%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU247+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:02:51 EDT 2023

% Result   : Theorem 100.64s 97.59s
% Output   : Proof 100.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU247+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n018.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 13:25:57 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 100.64/97.59  
% 100.64/97.59  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 100.64/97.59  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 100.64/97.59  %-----------------------------------------------------
% 100.64/97.59  ncf(matrix, plain, [(5051 ^ _441786) ^ [] : [relation_restriction(5047 ^ [], 5046 ^ []) = relation_rng_restriction(5046 ^ [], relation_dom_restriction(5047 ^ [], 5046 ^ []))], (5049 ^ _441786) ^ [] : [-(relation(5047 ^ []))], !, (3625 ^ _266965) ^ [_391513, _391515] : [subset(_391513, 3605 ^ [_391515]), -(are_equipotent(_391513, 3605 ^ [_391515])), -(in(_391513, 3605 ^ [_391515]))], (4181 ^ _266965) ^ [_409914, _409916] : [set_difference(_409916, _409914) = empty_set, -(subset(_409916, _409914))], (4171 ^ _266965) ^ [_409488, _409490] : [-(subset(set_difference(_409490, _409488), _409490))], (2750 ^ _266965) ^ [_362456, _362458] : [element(_362456, powerset(powerset(_362458))), -(element(union_of_subsets(_362458, _362456), powerset(_362458)))], (2833 ^ _266965) ^ [_365156, _365158] : [2840 ^ _266965 : [(2843 ^ _266965) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_365158, _365156)))], (2841 ^ _266965) ^ [] : [-(relation(relation_dom_restriction(_365158, _365156)))]], relation(_365158), relation_empty_yielding(_365158)], (3391 ^ _266965) ^ [] : [-(relation(3389 ^ []))], (3381 ^ _266965) ^ [] : [-(empty(3379 ^ []))], (2098 ^ _266965) ^ [_340666] : [relation(_340666), function(_340666), 2105 ^ _266965 : [(2106 ^ _266965) ^ [_340938] : [_340938 = relation_rng(_340666), 2109 ^ _266965 : [(2119 ^ _266965) ^ [_341468] : [-(in(_341468, _340938)), 2120 ^ _266965 : [(2121 ^ _266965) ^ [_341571] : [in(_341571, relation_dom(_340666)), _341468 = apply(_340666, _341571)]]], (2110 ^ _266965) ^ [_341126] : [in(_341126, _340938), 2114 ^ _266965 : [(2117 ^ _266965) ^ [] : [-(_341126 = apply(_340666, 2113 ^ [_340666, _340938, _341126]))], (2115 ^ _266965) ^ [] : [-(in(2113 ^ [_340666, _340938, _341126], relation_dom(_340666)))]]]]], (2129 ^ _266965) ^ [_341820] : [-(_341820 = relation_rng(_340666)), 2142 ^ _266965 : [(2147 ^ _266965) ^ [] : [in(2130 ^ [_340666, _341820], _341820)], (2145 ^ _266965) ^ [] : [-(2130 ^ [_340666, _341820] = apply(_340666, 2141 ^ [_340666, _341820]))], (2143 ^ _266965) ^ [] : [-(in(2141 ^ [_340666, _341820], relation_dom(_340666)))]], 2133 ^ _266965 : [(2136 ^ _266965) ^ [_342115] : [in(_342115, relation_dom(_340666)), 2130 ^ [_340666, _341820] = apply(_340666, _342115)], (2134 ^ _266965) ^ [] : [-(in(2130 ^ [_340666, _341820], _341820))]]]]], (4877 ^ _266965) ^ [_432986, _432988] : [set_difference(_432988, _432986) = _432988, -(disjoint(_432988, _432986))], (10 ^ _266965) ^ [_267400, _267402, _267404] : [-(_267404 = _267400), _267404 = _267402, _267402 = _267400], (2248 ^ _266965) ^ [_346051] : [relation(_346051), -(relation_field(_346051) = set_union2(relation_dom(_346051), relation_rng(_346051)))], (4713 ^ _266965) ^ [_427448] : [relation(_427448), 4716 ^ _266965 : [(4723 ^ _266965) ^ [] : [relation_rng(_427448) = empty_set, -(relation_dom(_427448) = empty_set)], (4717 ^ _266965) ^ [] : [relation_dom(_427448) = empty_set, -(relation_rng(_427448) = empty_set)]]], (3442 ^ _266965) ^ [] : [-(relation_empty_yielding(3438 ^ []))], (4671 ^ _266965) ^ [_426219, _426221] : [subset(_426221, _426219), proper_subset(_426219, _426221)], (3079 ^ _266965) ^ [_372908, _372910] : [element(_372908, powerset(powerset(_372910))), -(complements_of_subsets(_372910, complements_of_subsets(_372910, _372908)) = _372908)], (328 ^ _266965) ^ [_277199, _277201, _277203, _277205] : [-(in(_277203, _277199)), in(_277205, _277201), _277205 = _277203, _277201 = _277199], (1364 ^ _266965) ^ [_314544, _314546] : [_314544 = powerset(_314546), 1367 ^ _266965 : [(1374 ^ _266965) ^ [_314886] : [subset(_314886, _314546), -(in(_314886, _314544))], (1368 ^ _266965) ^ [_314714] : [in(_314714, _314544), -(subset(_314714, _314546))]]], (3584 ^ _266965) ^ [_389977, _389979] : [relation(_389977), -(relation_rng(relation_rng_restriction(_389979, _389977)) = set_intersection2(relation_rng(_389977), _389979))], (2798 ^ _266965) ^ [] : [true___, -(true___)], (2636 ^ _266965) ^ [] : [true___, -(true___)], (3364 ^ _266965) ^ [] : [-(ordinal(3358 ^ []))], (3051 ^ _266965) ^ [_371914, _371916] : [3058 ^ _266965 : [(3061 ^ _266965) ^ [] : [-(relation(relation_composition(_371916, _371914)))], (3059 ^ _266965) ^ [] : [-(empty(relation_composition(_371916, _371914)))]], empty(_371916), relation(_371914)], (3110 ^ _266965) ^ [_373926] : [singleton(_373926) = empty_set], (3939 ^ _266965) ^ [_401864, _401866] : [relation(_401864), function(_401864), 3946 ^ _266965 : [(3947 ^ _266965) ^ [_402110] : [relation(_402110), function(_402110), in(_401866, relation_dom(_401864)), -(apply(relation_composition(_401864, _402110), _401866) = apply(_402110, apply(_401864, _401866)))]]], (4223 ^ _266965) ^ [_411307, _411309] : [-(set_union2(_411309, set_difference(_411307, _411309)) = set_union2(_411309, _411307))], (3767 ^ _266965) ^ [_396394, _396396, _396398] : [relation(_396394), 3770 ^ _266965 : [(3779 ^ _266965) ^ [] : [-(in(_396398, relation_restriction(_396394, _396396))), in(_396398, _396394), in(_396398, cartesian_product2(_396396, _396396))], (3771 ^ _266965) ^ [] : [in(_396398, relation_restriction(_396394, _396396)), 3774 ^ _266965 : [(3777 ^ _266965) ^ [] : [-(in(_396398, cartesian_product2(_396396, _396396)))], (3775 ^ _266965) ^ [] : [-(in(_396398, _396394))]]]]], (2889 ^ _266965) ^ [] : [-(relation_empty_yielding(empty_set))], (2612 ^ _266965) ^ [] : [true___, -(true___)], (4883 ^ _266965) ^ [_433218, _433220, _433222] : [relation(_433218), 4886 ^ _266965 : [(4895 ^ _266965) ^ [] : [-(in(_433222, relation_dom(relation_dom_restriction(_433218, _433220)))), in(_433222, _433220), in(_433222, relation_dom(_433218))], (4887 ^ _266965) ^ [] : [in(_433222, relation_dom(relation_dom_restriction(_433218, _433220))), 4890 ^ _266965 : [(4893 ^ _266965) ^ [] : [-(in(_433222, relation_dom(_433218)))], (4891 ^ _266965) ^ [] : [-(in(_433222, _433220))]]]]], (4005 ^ _266965) ^ [_403928, _403930, _403932] : [subset(_403932, _403930), -(subset(set_intersection2(_403932, _403928), set_intersection2(_403930, _403928)))], (658 ^ _266965) ^ [_289164] : [empty(_289164), -(relation(_289164))], (4458 ^ _266965) ^ [_419193] : [-(set_difference(empty_set, _419193) = empty_set)], (2296 ^ _266965) ^ [_347934] : [relation(_347934), 2299 ^ _266965 : [(2300 ^ _266965) ^ [_348053] : [-(relation_restriction(_347934, _348053) = set_intersection2(_347934, cartesian_product2(_348053, _348053)))]]], (4124 ^ _266965) ^ [_407946, _407948, _407950, _407952] : [ordered_pair(_407952, _407950) = ordered_pair(_407948, _407946), 4127 ^ _266965 : [(4130 ^ _266965) ^ [] : [-(_407950 = _407946)], (4128 ^ _266965) ^ [] : [-(_407952 = _407948)]]], (704 ^ _266965) ^ [_290538, _290540] : [-(set_union2(_290540, _290538) = set_union2(_290538, _290540))], (2937 ^ _266965) ^ [_368283] : [ordinal(_368283), 2940 ^ _266965 : [(2943 ^ _266965) ^ [] : [-(epsilon_transitive(succ(_368283)))], (2945 ^ _266965) ^ [] : [-(epsilon_connected(succ(_368283)))], (2947 ^ _266965) ^ [] : [-(ordinal(succ(_368283)))], (2941 ^ _266965) ^ [] : [empty(succ(_368283))]]], (3676 ^ _266965) ^ [_393335, _393337] : [-(subset(relation_image(_393335, relation_inverse_image(_393335, _393337)), _393337)), relation(_393335), function(_393335)], (4856 ^ _266965) ^ [_432161, _432163] : [in(_432163, _432161), 4860 ^ _266965 : [(4863 ^ _266965) ^ [_432452] : [in(_432452, _432161), in(_432452, 4859 ^ [_432161, _432163])], (4861 ^ _266965) ^ [] : [-(in(4859 ^ [_432161, _432163], _432161))]]], (3369 ^ _266965) ^ [] : [-(relation(3365 ^ []))], (3386 ^ _266965) ^ [] : [-(empty(3382 ^ []))], (1154 ^ _266965) ^ [_306978, _306980, _306982, _306984] : [_306978 = unordered_triple(_306984, _306982, _306980), 1157 ^ _266965 : [(1158 ^ _266965) ^ [_307180] : [in(_307180, _306978), -(_307180 = _306984), -(_307180 = _306982), -(_307180 = _306980)], (1172 ^ _266965) ^ [_307580] : [1173 ^ _266965 : [(1178 ^ _266965) ^ [] : [_307580 = _306980], (1176 ^ _266965) ^ [] : [_307580 = _306982], (1174 ^ _266965) ^ [] : [_307580 = _306984]], -(in(_307580, _306978))]]], (392 ^ _266965) ^ [_279506, _279508, _279510, _279512] : [-(relation_inverse_image(_279512, _279508) = relation_inverse_image(_279510, _279506)), _279512 = _279510, _279508 = _279506], (3063 ^ _266965) ^ [_372277, _372279] : [-(set_union2(_372279, _372279) = _372279)], (1733 ^ _266965) ^ [_327861, _327863] : [subset(_327863, _327861), 1736 ^ _266965 : [(1737 ^ _266965) ^ [_327998] : [in(_327998, _327863), -(in(_327998, _327861))]]], (3819 ^ _266965) ^ [_397994, _397996] : [-(subset(set_intersection2(_397996, _397994), _397996))], (1993 ^ _266965) ^ [_337287, _337289] : [-(_337287 = union(_337289)), 2006 ^ _266965 : [(2011 ^ _266965) ^ [] : [in(1994 ^ [_337287, _337289], _337287)], (2009 ^ _266965) ^ [] : [-(in(2005 ^ [_337287, _337289], _337289))], (2007 ^ _266965) ^ [] : [-(in(1994 ^ [_337287, _337289], 2005 ^ [_337287, _337289]))]], 1997 ^ _266965 : [(2000 ^ _266965) ^ [_337570] : [in(1994 ^ [_337287, _337289], _337570), in(_337570, _337289)], (1998 ^ _266965) ^ [] : [-(in(1994 ^ [_337287, _337289], _337287))]]], (2666 ^ _266965) ^ [] : [true___, -(true___)], (366 ^ _266965) ^ [_278570, _278572, _278574, _278576] : [-(fiber(_278576, _278572) = fiber(_278574, _278570)), _278576 = _278574, _278572 = _278570], (3043 ^ _266965) ^ [_371635] : [empty(_371635), 3046 ^ _266965 : [(3049 ^ _266965) ^ [] : [-(relation(relation_rng(_371635)))], (3047 ^ _266965) ^ [] : [-(empty(relation_rng(_371635)))]]], (4286 ^ _266965) ^ [_413505] : [subset(_413505, empty_set), -(_413505 = empty_set)], (4193 ^ _266965) ^ [_410329, _410331] : [subset(singleton(_410331), _410329), -(in(_410331, _410329))], (3813 ^ _266965) ^ [_397783, _397785] : [relation(_397783), -(relation_restriction(_397783, _397785) = relation_dom_restriction(relation_rng_restriction(_397785, _397783), _397785))], (3403 ^ _266965) ^ [] : [-(ordinal(3389 ^ []))], (3506 ^ _266965) ^ [_387277, _387279, _387281, _387283] : [in(ordered_pair(_387283, _387281), cartesian_product2(_387279, _387277)), 3509 ^ _266965 : [(3512 ^ _266965) ^ [] : [-(in(_387281, _387277))], (3510 ^ _266965) ^ [] : [-(in(_387283, _387279))]]], (3367 ^ _266965) ^ [] : [-(empty(3365 ^ []))], (788 ^ _266965) ^ [_293345] : [relation(_293345), 791 ^ _266965 : [(792 ^ _266965) ^ [_293531, _293533] : [relation(_293531), 795 ^ _266965 : [(796 ^ _266965) ^ [] : [_293531 = relation_dom_restriction(_293345, _293533), 799 ^ _266965 : [(808 ^ _266965) ^ [_294135, _294137] : [-(in(ordered_pair(_294137, _294135), _293531)), in(_294137, _293533), in(ordered_pair(_294137, _294135), _293345)], (800 ^ _266965) ^ [_293856, _293858] : [in(ordered_pair(_293858, _293856), _293531), 803 ^ _266965 : [(806 ^ _266965) ^ [] : [-(in(ordered_pair(_293858, _293856), _293345))], (804 ^ _266965) ^ [] : [-(in(_293858, _293533))]]]]], (818 ^ _266965) ^ [] : [-(_293531 = relation_dom_restriction(_293345, _293533)), 831 ^ _266965 : [(836 ^ _266965) ^ [] : [in(ordered_pair(819 ^ [_293345, _293531, _293533], 820 ^ [_293345, _293531, _293533]), _293531)], (834 ^ _266965) ^ [] : [-(in(ordered_pair(819 ^ [_293345, _293531, _293533], 820 ^ [_293345, _293531, _293533]), _293345))], (832 ^ _266965) ^ [] : [-(in(819 ^ [_293345, _293531, _293533], _293533))]], 823 ^ _266965 : [(826 ^ _266965) ^ [] : [in(819 ^ [_293345, _293531, _293533], _293533), in(ordered_pair(819 ^ [_293345, _293531, _293533], 820 ^ [_293345, _293531, _293533]), _293345)], (824 ^ _266965) ^ [] : [-(in(ordered_pair(819 ^ [_293345, _293531, _293533], 820 ^ [_293345, _293531, _293533]), _293531))]]]]]]], (3488 ^ _266965) ^ [_386621, _386623] : [-(ordinal_subset(_386623, _386623)), ordinal(_386623), ordinal(_386621)], (4477 ^ _266965) ^ [_419885, _419887] : [4478 ^ _266965 : [(4479 ^ _266965) ^ [_419958] : [in(_419958, set_intersection2(_419887, _419885))]], disjoint(_419887, _419885)], (4294 ^ _266965) ^ [_413798] : [ordinal(_413798), 4297 ^ _266965 : [(4298 ^ _266965) ^ [] : [being_limit_ordinal(_413798), 4301 ^ _266965 : [(4302 ^ _266965) ^ [_414044] : [ordinal(_414044), in(_414044, _413798), -(in(succ(_414044), _413798))]]], (4312 ^ _266965) ^ [] : [4314 ^ _266965 : [(4319 ^ _266965) ^ [] : [in(succ(4313 ^ [_413798]), _413798)], (4317 ^ _266965) ^ [] : [-(in(4313 ^ [_413798], _413798))], (4315 ^ _266965) ^ [] : [-(ordinal(4313 ^ [_413798]))]], -(being_limit_ordinal(_413798))]]], (464 ^ _266965) ^ [_282112, _282114, _282116, _282118] : [-(meet_of_subsets(_282118, _282114) = meet_of_subsets(_282116, _282112)), _282118 = _282116, _282114 = _282112], (3971 ^ _266965) ^ [_402830] : [ordinal(_402830), 3974 ^ _266965 : [(3975 ^ _266965) ^ [_402980] : [ordinal(_402980), -(in(_402830, _402980)), -(_402830 = _402980), -(in(_402980, _402830))]]], (3897 ^ _266965) ^ [_400528] : [epsilon_transitive(_400528), 3900 ^ _266965 : [(3901 ^ _266965) ^ [_400664] : [ordinal(_400664), proper_subset(_400528, _400664), -(in(_400528, _400664))]]], (664 ^ _266965) ^ [_289350] : [675 ^ _266965 : [(680 ^ _266965) ^ [] : [-(one_to_one(_289350))], (678 ^ _266965) ^ [] : [-(function(_289350))], (676 ^ _266965) ^ [] : [-(relation(_289350))]], relation(_289350), empty(_289350), function(_289350)], (2354 ^ _266965) ^ [_350041] : [relation(_350041), function(_350041), 2361 ^ _266965 : [(2362 ^ _266965) ^ [] : [one_to_one(_350041), 2365 ^ _266965 : [(2366 ^ _266965) ^ [_350404, _350406] : [-(_350406 = _350404), in(_350406, relation_dom(_350041)), in(_350404, relation_dom(_350041)), apply(_350041, _350406) = apply(_350041, _350404)]]], (2380 ^ _266965) ^ [] : [2383 ^ _266965 : [(2386 ^ _266965) ^ [] : [-(in(2382 ^ [_350041], relation_dom(_350041)))], (2388 ^ _266965) ^ [] : [-(apply(_350041, 2381 ^ [_350041]) = apply(_350041, 2382 ^ [_350041]))], (2390 ^ _266965) ^ [] : [2381 ^ [_350041] = 2382 ^ [_350041]], (2384 ^ _266965) ^ [] : [-(in(2381 ^ [_350041], relation_dom(_350041)))]], -(one_to_one(_350041))]]], (4790 ^ _266965) ^ [_429989, _429991] : [subset(singleton(_429991), singleton(_429989)), -(_429991 = _429989)], (3118 ^ _266965) ^ [_374255, _374257] : [disjoint(singleton(_374257), _374255), in(_374257, _374255)], (2991 ^ _266965) ^ [] : [-(relation(empty_set))], (1831 ^ _266965) ^ [_331485] : [relation(_331485), function(_331485), 1838 ^ _266965 : [(1855 ^ _266965) ^ [_332229, _332231] : [-(in(_332231, relation_dom(_331485))), 1858 ^ _266965 : [(1865 ^ _266965) ^ [] : [_332229 = empty_set, -(_332229 = apply(_331485, _332231))], (1859 ^ _266965) ^ [] : [_332229 = apply(_331485, _332231), -(_332229 = empty_set)]]], (1839 ^ _266965) ^ [_331777, _331779] : [in(_331779, relation_dom(_331485)), 1842 ^ _266965 : [(1849 ^ _266965) ^ [] : [in(ordered_pair(_331779, _331777), _331485), -(_331777 = apply(_331485, _331779))], (1843 ^ _266965) ^ [] : [_331777 = apply(_331485, _331779), -(in(ordered_pair(_331779, _331777), _331485))]]]]], (3839 ^ _266965) ^ [_398740, _398742, _398744] : [-(subset(_398744, _398740)), subset(_398744, _398742), subset(_398742, _398740)], (76 ^ _266965) ^ [_269489, _269491] : [-(reflexive(_269489)), _269491 = _269489, reflexive(_269491)], (3003 ^ _266965) ^ [_370452, _370454] : [3010 ^ _266965 : [(3013 ^ _266965) ^ [] : [-(function(relation_rng_restriction(_370454, _370452)))], (3011 ^ _266965) ^ [] : [-(relation(relation_rng_restriction(_370454, _370452)))]], relation(_370452), function(_370452)], (1871 ^ _266965) ^ [_332747] : [ordinal(_332747), 1874 ^ _266965 : [(1877 ^ _266965) ^ [] : [-(epsilon_connected(_332747))], (1875 ^ _266965) ^ [] : [-(epsilon_transitive(_332747))]]], (546 ^ _266965) ^ [_285033, _285035] : [_285035 = _285033, -(relation_dom(_285035) = relation_dom(_285033))], (4213 ^ _266965) ^ [_411005, _411007, _411009] : [-(subset(unordered_pair(_411009, _411007), _411005)), in(_411009, _411005), in(_411007, _411005)], (3397 ^ _266965) ^ [] : [-(empty(3389 ^ []))], (2819 ^ _266965) ^ [_364714] : [empty(_364714), 2822 ^ _266965 : [(2825 ^ _266965) ^ [] : [-(relation(relation_inverse(_364714)))], (2823 ^ _266965) ^ [] : [-(empty(relation_inverse(_364714)))]]], (3708 ^ _266965) ^ [_394387, _394389] : [relation(_394387), function(_394387), subset(_394389, relation_rng(_394387)), -(relation_image(_394387, relation_inverse_image(_394387, _394389)) = _394389)], (3576 ^ _266965) ^ [_389660, _389662, _389664] : [subset(_389664, _389662), 3579 ^ _266965 : [(3582 ^ _266965) ^ [] : [-(subset(cartesian_product2(_389660, _389664), cartesian_product2(_389660, _389662)))], (3580 ^ _266965) ^ [] : [-(subset(cartesian_product2(_389664, _389660), cartesian_product2(_389662, _389660)))]]], (402 ^ _266965) ^ [_279865, _279867, _279869, _279871] : [-(cartesian_product2(_279871, _279867) = cartesian_product2(_279869, _279865)), _279871 = _279869, _279867 = _279865], (4019 ^ _266965) ^ [_404453, _404455] : [element(_404455, _404453), -(empty(_404453)), -(in(_404455, _404453))], (4593 ^ _266965) ^ [_423901] : [relation(_423901), function(_423901), one_to_one(_423901), 4604 ^ _266965 : [(4607 ^ _266965) ^ [] : [-(relation_dom(_423901) = relation_rng(function_inverse(_423901)))], (4605 ^ _266965) ^ [] : [-(relation_rng(_423901) = relation_dom(function_inverse(_423901)))]]], (1638 ^ _266965) ^ [_324171, _324173, _324175] : [-(_324171 = cartesian_product2(_324175, _324173)), 1656 ^ _266965 : [(1659 ^ _266965) ^ [] : [-(in(1655 ^ [_324171, _324173, _324175], _324173))], (1661 ^ _266965) ^ [] : [-(1639 ^ [_324171, _324173, _324175] = ordered_pair(1654 ^ [_324171, _324173, _324175], 1655 ^ [_324171, _324173, _324175]))], (1663 ^ _266965) ^ [] : [in(1639 ^ [_324171, _324173, _324175], _324171)], (1657 ^ _266965) ^ [] : [-(in(1654 ^ [_324171, _324173, _324175], _324175))]], 1642 ^ _266965 : [(1645 ^ _266965) ^ [_324509, _324511] : [in(_324511, _324175), in(_324509, _324173), 1639 ^ [_324171, _324173, _324175] = ordered_pair(_324511, _324509)], (1643 ^ _266965) ^ [] : [-(in(1639 ^ [_324171, _324173, _324175], _324171))]]], (5006 ^ _266965) ^ [_437257] : [-(in(_437257, 5004 ^ [_437257]))], (1689 ^ _266965) ^ [_326072] : [1692 ^ _266965 : [(1693 ^ _266965) ^ [] : [-(in(1690 ^ [_326072], _326072))], (1697 ^ _266965) ^ [] : [in(1690 ^ [_326072], 1691 ^ [_326072])], (1701 ^ _266965) ^ [] : [in(1691 ^ [_326072], 1690 ^ [_326072])], (1699 ^ _266965) ^ [] : [1690 ^ [_326072] = 1691 ^ [_326072]], (1695 ^ _266965) ^ [] : [-(in(1691 ^ [_326072], _326072))]], -(epsilon_connected(_326072))], (1232 ^ _266965) ^ [_309899] : [relation(_309899), 1235 ^ _266965 : [(1236 ^ _266965) ^ [_310073] : [is_reflexive_in(_309899, _310073), 1239 ^ _266965 : [(1240 ^ _266965) ^ [_310215] : [in(_310215, _310073), -(in(ordered_pair(_310215, _310215), _309899))]]], (1246 ^ _266965) ^ [_310398] : [1248 ^ _266965 : [(1251 ^ _266965) ^ [] : [in(ordered_pair(1247 ^ [_309899, _310398], 1247 ^ [_309899, _310398]), _309899)], (1249 ^ _266965) ^ [] : [-(in(1247 ^ [_309899, _310398], _310398))]], -(is_reflexive_in(_309899, _310398))]]], (4810 ^ _266965) ^ [_430640] : [-(relation_dom(identity_relation(_430640)) = _430640)], (4784 ^ _266965) ^ [_429787] : [empty(_429787), -(_429787 = empty_set)], (4118 ^ _266965) ^ [_407690, _407692, _407694] : [subset(_407694, _407692), -(subset(set_difference(_407694, _407690), set_difference(_407692, _407690)))], (2867 ^ _266965) ^ [_366164, _366166] : [-(relation(set_intersection2(_366166, _366164))), relation(_366166), relation(_366164)], (2949 ^ _266965) ^ [_368711, _368713] : [-(relation(set_difference(_368713, _368711))), relation(_368713), relation(_368711)], (3393 ^ _266965) ^ [] : [-(function(3389 ^ []))], (3570 ^ _266965) ^ [_389424, _389426] : [relation(_389424), -(subset(relation_rng(relation_rng_restriction(_389426, _389424)), relation_rng(_389424)))], (3408 ^ _266965) ^ [] : [-(relation(3404 ^ []))], (2831 ^ _266965) ^ [] : [-(relation_empty_yielding(empty_set))], (62 ^ _266965) ^ [_269073, _269075, _269077, _269079] : [-(is_reflexive_in(_269077, _269073)), is_reflexive_in(_269079, _269075), _269079 = _269077, _269075 = _269073], (126 ^ _266965) ^ [_270964, _270966] : [-(relation_empty_yielding(_270964)), _270966 = _270964, relation_empty_yielding(_270966)], (4814 ^ _266965) ^ [_430815, _430817, _430819] : [relation(_430815), function(_430815), in(_430817, _430819), -(apply(relation_dom_restriction(_430815, _430819), _430817) = apply(_430815, _430817))], (4796 ^ _266965) ^ [_430221, _430223, _430225] : [relation(_430221), function(_430221), in(_430223, relation_dom(relation_dom_restriction(_430221, _430225))), -(apply(relation_dom_restriction(_430221, _430225), _430223) = apply(_430221, _430223))], (510 ^ _266965) ^ [_283766, _283768, _283770, _283772] : [-(apply(_283772, _283768) = apply(_283770, _283766)), _283772 = _283770, _283768 = _283766], (434 ^ _266965) ^ [_281019, _281021, _281023, _281025] : [-(complements_of_subsets(_281025, _281021) = complements_of_subsets(_281023, _281019)), _281025 = _281023, _281021 = _281019], (2786 ^ _266965) ^ [_363778, _363780] : [relation(_363778), -(relation(relation_rng_restriction(_363780, _363778)))], (4641 ^ _266965) ^ [_425370, _425372, _425374] : [in(_425374, _425372), element(_425372, powerset(_425370)), empty(_425370)], (4276 ^ _266965) ^ [_413156, _413158] : [disjoint(_413158, _413156), 4277 ^ _266965 : [(4278 ^ _266965) ^ [_413248] : [in(_413248, _413158), in(_413248, _413156)]]], (2967 ^ _266965) ^ [_369321, _369323] : [2974 ^ _266965 : [(2977 ^ _266965) ^ [] : [-(function(relation_dom_restriction(_369323, _369321)))], (2975 ^ _266965) ^ [] : [-(relation(relation_dom_restriction(_369323, _369321)))]], relation(_369323), function(_369323)], (3235 ^ _266965) ^ [_378375] : [relation(_378375), 3238 ^ _266965 : [(3239 ^ _266965) ^ [] : [connected(_378375), 3242 ^ _266965 : [(3243 ^ _266965) ^ [_378669, _378671] : [in(_378671, relation_field(_378375)), in(_378669, relation_field(_378375)), -(_378671 = _378669), -(in(ordered_pair(_378671, _378669), _378375)), -(in(ordered_pair(_378669, _378671), _378375))]]], (3261 ^ _266965) ^ [] : [3264 ^ _266965 : [(3265 ^ _266965) ^ [] : [-(in(3262 ^ [_378375], relation_field(_378375)))], (3269 ^ _266965) ^ [] : [3262 ^ [_378375] = 3263 ^ [_378375]], (3273 ^ _266965) ^ [] : [in(ordered_pair(3263 ^ [_378375], 3262 ^ [_378375]), _378375)], (3271 ^ _266965) ^ [] : [in(ordered_pair(3262 ^ [_378375], 3263 ^ [_378375]), _378375)], (3267 ^ _266965) ^ [] : [-(in(3263 ^ [_378375], relation_field(_378375)))]], -(connected(_378375))]]], (3309 ^ _266965) ^ [_380951, _380953, _380955, _380957] : [-(in(ordered_pair(_380957, _380955), cartesian_product2(_380953, _380951))), in(_380957, _380953), in(_380955, _380951)], (424 ^ _266965) ^ [_280660, _280662, _280664, _280666] : [-(union_of_subsets(_280666, _280662) = union_of_subsets(_280664, _280660)), _280666 = _280664, _280662 = _280660], (4392 ^ _266965) ^ [_416970] : [relation(_416970), 4395 ^ _266965 : [(4396 ^ _266965) ^ [_417117] : [relation(_417117), subset(relation_rng(_416970), relation_dom(_417117)), -(relation_dom(relation_composition(_416970, _417117)) = relation_dom(_416970))]]], (3430 ^ _266965) ^ [] : [-(epsilon_connected(3424 ^ []))], (552 ^ _266965) ^ [_285279, _285281, _285283, _285285] : [-(relation_composition(_285285, _285281) = relation_composition(_285283, _285279)), _285285 = _285283, _285281 = _285279], (352 ^ _266965) ^ [_278082, _278084, _278086, _278088, _278090, _278092] : [-(unordered_triple(_278092, _278088, _278084) = unordered_triple(_278090, _278086, _278082)), _278092 = _278090, _278088 = _278086, _278084 = _278082], (3355 ^ _266965) ^ [] : [-(relation(3353 ^ []))], (1470 ^ _266965) ^ [_318144, _318146] : [empty(_318146), 1473 ^ _266965 : [(1480 ^ _266965) ^ [] : [empty(_318144), -(element(_318144, _318146))], (1474 ^ _266965) ^ [] : [element(_318144, _318146), -(empty(_318144))]]], (3073 ^ _266965) ^ [_372698] : [relation(_372698), -(relation_inverse(relation_inverse(_372698)) = _372698)], (722 ^ _266965) ^ [_291140, _291142] : [relation(_291140), 725 ^ _266965 : [(726 ^ _266965) ^ [] : [_291140 = identity_relation(_291142), 729 ^ _266965 : [(738 ^ _266965) ^ [_291713, _291715] : [-(in(ordered_pair(_291715, _291713), _291140)), in(_291715, _291142), _291715 = _291713], (730 ^ _266965) ^ [_291450, _291452] : [in(ordered_pair(_291452, _291450), _291140), 733 ^ _266965 : [(736 ^ _266965) ^ [] : [-(_291452 = _291450)], (734 ^ _266965) ^ [] : [-(in(_291452, _291142))]]]]], (748 ^ _266965) ^ [] : [-(_291140 = identity_relation(_291142)), 761 ^ _266965 : [(766 ^ _266965) ^ [] : [in(ordered_pair(749 ^ [_291140, _291142], 750 ^ [_291140, _291142]), _291140)], (764 ^ _266965) ^ [] : [-(749 ^ [_291140, _291142] = 750 ^ [_291140, _291142])], (762 ^ _266965) ^ [] : [-(in(749 ^ [_291140, _291142], _291142))]], 753 ^ _266965 : [(756 ^ _266965) ^ [] : [in(749 ^ [_291140, _291142], _291142), 749 ^ [_291140, _291142] = 750 ^ [_291140, _291142]], (754 ^ _266965) ^ [] : [-(in(ordered_pair(749 ^ [_291140, _291142], 750 ^ [_291140, _291142]), _291140))]]]]], (1414 ^ _266965) ^ [_316241] : [relation(_316241), 1417 ^ _266965 : [(1418 ^ _266965) ^ [_316399] : [relation(_316399), 1421 ^ _266965 : [(1422 ^ _266965) ^ [] : [_316241 = _316399, 1425 ^ _266965 : [(1432 ^ _266965) ^ [_316894, _316896] : [in(ordered_pair(_316896, _316894), _316399), -(in(ordered_pair(_316896, _316894), _316241))], (1426 ^ _266965) ^ [_316704, _316706] : [in(ordered_pair(_316706, _316704), _316241), -(in(ordered_pair(_316706, _316704), _316399))]]], (1438 ^ _266965) ^ [] : [-(_316241 = _316399), 1443 ^ _266965 : [(1446 ^ _266965) ^ [] : [in(ordered_pair(1439 ^ [_316241, _316399], 1440 ^ [_316241, _316399]), _316399)], (1444 ^ _266965) ^ [] : [-(in(ordered_pair(1439 ^ [_316241, _316399], 1440 ^ [_316241, _316399]), _316241))]], 1447 ^ _266965 : [(1450 ^ _266965) ^ [] : [in(ordered_pair(1439 ^ [_316241, _316399], 1440 ^ [_316241, _316399]), _316241)], (1448 ^ _266965) ^ [] : [-(in(ordered_pair(1439 ^ [_316241, _316399], 1440 ^ [_316241, _316399]), _316399))]]]]]]], (4669 ^ _266965) ^ [] : [-(relation_rng(empty_set) = empty_set)], (34 ^ _266965) ^ [_268185, _268187, _268189, _268191] : [-(is_connected_in(_268189, _268185)), is_connected_in(_268191, _268187), _268191 = _268189, _268187 = _268185], (3357 ^ _266965) ^ [] : [-(function(3353 ^ []))], (3067 ^ _266965) ^ [_372486, _372488] : [element(_372486, powerset(_372488)), -(subset_complement(_372488, subset_complement(_372488, _372486)) = _372486)], (4667 ^ _266965) ^ [] : [-(relation_dom(empty_set) = empty_set)], (4741 ^ _266965) ^ [_428329, _428331] : [relation(_428329), function(_428329), 4748 ^ _266965 : [(4749 ^ _266965) ^ [_428596] : [relation(_428596), function(_428596), 4756 ^ _266965 : [(4769 ^ _266965) ^ [] : [-(_428329 = relation_dom_restriction(_428596, _428331)), relation_dom(_428329) = set_intersection2(relation_dom(_428596), _428331), 4775 ^ _266965 : [(4778 ^ _266965) ^ [] : [apply(_428329, 4774 ^ [_428329, _428331, _428596]) = apply(_428596, 4774 ^ [_428329, _428331, _428596])], (4776 ^ _266965) ^ [] : [-(in(4774 ^ [_428329, _428331, _428596], relation_dom(_428329)))]]], (4757 ^ _266965) ^ [] : [_428329 = relation_dom_restriction(_428596, _428331), 4760 ^ _266965 : [(4763 ^ _266965) ^ [_429050] : [in(_429050, relation_dom(_428329)), -(apply(_428329, _429050) = apply(_428596, _429050))], (4761 ^ _266965) ^ [] : [-(relation_dom(_428329) = set_intersection2(relation_dom(_428596), _428331))]]]]]]], (622 ^ _266965) ^ [_287785, _287787, _287789, _287791] : [-(relation_dom_restriction(_287791, _287787) = relation_dom_restriction(_287789, _287785)), _287791 = _287789, _287787 = _287785], (770 ^ _266965) ^ [_292821, _292823] : [_292823 = _292821, 773 ^ _266965 : [(776 ^ _266965) ^ [] : [-(subset(_292821, _292823))], (774 ^ _266965) ^ [] : [-(subset(_292823, _292821))]]], (2740 ^ _266965) ^ [_362157, _362159] : [-(relation(relation_composition(_362159, _362157))), relation(_362159), relation(_362157)], (2 ^ _266965) ^ [_267089] : [-(_267089 = _267089)], (2887 ^ _266965) ^ [] : [-(relation(empty_set))], (2716 ^ _266965) ^ [] : [true___, -(true___)], (3035 ^ _266965) ^ [_371370] : [empty(_371370), 3038 ^ _266965 : [(3041 ^ _266965) ^ [] : [-(relation(relation_dom(_371370)))], (3039 ^ _266965) ^ [] : [-(empty(relation_dom(_371370)))]]], (218 ^ _266965) ^ [_273799, _273801, _273803, _273805] : [-(proper_subset(_273803, _273799)), proper_subset(_273805, _273801), _273805 = _273803, _273801 = _273799], (4782 ^ _266965) ^ [_429689] : [-(unordered_pair(_429689, _429689) = singleton(_429689))], (4460 ^ _266965) ^ [_419317, _419319, _419321] : [-(element(_419321, _419317)), in(_419321, _419319), element(_419319, powerset(_419317))], (2865 ^ _266965) ^ [_366056] : [empty(succ(_366056))], (382 ^ _266965) ^ [_279147, _279149, _279151, _279153] : [-(relation_image(_279153, _279149) = relation_image(_279151, _279147)), _279153 = _279151, _279149 = _279147], (2883 ^ _266965) ^ [_366680] : [-(relation(identity_relation(_366680)))], (4292 ^ _266965) ^ [_413694, _413696] : [-(set_difference(set_union2(_413696, _413694), _413694) = set_difference(_413696, _413694))], (2674 ^ _266965) ^ [] : [true___, -(true___)], (146 ^ _266965) ^ [_271582, _271584, _271586, _271588] : [-(ordinal_subset(_271586, _271582)), ordinal_subset(_271588, _271584), _271588 = _271586, _271584 = _271582], (4376 ^ _266965) ^ [_416396] : [relation(_416396), 4379 ^ _266965 : [(4380 ^ _266965) ^ [_416533] : [relation(_416533), -(subset(relation_rng(relation_composition(_416396, _416533)), relation_rng(_416533)))]]], (3173 ^ _266965) ^ [_376281, _376283] : [set_difference(_376283, _376281) = empty_set, -(subset(_376283, _376281))], (2302 ^ _266965) ^ [_348162] : [relation(_348162), 2305 ^ _266965 : [(2306 ^ _266965) ^ [_348322] : [relation(_348322), 2309 ^ _266965 : [(2310 ^ _266965) ^ [] : [_348322 = relation_inverse(_348162), 2313 ^ _266965 : [(2320 ^ _266965) ^ [_348821, _348823] : [in(ordered_pair(_348821, _348823), _348162), -(in(ordered_pair(_348823, _348821), _348322))], (2314 ^ _266965) ^ [_348631, _348633] : [in(ordered_pair(_348633, _348631), _348322), -(in(ordered_pair(_348631, _348633), _348162))]]], (2326 ^ _266965) ^ [] : [-(_348322 = relation_inverse(_348162)), 2331 ^ _266965 : [(2334 ^ _266965) ^ [] : [in(ordered_pair(2328 ^ [_348162, _348322], 2327 ^ [_348162, _348322]), _348162)], (2332 ^ _266965) ^ [] : [-(in(ordered_pair(2327 ^ [_348162, _348322], 2328 ^ [_348162, _348322]), _348322))]], 2335 ^ _266965 : [(2338 ^ _266965) ^ [] : [in(ordered_pair(2327 ^ [_348162, _348322], 2328 ^ [_348162, _348322]), _348322)], (2336 ^ _266965) ^ [] : [-(in(ordered_pair(2328 ^ [_348162, _348322], 2327 ^ [_348162, _348322]), _348162))]]]]]]], (3301 ^ _266965) ^ [_380686, _380688, _380690, _380692] : [in(ordered_pair(_380692, _380690), cartesian_product2(_380688, _380686)), 3304 ^ _266965 : [(3307 ^ _266965) ^ [] : [-(in(_380690, _380686))], (3305 ^ _266965) ^ [] : [-(in(_380692, _380688))]]], (1351 ^ _266965) ^ [_314074] : [_314074 = empty_set, 1354 ^ _266965 : [(1355 ^ _266965) ^ [_314187] : [in(_314187, _314074)]]], (86 ^ _266965) ^ [_269784, _269786] : [-(transitive(_269784)), _269786 = _269784, transitive(_269786)], (3831 ^ _266965) ^ [_398406] : [-(set_union2(_398406, empty_set) = _398406)], (2600 ^ _266965) ^ [] : [true___, -(true___)], (4979 ^ _266965) ^ [_436157, _436159] : [relation(_436157), -(relation_dom(relation_dom_restriction(_436157, _436159)) = set_intersection2(relation_dom(_436157), _436159))], (2921 ^ _266965) ^ [_367852] : [2932 ^ _266965 : [(2935 ^ _266965) ^ [] : [-(function(relation_inverse(_367852)))], (2933 ^ _266965) ^ [] : [-(relation(relation_inverse(_367852)))]], relation(_367852), function(_367852), one_to_one(_367852)], (3607 ^ _266965) ^ [_390886] : [-(in(_390886, 3605 ^ [_390886]))], (276 ^ _266965) ^ [_275572, _275574, _275576, _275578] : [-(well_orders(_275576, _275572)), well_orders(_275578, _275574), _275578 = _275576, _275574 = _275572], (376 ^ _266965) ^ [_278901, _278903] : [_278903 = _278901, -(set_meet(_278903) = set_meet(_278901))], (180 ^ _266965) ^ [_272616, _272618, _272620, _272622] : [-(element(_272620, _272616)), element(_272622, _272618), _272622 = _272620, _272618 = _272616], (3179 ^ _266965) ^ [_376449, _376451] : [subset(_376451, _376449), -(set_difference(_376451, _376449) = empty_set)], (1810 ^ _266965) ^ [_330746, _330748, _330750] : [-(_330746 = set_intersection2(_330750, _330748)), 1822 ^ _266965 : [(1827 ^ _266965) ^ [] : [in(1811 ^ [_330746, _330748, _330750], _330746)], (1825 ^ _266965) ^ [] : [-(in(1811 ^ [_330746, _330748, _330750], _330748))], (1823 ^ _266965) ^ [] : [-(in(1811 ^ [_330746, _330748, _330750], _330750))]], 1814 ^ _266965 : [(1817 ^ _266965) ^ [] : [in(1811 ^ [_330746, _330748, _330750], _330750), in(1811 ^ [_330746, _330748, _330750], _330748)], (1815 ^ _266965) ^ [] : [-(in(1811 ^ [_330746, _330748, _330750], _330746))]]], (300 ^ _266965) ^ [_276311, _276313, _276315, _276317] : [-(subset(_276315, _276311)), subset(_276317, _276313), _276317 = _276315, _276313 = _276311], (3635 ^ _266965) ^ [_391867, _391869, _391871] : [relation(_391867), -(relation_dom_restriction(relation_rng_restriction(_391871, _391867), _391869) = relation_rng_restriction(_391871, relation_dom_restriction(_391867, _391869)))], (1926 ^ _266965) ^ [_334682] : [relation(_334682), 1929 ^ _266965 : [(1930 ^ _266965) ^ [_334882] : [is_antisymmetric_in(_334682, _334882), 1933 ^ _266965 : [(1934 ^ _266965) ^ [_335064, _335066] : [-(_335066 = _335064), in(_335066, _334882), in(_335064, _334882), in(ordered_pair(_335066, _335064), _334682), in(ordered_pair(_335064, _335066), _334682)]]], (1952 ^ _266965) ^ [_335550] : [1955 ^ _266965 : [(1956 ^ _266965) ^ [] : [-(in(1953 ^ [_334682, _335550], _335550))], (1960 ^ _266965) ^ [] : [-(in(ordered_pair(1953 ^ [_334682, _335550], 1954 ^ [_334682, _335550]), _334682))], (1964 ^ _266965) ^ [] : [1953 ^ [_334682, _335550] = 1954 ^ [_334682, _335550]], (1962 ^ _266965) ^ [] : [-(in(ordered_pair(1954 ^ [_334682, _335550], 1953 ^ [_334682, _335550]), _334682))], (1958 ^ _266965) ^ [] : [-(in(1954 ^ [_334682, _335550], _335550))]], -(is_antisymmetric_in(_334682, _335550))]]], (4422 ^ _266965) ^ [_417966] : [relation(_417966), 4425 ^ _266965 : [(4426 ^ _266965) ^ [_418113] : [relation(_418113), subset(relation_dom(_417966), relation_rng(_418113)), -(relation_rng(relation_composition(_418113, _417966)) = relation_rng(_417966))]]], (1182 ^ _266965) ^ [_307942, _307944, _307946, _307948] : [-(_307942 = unordered_triple(_307948, _307946, _307944)), 1186 ^ _266965 : [(1189 ^ _266965) ^ [] : [1183 ^ [_307942, _307944, _307946, _307948] = _307948], (1191 ^ _266965) ^ [] : [1183 ^ [_307942, _307944, _307946, _307948] = _307946], (1193 ^ _266965) ^ [] : [1183 ^ [_307942, _307944, _307946, _307948] = _307944], (1187 ^ _266965) ^ [] : [-(in(1183 ^ [_307942, _307944, _307946, _307948], _307942))]], 1194 ^ _266965 : [(1195 ^ _266965) ^ [] : [-(1183 ^ [_307942, _307944, _307946, _307948] = _307948), -(1183 ^ [_307942, _307944, _307946, _307948] = _307946), -(1183 ^ [_307942, _307944, _307946, _307948] = _307944)], (1205 ^ _266965) ^ [] : [in(1183 ^ [_307942, _307944, _307946, _307948], _307942)]]], (2015 ^ _266965) ^ [_338120] : [relation(_338120), 2018 ^ _266965 : [(2033 ^ _266965) ^ [] : [-(well_ordering(_338120)), reflexive(_338120), transitive(_338120), antisymmetric(_338120), connected(_338120), well_founded_relation(_338120)], (2019 ^ _266965) ^ [] : [well_ordering(_338120), 2022 ^ _266965 : [(2023 ^ _266965) ^ [] : [-(reflexive(_338120))], (2027 ^ _266965) ^ [] : [-(antisymmetric(_338120))], (2031 ^ _266965) ^ [] : [-(well_founded_relation(_338120))], (2029 ^ _266965) ^ [] : [-(connected(_338120))], (2025 ^ _266965) ^ [] : [-(transitive(_338120))]]]]], (2594 ^ _266965) ^ [] : [true___, -(true___)], (342 ^ _266965) ^ [_277595, _277597] : [-(relation(_277595)), _277597 = _277595, relation(_277597)], (4323 ^ _266965) ^ [_414670] : [ordinal(_414670), 4326 ^ _266965 : [(4336 ^ _266965) ^ [] : [being_limit_ordinal(_414670), 4337 ^ _266965 : [(4338 ^ _266965) ^ [_415141] : [ordinal(_415141), _414670 = succ(_415141)]]], (4327 ^ _266965) ^ [] : [-(being_limit_ordinal(_414670)), 4331 ^ _266965 : [(4334 ^ _266965) ^ [] : [-(_414670 = succ(4330 ^ [_414670]))], (4332 ^ _266965) ^ [] : [-(ordinal(4330 ^ [_414670]))]]]]], (2236 ^ _266965) ^ [_345699] : [being_limit_ordinal(_345699), -(_345699 = union(_345699))], (2993 ^ _266965) ^ [_370146, _370148] : [empty(cartesian_product2(_370148, _370146)), -(empty(_370148)), -(empty(_370146))], (3961 ^ _266965) ^ [_402549, _402551] : [ordinal(_402549), in(_402551, _402549), -(ordinal(_402551))], (2686 ^ _266965) ^ [] : [true___, -(true___)], (708 ^ _266965) ^ [_290753, _290755] : [ordinal(_290755), ordinal(_290753), -(ordinal_subset(_290755, _290753)), -(ordinal_subset(_290753, _290755))], (444 ^ _266965) ^ [_281406, _281408, _281410, _281412, _281414, _281416] : [-(subset_difference(_281416, _281412, _281408) = subset_difference(_281414, _281410, _281406)), _281416 = _281414, _281412 = _281410, _281408 = _281406], (290 ^ _266965) ^ [_275988, _275990] : [-(well_ordering(_275988)), _275990 = _275988, well_ordering(_275990)], (4583 ^ _266965) ^ [_423595, _423597, _423599] : [element(_423595, powerset(_423599)), in(_423597, subset_complement(_423599, _423595)), in(_423597, _423595)], (2606 ^ _266965) ^ [] : [true___, -(true___)], (3600 ^ _266965) ^ [_390564, _390566] : [subset(_390566, _390564), -(set_union2(_390566, _390564) = _390564)], (3558 ^ _266965) ^ [_388992, _388994] : [relation(_388992), -(subset(relation_rng(relation_rng_restriction(_388994, _388992)), _388994))], (1608 ^ _266965) ^ [_322914, _322916, _322918] : [_322914 = cartesian_product2(_322918, _322916), 1611 ^ _266965 : [(1624 ^ _266965) ^ [_323675] : [-(in(_323675, _322914)), 