ordered_pair(4454 ^ [_463270, _463272, _463274, _463865], _463865), _463270))]]]]], (4458 ^ _310321) ^ [_464187, _464189] : [relation(_464187), connected(_464187), -(connected(relation_restriction(_464187, _464189)))], (4468 ^ _310321) ^ [_464472] : [ordinal(_464472), 4471 ^ _310321 : [(4472 ^ _310321) ^ [_464622] : [ordinal(_464622), -(in(_464472, _464622)), -(_464472 = _464622), -(in(_464622, _464472))]]], (4486 ^ _310321) ^ [_465025, _465027] : [relation(_465025), transitive(_465025), -(transitive(relation_restriction(_465025, _465027)))], (4496 ^ _310321) ^ [_465310] : [relation(_465310), 4499 ^ _310321 : [(4500 ^ _310321) ^ [_465460] : [relation(_465460), subset(_465310, _465460), 4507 ^ _310321 : [(4508 ^ _310321) ^ [] : [-(subset(relation_dom(_465310), relation_dom(_465460)))], (4510 ^ _310321) ^ [] : [-(subset(relation_rng(_465310), relation_rng(_465460)))]]]]], (4512 ^ _310321) ^ [_465855, _465857] : [relation(_465855), antisymmetric(_465855), -(antisymmetric(relation_restriction(_465855, _465857)))], (4522 ^ _310321) ^ [_466168, _466170, _466172] : [subset(_466172, _466170), -(subset(set_intersection2(_466172, _466168), set_intersection2(_466170, _466168)))], (4528 ^ _310321) ^ [_466396, _466398] : [subset(_466398, _466396), -(set_intersection2(_466398, _466396) = _466398)], (4534 ^ _310321) ^ [_466583] : [-(set_intersection2(_466583, empty_set) = empty_set)], (4536 ^ _310321) ^ [_466693, _466695] : [element(_466695, _466693), -(empty(_466693)), -(in(_466695, _466693))], (4546 ^ _310321) ^ [_466991, _466993] : [-(_466993 = _466991), 4550 ^ _310321 : [(4551 ^ _310321) ^ [] : [-(in(4547 ^ [_466991, _466993], _466993))], (4553 ^ _310321) ^ [] : [in(4547 ^ [_466991, _466993], _466991)]], 4554 ^ _310321 : [(4555 ^ _310321) ^ [] : [-(in(4547 ^ [_466991, _466993], _466991))], (4557 ^ _310321) ^ [] : [in(4547 ^ [_466991, _466993], _466993)]]], (4561 ^ _310321) ^ [_467492] : [-(subset(empty_set, _467492))], (4563 ^ _310321) ^ [_467613, _467615, _467617] : [relation(_467613), in(ordered_pair(_467617, _467615), _467613), 4570 ^ _310321 : [(4571 ^ _310321) ^ [] : [-(in(_467617, relation_field(_467613)))], (4573 ^ _310321) ^ [] : [-(in(_467615, relation_field(_467613)))]]], (4575 ^ _310321) ^ [_467997] : [-(ordinal(_467997)), 4577 ^ _310321 : [(4578 ^ _310321) ^ [] : [-(in(4576 ^ [_467997], _467997))], (4580 ^ _310321) ^ [] : [ordinal(4576 ^ [_467997]), subset(4576 ^ [_467997], _467997)]]], (4588 ^ _310321) ^ [_468427, _468429] : [relation(_468427), well_founded_relation(_468427), -(well_founded_relation(relation_restriction(_468427, _468429)))], (4598 ^ _310321) ^ [_468726, _468728] : [ordinal(_468726), subset(_468728, _468726), -(_468728 = empty_set), 4610 ^ _310321 : [(4611 ^ _310321) ^ [] : [-(ordinal(4609 ^ [_468726, _468728]))], (4613 ^ _310321) ^ [] : [-(in(4609 ^ [_468726, _468728], _468728))], (4615 ^ _310321) ^ [_469278] : [ordinal(_469278), in(_469278, _468728), -(ordinal_subset(4609 ^ [_468726, _468728], _469278))]]], (4625 ^ _310321) ^ [_469620, _469622] : [relation(_469620), well_ordering(_469620), -(well_ordering(relation_restriction(_469620, _469622)))], (4635 ^ _310321) ^ [_469905] : [ordinal(_469905), 4638 ^ _310321 : [(4639 ^ _310321) ^ [_470043] : [ordinal(_470043), 4642 ^ _310321 : [(4643 ^ _310321) ^ [] : [in(_469905, _470043), -(ordinal_subset(succ(_469905), _470043))], (4649 ^ _310321) ^ [] : [ordinal_subset(succ(_469905), _470043), -(in(_469905, _470043))]]]]], (4655 ^ _310321) ^ [_470528, _470530, _470532] : [subset(_470532, _470530), -(subset(set_difference(_470532, _470528), set_difference(_470530, _470528)))], (4661 ^ _310321) ^ [_470784, _470786, _470788, _470790] : [ordered_pair(_470790, _470788) = ordered_pair(_470786, _470784), 4664 ^ _310321 : [(4665 ^ _310321) ^ [] : [-(_470790 = _470786)], (4667 ^ _310321) ^ [] : [-(_470788 = _470784)]]], (4669 ^ _310321) ^ [_471097, _471099] : [relation(_471097), function(_471097), 4676 ^ _310321 : [(4677 ^ _310321) ^ [] : [_471097 = identity_relation(_471099), 4680 ^ _310321 : [(4681 ^ _310321) ^ [] : [-(relation_dom(_471097) = _471099)], (4683 ^ _310321) ^ [_471516] : [in(_471516, _471099), -(apply(_471097, _471516) = _471516)]]], (4689 ^ _310321) ^ [] : [-(_471097 = identity_relation(_471099)), relation_dom(_471097) = _471099, 4695 ^ _310321 : [(4696 ^ _310321) ^ [] : [-(in(4694 ^ [_471097, _471099], _471099))], (4698 ^ _310321) ^ [] : [apply(_471097, 4694 ^ [_471097, _471099]) = 4694 ^ [_471097, _471099]]]]]], (4702 ^ _310321) ^ [_472121, _472123] : [in(_472121, _472123), -(apply(identity_relation(_472123), _472121) = _472121)], (4708 ^ _310321) ^ [_472326, _472328] : [-(subset(set_difference(_472328, _472326), _472328))], (4710 ^ _310321) ^ [_472424] : [relation(_472424), 4713 ^ _310321 : [(4714 ^ _310321) ^ [] : [-(relation_rng(_472424) = relation_dom(relation_inverse(_472424)))], (4716 ^ _310321) ^ [] : [-(relation_dom(_472424) = relation_rng(relation_inverse(_472424)))]]], (4718 ^ _310321) ^ [_472752, _472754] : [set_difference(_472754, _472752) = empty_set, -(subset(_472754, _472752))], (4724 ^ _310321) ^ [_472920, _472922] : [subset(_472922, _472920), -(set_difference(_472922, _472920) = empty_set)], (4730 ^ _310321) ^ [_473167, _473169] : [subset(singleton(_473169), _473167), -(in(_473169, _473167))], (4736 ^ _310321) ^ [_473333, _473335] : [in(_473335, _473333), -(subset(singleton(_473335), _473333))], (4742 ^ _310321) ^ [_473592, _473594, _473596] : [subset(unordered_pair(_473596, _473594), _473592), 4745 ^ _310321 : [(4746 ^ _310321) ^ [] : [-(in(_473596, _473592))], (4748 ^ _310321) ^ [] : [-(in(_473594, _473592))]]], (4750 ^ _310321) ^ [_473843, _473845, _473847] : [-(subset(unordered_pair(_473847, _473845), _473843)), in(_473847, _473843), in(_473845, _473843)], (4760 ^ _310321) ^ [_474160, _474162] : [relation(_474160), -(relation_field(relation_restriction(_474160, _474162)) = _474162), well_ordering(_474160), subset(_474162, relation_field(_474160))], (4774 ^ _310321) ^ [_474543, _474545] : [-(set_union2(_474545, set_difference(_474543, _474545)) = set_union2(_474545, _474543))], (4786 ^ _310321) ^ [_474950, _474952] : [4787 ^ _310321 : [(4788 ^ _310321) ^ [] : [_474952 = empty_set], (4790 ^ _310321) ^ [] : [_474952 = singleton(_474950)]], -(subset(_474952, singleton(_474950)))], (4776 ^ _310321) ^ [_474690, _474692] : [subset(_474692, singleton(_474690)), -(_474692 = empty_set), -(_474692 = singleton(_474690))], (4794 ^ _310321) ^ [_475215] : [-(set_difference(_475215, empty_set) = _475215)], (4796 ^ _310321) ^ [_475339, _475341, _475343] : [in(_475343, _475341), in(_475341, _475339), in(_475339, _475343)], (4806 ^ _310321) ^ [_475676, _475678] : [element(_475678, powerset(_475676)), -(subset(_475678, _475676))], (4812 ^ _310321) ^ [_475842, _475844] : [subset(_475844, _475842), -(element(_475844, powerset(_475842)))], (4818 ^ _310321) ^ [_476078, _476080] : [-(disjoint(_476080, _476078)), 4822 ^ _310321 : [(4823 ^ _310321) ^ [] : [-(in(4821 ^ [_476078, _476080], _476080))], (4825 ^ _310321) ^ [] : [-(in(4821 ^ [_476078, _476080], _476078))]]], (4827 ^ _310321) ^ [_476392, _476394] : [disjoint(_476394, _476392), 4828 ^ _310321 : [(4829 ^ _310321) ^ [_476484] : [in(_476484, _476394), in(_476484, _476392)]]], (4837 ^ _310321) ^ [_476741] : [subset(_476741, empty_set), -(_476741 = empty_set)], (4843 ^ _310321) ^ [_476930, _476932] : [-(set_difference(set_union2(_476932, _476930), _476930) = set_difference(_476932, _476930))], (4845 ^ _310321) ^ [_477034] : [ordinal(_477034), 4848 ^ _310321 : [(4863 ^ _310321) ^ [] : [4865 ^ _310321 : [(4866 ^ _310321) ^ [] : [-(ordinal(4864 ^ [_477034]))], (4868 ^ _310321) ^ [] : [-(in(4864 ^ [_477034], _477034))], (4870 ^ _310321) ^ [] : [in(succ(4864 ^ [_477034]), _477034)]], -(being_limit_ordinal(_477034))], (4849 ^ _310321) ^ [] : [being_limit_ordinal(_477034), 4852 ^ _310321 : [(4853 ^ _310321) ^ [_477280] : [ordinal(_477280), in(_477280, _477034), -(in(succ(_477280), _477034))]]]]], (4874 ^ _310321) ^ [_477906] : [ordinal(_477906), 4877 ^ _310321 : [(4878 ^ _310321) ^ [] : [-(being_limit_ordinal(_477906)), 4882 ^ _310321 : [(4883 ^ _310321) ^ [] : [-(ordinal(4881 ^ [_477906]))], (4885 ^ _310321) ^ [] : [-(_477906 = succ(4881 ^ [_477906]))]]], (4887 ^ _310321) ^ [] : [being_limit_ordinal(_477906), 4888 ^ _310321 : [(4889 ^ _310321) ^ [_478377] : [ordinal(_478377), _477906 = succ(_478377)]]]]], (4897 ^ _310321) ^ [_478644, _478646] : [element(_478644, powerset(_478646)), 4900 ^ _310321 : [(4901 ^ _310321) ^ [_478796] : [element(_478796, powerset(_478646)), 4904 ^ _310321 : [(4905 ^ _310321) ^ [] : [disjoint(_478644, _478796), -(subset(_478644, subset_complement(_478646, _478796)))], (4911 ^ _310321) ^ [] : [subset(_478644, subset_complement(_478646, _478796)), -(disjoint(_478644, _478796))]]]]], (4917 ^ _310321) ^ [_479280] : [relation(_479280), 4920 ^ _310321 : [(4921 ^ _310321) ^ [_479417] : [relation(_479417), -(subset(relation_dom(relation_composition(_479280, _479417)), relation_dom(_479280)))]]], (4927 ^ _310321) ^ [_479632] : [relation(_479632), 4930 ^ _310321 : [(4931 ^ _310321) ^ [_479769] : [relation(_479769), -(subset(relation_rng(relation_composition(_479632, _479769)), relation_rng(_479769)))]]], (4937 ^ _310321) ^ [_479998, _480000] : [subset(_480000, _479998), -(_479998 = set_union2(_480000, set_difference(_479998, _480000)))], (4943 ^ _310321) ^ [_480206] : [relation(_480206), 4946 ^ _310321 : [(4947 ^ _310321) ^ [_480353] : [relation(_480353), subset(relation_rng(_480206), relation_dom(_480353)), -(relation_dom(relation_composition(_480206, _480353)) = relation_dom(_480206))]]], (4957 ^ _310321) ^ [_480679, _480681] : [element(_480679, powerset(powerset(_480681))), -(_480679 = empty_set), complements_of_subsets(_480681, _480679) = empty_set], (4967 ^ _310321) ^ [_480996, _480998] : [in(_480998, _480996), -(set_union2(singleton(_480998), _480996) = _480996)], (4973 ^ _310321) ^ [_481202] : [relation(_481202), 4976 ^ _310321 : [(4977 ^ _310321) ^ [_481349] : [relation(_481349), subset(relation_dom(_481202), relation_rng(_481349)), -(relation_rng(relation_composition(_481349, _481202)) = relation_rng(_481202))]]], (4987 ^ _310321) ^ [_481675, _481677] : [element(_481675, powerset(powerset(_481677))), -(_481675 = empty_set), -(subset_difference(_481677, cast_to_subset(_481677), union_of_subsets(_481677, _481675)) = meet_of_subsets(_481677, complements_of_subsets(_481677, _481675)))], (4997 ^ _310321) ^ [_482015, _482017] : [element(_482015, powerset(powerset(_482017))), -(_482015 = empty_set), -(union_of_subsets(_482017, complements_of_subsets(_482017, _482015)) = subset_difference(_482017, cast_to_subset(_482017), meet_of_subsets(_482017, _482015)))], (5007 ^ _310321) ^ [_482340, _482342] : [-(set_difference(_482342, set_difference(_482342, _482340)) = set_intersection2(_482342, _482340))], (5009 ^ _310321) ^ [_482444] : [relation(_482444), 5012 ^ _310321 : [(5013 ^ _310321) ^ [_482599] : [relation(_482599), 5016 ^ _310321 : [(5017 ^ _310321) ^ [_482750] : [relation(_482750), function(_482750), relation_isomorphism(_482444, _482599, _482750), -(relation_isomorphism(_482599, _482444, function_inverse(_482750)))]]]]], (5031 ^ _310321) ^ [_483143] : [-(set_difference(empty_set, _483143) = empty_set)], (5033 ^ _310321) ^ [_483267, _483269, _483271] : [-(element(_483271, _483267)), in(_483271, _483269), element(_483269, powerset(_483267))], (5043 ^ _310321) ^ [_483600, _483602] : [-(disjoint(_483602, _483600)), -(in(5046 ^ [_483600, _483602], set_intersection2(_483602, _483600)))], (5050 ^ _310321) ^ [_483835, _483837] : [5051 ^ _310321 : [(5052 ^ _310321) ^ [_483908] : [in(_483908, set_intersection2(_483837, _483835))]], disjoint(_483837, _483835)], (5056 ^ _310321) ^ [_484060] : [-(_484060 = empty_set), 5059 ^ _310321 : [(5060 ^ _310321) ^ [_484220] : [element(_484220, powerset(_484060)), 5063 ^ _310321 : [(5064 ^ _310321) ^ [_484374] : [element(_484374, _484060), -(in(_484374, _484220)), -(in(_484374, subset_complement(_484060, _484220)))]]]]], (5074 ^ _310321) ^ [_484692] : [relation(_484692), 5077 ^ _310321 : [(5078 ^ _310321) ^ [_484888] : [relation(_484888), 5081 ^ _310321 : [(5082 ^ _310321) ^ [_485080] : [relation(_485080), function(_485080), relation_isomorphism(_484692, _484888, _485080), 5093 ^ _310321 : [(5094 ^ _310321) ^ [] : [reflexive(_484692), -(reflexive(_484888))], (5100 ^ _310321) ^ [] : [transitive(_484692), -(transitive(_484888))], (5106 ^ _310321) ^ [] : [connected(_484692), -(connected(_484888))], (5112 ^ _310321) ^ [] : [antisymmetric(_484692), -(antisymmetric(_484888))], (5118 ^ _310321) ^ [] : [well_founded_relation(_484692), -(well_founded_relation(_484888))]]]]]]], (5124 ^ _310321) ^ [_486232] : [relation(_486232), function(_486232), one_to_one(_486232), 5135 ^ _310321 : [(5136 ^ _310321) ^ [_486619] : [relation(_486619), function(_486619), 5143 ^ _310321 : [(5174 ^ _310321) ^ [] : [-(_486619 = function_inverse(_486232)), relation_dom(_486619) = relation_rng(_486232), 5183 ^ _310321 : [(5184 ^ _310321) ^ [] : [-(in(5179 ^ [_486232, _486619], relation_rng(_486232)))], (5186 ^ _310321) ^ [] : [-(5180 ^ [_486232, _486619] = apply(_486619, 5179 ^ [_486232, _486619]))], (5188 ^ _310321) ^ [] : [in(5180 ^ [_486232, _486619], relation_dom(_486232)), 5179 ^ [_486232, _486619] = apply(_486232, 5180 ^ [_486232, _486619])]], 5193 ^ _310321 : [(5194 ^ _310321) ^ [] : [-(in(5180 ^ [_486232, _486619], relation_dom(_486232)))], (5196 ^ _310321) ^ [] : [-(5179 ^ [_486232, _486619] = apply(_486232, 5180 ^ [_486232, _486619]))], (5198 ^ _310321) ^ [] : [in(5179 ^ [_486232, _486619], relation_rng(_486232)), 5180 ^ [_486232, _486619] = apply(_486619, 5179 ^ [_486232, _486619])]]], (5144 ^ _310321) ^ [] : [_486619 = function_inverse(_486232), 5147 ^ _310321 : [(5148 ^ _310321) ^ [] : [-(relation_dom(_486619) = relation_rng(_486232))], (5150 ^ _310321) ^ [_487136, _487138] : [5157 ^ _310321 : [(5158 ^ _310321) ^ [] : [-(in(_487136, relation_dom(_486232)))], (5160 ^ _310321) ^ [] : [-(_487138 = apply(_486232, _487136))]], in(_487138, relation_rng(_486232)), _487136 = apply(_486619, _487138)], (5162 ^ _310321) ^ [_487510, _487512] : [5169 ^ _310321 : [(5170 ^ _310321) ^ [] : [-(in(_487512, relation_rng(_486232)))], (5172 ^ _310321) ^ [] : [-(_487510 = apply(_486619, _487512))]], in(_487510, relation_dom(_486232)), _487512 = apply(_486232, _487510)]]]]]]], (5206 ^ _310321) ^ [_489085, _489087, _489089] : [element(_489085, powerset(_489089)), in(_489087, subset_complement(_489089, _489085)), in(_489087, _489085)], (5216 ^ _310321) ^ [_489391] : [relation(_489391), 5219 ^ _310321 : [(5220 ^ _310321) ^ [_489547] : [relation(_489547), 5223 ^ _310321 : [(5224 ^ _310321) ^ [_489699] : [relation(_489699), function(_489699), -(well_ordering(_489547)), well_ordering(_489391), relation_isomorphism(_489391, _489547, _489699)]]]]], (5242 ^ _310321) ^ [_490190] : [relation(_490190), function(_490190), one_to_one(_490190), 5253 ^ _310321 : [(5254 ^ _310321) ^ [] : [-(relation_rng(_490190) = relation_dom(function_inverse(_490190)))], (5256 ^ _310321) ^ [] : [-(relation_dom(_490190) = relation_rng(function_inverse(_490190)))]]], (5258 ^ _310321) ^ [_490643] : [relation(_490643), -(in(ordered_pair(5263 ^ [_490643], 5264 ^ [_490643]), _490643)), -(_490643 = empty_set)], (5270 ^ _310321) ^ [_491061, _491063] : [relation(_491061), function(_491061), 5285 ^ _310321 : [(5286 ^ _310321) ^ [] : [-(_491063 = apply(_491061, apply(function_inverse(_491061), _491063)))], (5288 ^ _310321) ^ [] : [-(_491063 = apply(relation_composition(function_inverse(_491061), _491061), _491063))]], one_to_one(_491061), in(_491063, relation_rng(_491061))], (5290 ^ _310321) ^ [_491659, _491661, _491663] : [in(_491663, _491661), element(_491661, powerset(_491659)), empty(_491659)], (5300 ^ _310321) ^ [_491955] : [relation(_491955), 5303 ^ _310321 : [(5304 ^ _310321) ^ [] : [well_founded_relation(_491955), -(is_well_founded_in(_491955, relation_field(_491955)))], (5310 ^ _310321) ^ [] : [is_well_founded_in(_491955, relation_field(_491955)), -(well_founded_relation(_491955))]]], (5316 ^ _310321) ^ [] : [-(relation_dom(empty_set) = empty_set)], (5318 ^ _310321) ^ [] : [-(relation_rng(empty_set) = empty_set)], (5320 ^ _310321) ^ [_492508, _492510] : [subset(_492510, _492508), proper_subset(_492508, _492510)], (5326 ^ _310321) ^ [_492703] : [relation(_492703), function(_492703), one_to_one(_492703), -(one_to_one(function_inverse(_492703)))], (5340 ^ _310321) ^ [_493089, _493091, _493093] : [-(disjoint(_493093, _493089)), subset(_493093, _493091), disjoint(_493091, _493089)], (5350 ^ _310321) ^ [_493384] : [relation(_493384), 5355 ^ _310321 : [(5356 ^ _310321) ^ [] : [relation_dom(_493384) = empty_set], (5358 ^ _310321) ^ [] : [relation_rng(_493384) = empty_set]], -(_493384 = empty_set)], (5362 ^ _310321) ^ [_493737] : [relation(_493737), 5365 ^ _310321 : [(5366 ^ _310321) ^ [] : [relation_dom(_493737) = empty_set, -(relation_rng(_493737) = empty_set)], (5372 ^ _310321) ^ [] : [relation_rng(_493737) = empty_set, -(relation_dom(_493737) = empty_set)]]], (5378 ^ _310321) ^ [_494220, _494222] : [set_difference(_494222, singleton(_494220)) = _494222, in(_494220, _494222)], (5384 ^ _310321) ^ [_494393, _494395] : [-(in(_494393, _494395)), -(set_difference(_494395, singleton(_494393)) = _494395)], (5390 ^ _310321) ^ [_494618, _494620] : [relation(_494618), function(_494618), 5397 ^ _310321 : [(5398 ^ _310321) ^ [_494885] : [relation(_494885), function(_494885), 5405 ^ _310321 : [(5406 ^ _310321) ^ [] : [_494618 = relation_dom_restriction(_494885, _494620), 5409 ^ _310321 : [(5410 ^ _310321) ^ [] : [-(relation_dom(_494618) = set_intersection2(relation_dom(_494885), _494620))], (5412 ^ _310321) ^ [_495339] : [in(_495339, relation_dom(_494618)), -(apply(_494618, _495339) = apply(_494885, _495339))]]], (5418 ^ _310321) ^ [] : [-(_494618 = relation_dom_restriction(_494885, _494620)), relation_dom(_494618) = set_intersection2(relation_dom(_494885), _494620), 5424 ^ _310321 : [(5425 ^ _310321) ^ [] : [-(in(5423 ^ [_494618, _494620, _494885], relation_dom(_494618)))], (5427 ^ _310321) ^ [] : [apply(_494618, 5423 ^ [_494618, _494620, _494885]) = apply(_494885, 5423 ^ [_494618, _494620, _494885])]]]]]]], (5431 ^ _310321) ^ [_495978] : [-(unordered_pair(_495978, _495978) = singleton(_495978))], (5433 ^ _310321) ^ [_496076] : [empty(_496076), -(_496076 = empty_set)], (5439 ^ _310321) ^ [_496278, _496280] : [subset(singleton(_496280), singleton(_496278)), -(_496280 = _496278)], (5445 ^ _310321) ^ [_496510, _496512, _496514] : [relation(_496510), function(_496510), in(_496512, relation_dom(relation_dom_restriction(_496510, _496514))), -(apply(relation_dom_restriction(_496510, _496514), _496512) = apply(_496510, _496512))], (5459 ^ _310321) ^ [_496929] : [-(relation_dom(identity_relation(_496929)) = _496929)], (5461 ^ _310321) ^ [_496977] : [-(relation_rng(identity_relation(_496977)) = _496977)], (5463 ^ _310321) ^ [_497104, _497106, _497108] : [relation(_497104), function(_497104), in(_497106, _497108), -(apply(relation_dom_restriction(_497104, _497108), _497106) = apply(_497104, _497106))], (5477 ^ _310321) ^ [_497550, _497552, _497554, _497556] : [relation(_497550), 5480 ^ _310321 : [(5481 ^ _310321) ^ [] : [in(ordered_pair(_497556, _497554), relation_composition(identity_relation(_497552), _497550)), 5484 ^ _310321 : [(5485 ^ _310321) ^ [] : [-(in(_497556, _497552))], (5487 ^ _310321) ^ [] : [-(in(ordered_pair(_497556, _497554), _497550))]]], (5489 ^ _310321) ^ [] : [-(in(ordered_pair(_497556, _497554), relation_composition(identity_relation(_497552), _497550))), in(_497556, _497552), in(ordered_pair(_497556, _497554), _497550)]]], (5499 ^ _310321) ^ [_498243, _498245] : [in(_498245, _498243), empty(_498243)], (5505 ^ _310321) ^ [_498450, _498452] : [in(_498452, _498450), 5509 ^ _310321 : [(5510 ^ _310321) ^ [] : [-(in(5508 ^ [_498450, _498452], _498450))], (5512 ^ _310321) ^ [_498741] : [in(_498741, _498450), in(_498741, 5508 ^ [_498450, _498452])]]], (5518 ^ _310321) ^ [_498966, _498968] : [-(subset(_498968, set_union2(_498968, _498966)))], (5520 ^ _310321) ^ [_499107, _499109] : [disjoint(_499109, _499107), -(set_difference(_499109, _499107) = _499109)], (5526 ^ _310321) ^ [_499275, _499277] : [set_difference(_499277, _499275) = _499277, -(disjoint(_499277, _499275))], (5532 ^ _310321) ^ [_499507, _499509, _499511] : [relation(_499507), 5535 ^ _310321 : [(5536 ^ _310321) ^ [] : [in(_499511, relation_dom(relation_dom_restriction(_499507, _499509))), 5539 ^ _310321 : [(5540 ^ _310321) ^ [] : [-(in(_499511, _499509))], (5542 ^ _310321) ^ [] : [-(in(_499511, relation_dom(_499507)))]]], (5544 ^ _310321) ^ [] : [-(in(_499511, relation_dom(relation_dom_restriction(_499507, _499509)))), in(_499511, _499509), in(_499511, relation_dom(_499507))]]], (5554 ^ _310321) ^ [_500166, _500168] : [relation(_500166), -(subset(relation_dom_restriction(_500166, _500168), _500166))], (5560 ^ _310321) ^ [_500380, _500382] : [empty(_500382), -(_500382 = _500380), empty(_500380)], (5570 ^ _310321) ^ [_500691, _500693, _500695] : [relation(_500691), function(_500691), 5577 ^ _310321 : [(5578 ^ _310321) ^ [] : [in(ordered_pair(_500695, _500693), _500691), 5581 ^ _310321 : [(5582 ^ _310321) ^ [] : [-(in(_500695, relation_dom(_500691)))], (5584 ^ _310321) ^ [] : [-(_500693 = apply(_500691, _500695))]]], (5586 ^ _310321) ^ [] : [-(in(ordered_pair(_500695, _500693), _500691)), in(_500695, relation_dom(_500691)), _500693 = apply(_500691, _500695)]]], (5596 ^ _310321) ^ [_501432] : [relation(_501432), 5599 ^ _310321 : [(5600 ^ _310321) ^ [] : [well_orders(_501432, relation_field(_501432)), -(well_ordering(_501432))], (5606 ^ _310321) ^ [] : [well_ordering(_501432), -(well_orders(_501432, relation_field(_501432)))]]], (5612 ^ _310321) ^ [_501891, _501893, _501895] : [-(subset(set_union2(_501895, _501891), _501893)), subset(_501895, _501893), subset(_501891, _501893)], (5622 ^ _310321) ^ [_502220, _502222, _502224] : [singleton(_502224) = unordered_pair(_502222, _502220), -(_502224 = _502222)], (5628 ^ _310321) ^ [_502446, _502448] : [relation(_502446), -(relation_dom(relation_dom_restriction(_502446, _502448)) = set_intersection2(relation_dom(_502446), _502448))], (5634 ^ _310321) ^ [_502674, _502676] : [in(_502676, _502674), -(subset(_502676, union(_502674)))], (5640 ^ _310321) ^ [_502888, _502890] : [relation(_502888), -(relation_dom_restriction(_502888, _502890) = relation_composition(identity_relation(_502890), _502888))], (5646 ^ _310321) ^ [_503112, _503114] : [relation(_503112), -(subset(relation_rng(relation_dom_restriction(_503112, _503114)), relation_rng(_503112)))], (5652 ^ _310321) ^ [_503305] : [-(union(powerset(_503305)) = _503305)], (5690 ^ _310321) ^ [_504826, _504828, _504830] : [singleton(_504830) = unordered_pair(_504828, _504826), -(_504828 = _504826)], (5655 ^ _310321) ^ [_503546] : [-(in(_503546, 5653 ^ [_503546]))], (5657 ^ _310321) ^ [_503658, _503660, _503662] : [-(in(_503658, 5653 ^ [_503662])), in(_503660, 5653 ^ [_503662]), subset(_503658, _503660)], (5667 ^ _310321) ^ [_503973, _503975] : [in(_503973, 5653 ^ [_503975]), 5671 ^ _310321 : [(5672 ^ _310321) ^ [] : [-(in(5670 ^ [_503973, _503975], 5653 ^ [_503975]))], (5674 ^ _310321) ^ [_504285] : [subset(_504285, _503973), -(in(_504285, 5670 ^ [_503973, _503975]))]]], (5680 ^ _310321) ^ [_504492, _504494] : [subset(_504492, 5653 ^ [_504494]), -(are_equipotent(_504492, 5653 ^ [_504494])), -(in(_504492, 5653 ^ [_504494]))]], input).
