%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU250+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 12:02:52 EDT 2023

% Result   : Theorem 64.78s 63.46s
% Output   : Proof 64.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU250+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 13:50:42 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 64.78/63.46  
% 64.78/63.46  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 64.78/63.46  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.78/63.46  %-----------------------------------------------------
% 64.78/63.46  ncf(matrix, plain, [(5075 ^ _456708) ^ [] : [subset(relation_field(relation_restriction(5071 ^ [], 5070 ^ [])), relation_field(5071 ^ [])), subset(relation_field(relation_restriction(5071 ^ [], 5070 ^ [])), 5070 ^ [])], (5073 ^ _456708) ^ [] : [-(relation(5071 ^ []))], !, (1255 ^ _280972) ^ [_324805, _324807] : [-(_324807 = empty_set), 1258 ^ _280972 : [(1259 ^ _280972) ^ [] : [_324805 = set_meet(_324807), 1262 ^ _280972 : [(1263 ^ _280972) ^ [_325103] : [in(_325103, _324805), 1266 ^ _280972 : [(1267 ^ _280972) ^ [_325248] : [in(_325248, _324807), -(in(_325103, _325248))]]], (1273 ^ _280972) ^ [_325433] : [1275 ^ _280972 : [(1278 ^ _280972) ^ [] : [in(_325433, 1274 ^ [_324805, _324807, _325433])], (1276 ^ _280972) ^ [] : [-(in(1274 ^ [_324805, _324807, _325433], _324807))]], -(in(_325433, _324805))]]], (1282 ^ _280972) ^ [] : [-(_324805 = set_meet(_324807)), 1286 ^ _280972 : [(1292 ^ _280972) ^ [] : [in(1283 ^ [_324805, _324807], 1288 ^ [_324805, _324807])], (1290 ^ _280972) ^ [] : [-(in(1288 ^ [_324805, _324807], _324807))], (1287 ^ _280972) ^ [] : [-(in(1283 ^ [_324805, _324807], _324805))]], 1293 ^ _280972 : [(1294 ^ _280972) ^ [_326207] : [in(_326207, _324807), -(in(1283 ^ [_324805, _324807], _326207))], (1300 ^ _280972) ^ [] : [in(1283 ^ [_324805, _324807], _324805)]]]]], (540 ^ _280972) ^ [_298850, _298852, _298854, _298856] : [-(set_intersection2(_298856, _298852) = set_intersection2(_298854, _298850)), _298856 = _298854, _298852 = _298850], (3368 ^ _280972) ^ [] : [-(epsilon_connected(3364 ^ []))], (382 ^ _280972) ^ [_293154, _293156, _293158, _293160] : [-(relation_image(_293160, _293156) = relation_image(_293158, _293154)), _293160 = _293158, _293156 = _293154], (48 ^ _280972) ^ [_282636, _282638, _282640, _282642] : [-(is_transitive_in(_282640, _282636)), is_transitive_in(_282642, _282638), _282642 = _282640, _282638 = _282636], (4765 ^ _280972) ^ [_443196, _443198] : [relation(_443196), function(_443196), 4772 ^ _280972 : [(4773 ^ _280972) ^ [_443463] : [relation(_443463), function(_443463), 4780 ^ _280972 : [(4793 ^ _280972) ^ [] : [-(_443196 = relation_dom_restriction(_443463, _443198)), relation_dom(_443196) = set_intersection2(relation_dom(_443463), _443198), 4799 ^ _280972 : [(4802 ^ _280972) ^ [] : [apply(_443196, 4798 ^ [_443196, _443198, _443463]) = apply(_443463, 4798 ^ [_443196, _443198, _443463])], (4800 ^ _280972) ^ [] : [-(in(4798 ^ [_443196, _443198, _443463], relation_dom(_443196)))]]], (4781 ^ _280972) ^ [] : [_443196 = relation_dom_restriction(_443463, _443198), 4784 ^ _280972 : [(4787 ^ _280972) ^ [_443917] : [in(_443917, relation_dom(_443196)), -(apply(_443196, _443917) = apply(_443463, _443917))], (4785 ^ _280972) ^ [] : [-(relation_dom(_443196) = set_intersection2(relation_dom(_443463), _443198))]]]]]]], (2692 ^ _280972) ^ [] : [true___, -(true___)], (2055 ^ _280972) ^ [_353199, _353201, _353203] : [_353199 = set_difference(_353203, _353201), 2058 ^ _280972 : [(2067 ^ _280972) ^ [_353643] : [-(in(_353643, _353199)), in(_353643, _353203), -(in(_353643, _353201))], (2059 ^ _280972) ^ [_353383] : [in(_353383, _353199), 2062 ^ _280972 : [(2065 ^ _280972) ^ [] : [in(_353383, _353201)], (2063 ^ _280972) ^ [] : [-(in(_353383, _353203))]]]]], (3452 ^ _280972) ^ [_399502, _399504] : [element(_399502, powerset(powerset(_399504))), -(union_of_subsets(_399504, _399502) = union(_399502))], (2867 ^ _280972) ^ [_380171, _380173] : [-(relation(set_intersection2(_380173, _380171))), relation(_380173), relation(_380171)], (2554 ^ _280972) ^ [_371748, _371750] : [-(proper_subset(_371750, _371748)), subset(_371750, _371748), -(_371750 = _371748)], (2979 ^ _280972) ^ [_383692] : [ordinal(_383692), 2982 ^ _280972 : [(2987 ^ _280972) ^ [] : [-(ordinal(union(_383692)))], (2985 ^ _280972) ^ [] : [-(epsilon_connected(union(_383692)))], (2983 ^ _280972) ^ [] : [-(epsilon_transitive(union(_383692)))]]], (4893 ^ _280972) ^ [_447544, _447546] : [-(subset(_447546, set_union2(_447546, _447544)))], (644 ^ _280972) ^ [_302728] : [empty(_302728), -(function(_302728))], (1587 ^ _280972) ^ [_336127, _336129, _336131] : [-(_336127 = set_union2(_336131, _336129)), 1591 ^ _280972 : [(1596 ^ _280972) ^ [] : [in(1588 ^ [_336127, _336129, _336131], _336129)], (1594 ^ _280972) ^ [] : [in(1588 ^ [_336127, _336129, _336131], _336131)], (1592 ^ _280972) ^ [] : [-(in(1588 ^ [_336127, _336129, _336131], _336127))]], 1597 ^ _280972 : [(1598 ^ _280972) ^ [] : [-(in(1588 ^ [_336127, _336129, _336131], _336131)), -(in(1588 ^ [_336127, _336129, _336131], _336129))], (1604 ^ _280972) ^ [] : [in(1588 ^ [_336127, _336129, _336131], _336127)]]], (973 ^ _280972) ^ [_314207] : [relation(_314207), function(_314207), 980 ^ _280972 : [(981 ^ _280972) ^ [_314494, _314496] : [_314494 = relation_inverse_image(_314207, _314496), 984 ^ _280972 : [(993 ^ _280972) ^ [_314952] : [-(in(_314952, _314494)), in(_314952, relation_dom(_314207)), in(apply(_314207, _314952), _314496)], (985 ^ _280972) ^ [_314683] : [in(_314683, _314494), 988 ^ _280972 : [(991 ^ _280972) ^ [] : [-(in(apply(_314207, _314683), _314496))], (989 ^ _280972) ^ [] : [-(in(_314683, relation_dom(_314207)))]]]]], (1003 ^ _280972) ^ [_315246, _315248] : [-(_315246 = relation_inverse_image(_314207, _315248)), 