1625 ^ _266965 : [(1626 ^ _266965) ^ [_323805, _323807] : [in(_323807, _322918), in(_323805, _322916), _323675 = ordered_pair(_323807, _323805)]]], (1612 ^ _266965) ^ [_323115] : [in(_323115, _322914), 1617 ^ _266965 : [(1622 ^ _266965) ^ [] : [-(_323115 = ordered_pair(1615 ^ [_322914, _322916, _322918, _323115], 1616 ^ [_322914, _322916, _322918, _323115]))], (1620 ^ _266965) ^ [] : [-(in(1616 ^ [_322914, _322916, _322918, _323115], _322916))], (1618 ^ _266965) ^ [] : [-(in(1615 ^ [_322914, _322916, _322918, _323115], _322918))]]]]], (490 ^ _266965) ^ [_283048, _283050, _283052, _283054] : [-(set_difference(_283054, _283050) = set_difference(_283052, _283048)), _283054 = _283052, _283050 = _283048], (3590 ^ _266965) ^ [_390233, _390235, _390237, _390239] : [-(subset(cartesian_product2(_390239, _390235), cartesian_product2(_390237, _390233))), subset(_390239, _390237), subset(_390235, _390233)], (3761 ^ _266965) ^ [_396162, _396164] : [relation(_396162), -(subset(relation_inverse_image(_396162, _396164), relation_dom(_396162)))], (638 ^ _266965) ^ [_288524, _288526] : [proper_subset(_288526, _288524), proper_subset(_288524, _288526)], (3124 ^ _266965) ^ [_374468, _374470] : [-(in(_374470, _374468)), -(disjoint(singleton(_374470), _374468))], (2501 ^ _266965) ^ [_355912, _355914] : [element(_355912, powerset(powerset(_355914))), 2504 ^ _266965 : [(2505 ^ _266965) ^ [_356092] : [element(_356092, powerset(powerset(_355914))), 2508 ^ _266965 : [(2509 ^ _266965) ^ [] : [_356092 = complements_of_subsets(_355914, _355912), 2512 ^ _266965 : [(2513 ^ _266965) ^ [_356380] : [element(_356380, powerset(_355914)), 2516 ^ _266965 : [(2523 ^ _266965) ^ [] : [in(subset_complement(_355914, _356380), _355912), -(in(_356380, _356092))], (2517 ^ _266965) ^ [] : [in(_356380, _356092), -(in(subset_complement(_355914, _356380), _355912))]]]]], (2529 ^ _266965) ^ [] : [-(_356092 = complements_of_subsets(_355914, _355912)), 2531 ^ _266965 : [(2534 ^ _266965) ^ [] : [2535 ^ _266965 : [(2538 ^ _266965) ^ [] : [in(subset_complement(_355914, 2530 ^ [_355912, _355914, _356092]), _355912)], (2536 ^ _266965) ^ [] : [-(in(2530 ^ [_355912, _355914, _356092], _356092))]], 2539 ^ _266965 : [(2542 ^ _266965) ^ [] : [in(2530 ^ [_355912, _355914, _356092], _356092)], (2540 ^ _266965) ^ [] : [-(in(subset_complement(_355914, 2530 ^ [_355912, _355914, _356092]), _355912))]]], (2532 ^ _266965) ^ [] : [-(element(2530 ^ [_355912, _355914, _356092], powerset(_355914)))]]]]]]], (3395 ^ _266965) ^ [] : [-(one_to_one(3389 ^ []))], (3423 ^ _266965) ^ [] : [-(one_to_one(3417 ^ []))], (5041 ^ _266965) ^ [_438537, _438539, _438541] : [singleton(_438541) = unordered_pair(_438539, _438537), -(_438539 = _438537)], (3500 ^ _266965) ^ [_387010, _387012] : [disjoint(_387012, _387010), -(disjoint(_387010, _387012))], (4205 ^ _266965) ^ [_410754, _410756, _410758] : [subset(unordered_pair(_410758, _410756), _410754), 4208 ^ _266965 : [(4211 ^ _266965) ^ [] : [-(in(_410756, _410754))], (4209 ^ _266965) ^ [] : [-(in(_410758, _410754))]]], (1565 ^ _266965) ^ [_321395, _321397, _321399] : [_321395 = set_union2(_321399, _321397), 1568 ^ _266965 : [(1569 ^ _266965) ^ [_321577] : [in(_321577, _321395), -(in(_321577, _321399)), -(in(_321577, _321397))], (1579 ^ _266965) ^ [_321855] : [1580 ^ _266965 : [(1583 ^ _266965) ^ [] : [in(_321855, _321397)], (1581 ^ _266965) ^ [] : [in(_321855, _321399)]], -(in(_321855, _321395))]]], (3458 ^ _266965) ^ [_385743, _385745, _385747] : [-(subset_difference(_385747, _385745, _385743) = set_difference(_385745, _385743)), element(_385745, powerset(_385747)), element(_385743, powerset(_385747))], (692 ^ _266965) ^ [_290112] : [empty(_290112), 695 ^ _266965 : [(700 ^ _266965) ^ [] : [-(ordinal(_290112))], (698 ^ _266965) ^ [] : [-(epsilon_connected(_290112))], (696 ^ _266965) ^ [] : [-(epsilon_transitive(_290112))]]], (682 ^ _266965) ^ [_289843] : [-(ordinal(_289843)), epsilon_transitive(_289843), epsilon_connected(_289843)], (3732 ^ _266965) ^ [_395164, _395166, _395168] : [relation(_395164), 3735 ^ _266965 : [(3747 ^ _266965) ^ [] : [-(in(_395168, relation_inverse_image(_395164, _395166))), 3748 ^ _266965 : [(3749 ^ _266965) ^ [_395765] : [in(_395765, relation_rng(_395164)), in(ordered_pair(_395168, _395765), _395164), in(_395765, _395166)]]], (3736 ^ _266965) ^ [] : [in(_395168, relation_inverse_image(_395164, _395166)), 3740 ^ _266965 : [(3745 ^ _266965) ^ [] : [-(in(3739 ^ [_395164, _395166, _395168], _395166))], (3743 ^ _266965) ^ [] : [-(in(ordered_pair(_395168, 3739 ^ [_395164, _395166, _395168]), _395164))], (3741 ^ _266965) ^ [] : [-(in(3739 ^ [_395164, _395166, _395168], relation_rng(_395164)))]]]]], (4243 ^ _266965) ^ [_411979] : [-(set_difference(_411979, empty_set) = _411979)], (4973 ^ _266965) ^ [_435931, _435933, _435935] : [singleton(_435935) = unordered_pair(_435933, _435931), -(_435935 = _435933)], (3411 ^ _266965) ^ [_384182] : [-(element(3409 ^ [_384182], powerset(_384182)))], (1209 ^ _266965) ^ [_308915] : [-(succ(_308915) = set_union2(_308915, singleton(_308915)))], (3498 ^ _266965) ^ [_386901, _386903] : [-(subset(_386903, _386903))], (4 ^ _266965) ^ [_267196, _267198] : [_267198 = _267196, -(_267196 = _267198)], (2903 ^ _266965) ^ [_367273, _367275] : [-(relation(set_union2(_367275, _367273))), relation(_367275), relation(_367273)], (1889 ^ _266965) ^ [_333241] : [relation(_333241), 1892 ^ _266965 : [(1893 ^ _266965) ^ [_333422] : [_333422 = relation_dom(_333241), 1896 ^ _266965 : [(1904 ^ _266965) ^ [_333846] : [1905 ^ _266965 : [(1906 ^ _266965) ^ [_333925] : [in(ordered_pair(_333846, _333925), _333241)]], -(in(_333846, _333422))], (1897 ^ _266965) ^ [_333602] : [in(_333602, _333422), -(in(ordered_pair(_333602, 1900 ^ [_333241, _333422, _333602]), _333241))]]], (1910 ^ _266965) ^ [_334053] : [-(_334053 = relation_dom(_333241)), 1914 ^ _266965 : [(1917 ^ _266965) ^ [_334316] : [in(ordered_pair(1911 ^ [_333241, _334053], _334316), _333241)], (1915 ^ _266965) ^ [] : [-(in(1911 ^ [_333241, _334053], _334053))]], 1919 ^ _266965 : [(1922 ^ _266965) ^ [] : [in(1911 ^ [_333241, _334053], _334053)], (1920 ^ _266965) ^ [] : [-(in(ordered_pair(1911 ^ [_333241, _334053], 1918 ^ [_333241, _334053]), _333241))]]]]], (2254 ^ _266965) ^ [_346257] : [relation(_346257), 2257 ^ _266965 : [(2258 ^ _266965) ^ [_346465] : [is_connected_in(_346257, _346465), 2261 ^ _266965 : [(2262 ^ _266965) ^ [_346655, _346657] : [in(_346657, _346465), in(_346655, _346465), -(_346657 = _346655), -(in(ordered_pair(_346657, _346655), _346257)), -(in(ordered_pair(_346655, _346657), _346257))]]], (2280 ^ _266965) ^ [_347149] : [2283 ^ _266965 : [(2284 ^ _266965) ^ [] : [-(in(2281 ^ [_346257, _347149], _347149))], (2288 ^ _266965) ^ [] : [2281 ^ [_346257, _347149] = 2282 ^ [_346257, _347149]], (2292 ^ _266965) ^ [] : [in(ordered_pair(2282 ^ [_346257, _347149], 2281 ^ [_346257, _347149]), _346257)], (2290 ^ _266965) ^ [] : [in(ordered_pair(2281 ^ [_346257, _347149], 2282 ^ [_346257, _347149]), _346257)], (2286 ^ _266965) ^ [] : [-(in(2282 ^ [_346257, _347149], _347149))]], -(is_connected_in(_346257, _347149))]]], (3401 ^ _266965) ^ [] : [-(epsilon_connected(3389 ^ []))], (2704 ^ _266965) ^ [_361267, _361269] : [element(_361267, powerset(_361269)), -(element(subset_complement(_361269, _361267), powerset(_361269)))], (1743 ^ _266965) ^ [_328175, _328177] : [1745 ^ _266965 : [(1748 ^ _266965) ^ [] : [in(1744 ^ [_328175, _328177], _328175)], (1746 ^ _266965) ^ [] : [-(in(1744 ^ [_328175, _328177], _328177))]], -(subset(_328177, _328175))], (2891 ^ _266965) ^ [] : [-(function(empty_set))], (973 ^ _266965) ^ [_300200] : [relation(_300200), function(_300200), 980 ^ _266965 : [(981 ^ _266965) ^ [_300487, _300489] : [_300487 = relation_inverse_image(_300200, _300489), 984 ^ _266965 : [(993 ^ _266965) ^ [_300945] : [-(in(_300945, _300487)), in(_300945, relation_dom(_300200)), in(apply(_300200, _300945), _300489)], (985 ^ _266965) ^ [_300676] : [in(_300676, _300487), 988 ^ _266965 : [(991 ^ _266965) ^ [] : [-(in(apply(_300200, _300676), _300489))], (989 ^ _266965) ^ [] : [-(in(_300676, relation_dom(_300200)))]]]]], (1003 ^ _266965) ^ [_301239, _301241] : [-(_301239 = relation_inverse_image(_300200, _301241)), 1015 ^ _266965 : [(1020 ^ _266965) ^ [] : [in(1004 ^ [_300200, _301239, _301241], _301239)], (1018 ^ _266965) ^ [] : [-(in(apply(_300200, 1004 ^ [_300200, _301239, _301241]), _301241))], (1016 ^ _266965) ^ [] : [-(in(1004 ^ [_300200, _301239, _301241], relation_dom(_300200)))]], 1007 ^ _266965 : [(1010 ^ _266965) ^ [] : [in(1004 ^ [_300200, _301239, _301241], relation_dom(_300200)), in(apply(_300200, 1004 ^ [_300200, _301239, _301241]), _301241)], (1008 ^ _266965) ^ [] : [-(in(1004 ^ [_300200, _301239, _301241], _301239))]]]]], (3328 ^ _266965) ^ [_381657, _381659, _381661] : [relation(_381657), function(_381657), 3335 ^ _266965 : [(3344 ^ _266965) ^ [] : [-(in(_381659, relation_dom(relation_dom_restriction(_381657, _381661)))), in(_381659, relation_dom(_381657)), in(_381659, _381661)], (3336 ^ _266965) ^ [] : [in(_381659, relation_dom(relation_dom_restriction(_381657, _381661))), 3339 ^ _266965 : [(3342 ^ _266965) ^ [] : [-(in(_381659, _381661))], (3340 ^ _266965) ^ [] : [-(in(_381659, relation_dom(_381657)))]]]]], (3437 ^ _266965) ^ [] : [-(relation_empty_yielding(3433 ^ []))], (3384 ^ _266965) ^ [] : [-(relation(3382 ^ []))], (2734 ^ _266965) ^ [] : [true___, -(true___)], (526 ^ _266965) ^ [_284343, _284345, _284347, _284349] : [-(set_union2(_284349, _284345) = set_union2(_284347, _284343)), _284349 = _284347, _284345 = _284343], (2897 ^ _266965) ^ [] : [-(epsilon_transitive(empty_set))], (2564 ^ _266965) ^ [_358031] : [relation(_358031), function(_358031), one_to_one(_358031), -(function_inverse(_358031) = relation_inverse(_358031))], (702 ^ _266965) ^ [_290438, _290440] : [-(unordered_pair(_290440, _290438) = unordered_pair(_290438, _290440))], (2879 ^ _266965) ^ [] : [-(empty(empty_set))], (2654 ^ _266965) ^ [_360016] : [2661 ^ _266965 : [(2664 ^ _266965) ^ [] : [-(function(function_inverse(_360016)))], (2662 ^ _266965) ^ [] : [-(relation(function_inverse(_360016)))]], relation(_360016), function(_360016)], (2807 ^ _266965) ^ [_364350, _364352] : [2814 ^ _266965 : [(2817 ^ _266965) ^ [] : [-(relation(relation_composition(_364350, _364352)))], (2815 ^ _266965) ^ [] : [-(empty(relation_composition(_364350, _364352)))]], empty(_364352), relation(_364350)], (3917 ^ _266965) ^ [_401170, _401172] : [relation(_401170), function(_401170), 3924 ^ _266965 : [(3925 ^ _266965) ^ [_401419] : [relation(_401419), function(_401419), in(_401172, relation_dom(relation_composition(_401419, _401170))), -(apply(relation_composition(_401419, _401170), _401172) = apply(_401170, apply(_401419, _401172)))]]], (3360 ^ _266965) ^ [] : [-(epsilon_transitive(3358 ^ []))], (632 ^ _266965) ^ [_288313, _288315] : [in(_288315, _288313), in(_288313, _288315)], (4245 ^ _266965) ^ [_412103, _412105, _412107] : [in(_412107, _412105), in(_412105, _412103), in(_412103, _412107)], (4701 ^ _266965) ^ [_427095] : [relation(_427095), 4706 ^ _266965 : [(4709 ^ _266965) ^ [] : [relation_rng(_427095) = empty_set], (4707 ^ _266965) ^ [] : [relation_dom(_427095) = empty_set]], -(_427095 = empty_set)], (4406 ^ _266965) ^ [_417443, _417445] : [element(_417443, powerset(powerset(_417445))), -(_417443 = empty_set), complements_of_subsets(_417445, _417443) = empty_set], (2827 ^ _266965) ^ [] : [-(empty(empty_set))], (170 ^ _266965) ^ [_272293, _272295] : [-(being_limit_ordinal(_272293)), _272295 = _272293, being_limit_ordinal(_272295)], (2792 ^ _266965) ^ [] : [true___, -(true___)], (2710 ^ _266965) ^ [] : [true___, -(true___)], (3085 ^ _266965) ^ [_373122, _373124] : [proper_subset(_373124, _373124)], (3406 ^ _266965) ^ [] : [empty(3404 ^ [])], (1752 ^ _266965) ^ [_328518] : [relation(_328518), 1755 ^ _266965 : [(1756 ^ _266965) ^ [_328715] : [is_well_founded_in(_328518, _328715), 1759 ^ _266965 : [(1760 ^ _266965) ^ [_328880] : [subset(_328880, _328715), -(_328880 = empty_set), 1768 ^ _266965 : [(1771 ^ _266965) ^ [] : [-(disjoint(fiber(_328518, 1767 ^ [_328518, _328715, _328880]), _328880))], (1769 ^ _266965) ^ [] : [-(in(1767 ^ [_328518, _328715, _328880], _328880))]]]]], (1773 ^ _266965) ^ [_329321] : [-(is_well_founded_in(_328518, _329321)), 1775 ^ _266965 : [(1780 ^ _266965) ^ [_329663] : [in(_329663, 1774 ^ [_328518, _329321]), disjoint(fiber(_328518, _329663), 1774 ^ [_328518, _329321])], (1778 ^ _266965) ^ [] : [1774 ^ [_328518, _329321] = empty_set], (1776 ^ _266965) ^ [] : [-(subset(1774 ^ [_328518, _329321], _329321))]]]]], (3112 ^ _266965) ^ [_374035, _374037] : [in(_374037, _374035), -(set_union2(singleton(_374037), _374035) = _374035)], (474 ^ _266965) ^ [_282471, _282473, _282475, _282477] : [-(subset_complement(_282477, _282473) = subset_complement(_282475, _282471)), _282477 = _282475, _282473 = _282471], (2554 ^ _266965) ^ [_357741, _357743] : [-(proper_subset(_357743, _357741)), subset(_357743, _357741), -(_357743 = _357741)], (4098 ^ _266965) ^ [_407067] : [ordinal(_407067), 4101 ^ _266965 : [(4102 ^ _266965) ^ [_407205] : [ordinal(_407205), 4105 ^ _266965 : [(4112 ^ _266965) ^ [] : [ordinal_subset(succ(_407067), _407205), -(in(_407067, _407205))], (4106 ^ _266965) ^ [] : [in(_407067, _407205), -(ordinal_subset(succ(_407067), _407205))]]]]], (612 ^ _266965) ^ [_287446, _287448, _287450, _287452] : [-(relation_rng_restriction(_287452, _287448) = relation_rng_restriction(_287450, _287446)), _287452 = _287450, _287448 = _287446], (3167 ^ _266965) ^ [_376036, _376038] : [in(_376038, _376036), -(subset(singleton(_376038), _376036))], (4609 ^ _266965) ^ [_424354] : [relation(_424354), -(in(ordered_pair(4614 ^ [_424354], 4615 ^ [_424354]), _424354)), -(_424354 = empty_set)], (2764 ^ _266965) ^ [_363005, _363007, _363009] : [-(element(subset_difference(_363009, _363007, _363005), powerset(_363009))), element(_363007, powerset(_363009)), element(_363005, powerset(_363009))], (4436 ^ _266965) ^ [_418439, _418441] : [element(_418439, powerset(powerset(_418441))), -(_418439 = empty_set), -(subset_difference(_418441, cast_to_subset(_418441), union_of_subsets(_418441, _418439)) = meet_of_subsets(_418441, complements_of_subsets(_418441, _418439)))], (4261 ^ _266965) ^ [_412606, _412608] : [subset(_412608, _412606), -(element(_412608, powerset(_412606)))], (2452 ^ _266965) ^ [_353853] : [relation(_353853), 2455 ^ _266965 : [(2456 ^ _266965) ^ [_354067] : [is_transitive_in(_353853, _354067), 2459 ^ _266965 : [(2460 ^ _266965) ^ [_354277, _354279, _354281] : [-(in(ordered_pair(_354281, _354277), _353853)), in(_354281, _354067), in(_354279, _354067), in(_354277, _354067), in(ordered_pair(_354281, _354279), _353853), in(ordered_pair(_354279, _354277), _353853)]]], (2482 ^ _266965) ^ [_354888] : [2486 ^ _266965 : [(2489 ^ _266965) ^ [] : [-(in(2484 ^ [_353853, _354888], _354888))], (2487 ^ _266965) ^ [] : [-(in(2483 ^ [_353853, _354888], _354888))], (2497 ^ _266965) ^ [] : [in(ordered_pair(2483 ^ [_353853, _354888], 2485 ^ [_353853, _354888]), _353853)], (2493 ^ _266965) ^ [] : [-(in(ordered_pair(2483 ^ [_353853, _354888], 2484 ^ [_353853, _354888]), _353853))], (2495 ^ _266965) ^ [] : [-(in(ordered_pair(2484 ^ [_353853, _354888], 2485 ^ [_353853, _354888]), _353853))], (2491 ^ _266965) ^ [] : [-(in(2485 ^ [_353853, _354888], _354888))]], -(is_transitive_in(_353853, _354888))]]], (4416 ^ _266965) ^ [_417760, _417762] : [in(_417762, _417760), -(set_union2(singleton(_417762), _417760) = _417760)], (592 ^ _266965) ^ [_286728, _286730, _286732, _286734] : [-(unordered_pair(_286734, _286730) = unordered_pair(_286732, _286728)), _286734 = _286732, _286730 = _286728], (266 ^ _266965) ^ [_275249, _275251] : [-(function(_275249)), _275251 = _275249, function(_275251)], (4691 ^ _266965) ^ [_426800, _426802, _426804] : [-(disjoint(_426804, _426800)), subset(_426804, _426802), disjoint(_426802, _426800)], (2578 ^ _266965) ^ [_358395] : [relation(_358395), 2581 ^ _266965 : [(2588 ^ _266965) ^ [] : [is_reflexive_in(_358395, relation_field(_358395)), -(reflexive(_358395))], (2582 ^ _266965) ^ [] : [reflexive(_358395), -(is_reflexive_in(_358395, relation_field(_358395)))]]], (3432 ^ _266965) ^ [] : [-(ordinal(3424 ^ []))], (650 ^ _266965) ^ [_288907] : [ordinal(_288907), 653 ^ _266965 : [(656 ^ _266965) ^ [] : [-(epsilon_connected(_288907))], (654 ^ _266965) ^ [] : [-(epsilon_transitive(_288907))]]], (4729 ^ _266965) ^ [_427931, _427933] : [set_difference(_427933, singleton(_427931)) = _427933, in(_427931, _427933)], (4386 ^ _266965) ^ [_416762, _416764] : [subset(_416764, _416762), -(_416762 = set_union2(_416764, set_difference(_416762, _416764)))], (232 ^ _266965) ^ [_274215, _274217] : [-(one_to_one(_274215)), _274217 = _274215, one_to_one(_274217)], (574 ^ _266965) ^ [_286046, _286048] : [_286048 = _286046, -(union(_286048) = union(_286046))], (4735 ^ _266965) ^ [_428104, _428106] : [-(in(_428104, _428106)), -(set_difference(_428106, singleton(_428104)) = _428106)], (4029 ^ _266965) ^ [_404751, _404753] : [-(_404753 = _404751), 4033 ^ _266965 : [(4036 ^ _266965) ^ [] : [in(4030 ^ [_404751, _404753], _404751)], (4034 ^ _266965) ^ [] : [-(in(4030 ^ [_404751, _404753], _404753))]], 4037 ^ _266965 : [(4040 ^ _266965) ^ [] : [in(4030 ^ [_404751, _404753], _404753)], (4038 ^ _266965) ^ [] : [-(in(4030 ^ [_404751, _404753], _404751))]]], (4621 ^ _266965) ^ [_424772, _424774] : [relation(_424772), function(_424772), 4636 ^ _266965 : [(4639 ^ _266965) ^ [] : [-(_424774 = apply(relation_composition(function_inverse(_424772), _424772), _424774))], (4637 ^ _266965) ^ [] : [-(_424774 = apply(_424772, apply(function_inverse(_424772), _424774)))]], one_to_one(_424772), in(_424774, relation_rng(_424772))], (2885 ^ _266965) ^ [_366725] : [-(function(identity_relation(_366725)))], (3195 ^ _266965) ^ [_377019] : [relation(_377019), 3198 ^ _266965 : [(3199 ^ _266965) ^ [] : [antisymmetric(_377019), 3202 ^ _266965 : [(3203 ^ _266965) ^ [_377289, _377291] : [-(_377291 = _377289), in(ordered_pair(_377291, _377289), _377019), in(ordered_pair(_377289, _377291), _377019)]]], (3213 ^ _266965) ^ [] : [3216 ^ _266965 : [(3221 ^ _266965) ^ [] : [3214 ^ [_377019] = 3215 ^ [_377019]], (3219 ^ _266965) ^ [] : [-(in(ordered_pair(3215 ^ [_377019], 3214 ^ [_377019]), _377019))], (3217 ^ _266965) ^ [] : [-(in(ordered_pair(3214 ^ [_377019], 3215 ^ [_377019]), _377019))]], -(antisymmetric(_377019))]]], (418 ^ _266965) ^ [_280414, _280416] : [_280416 = _280414, -(succ(_280416) = succ(_280414))], (1255 ^ _266965) ^ [_310798, _310800] : [-(_310800 = empty_set), 1258 ^ _266965 : [(1259 ^ _266965) ^ [] : [_310798 = set_meet(_310800), 1262 ^ _266965 : [(1263 ^ _266965) ^ [_311096] : [in(_311096, _310798), 1266 ^ _266965 : [(1267 ^ _266965) ^ [_311241] : [in(_311241, _310800), -(in(_311096, _311241))]]], (1273 ^ _266965) ^ [_311426] : [1275 ^ _266965 : [(1278 ^ _266965) ^ [] : [in(_311426, 1274 ^ [_310798, _310800, _311426])], (1276 ^ _266965) ^ [] : [-(in(1274 ^ [_310798, _310800, _311426], _310800))]], -(in(_311426, _310798))]]], (1282 ^ _266965) ^ [] : [-(_310798 = set_meet(_310800)), 1286 ^ _266965 : [(1292 ^ _266965) ^ [] : [in(1283 ^ [_310798, _310800], 1288 ^ [_310798, _310800])], (1290 ^ _266965) ^ [] : [-(in(1288 ^ [_310798, _310800], _310800))], (1287 ^ _266965) ^ [] : [-(in(1283 ^ [_310798, _310800], _310798))]], 1293 ^ _266965 : [(1294 ^ _266965) ^ [_312200] : [in(_312200, _310800), -(in(1283 ^ [_310798, _310800], _312200))], (1300 ^ _266965) ^ [] : [in(1283 ^ [_310798, _310800], _310798)]]]]], (1357 ^ _266965) ^ [_314253] : [-(in(1358 ^ [_314253], _314253)), -(_314253 = empty_set)], (1667 ^ _266965) ^ [_325434] : [epsilon_connected(_325434), 1670 ^ _266965 : [(1671 ^ _266965) ^ [_325610, _325612] : [in(_325612, _325434), in(_325610, _325434), -(in(_325612, _325610)), -(_325612 = _325610), -(in(_325610, _325612))]]], (4071 ^ _266965) ^ [_406187, _406189] : [ordinal(_406187), subset(_406189, _406187), -(_406189 = empty_set), 4083 ^ _266965 : [(4088 ^ _266965) ^ [_406739] : [ordinal(_406739), in(_406739, _406189), -(ordinal_subset(4082 ^ [_406187, _406189], _406739))], (4086 ^ _266965) ^ [] : [-(in(4082 ^ [_406187, _406189], _406189))], (4084 ^ _266965) ^ [] : [-(ordinal(4082 ^ [_406187, _406189]))]]], (2348 ^ _266965) ^ [_349837, _349839] : [set_intersection2(_349839, _349837) = empty_set, -(disjoint(_349839, _349837))], (4905 ^ _266965) ^ [_433877, _433879] : [relation(_433877), -(subset(relation_dom_restriction(_433877, _433879), _433877))], (458 ^ _266965) ^ [_281866, _281868] : [_281868 = _281866, -(cast_to_subset(_281868) = cast_to_subset(_281866))], (3295 ^ _266965) ^ [_380415, _380417] : [in(_380417, _380415), -(subset(_380417, union(_380415)))], (2077 ^ _266965) ^ [_339923, _339925, _339927] : [-(_339923 = set_difference(_339927, _339925)), 2089 ^ _266965 : [(2094 ^ _266965) ^ [] : [in(2078 ^ [_339923, _339925, _339927], _339923)], (2092 ^ _266965) ^ [] : [in(2078 ^ [_339923, _339925, _339927], _339925)], (2090 ^ _266965) ^ [] : [-(in(2078 ^ [_339923, _339925, _339927], _339927))]], 2081 ^ _266965 : [(2084 ^ _266965) ^ [] : [in(2078 ^ [_339923, _339925, _339927], _339927), -(in(2078 ^ [_339923, _339925, _339927], _339925))], (2082 ^ _266965) ^ [] : [-(in(2078 ^ [_339923, _339925, _339927], _339923))]]], (412 ^ _266965) ^ [_280196, _280198] : [_280198 = _280196, -(relation_inverse(_280198) = relation_inverse(_280196))], (1320 ^ _266965) ^ [_313002, _313004] : [_313002 = singleton(_313004), 1323 ^ _266965 : [(1330 ^ _266965) ^ [_313344] : [_313344 = _313004, -(in(_313344, _313002))], (1324 ^ _266965) ^ [_313172] : [in(_313172, _313002), -(_313172 = _313004)]]], (562 ^ _266965) ^ [_285610, _285612] : [_285612 = _285610, -(identity_relation(_285612) = identity_relation(_285610))], (1454 ^ _266965) ^ [_317731, _317733] : [-(empty(_317733)), 1457 ^ _266965 : [(1464 ^ _266965) ^ [] : [in(_317731, _317733), -(element(_317731, _317733))], (1458 ^ _266965) ^ [] : [element(_317731, _317733), -(in(_317731, _317733))]]], (4985 ^ _266965) ^ [_436385, _436387] : [in(_436387, _436385), -(subset(_436387, union(_436385)))], (4850 ^ _266965) ^ [_431954, _431956] : [in(_431956, _431954), empty(_431954)], (4828 ^ _266965) ^ [_431261, _431263, _431265, _431267] : [relation(_431261), 4831 ^ _266965 : [(4840 ^ _266965) ^ [] : [-(in(ordered_pair(_431267, _431265), relation_composition(identity_relation(_431263), _431261))), in(_431267, _431263), in(ordered_pair(_431267, _431265), _431261)], (4832 ^ _266965) ^ [] : [in(ordered_pair(_431267, _431265), relation_composition(identity_relation(_431263), _431261)), 4835 ^ _266965 : [(4838 ^ _266965) ^ [] : [-(in(ordered_pair(_431267, _431265), _431261))], (4836 ^ _266965) ^ [] : [-(in(_431267, _431263))]]]]], (256 ^ _266965) ^ [_274954, _274956] : [-(empty(_274954)), _274956 = _274954, empty(_274956)], (1024 ^ _266965) ^ [_302007] : [relation(_302007), 1027 ^ _266965 : [(1028 ^ _266965) ^ [_302214, _302216] : [_302214 = relation_image(_302007, _302216), 1031 ^ _266965 : [(1041 ^ _266965) ^ [_302760] : [-(in(_302760, _302214)), 1042 ^ _266965 : [(1043 ^ _266965) ^ [_302865] : [in(ordered_pair(_302865, _302760), _302007), in(_302865, _302216)]]], (1032 ^ _266965) ^ [_302406] : [in(_302406, _302214), 1036 ^ _266965 : [(1039 ^ _266965) ^ [] : [-(in(1035 ^ [_302007, _302214, _302216, _302406], _302216))], (1037 ^ _266965) ^ [] : [-(in(ordered_pair(1035 ^ [_302007, _302214, _302216, _302406], _302406), _302007))]]]]], (1051 ^ _266965) ^ [_303120, _303122] : [-(_303120 = relation_image(_302007, _303122)), 1064 ^ _266965 : [(1069 ^ _266965) ^ [] : [in(1052 ^ [_302007, _303120, _303122], _303120)], (1067 ^ _266965) ^ [] : [-(in(1063 ^ [_302007, _303120, _303122], _303122))], (1065 ^ _266965) ^ [] : [-(in(ordered_pair(1063 ^ [_302007, _303120, _303122], 1052 ^ [_302007, _303120, _303122]), _302007))]], 1055 ^ _266965 : [(1058 ^ _266965) ^ [_303424] : [in(ordered_pair(_303424, 1052 ^ [_302007, _303120, _303122]), _302007), in(_303424, _303122)], (1056 ^ _266965) ^ [] : [-(in(1052 ^ [_302007, _303120, _303122], _303120))]]]]], (4173 ^ _266965) ^ [_409586] : [relation(_409586), 4176 ^ _266965 : [(4179 ^ _266965) ^ [] : [-(relation_dom(_409586) = relation_rng(relation_inverse(_409586)))], (4177 ^ _266965) ^ [] : [-(relation_rng(_409586) = relation_dom(relation_inverse(_409586)))]]], (4132 ^ _266965) ^ [_408259, _408261] : [relation(_408259), function(_408259), 4139 ^ _266965 : [(4152 ^ _266965) ^ [] : [-(_408259 = identity_relation(_408261)), relation_dom(_408259) = _408261, 4158 ^ _266965 : [(4161 ^ _266965) ^ [] : [apply(_408259, 4157 ^ [_408259, _408261]) = 4157 ^ [_408259, _408261]], (4159 ^ _266965) ^ [] : [-(in(4157 ^ [_408259, _408261], _408261))]]], (4140 ^ _266965) ^ [] : [_408259 = identity_relation(_408261), 4143 ^ _266965 : [(4146 ^ _266965) ^ [_408678] : [in(_408678, _408261), -(apply(_408259, _408678) = _408678)], (4144 ^ _266965) ^ [] : [-(relation_dom(_408259) = _408261)]]]]], (106 ^ _266965) ^ [_270374, _270376] : [-(connected(_270374)), _270376 = _270374, connected(_270376)], (706 ^ _266965) ^ [_290638, _290640] : [-(set_intersection2(_290640, _290638) = set_intersection2(_290638, _290640))], (568 ^ _266965) ^ [_285828, _285830] : [_285830 = _285828, -(relation_rng(_285830) = relation_rng(_285828))], (2756 ^ _266965) ^ [_362655] : [-(relation(identity_relation(_362655)))], (484 ^ _266965) ^ [_282802, _282804] : [_282804 = _282802, -(function_inverse(_282804) = function_inverse(_282802))], (3692 ^ _266965) ^ [_393872, _393874] : [relation(_393872), subset(_393874, relation_dom(_393872)), -(subset(_393874, relation_inverse_image(_393872, relation_image(_393872, _393874))))], (3702 ^ _266965) ^ [_394171] : [relation(_394171), -(relation_image(_394171, relation_dom(_394171)) = relation_rng(_394171))], (160 ^ _266965) ^ [_271998, _272000] : [-(ordinal(_271998)), _272000 = _271998, ordinal(_272000)], (3446 ^ _266965) ^ [_385273, _385275] : [element(_385273, powerset(powerset(_385275))), -(union_of_subsets(_385275, _385273) = union(_385273))], (3641 ^ _266965) ^ [_392119, _392121, _392123] : [relation(_392119), 3644 ^ _266965 : [(3656 ^ _266965) ^ [] : [-(in(_392123, relation_image(_392119, _392121))), 3657 ^ _266965 : [(3658 ^ _266965) ^ [_392720] : [in(_392720, relation_dom(_392119)), in(ordered_pair(_392720, _392123), _392119), in(_392720, _392121)]]], (3645 ^ _266965) ^ [] : [in(_392123, relation_image(_392119, _392121)), 3649 ^ _266965 : [(3654 ^ _266965) ^ [] : [-(in(3648 ^ [_392119, _392121, _392123], _392121))], (3652 ^ _266965) ^ [] : [-(in(ordered_pair(3648 ^ [_392119, _392121, _392123], _392123), _392119))], (3650 ^ _266965) ^ [] : [-(in(3648 ^ [_392119, _392121, _392123], relation_dom(_392119)))]]]]], (4921 ^ _266965) ^ [_434402, _434404, _434406] : [relation(_434402), function(_434402), 4928 ^ _266965 : [(4937 ^ _266965) ^ [] : [-(in(ordered_pair(_434406, _434404), _434402)), in(_434406, relation_dom(_434402)), _434404 = apply(_434402, _434406)], (4929 ^ _266965) ^ [] : [in(ordered_pair(_434406, _434404), _434402), 4932 ^ _266965 : [(4935 ^ _266965) ^ [] : [-(_434404 = apply(_434402, _434406))], (4933 ^ _266965) ^ [] : [-(in(_434406, relation_dom(_434402)))]]]]], (1211 ^ _266965) ^ [_309044] : [relation(_309044), 1214 ^ _266965 : [(1215 ^ _266965) ^ [_309192] : [in(_309192, _309044), -(_309192 = ordered_pair(1218 ^ [_309044, _309192], 1219 ^ [_309044, _309192]))]]], (3225 ^ _266965) ^ [_378069, _378071, _378073] : [subset(_378073, _378071), -(in(_378069, _378073)), -(subset(_378073, set_difference(_378071, singleton(_378069))))], (3609 ^ _266965) ^ [_390998, _391000, _391002] : [-(in(_390998, 3605 ^ [_391002])), in(_391000, 3605 ^ [_391002]), subset(_390998, _391000)], (4456 ^ _266965) ^ [_419104, _419106] : [-(set_difference(_419106, set_difference(_419106, _419104)) = set_intersection2(_419106, _419104))], (4911 ^ _266965) ^ [_434091, _434093] : [empty(_434093), -(_434093 = _434091), empty(_434091)], (2680 ^ _266965) ^ [_360698, _360700] : [relation(_360700), -(relation(relation_restriction(_360700, _360698)))], (4044 ^ _266965) ^ [_405252] : [-(subset(empty_set, _405252))], (3371 ^ _266965) ^ [_382902] : [-(empty(_382902)), 3375 ^ _266965 : [(3378 ^ _266965) ^ [] : [empty(3374 ^ [_382902])], (3376 ^ _266965) ^ [] : [-(element(3374 ^ [_382902], powerset(_382902)))]]], (4235 ^ _266965) ^ [_411714, _411716] : [4236 ^ _266965 : [(4239 ^ _266965) ^ [] : [_411716 = singleton(_411714)], (4237 ^ _266965) ^ [] : [_411716 = empty_set]], -(subset(_411716, singleton(_411714)))], (1968 ^ _266965) ^ [_336304] : [-(cast_to_subset(_336304) = _336304)], (3452 ^ _266965) ^ [_385501, _385503] : [element(_385501, powerset(powerset(_385503))), -(meet_of_subsets(_385503, _385501) = set_meet(_385501))], (3388 ^ _266965) ^ [] : [-(function(3382 ^ []))], (242 ^ _266965) ^ [_274538, _274540, _274542, _274544] : [-(disjoint(_274542, _274538)), disjoint(_274544, _274540), _274544 = _274542, _274540 = _274538], (2188 ^ _266965) ^ [_344147, _344149] : [element(_344147, powerset(_344149)), -(subset_complement(_344149, _344147) = set_difference(_344149, _344147))], (3444 ^ _266965) ^ [] : [-(function(3438 ^ []))], (520 ^ _266965) ^ [_284097, _284099] : [_284099 = _284097, -(relation_field(_284099) = relation_field(_284097))], (3803 ^ _266965) ^ [_397464, _397466, _397468] : [relation(_397464), subset(_397468, _397466), -(subset(relation_inverse_image(_397464, _397468), relation_inverse_image(_397464, _397466)))], (136 ^ _266965) ^ [_271259, _271261] : [-(epsilon_transitive(_271259)), _271261 = _271259, epsilon_transitive(_271261)], (2394 ^ _266965) ^ [_351351] : [relation(_351351), 2397 ^ _266965 : [(2398 ^ _266965) ^ [_351536] : [relation(_351536), 2401 ^ _266965 : [(2402 ^ _266965) ^ [_351717] : [relation(_351717), 2405 ^ _266965 : [(2406 ^ _266965) ^ [] : [_351717 = relation_composition(_351351, _351536), 2409 ^ _266965 : [(2419 ^ _266965) ^ [_352437, _352439] : [-(in(ordered_pair(_352439, _352437), _351717)), 2420 ^ _266965 : [(2421 ^ _266965) ^ [_352550] : [in(ordered_pair(_352439, _352550), _351351), in(ordered_pair(_352550, _352437), _351536)]]], (2410 ^ _266965) ^ [_352052, _352054] : [in(ordered_pair(_352054, _352052), _351717), 2414 ^ _266965 : [(2417 ^ _266965) ^ [] : [-(in(ordered_pair(2413 ^ [_351351, _351536, _351717, _352052, _352054], _352052), _351536))], (2415 ^ _266965) ^ [] : [-(in(ordered_pair(_352054, 2413 ^ [_351351, _351536, _351717, _352052, _352054]), _351351))]]]]], (2429 ^ _266965) ^ [] : [-(_351717 = relation_composition(_351351, _351536)), 2443 ^ _266965 : [(2448 ^ _266965) ^ [] : [in(ordered_pair(2430 ^ [_351351, _351536, _351717], 2431 ^ [_351351, _351536, _351717]), _351717)], (2446 ^ _266965) ^ [] : [-(in(ordered_pair(2442 ^ [_351351, _351536, _351717], 2431 ^ [_351351, _351536, _351717]), _351536))], (2444 ^ _266965) ^ [] : [-(in(ordered_pair(2430 ^ [_351351, _351536, _351717], 2442 ^ [_351351, _351536, _351717]), _351351))]], 2434 ^ _266965 : [(2437 ^ _266965) ^ [_353181] : [in(ordered_pair(2430 ^ [_351351, _351536, _351717], _353181), _351351), in(ordered_pair(_353181, 2431 ^ [_351351, _351536, _351717]), _351536)], (2435 ^ _266965) ^ [] : [-(in(ordered_pair(2430 ^ [_351351, _351536, _351717], 2431 ^ [_351351, _351536, _351717]), _351717))]]]]]]]]], (3564 ^ _266965) ^ [_389210, _389212] : [relation(_389210), -(subset(relation_rng_restriction(_389212, _389210), _389210))], (5008 ^ _266965) ^ [_437369, _437371, _437373] : [-(in(_437369, 5004 ^ [_437373])), in(_437371, 5004 ^ [_437373]), subset(_437369, _437371)], (2899 ^ _266965) ^ [] : [-(epsilon_connected(empty_set))], (602 ^ _266965) ^ [_287087, _287089, _287091, _287093] : [-(relation_restriction(_287093, _287089) = relation_restriction(_287091, _287087)), _287093 = _287091, _287089 = _287087], (3536 ^ _266965) ^ [_388333, _388335, _388337] : [relation(_388333), 3539 ^ _266965 : [(3548 ^ _266965) ^ [] : [-(in(_388337, relation_rng(relation_rng_restriction(_388335, _388333)))), in(_388337, _388335), in(_388337, relation_rng(_388333))], (3540 ^ _266965) ^ [] : [in(_388337, relation_rng(relation_rng_restriction(_388335, _388333))), 3543 ^ _266965 : [(3546 ^ _266965) ^ [] : [-(in(_388337, relation_rng(_388333)))], (3544 ^ _266965) ^ [] : [-(in(_388337, _388335))]]]]], (2805 ^ _266965) ^ [_364238] : [-(element(2803 ^ [_364238], _364238))], (48 ^ _266965) ^ [_268629, _268631, _268633, _268635] : [-(is_transitive_in(_268633, _268629)), is_transitive_in(_268635, _268631), _268635 = _268633, _268631 = _268629], (2242 ^ _266965) ^ [_345857] : [_345857 = union(_345857), -(being_limit_ordinal(_345857))], (5003 ^ _266965) ^ [_437016] : [-(union(powerset(_437016)) = _437016)], (905 ^ _266965) ^ [_297846, _297848] : [relation(_297846), 908 ^ _266965 : [(909 ^ _266965) ^ [_298017] : [relation(_298017), 912 ^ _266965 : [(913 ^ _266965) ^ [] : [_298017 = relation_rng_restriction(_297848, _297846), 916 ^ _266965 : [(925 ^ _266965) ^ [_298623, _298625] : [-(in(ordered_pair(_298625, _298623), _298017)), in(_298623, _297848), in(ordered_pair(_298625, _298623), _297846)], (917 ^ _266965) ^ [_298344, _298346] : [in(ordered_pair(_298346, _298344), _298017), 920 ^ _266965 : [(923 ^ _266965) ^ [] : [-(in(ordered_pair(_298346, _298344), _297846))], (921 ^ _266965) ^ [] : [-(in(_298344, _297848))]]]]], (935 ^ _266965) ^ [] : [-(_298017 = relation_rng_restriction(_297848, _297846)), 948 ^ _266965 : [(953 ^ _266965) ^ [] : [in(ordered_pair(936 ^ [_297846, _297848, _298017], 937 ^ [_297846, _297848, _298017]), _298017)], (951 ^ _266965) ^ [] : [-(in(ordered_pair(936 ^ [_297846, _297848, _298017], 937 ^ [_297846, _297848, _298017]), _297846))], (949 ^ _266965) ^ [] : [-(in(937 ^ [_297846, _297848, _298017], _297848))]], 940 ^ _266965 : [(943 ^ _266965) ^ [] : [in(937 ^ [_297846, _297848, _298017], _297848), in(ordered_pair(936 ^ [_297846, _297848, _298017], 937 ^ [_297846, _297848, _298017]), _297846)], (941 ^ _266965) ^ [] : [-(in(ordered_pair(936 ^ [_297846, _297848, _298017], 937 ^ [_297846, _297848, _298017]), _298017))]]]]]]], (1073 ^ _266965) ^ [_304026] : [relation(_304026), 1076 ^ _266965 : [(1077 ^ _266965) ^ [_304233, _304235] : [_304233 = relation_inverse_image(_304026, _304235), 1080 ^ _266965 : [(1090 ^ _266965) ^ [_304779] : [-(in(_304779, _304233)), 1091 ^ _266965 : [(1092 ^ _266965) ^ [_304884] : [in(ordered_pair(_304779, _304884), _304026), in(_304884, _304235)]]], (1081 ^ _266965) ^ [_304425] : [in(_304425, _304233), 1085 ^ _266965 : [(1088 ^ _266965) ^ [] : [-(in(1084 ^ [_304026, _304233, _304235, _304425], _304235))], (1086 ^ _266965) ^ [] : [-(in(ordered_pair(_304425, 1084 ^ [_304026, _304233, _304235, _304425]), _304026))]]]]], (1100 ^ _266965) ^ [_305139, _305141] : [-(_305139 = relation_inverse_image(_304026, _305141)), 1113 ^ _266965 : [(1118 ^ _266965) ^ [] : [in(1101 ^ [_304026, _305139, _305141], _305139)], (1116 ^ _266965) ^ [] : [-(in(1112 ^ [_304026, _305139, _305141], _305141))], (1114 ^ _266965) ^ [] : [-(in(ordered_pair(1101 ^ [_304026, _305139, _305141], 1112 ^ [_304026, _305139, _305141]), _304026))]], 1104 ^ _266965 : [(1107 ^ _266965) ^ [_305443] : [in(ordered_pair(1101 ^ [_304026, _305139, _305141], _305443), _304026), in(_305443, _305141)], (1105 ^ _266965) ^ [] : [-(in(1101 ^ [_304026, _305139, _305141], _305139))]]]]], (3428 ^ _266965) ^ [] : [-(epsilon_transitive(3424 ^ []))], (586 ^ _266965) ^ [_286482, _286484] : [_286484 = _286482, -(singleton(_286484) = singleton(_286482))], (3421 ^ _266965) ^ [] : [-(function(3417 ^ []))], (4017 ^ _266965) ^ [_404343] : [-(set_intersection2(_404343, empty_set) = empty_set)], (3849 ^ _266965) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2618 ^ _266965) ^ [] : [true___, -(true___)], (2194 ^ _266965) ^ [_344358, _344360] : [-(ordered_pair(_344360, _344358) = unordered_pair(unordered_pair(_344360, _344358), singleton(_344360)))], (3526 ^ _266965) ^ [_387983, _387985, _387987, _387989] : [unordered_pair(_387989, _387987) = unordered_pair(_387985, _387983), -(_387989 = _387985), -(_387989 = _387983)], (3911 ^ _266965) ^ [_400954] : [relation(_400954), -(subset(_400954, cartesian_product2(relation_dom(_400954), relation_rng(_400954))))], (5031 ^ _266965) ^ [_438203, _438205] : [subset(_438203, 5004 ^ [_438205]), -(are_equipotent(_438203, 5004 ^ [_438205])), -(in(_438203, 5004 ^ [_438205]))], (3722 ^ _266965) ^ [_394775] : [relation(_394775), 3725 ^ _266965 : [(3726 ^ _266965) ^ [_394915] : [relation(_394915), -(relation_rng(relation_composition(_394775, _394915)) = relation_image(_394915, relation_rng(_394775)))]]], (3524 ^ _266965) ^ [_387846] : [-(in(_387846, succ(_387846)))], (4346 ^ _266965) ^ [_415408, _415410] : [element(_415408, powerset(_415410)), 4349 ^ _266965 : [(4350 ^ _266965) ^ [_415560] : [element(_415560, powerset(_415410)), 4353 ^ _266965 : [(4360 ^ _266965) ^ [] : [subset(_415408, subset_complement(_415410, _415560)), -(disjoint(_415408, _415560))], (4354 ^ _266965) ^ [] : [disjoint(_415408, _415560), -(subset(_415408, subset_complement(_415410, _415560)))]]]]], (3686 ^ _266965) ^ [_393642, _393644] : [relation(_393642), -(relation_image(_393642, _393644) = relation_image(_393642, set_intersection2(relation_dom(_393642), _393644)))], (3514 ^ _266965) ^ [_387542, _387544, _387546, _387548] : [-(in(ordered_pair(_387548, _387546), cartesian_product2(_387544, _387542))), in(_387548, _387544), in(_387546, _387542)], (3833 ^ _266965) ^ [_398516, _398518] : [in(_398518, _398516), -(element(_398518, _398516))], (536 ^ _266965) ^ [_284702, _284704, _284706, _284708] : [-(set_intersection2(_284708, _284704) = set_intersection2(_284706, _284702)), _284708 = _284706, _284704 = _284702], (2642 ^ _266965) ^ [] : [true___, -(true___)], (2901 ^ _266965) ^ [] : [-(ordinal(empty_set))], (3416 ^ _266965) ^ [] : [empty(3414 ^ [])], (4366 ^ _266965) ^ [_416044] : [relation(_416044), 4369 ^ _266965 : [(4370 ^ _266965) ^ [_416181] : [relation(_416181), -(subset(relation_dom(relation_composition(_416044, _416181)), relation_dom(_416044)))]]], (2342 ^ _266965) ^ [_349669, _349671] : [disjoint(_349671, _349669), -(set_intersection2(_349671, _349669) = empty_set)], (2895 ^ _266965) ^ [] : [-(empty(empty_set))], (1705 ^ _266965) ^ [_326778] : [relation(_326778), 1708 ^ _266965 : [(1709 ^ _266965) ^ [_326936] : [relation(_326936), 