% 1.66/2.42  ncf('1',plain,[pair_first(ordered_pair(5695 ^ [], 5696 ^ [])) = 5695 ^ [], pair_second(ordered_pair(5695 ^ [], 5696 ^ [])) = 5696 ^ []],start(5698 ^ 0)).
% 1.66/2.42  ncf('1.1',plain,[-(pair_first(ordered_pair(5695 ^ [], 5696 ^ [])) = 5695 ^ []), 1317 : ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ []), 1317 : pair_first(ordered_pair(5695 ^ [], 5696 ^ [])) = pair_first(ordered_pair(5695 ^ [], 5696 ^ [])), 1311 : ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ [])],extension(1309 ^ 1,bind([[_355889, _356120, _356285, _356287, _356011, _356013], [ordered_pair(5695 ^ [], 5696 ^ []), pair_first(ordered_pair(5695 ^ [], 5696 ^ [])), 5696 ^ [], 5695 ^ [], 5696 ^ [], 5695 ^ []]]))).
% 1.66/2.42  ncf('1.1.1',plain,[-(ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ []))],extension(2 ^ 6,bind([[_310465], [ordered_pair(5695 ^ [], 5696 ^ [])]]))).
% 1.66/2.42  ncf('1.1.2',plain,[-(pair_first(ordered_pair(5695 ^ [], 5696 ^ [])) = pair_first(ordered_pair(5695 ^ [], 5696 ^ [])))],extension(2 ^ 4,bind([[_310465], [pair_first(ordered_pair(5695 ^ [], 5696 ^ []))]]))).
% 1.66/2.42  ncf('1.1.3',plain,[-(ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ []))],extension(2 ^ 4,bind([[_310465], [ordered_pair(5695 ^ [], 5696 ^ [])]]))).
% 1.66/2.42  ncf('1.2',plain,[-(pair_second(ordered_pair(5695 ^ [], 5696 ^ [])) = 5696 ^ []), 1586 : ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ []), 1586 : pair_second(ordered_pair(5695 ^ [], 5696 ^ [])) = pair_second(ordered_pair(5695 ^ [], 5696 ^ [])), 1580 : ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ [])],extension(1578 ^ 1,bind([[_365739, _365970, _366135, _366137, _365861, _365863], [ordered_pair(5695 ^ [], 5696 ^ []), pair_second(ordered_pair(5695 ^ [], 5696 ^ [])), 5696 ^ [], 5695 ^ [], 5696 ^ [], 5695 ^ []]]))).
% 1.66/2.42  ncf('1.2.1',plain,[-(ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ []))],extension(2 ^ 6,bind([[_310465], [ordered_pair(5695 ^ [], 5696 ^ [])]]))).
% 1.66/2.42  ncf('1.2.2',plain,[-(pair_second(ordered_pair(5695 ^ [], 5696 ^ [])) = pair_second(ordered_pair(5695 ^ [], 5696 ^ [])))],extension(2 ^ 4,bind([[_310465], [pair_second(ordered_pair(5695 ^ [], 5696 ^ []))]]))).
% 1.66/2.42  ncf('1.2.3',plain,[-(ordered_pair(5695 ^ [], 5696 ^ []) = ordered_pair(5695 ^ [], 5696 ^ []))],extension(2 ^ 4,bind([[_310465], [ordered_pair(5695 ^ [], 5696 ^ [])]]))).
% 1.66/2.42  %-----------------------------------------------------
% 1.66/2.42  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------