1712 ^ _266965 : [(1713 ^ _266965) ^ [] : [subset(_326778, _326936), 1716 ^ _266965 : [(1717 ^ _266965) ^ [_327212, _327214] : [in(ordered_pair(_327214, _327212), _326778), -(in(ordered_pair(_327214, _327212), _326936))]]], (1723 ^ _266965) ^ [] : [1726 ^ _266965 : [(1729 ^ _266965) ^ [] : [in(ordered_pair(1724 ^ [_326778, _326936], 1725 ^ [_326778, _326936]), _326936)], (1727 ^ _266965) ^ [] : [-(in(ordered_pair(1724 ^ [_326778, _326936], 1725 ^ [_326778, _326936]), _326778))]], -(subset(_326778, _326936))]]]]], (2893 ^ _266965) ^ [] : [-(one_to_one(empty_set))], (2728 ^ _266965) ^ [] : [true___, -(true___)], (3419 ^ _266965) ^ [] : [-(relation(3417 ^ []))], (2151 ^ _266965) ^ [_342692] : [relation(_342692), 2154 ^ _266965 : [(2155 ^ _266965) ^ [_342873] : [_342873 = relation_rng(_342692), 2158 ^ _266965 : [(2166 ^ _266965) ^ [_343297] : [2167 ^ _266965 : [(2168 ^ _266965) ^ [_343376] : [in(ordered_pair(_343376, _343297), _342692)]], -(in(_343297, _342873))], (2159 ^ _266965) ^ [_343053] : [in(_343053, _342873), -(in(ordered_pair(2162 ^ [_342692, _342873, _343053], _343053), _342692))]]], (2172 ^ _266965) ^ [_343504] : [-(_343504 = relation_rng(_342692)), 2176 ^ _266965 : [(2179 ^ _266965) ^ [_343767] : [in(ordered_pair(_343767, 2173 ^ [_342692, _343504]), _342692)], (2177 ^ _266965) ^ [] : [-(in(2173 ^ [_342692, _343504], _343504))]], 2181 ^ _266965 : [(2184 ^ _266965) ^ [] : [in(2173 ^ [_342692, _343504], _343504)], (2182 ^ _266965) ^ [] : [-(in(ordered_pair(2180 ^ [_342692, _343504], 2173 ^ [_342692, _343504]), _342692))]]]]], (3087 ^ _266965) ^ [_373217] : [relation(_373217), 3090 ^ _266965 : [(3091 ^ _266965) ^ [] : [reflexive(_373217), 3094 ^ _266965 : [(3095 ^ _266965) ^ [_373461] : [in(_373461, relation_field(_373217)), -(in(ordered_pair(_373461, _373461), _373217))]]], (3101 ^ _266965) ^ [] : [3103 ^ _266965 : [(3106 ^ _266965) ^ [] : [in(ordered_pair(3102 ^ [_373217], 3102 ^ [_373217]), _373217)], (3104 ^ _266965) ^ [] : [-(in(3102 ^ [_373217], relation_field(_373217)))]], -(reflexive(_373217))]]], (2959 ^ _266965) ^ [_368994, _368996] : [empty(unordered_pair(_368996, _368994))], (4483 ^ _266965) ^ [_420110] : [-(_420110 = empty_set), 4486 ^ _266965 : [(4487 ^ _266965) ^ [_420270] : [element(_420270, powerset(_420110)), 4490 ^ _266965 : [(4491 ^ _266965) ^ [_420424] : [element(_420424, _420110), -(in(_420424, _420270)), -(in(_420424, subset_complement(_420110, _420270)))]]]]], (3413 ^ _266965) ^ [_384233] : [-(empty(3409 ^ [_384233]))], (4225 ^ _266965) ^ [_411454, _411456] : [subset(_411456, singleton(_411454)), -(_411456 = empty_set), -(_411456 = singleton(_411454))], (4470 ^ _266965) ^ [_419650, _419652] : [-(disjoint(_419652, _419650)), -(in(4473 ^ [_419650, _419652], set_intersection2(_419652, _419650)))], (194 ^ _266965) ^ [_273032, _273034] : [-(well_founded_relation(_273032)), _273034 = _273032, well_founded_relation(_273034)], (3161 ^ _266965) ^ [_375870, _375872] : [subset(singleton(_375872), _375870), -(in(_375872, _375870))], (4187 ^ _266965) ^ [_410082, _410084] : [subset(_410084, _410082), -(set_difference(_410084, _410082) = empty_set)], (3821 ^ _266965) ^ [_398120, _398122, _398124] : [-(subset(_398124, set_intersection2(_398122, _398120))), subset(_398124, _398122), subset(_398124, _398120)], (644 ^ _266965) ^ [_288721] : [empty(_288721), -(function(_288721))], (3319 ^ _266965) ^ [_381284, _381286] : [3321 ^ _266965 : [(3324 ^ _266965) ^ [] : [in(3320 ^ [_381284, _381286], _381284)], (3322 ^ _266965) ^ [] : [-(in(3320 ^ [_381284, _381286], _381286))]], -(element(_381286, powerset(_381284)))], (580 ^ _266965) ^ [_286264, _286266] : [_286266 = _286264, -(powerset(_286266) = powerset(_286264))], (2915 ^ _266965) ^ [_367650, _367652] : [-(empty(_367652)), empty(set_union2(_367652, _367650))], (3287 ^ _266965) ^ [_380121, _380123] : [3288 ^ _266965 : [(3291 ^ _266965) ^ [] : [_380123 = singleton(_380121)], (3289 ^ _266965) ^ [] : [_380123 = empty_set]], -(subset(_380123, singleton(_380121)))], (204 ^ _266965) ^ [_273355, _273357, _273359, _273361] : [-(is_well_founded_in(_273359, _273355)), is_well_founded_in(_273361, _273357), _273361 = _273359, _273357 = _273355], (4501 ^ _266965) ^ [_420742] : [relation(_420742), function(_420742), one_to_one(_420742), 4512 ^ _266965 : [(4513 ^ _266965) ^ [_421129] : [relation(_421129), function(_421129), 4520 ^ _266965 : [(4521 ^ _266965) ^ [] : [_421129 = function_inverse(_420742), 4524 ^ _266965 : [(4539 ^ _266965) ^ [_422020, _422022] : [4546 ^ _266965 : [(4549 ^ _266965) ^ [] : [-(_422020 = apply(_421129, _422022))], (4547 ^ _266965) ^ [] : [-(in(_422022, relation_rng(_420742)))]], in(_422020, relation_dom(_420742)), _422022 = apply(_420742, _422020)], (4527 ^ _266965) ^ [_421646, _421648] : [4534 ^ _266965 : [(4537 ^ _266965) ^ [] : [-(_421648 = apply(_420742, _421646))], (4535 ^ _266965) ^ [] : [-(in(_421646, relation_dom(_420742)))]], in(_421648, relation_rng(_420742)), _421646 = apply(_421129, _421648)], (4525 ^ _266965) ^ [] : [-(relation_dom(_421129) = relation_rng(_420742))]]], (4551 ^ _266965) ^ [] : [-(_421129 = function_inverse(_420742)), relation_dom(_421129) = relation_rng(_420742), 4560 ^ _266965 : [(4565 ^ _266965) ^ [] : [in(4557 ^ [_420742, _421129], relation_dom(_420742)), 4556 ^ [_420742, _421129] = apply(_420742, 4557 ^ [_420742, _421129])], (4563 ^ _266965) ^ [] : [-(4557 ^ [_420742, _421129] = apply(_421129, 4556 ^ [_420742, _421129]))], (4561 ^ _266965) ^ [] : [-(in(4556 ^ [_420742, _421129], relation_rng(_420742)))]], 4570 ^ _266965 : [(4575 ^ _266965) ^ [] : [in(4556 ^ [_420742, _421129], relation_rng(_420742)), 4557 ^ [_420742, _421129] = apply(_421129, 4556 ^ [_420742, _421129])], (4573 ^ _266965) ^ [] : [-(4556 ^ [_420742, _421129] = apply(_420742, 4557 ^ [_420742, _421129]))], (4571 ^ _266965) ^ [] : [-(in(4557 ^ [_420742, _421129], relation_dom(_420742)))]]]]]]], (1879 ^ _266965) ^ [_332970] : [-(ordinal(_332970)), epsilon_transitive(_332970), epsilon_connected(_332970)], (4011 ^ _266965) ^ [_404156, _404158] : [subset(_404158, _404156), -(set_intersection2(_404158, _404156) = _404158)], (1395 ^ _266965) ^ [_315616] : [epsilon_transitive(_315616), 1398 ^ _266965 : [(1399 ^ _266965) ^ [_315747] : [in(_315747, _315616), -(subset(_315747, _315616))]]], (2829 ^ _266965) ^ [] : [-(relation(empty_set))], (1970 ^ _266965) ^ [_336442, _336444] : [_336442 = union(_336444), 1973 ^ _266965 : [(1983 ^ _266965) ^ [_336950] : [-(in(_336950, _336442)), 1984 ^ _266965 : [(1985 ^ _266965) ^ [_337048] : [in(_336950, _337048), in(_337048, _336444)]]], (1974 ^ _266965) ^ [_336623] : [in(_336623, _336442), 1978 ^ _266965 : [(1981 ^ _266965) ^ [] : [-(in(1977 ^ [_336442, _336444, _336623], _336444))], (1979 ^ _266965) ^ [] : [-(in(_336623, 1977 ^ [_336442, _336444, _336623]))]]]]], (4871 ^ _266965) ^ [_432818, _432820] : [disjoint(_432820, _432818), -(set_difference(_432820, _432818) = _432820)], (2881 ^ _266965) ^ [_366578, _366580] : [empty(ordered_pair(_366580, _366578))], (5018 ^ _266965) ^ [_437684, _437686] : [in(_437684, 5004 ^ [_437686]), 5022 ^ _266965 : [(5025 ^ _266965) ^ [_437996] : [subset(_437996, _437684), -(in(_437996, 5021 ^ [_437684, _437686]))], (5023 ^ _266965) ^ [] : [-(in(5021 ^ [_437684, _437686], 5004 ^ [_437686]))]]], (2961 ^ _266965) ^ [_369105, _369107] : [-(empty(_369107)), empty(set_union2(_369105, _369107))], (1405 ^ _266965) ^ [_315916] : [1407 ^ _266965 : [(1410 ^ _266965) ^ [] : [subset(1406 ^ [_315916], _315916)], (1408 ^ _266965) ^ [] : [-(in(1406 ^ [_315916], _315916))]], -(epsilon_transitive(_315916))], (3670 ^ _266965) ^ [_393117, _393119] : [relation(_393117), -(subset(relation_image(_393117, _393119), relation_rng(_393117)))], (4046 ^ _266965) ^ [_405373, _405375, _405377] : [relation(_405373), in(ordered_pair(_405377, _405375), _405373), 4053 ^ _266965 : [(4056 ^ _266965) ^ [] : [-(in(_405375, relation_field(_405373)))], (4054 ^ _266965) ^ [] : [-(in(_405377, relation_field(_405373)))]]], (2698 ^ _266965) ^ [] : [true___, -(true___)], (1508 ^ _266965) ^ [_319369, _319371, _319373] : [-(_319369 = unordered_pair(_319373, _319371)), 1512 ^ _266965 : [(1517 ^ _266965) ^ [] : [1509 ^ [_319369, _319371, _319373] = _319371], (1515 ^ _266965) ^ [] : [1509 ^ [_319369, _319371, _319373] = _319373], (1513 ^ _266965) ^ [] : [-(in(1509 ^ [_319369, _319371, _319373], _319369))]], 1518 ^ _266965 : [(1519 ^ _266965) ^ [] : [-(1509 ^ [_319369, _319371, _319373] = _319373), -(1509 ^ [_319369, _319371, _319373] = _319371)], (1525 ^ _266965) ^ [] : [in(1509 ^ [_319369, _319371, _319373], _319369)]]], (3440 ^ _266965) ^ [] : [-(relation(3438 ^ []))], (1587 ^ _266965) ^ [_322120, _322122, _322124] : [-(_322120 = set_union2(_322124, _322122)), 1591 ^ _266965 : [(1596 ^ _266965) ^ [] : [in(1588 ^ [_322120, _322122, _322124], _322122)], (1594 ^ _266965) ^ [] : [in(1588 ^ [_322120, _322122, _322124], _322124)], (1592 ^ _266965) ^ [] : [-(in(1588 ^ [_322120, _322122, _322124], _322120))]], 1597 ^ _266965 : [(1598 ^ _266965) ^ [] : [-(in(1588 ^ [_322120, _322122, _322124], _322124)), -(in(1588 ^ [_322120, _322122, _322124], _322122))], (1604 ^ _266965) ^ [] : [in(1588 ^ [_322120, _322122, _322124], _322120)]]], (4255 ^ _266965) ^ [_412440, _412442] : [element(_412442, powerset(_412440)), -(subset(_412442, _412440))], (3025 ^ _266965) ^ [_371093] : [empty(relation_rng(_371093)), -(empty(_371093)), relation(_371093)], (2546 ^ _266965) ^ [_357503, _357505] : [proper_subset(_357505, _357503), 2549 ^ _266965 : [(2552 ^ _266965) ^ [] : [_357505 = _357503], (2550 ^ _266965) ^ [] : [-(subset(_357505, _357503))]]], (3468 ^ _266965) ^ [_386074, _386076] : [ordinal(_386076), ordinal(_386074), 3475 ^ _266965 : [(3482 ^ _266965) ^ [] : [subset(_386076, _386074), -(ordinal_subset(_386076, _386074))], (3476 ^ _266965) ^ [] : [ordinal_subset(_386076, _386074), -(subset(_386076, _386074))]]], (840 ^ _266965) ^ [_295290] : [relation(_295290), function(_295290), 847 ^ _266965 : [(848 ^ _266965) ^ [_295588, _295590] : [_295588 = relation_image(_295290, _295590), 851 ^ _266965 : [(863 ^ _266965) ^ [_296243] : [-(in(_296243, _295588)), 864 ^ _266965 : [(865 ^ _266965) ^ [_296356] : [in(_296356, relation_dom(_295290)), in(_296356, _295590), _296243 = apply(_295290, _296356)]]], (852 ^ _266965) ^ [_295788] : [in(_295788, _295588), 856 ^ _266965 : [(861 ^ _266965) ^ [] : [-(_295788 = apply(_295290, 855 ^ [_295290, _295588, _295590, _295788]))], (859 ^ _266965) ^ [] : [-(in(855 ^ [_295290, _295588, _295590, _295788], _295590))], (857 ^ _266965) ^ [] : [-(in(855 ^ [_295290, _295588, _295590, _295788], relation_dom(_295290)))]]]]], (877 ^ _266965) ^ [_296716, _296718] : [-(_296716 = relation_image(_295290, _296718)), 894 ^ _266965 : [(897 ^ _266965) ^ [] : [-(in(893 ^ [_295290, _296716, _296718], _296718))], (899 ^ _266965) ^ [] : [-(878 ^ [_295290, _296716, _296718] = apply(_295290, 893 ^ [_295290, _296716, _296718]))], (901 ^ _266965) ^ [] : [in(878 ^ [_295290, _296716, _296718], _296716)], (895 ^ _266965) ^ [] : [-(in(893 ^ [_295290, _296716, _296718], relation_dom(_295290)))]], 881 ^ _266965 : [(884 ^ _266965) ^ [_297036] : [in(_297036, relation_dom(_295290)), in(_297036, _296718), 878 ^ [_295290, _296716, _296718] = apply(_295290, _297036)], (882 ^ _266965) ^ [] : [-(in(878 ^ [_295290, _296716, _296718], _296716))]]]]], (314 ^ _266965) ^ [_276755, _276757, _276759, _276761] : [-(are_equipotent(_276759, _276755)), are_equipotent(_276761, _276757), _276761 = _276759, _276757 = _276755], (2979 ^ _266965) ^ [_369685] : [ordinal(_369685), 2982 ^ _266965 : [(2987 ^ _266965) ^ [] : [-(ordinal(union(_369685)))], (2985 ^ _266965) ^ [] : [-(epsilon_connected(union(_369685)))], (2983 ^ _266965) ^ [] : [-(epsilon_transitive(union(_369685)))]]], (3435 ^ _266965) ^ [] : [-(relation(3433 ^ []))], (2196 ^ _266965) ^ [_344464] : [relation(_344464), 2199 ^ _266965 : [(2214 ^ _266965) ^ [_345109] : [-(well_orders(_344464, _345109)), is_reflexive_in(_344464, _345109), is_transitive_in(_344464, _345109), is_antisymmetric_in(_344464, _345109), is_connected_in(_344464, _345109), is_well_founded_in(_344464, _345109)], (2200 ^ _266965) ^ [_344648] : [well_orders(_344464, _344648), 2203 ^ _266965 : [(2204 ^ _266965) ^ [] : [-(is_reflexive_in(_344464, _344648))], (2208 ^ _266965) ^ [] : [-(is_antisymmetric_in(_344464, _344648))], (2212 ^ _266965) ^ [] : [-(is_well_founded_in(_344464, _344648))], (2210 ^ _266965) ^ [] : [-(is_connected_in(_344464, _344648))], (2206 ^ _266965) ^ [] : [-(is_transitive_in(_344464, _344648))]]]]], (4165 ^ _266965) ^ [_409283, _409285] : [in(_409283, _409285), -(apply(identity_relation(_409285), _409283) = _409283)], (2845 ^ _266965) ^ [_365534, _365536] : [2860 ^ _266965 : [(2863 ^ _266965) ^ [] : [-(function(relation_composition(_365536, _365534)))], (2861 ^ _266965) ^ [] : [-(relation(relation_composition(_365536, _365534)))]], relation(_365536), function(_365536), relation(_365534), function(_365534)], (1486 ^ _266965) ^ [_318644, _318646, _318648] : [_318644 = unordered_pair(_318648, _318646), 1489 ^ _266965 : [(1490 ^ _266965) ^ [_318826] : [in(_318826, _318644), -(_318826 = _318648), -(_318826 = _318646)], (1500 ^ _266965) ^ [_319104] : [1501 ^ _266965 : [(1504 ^ _266965) ^ [] : [_319104 = _318646], (1502 ^ _266965) ^ [] : [_319104 = _318648]], -(in(_319104, _318644))]]], (1304 ^ _266965) ^ [_312505, _312507] : [_312507 = empty_set, 1307 ^ _266965 : [(1314 ^ _266965) ^ [] : [_312505 = empty_set, -(_312505 = set_meet(_312507))], (1308 ^ _266965) ^ [] : [_312505 = set_meet(_312507), -(_312505 = empty_set)]]], (2055 ^ _266965) ^ [_339192, _339194, _339196] : [_339192 = set_difference(_339196, _339194), 2058 ^ _266965 : [(2067 ^ _266965) ^ [_339636] : [-(in(_339636, _339192)), in(_339636, _339196), -(in(_339636, _339194))], (2059 ^ _266965) ^ [_339376] : [in(_339376, _339192), 2062 ^ _266965 : [(2065 ^ _266965) ^ [] : [in(_339376, _339194)], (2063 ^ _266965) ^ [] : [-(in(_339376, _339196))]]]]], (3277 ^ _266965) ^ [_379861, _379863] : [subset(_379863, singleton(_379861)), -(_379863 = empty_set), -(_379863 = singleton(_379861))], (3130 ^ _266965) ^ [_374671] : [relation(_374671), 3133 ^ _266965 : [(3134 ^ _266965) ^ [] : [transitive(_374671), 3137 ^ _266965 : [(3138 ^ _266965) ^ [_374963, _374965, _374967] : [-(in(ordered_pair(_374967, _374963), _374671)), in(ordered_pair(_374967, _374965), _374671), in(ordered_pair(_374965, _374963), _374671)]]], (3148 ^ _266965) ^ [] : [3152 ^ _266965 : [(3157 ^ _266965) ^ [] : [in(ordered_pair(3149 ^ [_374671], 3151 ^ [_374671]), _374671)], (3155 ^ _266965) ^ [] : [-(in(ordered_pair(3150 ^ [_374671], 3151 ^ [_374671]), _374671))], (3153 ^ _266965) ^ [] : [-(in(ordered_pair(3149 ^ [_374671], 3150 ^ [_374671]), _374671))]], -(transitive(_374671))]]], (20 ^ _266965) ^ [_267741, _267743, _267745, _267747] : [-(is_antisymmetric_in(_267745, _267741)), is_antisymmetric_in(_267747, _267743), _267747 = _267745, _267743 = _267741], (1336 ^ _266965) ^ [_313523, _313525] : [-(_313523 = singleton(_313525)), 1340 ^ _266965 : [(1343 ^ _266965) ^ [] : [1337 ^ [_313523, _313525] = _313525], (1341 ^ _266965) ^ [] : [-(in(1337 ^ [_313523, _313525], _313523))]], 1344 ^ _266965 : [(1347 ^ _266965) ^ [] : [in(1337 ^ [_313523, _313525], _313523)], (1345 ^ _266965) ^ [] : [-(1337 ^ [_313523, _313525] = _313525)]]], (778 ^ _266965) ^ [_293058, _293060] : [-(_293060 = _293058), subset(_293060, _293058), subset(_293058, _293060)], (4199 ^ _266965) ^ [_410495, _410497] : [in(_410497, _410495), -(subset(singleton(_410497), _410495))], (3065 ^ _266965) ^ [_372374, _372376] : [-(set_intersection2(_372376, _372376) = _372376)], (3863 ^ _266965) ^ [_399514, _399516] : [relation(_399514), function(_399514), 3870 ^ _266965 : [(3871 ^ _266965) ^ [_399764] : [relation(_399764), function(_399764), 3878 ^ _266965 : [(3887 ^ _266965) ^ [] : [-(in(_399516, relation_dom(relation_composition(_399764, _399514)))), in(_399516, relation_dom(_399764)), in(apply(_399764, _399516), relation_dom(_399514))], (3879 ^ _266965) ^ [] : [in(_399516, relation_dom(relation_composition(_399764, _399514))), 3882 ^ _266965 : [(3885 ^ _266965) ^ [] : [-(in(apply(_399764, _399516), relation_dom(_399514)))], (3883 ^ _266965) ^ [] : [-(in(_399516, relation_dom(_399764)))]]]]]]], (4991 ^ _266965) ^ [_436599, _436601] : [relation(_436599), -(relation_dom_restriction(_436599, _436601) = relation_composition(identity_relation(_436601), _436599))], (4267 ^ _266965) ^ [_412842, _412844] : [-(disjoint(_412844, _412842)), 4271 ^ _266965 : [(4274 ^ _266965) ^ [] : [-(in(4270 ^ [_412842, _412844], _412842))], (4272 ^ _266965) ^ [] : [-(in(4270 ^ [_412842, _412844], _412844))]]], (2722 ^ _266965) ^ [_361715] : [relation(_361715), -(relation(relation_inverse(_361715)))], (2648 ^ _266965) ^ [] : [true___, -(true___)], (96 ^ _266965) ^ [_270079, _270081] : [-(antisymmetric(_270079)), _270081 = _270079, antisymmetric(_270081)], (2672 ^ _266965) ^ [_360468] : [-(element(cast_to_subset(_360468), powerset(_360468)))], (3362 ^ _266965) ^ [] : [-(epsilon_connected(3358 ^ []))], (3399 ^ _266965) ^ [] : [-(epsilon_transitive(3389 ^ []))], (4651 ^ _266965) ^ [_425666] : [relation(_425666), 4654 ^ _266965 : [(4661 ^ _266965) ^ [] : [is_well_founded_in(_425666, relation_field(_425666)), -(well_founded_relation(_425666))], (4655 ^ _266965) ^ [] : [well_founded_relation(_425666), -(is_well_founded_in(_425666, relation_field(_425666)))]]], (4997 ^ _266965) ^ [_436823, _436825] : [relation(_436823), -(subset(relation_rng(relation_dom_restriction(_436823, _436825)), relation_rng(_436823)))], (1380 ^ _266965) ^ [_315065, _315067] : [-(_315065 = powerset(_315067)), 1384 ^ _266965 : [(1387 ^ _266965) ^ [] : [subset(1381 ^ [_315065, _315067], _315067)], (1385 ^ _266965) ^ [] : [-(in(1381 ^ [_315065, _315067], _315065))]], 1388 ^ _266965 : [(1391 ^ _266965) ^ [] : [in(1381 ^ [_315065, _315067], _315065)], (1389 ^ _266965) ^ [] : [-(subset(1381 ^ [_315065, _315067], _315067))]]], (4058 ^ _266965) ^ [_405757] : [-(ordinal(_405757)), 4060 ^ _266965 : [(4063 ^ _266965) ^ [] : [ordinal(4059 ^ [_405757]), subset(4059 ^ [_405757], _405757)], (4061 ^ _266965) ^ [] : [-(in(4059 ^ [_405757], _405757))]]], (116 ^ _266965) ^ [_270669, _270671] : [-(epsilon_connected(_270669)), _270671 = _270669, epsilon_connected(_270671)], (4677 ^ _266965) ^ [_426414] : [relation(_426414), function(_426414), one_to_one(_426414), -(one_to_one(function_inverse(_426414)))], (1223 ^ _266965) ^ [_309505] : [1225 ^ _266965 : [(1228 ^ _266965) ^ [_309742, _309744] : [1224 ^ [_309505] = ordered_pair(_309744, _309742)], (1226 ^ _266965) ^ [] : [-(in(1224 ^ [_309505], _309505))]], -(relation(_309505))], (3015 ^ _266965) ^ [_370816] : [empty(relation_dom(_370816)), -(empty(_370816)), relation(_370816)], (957 ^ _266965) ^ [_299769] : [relation(_299769), 960 ^ _266965 : [(967 ^ _266965) ^ [] : [is_antisymmetric_in(_299769, relation_field(_299769)), -(antisymmetric(_299769))], (961 ^ _266965) ^ [] : [antisymmetric(_299769), -(is_antisymmetric_in(_299769, relation_field(_299769)))]]], (2780 ^ _266965) ^ [_363546, _363548] : [element(_363546, powerset(powerset(_363548))), -(element(complements_of_subsets(_363548, _363546), powerset(powerset(_363548))))], (4446 ^ _266965) ^ [_418779, _418781] : [element(_418779, powerset(powerset(_418781))), -(_418779 = empty_set), -(union_of_subsets(_418781, complements_of_subsets(_418781, _418779)) = subset_difference(_418781, cast_to_subset(_418781), meet_of_subsets(_418781, _418779)))], (1138 ^ _266965) ^ [_306476] : [relation(_306476), 1141 ^ _266965 : [(1148 ^ _266965) ^ [] : [is_transitive_in(_306476, relation_field(_306476)), -(transitive(_306476))], (1142 ^ _266965) ^ [] : [transitive(_306476), -(is_transitive_in(_306476, relation_field(_306476)))]]], (3851 ^ _266965) ^ [_399116, _399118, _399120] : [relation(_399116), in(ordered_pair(_399120, _399118), _399116), 3858 ^ _266965 : [(3861 ^ _266965) ^ [] : [-(in(_399118, relation_rng(_399116)))], (3859 ^ _266965) ^ [] : [-(in(_399120, relation_dom(_399116)))]]], (2692 ^ _266965) ^ [] : [true___, -(true___)], (3426 ^ _266965) ^ [] : [empty(3424 ^ [])], (1529 ^ _266965) ^ [_320106] : [relation(_320106), 1532 ^ _266965 : [(1533 ^ _266965) ^ [] : [well_founded_relation(_320106), 1536 ^ _266965 : [(1537 ^ _266965) ^ [_320373] : [subset(_320373, relation_field(_320106)), -(_320373 = empty_set), 1545 ^ _266965 : [(1548 ^ _266965) ^ [] : [-(disjoint(fiber(_320106, 1544 ^ [_320106, _320373]), _320373))], (1546 ^ _266965) ^ [] : [-(in(1544 ^ [_320106, _320373], _320373))]]]]], (1550 ^ _266965) ^ [] : [-(well_founded_relation(_320106)), 1552 ^ _266965 : [(1557 ^ _266965) ^ [_321056] : [in(_321056, 1551 ^ [_320106]), disjoint(fiber(_320106, _321056), 1551 ^ [_320106])], (1555 ^ _266965) ^ [] : [1551 ^ [_320106] = empty_set], (1553 ^ _266965) ^ [] : [-(subset(1551 ^ [_320106], relation_field(_320106)))]]]]], (1122 ^ _266965) ^ [_306045] : [relation(_306045), 1125 ^ _266965 : [(1132 ^ _266965) ^ [] : [is_connected_in(_306045, relation_field(_306045)), -(connected(_306045))], (1126 ^ _266965) ^ [] : [connected(_306045), -(is_connected_in(_306045, relation_field(_306045)))]]], (1788 ^ _266965) ^ [_330021, _330023, _330025] : [_330021 = set_intersection2(_330025, _330023), 1791 ^ _266965 : [(1800 ^ _266965) ^ [_330462] : [-(in(_330462, _330021)), in(_330462, _330025), in(_330462, _330023)], (1792 ^ _266965) ^ [_330203] : [in(_330203, _330021), 1795 ^ _266965 : [(1798 ^ _266965) ^ [] : [-(in(_330203, _330023))], (1796 ^ _266965) ^ [] : [-(in(_330203, _330025))]]]]], (500 ^ _266965) ^ [_283407, _283409, _283411, _283413] : [-(ordered_pair(_283413, _283409) = ordered_pair(_283411, _283407)), _283413 = _283411, _283409 = _283407], (4947 ^ _266965) ^ [_435143] : [relation(_435143), 4950 ^ _266965 : [(4957 ^ _266965) ^ [] : [well_ordering(_435143), -(well_orders(_435143, relation_field(_435143)))], (4951 ^ _266965) ^ [] : [well_orders(_435143, relation_field(_435143)), -(well_ordering(_435143))]]], (4963 ^ _266965) ^ [_435602, _435604, _435606] : [-(subset(set_union2(_435606, _435602), _435604)), subset(_435606, _435604), subset(_435602, _435604)], (2913 ^ _266965) ^ [_367542] : [empty(singleton(_367542))], (2774 ^ _266965) ^ [_363334, _363336] : [relation(_363336), -(relation(relation_dom_restriction(_363336, _363334)))], (3185 ^ _266965) ^ [_376667, _376669] : [element(_376667, powerset(_376669)), 3188 ^ _266965 : [(3189 ^ _266965) ^ [_376808] : [in(_376808, _376667), -(in(_376808, _376669))]]], (2758 ^ _266965) ^ [_362763, _362765] : [element(_362763, powerset(powerset(_362765))), -(element(meet_of_subsets(_362765, _362763), powerset(_362765)))], (4812 ^ _266965) ^ [_430688] : [-(relation_rng(identity_relation(_430688)) = _430688)], (2877 ^ _266965) ^ [_366433] : [empty(powerset(_366433))], (4869 ^ _266965) ^ [_432677, _432679] : [-(subset(_432679, set_union2(_432679, _432677)))], (2630 ^ _266965) ^ [] : [true___, -(true___)], (3789 ^ _266965) ^ [_397050, _397052] : [relation(_397050), -(_397052 = empty_set), subset(_397052, relation_rng(_397050)), relation_inverse_image(_397050, _397052) = empty_set], (3619 ^ _266965) ^ [_391313, _391315] : [in(_391313, 3605 ^ [_391315]), -(in(powerset(_391313), 3605 ^ [_391315]))], (3989 ^ _266965) ^ [_403369] : [relation(_403369), 3992 ^ _266965 : [(3993 ^ _266965) ^ [_403519] : [relation(_403519), subset(_403369, _403519), 4000 ^ _266965 : [(4003 ^ _266965) ^ [] : [-(subset(relation_rng(_403369), relation_rng(_403519)))], (4001 ^ _266965) ^ [] : [-(subset(relation_dom(_403369), relation_dom(_403519)))]]]]], (2624 ^ _266965) ^ [] : [true___, -(true___)], (2989 ^ _266965) ^ [] : [-(empty(empty_set))]], input).
% 100.64/97.59  ncf('1',plain,[-(relation(5047 ^ []))],start(5049 ^ 0)).
% 100.64/97.59  ncf('1.1',plain,[relation(5047 ^ []), -(relation_restriction(5047 ^ [], 5046 ^ []) = relation_dom_restriction(relation_rng_restriction(5046 ^ [], 5047 ^ []), 5046 ^ []))],extension(3813 ^ 1,bind([[_397783, _397785], [5047 ^ [], 5046 ^ []]]))).
% 100.64/97.59  ncf('1.1.1',plain,[relation_restriction(5047 ^ [], 5046 ^ []) = relation_dom_restriction(relation_rng_restriction(5046 ^ [], 5047 ^ []), 5046 ^ []), -(relation_restriction(5047 ^ [], 5046 ^ []) = relation_rng_restriction(5046 ^ [], relation_dom_restriction(5047 ^ [], 5046 ^ []))), relation_dom_restriction(relation_rng_restriction(5046 ^ [], 5047 ^ []), 5046 ^ []) = relation_rng_restriction(5046 ^ [], relation_dom_restriction(5047 ^ [], 5046 ^ []))],extension(10 ^ 2,bind([[_267400, _267402, _267404], [relation_rng_restriction(5046 ^ [], relation_dom_restriction(5047 ^ [], 5046 ^ [])), relation_dom_restriction(relation_rng_restriction(5046 ^ [], 5047 ^ []), 5046 ^ []), relation_restriction(5047 ^ [], 5046 ^ [])]]))).
% 100.64/97.59  ncf('1.1.1.1',plain,[relation_restriction(5047 ^ [], 5046 ^ []) = relation_rng_restriction(5046 ^ [], relation_dom_restriction(5047 ^ [], 5046 ^ []))],extension(5051 ^ 3)).
% 100.64/97.59  ncf('1.1.1.2',plain,[-(relation_dom_restriction(relation_rng_restriction(5046 ^ [], 5047 ^ []), 5046 ^ []) = relation_rng_restriction(5046 ^ [], relation_dom_restriction(5047 ^ [], 5046 ^ []))), relation(5047 ^ [])],extension(3635 ^ 3,bind([[_391867, _391869, _391871], [5047 ^ [], 5046 ^ [], 5046 ^ []]]))).
% 100.64/97.59  ncf('1.1.1.2.1',plain,[-(relation(5047 ^ []))],reduction('1')).
% 100.64/97.59  %-----------------------------------------------------
% 100.64/97.59  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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