1015 ^ _280972 : [(1020 ^ _280972) ^ [] : [in(1004 ^ [_314207, _315246, _315248], _315246)], (1018 ^ _280972) ^ [] : [-(in(apply(_314207, 1004 ^ [_314207, _315246, _315248]), _315248))], (1016 ^ _280972) ^ [] : [-(in(1004 ^ [_314207, _315246, _315248], relation_dom(_314207)))]], 1007 ^ _280972 : [(1010 ^ _280972) ^ [] : [in(1004 ^ [_314207, _315246, _315248], relation_dom(_314207)), in(apply(_314207, 1004 ^ [_314207, _315246, _315248]), _315248)], (1008 ^ _280972) ^ [] : [-(in(1004 ^ [_314207, _315246, _315248], _315246))]]]]], (4460 ^ _280972) ^ [_433306, _433308] : [element(_433306, powerset(powerset(_433308))), -(_433306 = empty_set), -(subset_difference(_433308, cast_to_subset(_433308), union_of_subsets(_433308, _433306)) = meet_of_subsets(_433308, complements_of_subsets(_433308, _433306)))], (4874 ^ _280972) ^ [_446821, _446823] : [in(_446823, _446821), empty(_446821)], (3315 ^ _280972) ^ [_395180, _395182, _395184, _395186] : [-(in(ordered_pair(_395186, _395184), cartesian_product2(_395182, _395180))), in(_395186, _395182), in(_395184, _395180)], (582 ^ _280972) ^ [_300335, _300337] : [_300337 = _300335, -(relation_rng(_300337) = relation_rng(_300335))], (2188 ^ _280972) ^ [_358154, _358156] : [element(_358154, powerset(_358156)), -(subset_complement(_358156, _358154) = set_difference(_358156, _358154))], (1879 ^ _280972) ^ [_346977] : [-(ordinal(_346977)), epsilon_transitive(_346977), epsilon_connected(_346977)], (3504 ^ _280972) ^ [_401130, _401132] : [-(subset(_401132, _401132))], (3887 ^ _280972) ^ [_414381, _414383] : [relation(_414381), function(_414381), 3894 ^ _280972 : [(3895 ^ _280972) ^ [_414631] : [relation(_414631), function(_414631), 3902 ^ _280972 : [(3911 ^ _280972) ^ [] : [-(in(_414383, relation_dom(relation_composition(_414631, _414381)))), in(_414383, relation_dom(_414631)), in(apply(_414631, _414383), relation_dom(_414381))], (3903 ^ _280972) ^ [] : [in(_414383, relation_dom(relation_composition(_414631, _414381))), 3906 ^ _280972 : [(3909 ^ _280972) ^ [] : [-(in(apply(_414631, _414383), relation_dom(_414381)))], (3907 ^ _280972) ^ [] : [-(in(_414383, relation_dom(_414631)))]]]]]]], (3112 ^ _280972) ^ [_388042, _388044] : [in(_388044, _388042), -(set_union2(singleton(_388044), _388042) = _388042)], (1689 ^ _280972) ^ [_340079] : [1692 ^ _280972 : [(1693 ^ _280972) ^ [] : [-(in(1690 ^ [_340079], _340079))], (1697 ^ _280972) ^ [] : [in(1690 ^ [_340079], 1691 ^ [_340079])], (1701 ^ _280972) ^ [] : [in(1691 ^ [_340079], 1690 ^ [_340079])], (1699 ^ _280972) ^ [] : [1690 ^ [_340079] = 1691 ^ [_340079]], (1695 ^ _280972) ^ [] : [-(in(1691 ^ [_340079], _340079))]], -(epsilon_connected(_340079))], (3293 ^ _280972) ^ [_394350, _394352] : [3294 ^ _280972 : [(3297 ^ _280972) ^ [] : [_394352 = singleton(_394350)], (3295 ^ _280972) ^ [] : [_394352 = empty_set]], -(subset(_394352, singleton(_394350)))], (4820 ^ _280972) ^ [_445088, _445090, _445092] : [relation(_445088), function(_445088), in(_445090, relation_dom(relation_dom_restriction(_445088, _445092))), -(apply(relation_dom_restriction(_445088, _445092), _445090) = apply(_445088, _445090))], (3110 ^ _280972) ^ [_387933] : [singleton(_387933) = empty_set], (392 ^ _280972) ^ [_293513, _293515, _293517, _293519] : [-(relation_inverse_image(_293519, _293515) = relation_inverse_image(_293517, _293513)), _293519 = _293517, _293515 = _293513], (5042 ^ _280972) ^ [_452551, _452553] : [in(_452551, 5028 ^ [_452553]), 5046 ^ _280972 : [(5049 ^ _280972) ^ [_452863] : [subset(_452863, _452551), -(in(_452863, 5045 ^ [_452551, _452553]))], (5047 ^ _280972) ^ [] : [-(in(5045 ^ [_452551, _452553], 5028 ^ [_452553]))]]], (3394 ^ _280972) ^ [] : [-(function(3388 ^ []))], (2887 ^ _280972) ^ [] : [-(relation(empty_set))], (2959 ^ _280972) ^ [_383001, _383003] : [empty(unordered_pair(_383003, _383001))], (180 ^ _280972) ^ [_286623, _286625, _286627, _286629] : [-(element(_286627, _286623)), element(_286629, _286625), _286629 = _286627, _286625 = _286623], (957 ^ _280972) ^ [_313776] : [relation(_313776), 960 ^ _280972 : [(967 ^ _280972) ^ [] : [is_antisymmetric_in(_313776, relation_field(_313776)), -(antisymmetric(_313776))], (961 ^ _280972) ^ [] : [antisymmetric(_313776), -(is_antisymmetric_in(_313776, relation_field(_313776)))]]], (3773 ^ _280972) ^ [_410623, _410625, _410627] : [relation(_410623), 3776 ^ _280972 : [(3785 ^ _280972) ^ [] : [-(in(_410627, relation_restriction(_410623, _410625))), in(_410627, _410623), in(_410627, cartesian_product2(_410625, _410625))], (3777 ^ _280972) ^ [] : [in(_410627, relation_restriction(_410623, _410625)), 3780 ^ _280972 : [(3783 ^ _280972) ^ [] : [-(in(_410627, cartesian_product2(_410625, _410625)))], (3781 ^ _280972) ^ [] : [-(in(_410627, _410623))]]]]], (2845 ^ _280972) ^ [_379541, _379543] : [2860 ^ _280972 : [(2863 ^ _280972) ^ [] : [-(function(relation_composition(_379543, _379541)))], (2861 ^ _280972) ^ [] : [-(relation(relation_composition(_379543, _379541)))]], relation(_379543), function(_379543), relation(_379541), function(_379541)], (170 ^ _280972) ^ [_286300, _286302] : [-(being_limit_ordinal(_286300)), _286302 = _286300, being_limit_ordinal(_286302)], (352 ^ _280972) ^ [_292089, _292091, _292093, _292095, _292097, _292099] : [-(unordered_triple(_292099, _292095, _292091) = unordered_triple(_292097, _292093, _292089)), _292099 = _292097, _292095 = _292093, _292091 = _292089], (4279 ^ _280972) ^ [_427307, _427309] : [element(_427309, powerset(_427307)), -(subset(_427309, _427307))], (2354 ^ _280972) ^ [_364048] : [relation(_364048), function(_364048), 2361 ^ _280972 : [(2362 ^ _280972) ^ [] : [one_to_one(_364048), 2365 ^ _280972 : [(2366 ^ _280972) ^ [_364411, _364413] : [-(_364413 = _364411), in(_364413, relation_dom(_364048)), in(_364411, relation_dom(_364048)), apply(_364048, _364413) = apply(_364048, _364411)]]], (2380 ^ _280972) ^ [] : [2383 ^ _280972 : [(2386 ^ _280972) ^ [] : [-(in(2382 ^ [_364048], relation_dom(_364048)))], (2388 ^ _280972) ^ [] : [-(apply(_364048, 2381 ^ [_364048]) = apply(_364048, 2382 ^ [_364048]))], (2390 ^ _280972) ^ [] : [2381 ^ [_364048] = 2382 ^ [_364048]], (2384 ^ _280972) ^ [] : [-(in(2381 ^ [_364048], relation_dom(_364048)))]], -(one_to_one(_364048))]]], (4291 ^ _280972) ^ [_427709, _427711] : [-(disjoint(_427711, _427709)), 4295 ^ _280972 : [(4298 ^ _280972) ^ [] : [-(in(4294 ^ [_427709, _427711], _427709))], (4296 ^ _280972) ^ [] : [-(in(4294 ^ [_427709, _427711], _427711))]]], (3397 ^ _280972) ^ [] : [-(relation(3395 ^ []))], (3063 ^ _280972) ^ [_386284, _386286] : [-(set_union2(_386286, _386286) = _386286)], (2895 ^ _280972) ^ [] : [-(empty(empty_set))], (4300 ^ _280972) ^ [_428023, _428025] : [disjoint(_428025, _428023), 4301 ^ _280972 : [(4302 ^ _280972) ^ [_428115] : [in(_428115, _428025), in(_428115, _428023)]]], (4347 ^ _280972) ^ [_429537] : [ordinal(_429537), 4350 ^ _280972 : [(4360 ^ _280972) ^ [] : [being_limit_ordinal(_429537), 4361 ^ _280972 : [(4362 ^ _280972) ^ [_430008] : [ordinal(_430008), _429537 = succ(_430008)]]], (4351 ^ _280972) ^ [] : [-(being_limit_ordinal(_429537)), 4355 ^ _280972 : [(4358 ^ _280972) ^ [] : [-(_429537 = succ(4354 ^ [_429537]))], (4356 ^ _280972) ^ [] : [-(ordinal(4354 ^ [_429537]))]]]]], (4229 ^ _280972) ^ [_425621, _425623, _425625] : [subset(unordered_pair(_425625, _425623), _425621), 4232 ^ _280972 : [(4235 ^ _280972) ^ [] : [-(in(_425623, _425621))], (4233 ^ _280972) ^ [] : [-(in(_425625, _425621))]]], (160 ^ _280972) ^ [_286005, _286007] : [-(ordinal(_286005)), _286007 = _286005, ordinal(_286007)], (242 ^ _280972) ^ [_288545, _288547, _288549, _288551] : [-(disjoint(_288549, _288545)), disjoint(_288551, _288547), _288551 = _288549, _288547 = _288545], (1405 ^ _280972) ^ [_329923] : [1407 ^ _280972 : [(1410 ^ _280972) ^ [] : [subset(1406 ^ [_329923], _329923)], (1408 ^ _280972) ^ [] : [-(in(1406 ^ [_329923], _329923))]], -(epsilon_transitive(_329923))], (3130 ^ _280972) ^ [_388692, _388694] : [relation(_388692), -(subset(relation_dom(relation_rng_restriction(_388694, _388692)), relation_dom(_388692)))], (3405 ^ _280972) ^ [] : [-(epsilon_transitive(3395 ^ []))], (2674 ^ _280972) ^ [] : [true___, -(true___)], (2899 ^ _280972) ^ [] : [-(epsilon_connected(empty_set))], (4645 ^ _280972) ^ [_439639, _439641] : [relation(_439639), function(_439639), 4660 ^ _280972 : [(4663 ^ _280972) ^ [] : [-(_439641 = apply(relation_composition(function_inverse(_439639), _439639), _439641))], (4661 ^ _280972) ^ [] : [-(_439641 = apply(_439639, apply(function_inverse(_439639), _439641)))]], one_to_one(_439639), in(_439641, relation_rng(_439639))], (1667 ^ _280972) ^ [_339441] : [epsilon_connected(_339441), 1670 ^ _280972 : [(1671 ^ _280972) ^ [_339617, _339619] : [in(_339619, _339441), in(_339617, _339441), -(in(_339619, _339617)), -(_339619 = _339617), -(in(_339617, _339619))]]], (2642 ^ _280972) ^ [] : [true___, -(true___)], (1122 ^ _280972) ^ [_320052] : [relation(_320052), 1125 ^ _280972 : [(1132 ^ _280972) ^ [] : [is_connected_in(_320052, relation_field(_320052)), -(connected(_320052))], (1126 ^ _280972) ^ [] : [connected(_320052), -(is_connected_in(_320052, relation_field(_320052)))]]], (428 ^ _280972) ^ [_294780, _294782] : [_294782 = _294780, -(succ(_294782) = succ(_294780))], (4285 ^ _280972) ^ [_427473, _427475] : [subset(_427475, _427473), -(element(_427475, powerset(_427473)))], (3399 ^ _280972) ^ [] : [-(function(3395 ^ []))], (3191 ^ _280972) ^ [_390896, _390898] : [element(_390896, powerset(_390898)), 3194 ^ _280972 : [(3195 ^ _280972) ^ [_391037] : [in(_391037, _390896), -(in(_391037, _390898))]]], (2915 ^ _280972) ^ [_381657, _381659] : [-(empty(_381659)), empty(set_union2(_381659, _381657))], (3985 ^ _280972) ^ [_417416, _417418] : [ordinal(_417416), in(_417418, _417416), -(ordinal(_417418))], (1223 ^ _280972) ^ [_323512] : [1225 ^ _280972 : [(1228 ^ _280972) ^ [_323749, _323751] : [1224 ^ [_323512] = ordered_pair(_323751, _323749)], (1226 ^ _280972) ^ [] : [-(in(1224 ^ [_323512], _323512))]], -(relation(_323512))], (2077 ^ _280972) ^ [_353930, _353932, _353934] : [-(_353930 = set_difference(_353934, _353932)), 2089 ^ _280972 : [(2094 ^ _280972) ^ [] : [in(2078 ^ [_353930, _353932, _353934], _353930)], (2092 ^ _280972) ^ [] : [in(2078 ^ [_353930, _353932, _353934], _353932)], (2090 ^ _280972) ^ [] : [-(in(2078 ^ [_353930, _353932, _353934], _353934))]], 2081 ^ _280972 : [(2084 ^ _280972) ^ [] : [in(2078 ^ [_353930, _353932, _353934], _353934), -(in(2078 ^ [_353930, _353932, _353934], _353932))], (2082 ^ _280972) ^ [] : [-(in(2078 ^ [_353930, _353932, _353934], _353930))]]], (2901 ^ _280972) ^ [] : [-(ordinal(empty_set))], (4035 ^ _280972) ^ [_419023, _419025] : [subset(_419025, _419023), -(set_intersection2(_419025, _419023) = _419025)], (2967 ^ _280972) ^ [_383328, _383330] : [2974 ^ _280972 : [(2977 ^ _280972) ^ [] : [-(function(relation_dom_restriction(_383330, _383328)))], (2975 ^ _280972) ^ [] : [-(relation(relation_dom_restriction(_383330, _383328)))]], relation(_383330), function(_383330)], (905 ^ _280972) ^ [_311853, _311855] : [relation(_311853), 908 ^ _280972 : [(909 ^ _280972) ^ [_312024] : [relation(_312024), 912 ^ _280972 : [(913 ^ _280972) ^ [] : [_312024 = relation_rng_restriction(_311855, _311853), 916 ^ _280972 : [(925 ^ _280972) ^ [_312630, _312632] : [-(in(ordered_pair(_312632, _312630), _312024)), in(_312630, _311855), in(ordered_pair(_312632, _312630), _311853)], (917 ^ _280972) ^ [_312351, _312353] : [in(ordered_pair(_312353, _312351), _312024), 920 ^ _280972 : [(923 ^ _280972) ^ [] : [-(in(ordered_pair(_312353, _312351), _311853))], (921 ^ _280972) ^ [] : [-(in(_312351, _311855))]]]]], (935 ^ _280972) ^ [] : [-(_312024 = relation_rng_restriction(_311855, _311853)), 948 ^ _280972 : [(953 ^ _280972) ^ [] : [in(ordered_pair(936 ^ [_311853, _311855, _312024], 937 ^ [_311853, _311855, _312024]), _312024)], (951 ^ _280972) ^ [] : [-(in(ordered_pair(936 ^ [_311853, _311855, _312024], 937 ^ [_311853, _311855, _312024]), _311853))], (949 ^ _280972) ^ [] : [-(in(937 ^ [_311853, _311855, _312024], _311855))]], 940 ^ _280972 : [(943 ^ _280972) ^ [] : [in(937 ^ [_311853, _311855, _312024], _311855), in(ordered_pair(936 ^ [_311853, _311855, _312024], 937 ^ [_311853, _311855, _312024]), _311853)], (941 ^ _280972) ^ [] : [-(in(ordered_pair(936 ^ [_311853, _311855, _312024], 937 ^ [_311853, _311855, _312024]), _312024))]]]]]]], (650 ^ _280972) ^ [_302914] : [ordinal(_302914), 653 ^ _280972 : [(656 ^ _280972) ^ [] : [-(epsilon_connected(_302914))], (654 ^ _280972) ^ [] : [-(epsilon_transitive(_302914))]]], (2698 ^ _280972) ^ [] : [true___, -(true___)], (2248 ^ _280972) ^ [_360058] : [relation(_360058), -(relation_field(_360058) = set_union2(relation_dom(_360058), relation_rng(_360058)))], (2612 ^ _280972) ^ [] : [true___, -(true___)], (3425 ^ _280972) ^ [] : [-(relation(3423 ^ []))], (3167 ^ _280972) ^ [_390099, _390101] : [subset(singleton(_390101), _390099), -(in(_390101, _390099))], (3412 ^ _280972) ^ [] : [empty(3410 ^ [])], (1810 ^ _280972) ^ [_344753, _344755, _344757] : [-(_344753 = set_intersection2(_344757, _344755)), 1822 ^ _280972 : [(1827 ^ _280972) ^ [] : [in(1811 ^ [_344753, _344755, _344757], _344753)], (1825 ^ _280972) ^ [] : [-(in(1811 ^ [_344753, _344755, _344757], _344755))], (1823 ^ _280972) ^ [] : [-(in(1811 ^ [_344753, _344755, _344757], _344757))]], 1814 ^ _280972 : [(1817 ^ _280972) ^ [] : [in(1811 ^ [_344753, _344755, _344757], _344757), in(1811 ^ [_344753, _344755, _344757], _344755)], (1815 ^ _280972) ^ [] : [-(in(1811 ^ [_344753, _344755, _344757], _344753))]]], (3795 ^ _280972) ^ [_411279, _411281] : [relation(_411279), -(_411281 = empty_set), subset(_411281, relation_rng(_411279)), relation_inverse_image(_411279, _411281) = empty_set], (3136 ^ _280972) ^ [_388900] : [relation(_388900), 3139 ^ _280972 : [(3140 ^ _280972) ^ [] : [transitive(_388900), 3143 ^ _280972 : [(3144 ^ _280972) ^ [_389192, _389194, _389196] : [-(in(ordered_pair(_389196, _389192), _388900)), in(ordered_pair(_389196, _389194), _388900), in(ordered_pair(_389194, _389192), _388900)]]], (3154 ^ _280972) ^ [] : [3158 ^ _280972 : [(3163 ^ _280972) ^ [] : [in(ordered_pair(3155 ^ [_388900], 3157 ^ [_388900]), _388900)], (3161 ^ _280972) ^ [] : [-(in(ordered_pair(3156 ^ [_388900], 3157 ^ [_388900]), _388900))], (3159 ^ _280972) ^ [] : [-(in(ordered_pair(3155 ^ [_388900], 3156 ^ [_388900]), _388900))]], -(transitive(_388900))]]], (702 ^ _280972) ^ [_304445, _304447] : [-(unordered_pair(_304447, _304445) = unordered_pair(_304445, _304447))], (4691 ^ _280972) ^ [] : [-(relation_dom(empty_set) = empty_set)], (4838 ^ _280972) ^ [_445682, _445684, _445686] : [relation(_445682), function(_445682), in(_445684, _445686), -(apply(relation_dom_restriction(_445682, _445686), _445684) = apply(_445682, _445684))], (218 ^ _280972) ^ [_287806, _287808, _287810, _287812] : [-(proper_subset(_287810, _287806)), proper_subset(_287812, _287808), _287812 = _287810, _287808 = _287806], (2630 ^ _280972) ^ [] : [true___, -(true___)], (3532 ^ _280972) ^ [_402212, _402214, _402216, _402218] : [unordered_pair(_402218, _402216) = unordered_pair(_402214, _402212), -(_402218 = _402214), -(_402218 = _402212)], (4935 ^ _280972) ^ [_448958, _448960] : [empty(_448960), -(_448960 = _448958), empty(_448958)], (3935 ^ _280972) ^ [_415821] : [relation(_415821), -(subset(_415821, cartesian_product2(relation_dom(_415821), relation_rng(_415821))))], (2672 ^ _280972) ^ [_374475] : [-(element(cast_to_subset(_374475), powerset(_374475)))], (1970 ^ _280972) ^ [_350449, _350451] : [_350449 = union(_350451), 1973 ^ _280972 : [(1983 ^ _280972) ^ [_350957] : [-(in(_350957, _350449)), 1984 ^ _280972 : [(1985 ^ _280972) ^ [_351055] : [in(_350957, _351055), in(_351055, _350451)]]], (1974 ^ _280972) ^ [_350630] : [in(_350630, _350449), 1978 ^ _280972 : [(1981 ^ _280972) ^ [] : [-(in(1977 ^ [_350449, _350451, _350630], _350451))], (1979 ^ _280972) ^ [] : [-(in(_350630, 1977 ^ [_350449, _350451, _350630]))]]]]], (2734 ^ _280972) ^ [] : [true___, -(true___)], (2710 ^ _280972) ^ [] : [true___, -(true___)], (1024 ^ _280972) ^ [_316014] : [relation(_316014), 1027 ^ _280972 : [(1028 ^ _280972) ^ [_316221, _316223] : [_316221 = relation_image(_316014, _316223), 1031 ^ _280972 : [(1041 ^ _280972) ^ [_316767] : [-(in(_316767, _316221)), 1042 ^ _280972 : [(1043 ^ _280972) ^ [_316872] : [in(ordered_pair(_316872, _316767), _316014), in(_316872, _316223)]]], (1032 ^ _280972) ^ [_316413] : [in(_316413, _316221), 1036 ^ _280972 : [(1039 ^ _280972) ^ [] : [-(in(1035 ^ [_316014, _316221, _316223, _316413], _316223))], (1037 ^ _280972) ^ [] : [-(in(ordered_pair(1035 ^ [_316014, _316221, _316223, _316413], _316413), _316014))]]]]], (1051 ^ _280972) ^ [_317127, _317129] : [-(_317127 = relation_image(_316014, _317129)), 1064 ^ _280972 : [(1069 ^ _280972) ^ [] : [in(1052 ^ [_316014, _317127, _317129], _317127)], (1067 ^ _280972) ^ [] : [-(in(1063 ^ [_316014, _317127, _317129], _317129))], (1065 ^ _280972) ^ [] : [-(in(ordered_pair(1063 ^ [_316014, _317127, _317129], 1052 ^ [_316014, _317127, _317129]), _316014))]], 1055 ^ _280972 : [(1058 ^ _280972) ^ [_317431] : [in(ordered_pair(_317431, 1052 ^ [_316014, _317127, _317129]), _316014), in(_317431, _317129)], (1056 ^ _280972) ^ [] : [-(in(1052 ^ [_316014, _317127, _317129], _317127))]]]]], (2686 ^ _280972) ^ [] : [true___, -(true___)], (500 ^ _280972) ^ [_297414, _297416, _297418, _297420] : [-(set_difference(_297420, _297416) = set_difference(_297418, _297414)), _297420 = _297418, _297416 = _297414], (3767 ^ _280972) ^ [_410391, _410393] : [relation(_410391), -(subset(relation_inverse_image(_410391, _410393), relation_dom(_410391)))], (3582 ^ _280972) ^ [_403889, _403891, _403893] : [subset(_403893, _403891), 3585 ^ _280972 : [(3588 ^ _280972) ^ [] : [-(subset(cartesian_product2(_403889, _403893), cartesian_product2(_403889, _403891)))], (3586 ^ _280972) ^ [] : [-(subset(cartesian_product2(_403893, _403889), cartesian_product2(_403891, _403889)))]]], (2606 ^ _280972) ^ [] : [true___, -(true___)], (434 ^ _280972) ^ [_295026, _295028, _295030, _295032] : [-(union_of_subsets(_295032, _295028) = union_of_subsets(_295030, _295026)), _295032 = _295030, _295028 = _295026], (2758 ^ _280972) ^ [_376770, _376772] : [element(_376770, powerset(powerset(_376772))), -(element(meet_of_subsets(_376772, _376770), powerset(_376772)))], (2578 ^ _280972) ^ [_372402] : [relation(_372402), 2581 ^ _280972 : [(2588 ^ _280972) ^ [] : [is_reflexive_in(_372402, relation_field(_372402)), -(reflexive(_372402))], (2582 ^ _280972) ^ [] : [reflexive(_372402), -(is_reflexive_in(_372402, relation_field(_372402)))]]], (788 ^ _280972) ^ [_307352] : [relation(_307352), 791 ^ _280972 : [(792 ^ _280972) ^ [_307538, _307540] : [relation(_307538), 795 ^ _280972 : [(796 ^ _280972) ^ [] : [_307538 = relation_dom_restriction(_307352, _307540), 799 ^ _280972 : [(808 ^ _280972) ^ [_308142, _308144] : [-(in(ordered_pair(_308144, _308142), _307538)), in(_308144, _307540), in(ordered_pair(_308144, _308142), _307352)], (800 ^ _280972) ^ [_307863, _307865] : [in(ordered_pair(_307865, _307863), _307538), 803 ^ _280972 : [(806 ^ _280972) ^ [] : [-(in(ordered_pair(_307865, _307863), _307352))], (804 ^ _280972) ^ [] : [-(in(_307865, _307540))]]]]], (818 ^ _280972) ^ [] : [-(_307538 = relation_dom_restriction(_307352, _307540)), 831 ^ _280972 : [(836 ^ _280972) ^ [] : [in(ordered_pair(819 ^ [_307352, _307538, _307540], 820 ^ [_307352, _307538, _307540]), _307538)], (834 ^ _280972) ^ [] : [-(in(ordered_pair(819 ^ [_307352, _307538, _307540], 820 ^ [_307352, _307538, _307540]), _307352))], (832 ^ _280972) ^ [] : [-(in(819 ^ [_307352, _307538, _307540], _307540))]], 823 ^ _280972 : [(826 ^ _280972) ^ [] : [in(819 ^ [_307352, _307538, _307540], _307540), in(ordered_pair(819 ^ [_307352, _307538, _307540], 820 ^ [_307352, _307538, _307540]), _307352)], (824 ^ _280972) ^ [] : [-(in(ordered_pair(819 ^ [_307352, _307538, _307540], 820 ^ [_307352, _307538, _307540]), _307538))]]]]]]], (1871 ^ _280972) ^ [_346754] : [ordinal(_346754), 1874 ^ _280972 : [(1877 ^ _280972) ^ [] : [-(epsilon_connected(_346754))], (1875 ^ _280972) ^ [] : [-(epsilon_transitive(_346754))]]], (4053 ^ _280972) ^ [_419618, _419620] : [-(_419620 = _419618), 4057 ^ _280972 : [(4060 ^ _280972) ^ [] : [in(4054 ^ [_419618, _419620], _419618)], (4058 ^ _280972) ^ [] : [-(in(4054 ^ [_419618, _419620], _419620))]], 4061 ^ _280972 : [(4064 ^ _280972) ^ [] : [in(4054 ^ [_419618, _419620], _419620)], (4062 ^ _280972) ^ [] : [-(in(4054 ^ [_419618, _419620], _419618))]]], (116 ^ _280972) ^ [_284676, _284678] : [-(epsilon_connected(_284676)), _284678 = _284676, epsilon_connected(_284678)], (4808 ^ _280972) ^ [_444654] : [empty(_444654), -(_444654 = empty_set)], (3875 ^ _280972) ^ [_413983, _413985, _413987] : [relation(_413983), in(ordered_pair(_413987, _413985), _413983), 3882 ^ _280972 : [(3885 ^ _280972) ^ [] : [-(in(_413985, relation_rng(_413983)))], (3883 ^ _280972) ^ [] : [-(in(_413987, relation_dom(_413983)))]]], (2151 ^ _280972) ^ [_356699] : [relation(_356699), 2154 ^ _280972 : [(2155 ^ _280972) ^ [_356880] : [_356880 = relation_rng(_356699), 2158 ^ _280972 : [(2166 ^ _280972) ^ [_357304] : [2167 ^ _280972 : [(2168 ^ _280972) ^ [_357383] : [in(ordered_pair(_357383, _357304), _356699)]], -(in(_357304, _356880))], (2159 ^ _280972) ^ [_357060] : [in(_357060, _356880), -(in(ordered_pair(2162 ^ [_356699, _356880, _357060], _357060), _356699))]]], (2172 ^ _280972) ^ [_357511] : [-(_357511 = relation_rng(_356699)), 2176 ^ _280972 : [(2179 ^ _280972) ^ [_357774] : [in(ordered_pair(_357774, 2173 ^ [_356699, _357511]), _356699)], (2177 ^ _280972) ^ [] : [-(in(2173 ^ [_356699, _357511], _357511))]], 2181 ^ _280972 : [(2184 ^ _280972) ^ [] : [in(2173 ^ [_356699, _357511], _357511)], (2182 ^ _280972) ^ [] : [-(in(ordered_pair(2180 ^ [_356699, _357511], 2173 ^ [_356699, _357511]), _356699))]]]]], (3432 ^ _280972) ^ [] : [empty(3430 ^ [])], (4607 ^ _280972) ^ [_438462, _438464, _438466] : [element(_438462, powerset(_438466)), in(_438464, subset_complement(_438466, _438462)), in(_438464, _438462)], (4675 ^ _280972) ^ [_440533] : [relation(_440533), 4678 ^ _280972 : [(4685 ^ _280972) ^ [] : [is_well_founded_in(_440533, relation_field(_440533)), -(well_founded_relation(_440533))], (4679 ^ _280972) ^ [] : [well_founded_relation(_440533), -(is_well_founded_in(_440533, relation_field(_440533)))]]], (510 ^ _280972) ^ [_297773, _297775, _297777, _297779] : [-(ordered_pair(_297779, _297775) = ordered_pair(_297777, _297773)), _297779 = _297777, _297775 = _297773], (3422 ^ _280972) ^ [] : [empty(3420 ^ [])], (4070 ^ _280972) ^ [_420240, _420242, _420244] : [relation(_420240), in(ordered_pair(_420244, _420242), _420240), 4077 ^ _280972 : [(4080 ^ _280972) ^ [] : [-(in(_420242, relation_field(_420240)))], (4078 ^ _280972) ^ [] : [-(in(_420244, relation_field(_420240)))]]], (3615 ^ _280972) ^ [_405227, _405229, _405231] : [-(in(_405227, 3611 ^ [_405231])), in(_405229, 3611 ^ [_405231]), subset(_405227, _405229)], (4494 ^ _280972) ^ [_434517, _434519] : [-(disjoint(_434519, _434517)), -(in(4497 ^ [_434517, _434519], set_intersection2(_434519, _434517)))], (3373 ^ _280972) ^ [] : [-(empty(3371 ^ []))], (2879 ^ _280972) ^ [] : [-(empty(empty_set))], (5032 ^ _280972) ^ [_452236, _452238, _452240] : [-(in(_452236, 5028 ^ [_452240])), in(_452238, 5028 ^ [_452240]), subset(_452236, _452238)], (3530 ^ _280972) ^ [_402075] : [-(in(_402075, succ(_402075)))], (3512 ^ _280972) ^ [_401506, _401508, _401510, _401512] : [in(ordered_pair(_401512, _401510), cartesian_product2(_401508, _401506)), 3515 ^ _280972 : [(3518 ^ _280972) ^ [] : [-(in(_401510, _401506))], (3516 ^ _280972) ^ [] : [-(in(_401512, _401508))]]], (682 ^ _280972) ^ [_303850] : [-(ordinal(_303850)), epsilon_transitive(_303850), epsilon_connected(_303850)], (3450 ^ _280972) ^ [] : [-(function(3444 ^ []))], (1380 ^ _280972) ^ [_329072, _329074] : [-(_329072 = powerset(_329074)), 1384 ^ _280972 : [(1387 ^ _280972) ^ [] : [subset(1381 ^ [_329072, _329074], _329074)], (1385 ^ _280972) ^ [] : [-(in(1381 ^ [_329072, _329074], _329072))]], 1388 ^ _280972 : [(1391 ^ _280972) ^ [] : [in(1381 ^ [_329072, _329074], _329072)], (1389 ^ _280972) ^ [] : [-(subset(1381 ^ [_329072, _329074], _329074))]]], (4068 ^ _280972) ^ [_420119] : [-(subset(empty_set, _420119))], (1486 ^ _280972) ^ [_332651, _332653, _332655] : [_332651 = unordered_pair(_332655, _332653), 1489 ^ _280972 : [(1490 ^ _280972) ^ [_332833] : [in(_332833, _332651), -(_332833 = _332655), -(_332833 = _332653)], (1500 ^ _280972) ^ [_333111] : [1501 ^ _280972 : [(1504 ^ _280972) ^ [] : [_333111 = _332653], (1502 ^ _280972) ^ [] : [_333111 = _332655]], -(in(_333111, _332651))]]], (3446 ^ _280972) ^ [] : [-(relation(3444 ^ []))], (840 ^ _280972) ^ [_309297] : [relation(_309297), function(_309297), 847 ^ _280972 : [(848 ^ _280972) ^ [_309595, _309597] : [_309595 = relation_image(_309297, _309597), 851 ^ _280972 : [(863 ^ _280972) ^ [_310250] : [-(in(_310250, _309595)), 864 ^ _280972 : [(865 ^ _280972) ^ [_310363] : [in(_310363, relation_dom(_309297)), in(_310363, _309597), _310250 = apply(_309297, _310363)]]], (852 ^ _280972) ^ [_309795] : [in(_309795, _309595), 856 ^ _280972 : [(861 ^ _280972) ^ [] : [-(_309795 = apply(_309297, 855 ^ [_309297, _309595, _309597, _309795]))], (859 ^ _280972) ^ [] : [-(in(855 ^ [_309297, _309595, _309597, _309795], _309597))], (857 ^ _280972) ^ [] : [-(in(855 ^ [_309297, _309595, _309597, _309795], relation_dom(_309297)))]]]]], (877 ^ _280972) ^ [_310723, _310725] : [-(_310723 = relation_image(_309297, _310725)), 894 ^ _280972 : [(897 ^ _280972) ^ [] : [-(in(893 ^ [_309297, _310723, _310725], _310725))], (899 ^ _280972) ^ [] : [-(878 ^ [_309297, _310723, _310725] = apply(_309297, 893 ^ [_309297, _310723, _310725]))], (901 ^ _280972) ^ [] : [in(878 ^ [_309297, _310723, _310725], _310723)], (895 ^ _280972) ^ [] : [-(in(893 ^ [_309297, _310723, _310725], relation_dom(_309297)))]], 881 ^ _280972 : [(884 ^ _280972) ^ [_311043] : [in(_311043, relation_dom(_309297)), in(_311043, _310725), 878 ^ [_309297, _310723, _310725] = apply(_309297, _311043)], (882 ^ _280972) ^ [] : [-(in(878 ^ [_309297, _310723, _310725], _310723))]]]]], (3819 ^ _280972) ^ [_412012, _412014] : [relation(_412012), -(relation_restriction(_412012, _412014) = relation_dom_restriction(relation_rng_restriction(_412014, _412012), _412014))], (300 ^ _280972) ^ [_290318, _290320, _290322, _290324] : [-(are_equipotent(_290322, _290318)), are_equipotent(_290324, _290320), _290324 = _290322, _290320 = _290318], (4189 ^ _280972) ^ [_424150, _424152] : [in(_424150, _424152), -(apply(identity_relation(_424152), _424150) = _424150)], (3179 ^ _280972) ^ [_390510, _390512] : [set_difference(_390512, _390510) = empty_set, -(subset(_390512, _390510))], (2254 ^ _280972) ^ [_360264] : [relation(_360264), 2257 ^ _280972 : [(2258 ^ _280972) ^ [_360472] : [is_connected_in(_360264, _360472), 2261 ^ _280972 : [(2262 ^ _280972) ^ [_360662, _360664] : [in(_360664, _360472), in(_360662, _360472), -(_360664 = _360662), -(in(ordered_pair(_360664, _360662), _360264)), -(in(ordered_pair(_360662, _360664), _360264))]]], (2280 ^ _280972) ^ [_361156] : [2283 ^ _280972 : [(2284 ^ _280972) ^ [] : [-(in(2281 ^ [_360264, _361156], _361156))], (2288 ^ _280972) ^ [] : [2281 ^ [_360264, _361156] = 2282 ^ [_360264, _361156]], (2292 ^ _280972) ^ [] : [in(ordered_pair(2282 ^ [_360264, _361156], 2281 ^ [_360264, _361156]), _360264)], (2290 ^ _280972) ^ [] : [in(ordered_pair(2281 ^ [_360264, _361156], 2282 ^ [_360264, _361156]), _360264)], (2286 ^ _280972) ^ [] : [-(in(2282 ^ [_360264, _361156], _361156))]], -(is_connected_in(_360264, _361156))]]], (2342 ^ _280972) ^ [_363676, _363678] : [disjoint(_363678, _363676), -(set_intersection2(_363678, _363676) = empty_set)], (520 ^ _280972) ^ [_298132, _298134, _298136, _298138] : [-(apply(_298138, _298134) = apply(_298136, _298132)), _298138 = _298136, _298134 = _298132], (2877 ^ _280972) ^ [_380440] : [empty(powerset(_380440))], (708 ^ _280972) ^ [_304760, _304762] : [ordinal(_304762), ordinal(_304760), -(ordinal_subset(_304762, _304760)), -(ordinal_subset(_304760, _304762))], (4430 ^ _280972) ^ [_432310, _432312] : [element(_432310, powerset(powerset(_432312))), -(_432310 = empty_set), complements_of_subsets(_432312, _432310) = empty_set], (3307 ^ _280972) ^ [_394915, _394917, _394919, _394921] : [in(ordered_pair(_394921, _394919), cartesian_product2(_394917, _394915)), 3310 ^ _280972 : [(3313 ^ _280972) ^ [] : [-(in(_394919, _394915))], (3311 ^ _280972) ^ [] : [-(in(_394921, _394917))]]], (4737 ^ _280972) ^ [_442315] : [relation(_442315), 4740 ^ _280972 : [(4747 ^ _280972) ^ [] : [relation_rng(_442315) = empty_set, -(relation_dom(_442315) = empty_set)], (4741 ^ _280972) ^ [] : [relation_dom(_442315) = empty_set, -(relation_rng(_442315) = empty_set)]]], (4470 ^ _280972) ^ [_433646, _433648] : [element(_433646, powerset(powerset(_433648))), -(_433646 = empty_set), -(union_of_subsets(_433648, complements_of_subsets(_433648, _433646)) = subset_difference(_433648, cast_to_subset(_433648), meet_of_subsets(_433648, _433646)))], (3185 ^ _280972) ^ [_390678, _390680] : [subset(_390680, _390678), -(set_difference(_390680, _390678) = empty_set)], (606 ^ _280972) ^ [_301235, _301237, _301239, _301241] : [-(unordered_pair(_301241, _301237) = unordered_pair(_301239, _301235)), _301241 = _301239, _301237 = _301235], (4836 ^ _280972) ^ [_445555] : [-(relation_rng(identity_relation(_445555)) = _445555)], (62 ^ _280972) ^ [_283080, _283082, _283084, _283086] : [-(is_reflexive_in(_283084, _283080)), is_reflexive_in(_283086, _283082), _283086 = _283084, _283082 = _283080], (2666 ^ _280972) ^ [] : [true___, -(true___)], (2296 ^ _280972) ^ [_361941] : [relation(_361941), 2299 ^ _280972 : [(2300 ^ _280972) ^ [_362060] : [-(relation_restriction(_361941, _362060) = set_intersection2(_361941, cartesian_product2(_362060, _362060)))]]], (3065 ^ _280972) ^ [_386381, _386383] : [-(set_intersection2(_386383, _386383) = _386383)], (4142 ^ _280972) ^ [_422557, _422559, _422561] : [subset(_422561, _422559), -(subset(set_difference(_422561, _422557), set_difference(_422559, _422557)))], (1508 ^ _280972) ^ [_333376, _333378, _333380] : [-(_333376 = unordered_pair(_333380, _333378)), 1512 ^ _280972 : [(1517 ^ _280972) ^ [] : [1509 ^ [_333376, _333378, _333380] = _333378], (1515 ^ _280972) ^ [] : [1509 ^ [_333376, _333378, _333380] = _333380], (1513 ^ _280972) ^ [] : [-(in(1509 ^ [_333376, _333378, _333380], _333376))]], 1518 ^ _280972 : [(1519 ^ _280972) ^ [] : [-(1509 ^ [_333376, _333378, _333380] = _333380), -(1509 ^ [_333376, _333378, _333380] = _333378)], (1525 ^ _280972) ^ [] : [in(1509 ^ [_333376, _333378, _333380], _333376)]]], (1565 ^ _280972) ^ [_335402, _335404, _335406] : [_335402 = set_union2(_335406, _335404), 1568 ^ _280972 : [(1569 ^ _280972) ^ [_335584] : [in(_335584, _335402), -(in(_335584, _335406)), -(in(_335584, _335404))], (1579 ^ _280972) ^ [_335862] : [1580 ^ _280972 : [(1583 ^ _280972) ^ [] : [in(_335862, _335404)], (1581 ^ _280972) ^ [] : [in(_335862, _335406)]], -(in(_335862, _335402))]]], (3414 ^ _280972) ^ [] : [-(relation(3410 ^ []))], (3043 ^ _280972) ^ [_385642] : [empty(_385642), 3046 ^ _280972 : [(3049 ^ _280972) ^ [] : [-(relation(relation_rng(_385642)))], (3047 ^ _280972) ^ [] : [-(empty(relation_rng(_385642)))]]], (704 ^ _280972) ^ [_304545, _304547] : [-(set_union2(_304547, _304545) = set_union2(_304545, _304547))], (3682 ^ _280972) ^ [_407564, _407566] : [-(subset(relation_image(_407564, relation_inverse_image(_407564, _407566)), _407566)), relation(_407564), function(_407564)], (3361 ^ _280972) ^ [] : [-(relation(3359 ^ []))], (3087 ^ _280972) ^ [_387224] : [relation(_387224), 3090 ^ _280972 : [(3091 ^ _280972) ^ [] : [reflexive(_387224), 3094 ^ _280972 : [(3095 ^ _280972) ^ [_387468] : [in(_387468, relation_field(_387224)), -(in(ordered_pair(_387468, _387468), _387224))]]], (3101 ^ _280972) ^ [] : [3103 ^ _280972 : [(3106 ^ _280972) ^ [] : [in(ordered_pair(3102 ^ [_387224], 3102 ^ [_387224]), _387224)], (3104 ^ _280972) ^ [] : [-(in(3102 ^ [_387224], relation_field(_387224)))]], -(reflexive(_387224))]]], (3708 ^ _280972) ^ [_408400] : [relation(_408400), -(relation_image(_408400, relation_dom(_408400)) = relation_rng(_408400))], (2098 ^ _280972) ^ [_354673] : [relation(_354673), function(_354673), 2105 ^ _280972 : [(2106 ^ _280972) ^ [_354945] : [_354945 = relation_rng(_354673), 2109 ^ _280972 : [(2119 ^ _280972) ^ [_355475] : [-(in(_355475, _354945)), 2120 ^ _280972 : [(2121 ^ _280972) ^ [_355578] : [in(_355578, relation_dom(_354673)), _355475 = apply(_354673, _355578)]]], (2110 ^ _280972) ^ [_355133] : [in(_355133, _354945), 2114 ^ _280972 : [(2117 ^ _280972) ^ [] : [-(_355133 = apply(_354673, 2113 ^ [_354673, _354945, _355133]))], (2115 ^ _280972) ^ [] : [-(in(2113 ^ [_354673, _354945, _355133], relation_dom(_354673)))]]]]], (2129 ^ _280972) ^ [_355827] : [-(_355827 = relation_rng(_354673)), 2142 ^ _280972 : [(2147 ^ _280972) ^ [] : [in(2130 ^ [_354673, _355827], _355827)], (2145 ^ _280972) ^ [] : [-(2130 ^ [_354673, _355827] = apply(_354673, 2141 ^ [_354673, _355827]))], (2143 ^ _280972) ^ [] : [-(in(2141 ^ [_354673, _355827], relation_dom(_354673)))]], 2133 ^ _280972 : [(2136 ^ _280972) ^ [_356122] : [in(_356122, relation_dom(_354673)), 2130 ^ [_354673, _355827] = apply(_354673, _356122)], (2134 ^ _280972) ^ [] : [-(in(2130 ^ [_354673, _355827], _355827))]]]]], (4814 ^ _280972) ^ [_444856, _444858] : [subset(singleton(_444858), singleton(_444856)), -(_444858 = _444856)], (3003 ^ _280972) ^ [_384459, _384461] : [3010 ^ _280972 : [(3013 ^ _280972) ^ [] : [-(function(relation_rng_restriction(_384461, _384459)))], (3011 ^ _280972) ^ [] : [-(relation(relation_rng_restriction(_384461, _384459)))]], relation(_384459), function(_384459)], (2991 ^ _280972) ^ [] : [-(relation(empty_set))], (4316 ^ _280972) ^ [_428561, _428563] : [-(set_difference(set_union2(_428563, _428561), _428561) = set_difference(_428563, _428561))], (622 ^ _280972) ^ [_301792, _301794, _301796, _301798] : [-(relation_restriction(_301798, _301794) = relation_restriction(_301796, _301792)), _301798 = _301796, _301794 = _301792], (5030 ^ _280972) ^ [_452124] : [-(in(_452124, 5028 ^ [_452124]))], (96 ^ _280972) ^ [_284086, _284088] : [-(antisymmetric(_284086)), _284088 = _284086, antisymmetric(_284088)], (3392 ^ _280972) ^ [] : [-(empty(3388 ^ []))], (2394 ^ _280972) ^ [_365358] : [relation(_365358), 2397 ^ _280972 : [(2398 ^ _280972) ^ [_365543] : [relation(_365543), 2401 ^ _280972 : [(2402 ^ _280972) ^ [_365724] : [relation(_365724), 2405 ^ _280972 : [(2406 ^ _280972) ^ [] : [_365724 = relation_composition(_365358, _365543), 2409 ^ _280972 : [(2419 ^ _280972) ^ [_366444, _366446] : [-(in(ordered_pair(_366446, _366444), _365724)), 2420 ^ _280972 : [(2421 ^ _280972) ^ [_366557] : [in(ordered_pair(_366446, _366557), _365358), in(ordered_pair(_366557, _366444), _365543)]]], (2410 ^ _280972) ^ [_366059, _366061] : [in(ordered_pair(_366061, _366059), _365724), 2414 ^ _280972 : [(2417 ^ _280972) ^ [] : [-(in(ordered_pair(2413 ^ [_365358, _365543, _365724, _366059, _366061], _366059), _365543))], (2415 ^ _280972) ^ [] : [-(in(ordered_pair(_366061, 2413 ^ [_365358, _365543, _365724, _366059, _366061]), _365358))]]]]], (2429 ^ _280972) ^ [] : [-(_365724 = relation_composition(_365358, _365543)), 2443 ^ _280972 : [(2448 ^ _280972) ^ [] : [in(ordered_pair(2430 ^ [_365358, _365543, _365724], 2431 ^ [_365358, _365543, _365724]), _365724)], (2446 ^ _280972) ^ [] : [-(in(ordered_pair(2442 ^ [_365358, _365543, _365724], 2431 ^ [_365358, _365543, _365724]), _365543))], (2444 ^ _280972) ^ [] : [-(in(ordered_pair(2430 ^ [_365358, _365543, _365724], 2442 ^ [_365358, _365543, _365724]), _365358))]], 2434 ^ _280972 : [(2437 ^ _280972) ^ [_367188] : [in(ordered_pair(2430 ^ [_365358, _365543, _365724], _367188), _365358), in(ordered_pair(_367188, 2431 ^ [_365358, _365543, _365724]), _365543)], (2435 ^ _280972) ^ [] : [-(in(ordered_pair(2430 ^ [_365358, _365543, _365724], 2431 ^ [_365358, _365543, _365724]), _365724))]]]]]]]]], (3283 ^ _280972) ^ [_394090, _394092] : [subset(_394092, singleton(_394090)), -(_394092 = empty_set), -(_394092 = singleton(_394090))], (4665 ^ _280972) ^ [_440237, _440239, _440241] : [in(_440241, _440239), element(_440239, powerset(_440237)), empty(_440237)], (366 ^ _280972) ^ [_292577, _292579, _292581, _292583] : [-(fiber(_292583, _292579) = fiber(_292581, _292577)), _292583 = _292581, _292579 = _292577], (20 ^ _280972) ^ [_281748, _281750, _281752, _281754] : [-(is_antisymmetric_in(_281752, _281748)), is_antisymmetric_in(_281754, _281750), _281754 = _281752, _281750 = _281748], (2827 ^ _280972) ^ [] : [-(empty(empty_set))], (2819 ^ _280972) ^ [_378721] : [empty(_378721), 2822 ^ _280972 : [(2825 ^ _280972) ^ [] : [-(relation(relation_inverse(_378721)))], (2823 ^ _280972) ^ [] : [-(empty(relation_inverse(_378721)))]]], (4223 ^ _280972) ^ [_425362, _425364] : [in(_425364, _425362), -(subset(singleton(_425364), _425362))], (3941 ^ _280972) ^ [_416037, _416039] : [relation(_416037), function(_416037), 3948 ^ _280972 : [(3949 ^ _280972) ^ [_416286] : [relation(_416286), function(_416286), in(_416039, relation_dom(relation_composition(_416286, _416037))), -(apply(relation_composition(_416286, _416037), _416039) = apply(_416037, apply(_416286, _416039)))]]], (3118 ^ _280972) ^ [_388262, _388264] : [disjoint(singleton(_388264), _388262), in(_388264, _388262)], (4929 ^ _280972) ^ [_448744, _448746] : [relation(_448744), -(subset(relation_dom_restriction(_448744, _448746), _448744))], (2913 ^ _280972) ^ [_381549] : [empty(singleton(_381549))], (484 ^ _280972) ^ [_296837, _296839, _296841, _296843] : [-(subset_complement(_296843, _296839) = subset_complement(_296841, _296837)), _296843 = _296841, _296839 = _296837], (2015 ^ _280972) ^ [_352127] : [relation(_352127), 2018 ^ _280972 : [(2033 ^ _280972) ^ [] : [-(well_ordering(_352127)), reflexive(_352127), transitive(_352127), antisymmetric(_352127), connected(_352127), well_founded_relation(_352127)], (2019 ^ _280972) ^ [] : [well_ordering(_352127), 2022 ^ _280972 : [(2023 ^ _280972) ^ [] : [-(reflexive(_352127))], (2027 ^ _280972) ^ [] : [-(antisymmetric(_352127))], (2031 ^ _280972) ^ [] : [-(well_founded_relation(_352127))], (2029 ^ _280972) ^ [] : [-(connected(_352127))], (2025 ^ _280972) ^ [] : [-(transitive(_352127))]]]]], (4695 ^ _280972) ^ [_441086, _441088] : [subset(_441088, _441086), proper_subset(_441086, _441088)], (3301 ^ _280972) ^ [_394644, _394646] : [in(_394646, _394644), -(subset(_394646, union(_394644)))], (4416 ^ _280972) ^ [_431837] : [relation(_431837), 4419 ^ _280972 : [(4420 ^ _280972) ^ [_431984] : [relation(_431984), subset(relation_rng(_431837), relation_dom(_431984)), -(relation_dom(relation_composition(_431837, _431984)) = relation_dom(_431837))]]], (4267 ^ _280972) ^ [_426846] : [-(set_difference(_426846, empty_set) = _426846)], (76 ^ _280972) ^ [_283496, _283498] : [-(reflexive(_283496)), _283498 = _283496, reflexive(_283498)], (3387 ^ _280972) ^ [] : [-(empty(3385 ^ []))], (3698 ^ _280972) ^ [_408101, _408103] : [relation(_408101), subset(_408103, relation_dom(_408101)), -(subset(_408103, relation_inverse_image(_408101, relation_image(_408101, _408103))))], (3564 ^ _280972) ^ [_403221, _403223] : [relation(_403221), -(subset(relation_rng(relation_rng_restriction(_403223, _403221)), _403223))], (2722 ^ _280972) ^ [_375722] : [relation(_375722), -(relation(relation_inverse(_375722)))], (3855 ^ _280972) ^ [_413273] : [-(set_union2(_413273, empty_set) = _413273)], (4 ^ _280972) ^ [_281203, _281205] : [_281205 = _281203, -(_281203 = _281205)], (4715 ^ _280972) ^ [_441667, _441669, _441671] : [-(disjoint(_441671, _441667)), subset(_441671, _441669), disjoint(_441669, _441667)], (2740 ^ _280972) ^ [_376164, _376166] : [-(relation(relation_composition(_376166, _376164))), relation(_376166), relation(_376164)], (328 ^ _280972) ^ [_291178, _291180] : [-(relation(_291178)), _291180 = _291178, relation(_291180)], (4259 ^ _280972) ^ [_426581, _426583] : [4260 ^ _280972 : [(4263 ^ _280972) ^ [] : [_426583 = singleton(_426581)], (4261 ^ _280972) ^ [] : [_426583 = empty_set]], -(subset(_426583, singleton(_426581)))], (276 ^ _280972) ^ [_289579, _289581, _289583, _289585] : [-(well_orders(_289583, _289579)), well_orders(_289585, _289581), _289585 = _289583, _289581 = _289579], (3363 ^ _280972) ^ [] : [-(function(3359 ^ []))], (4525 ^ _280972) ^ [_435609] : [relation(_435609), function(_435609), one_to_one(_435609), 4536 ^ _280972 : [(4537 ^ _280972) ^ [_435996] : [relation(_435996), function(_435996), 4544 ^ _280972 : [(4545 ^ _280972) ^ [] : [_435996 = function_inverse(_435609), 4548 ^ _280972 : [(4563 ^ _280972) ^ [_436887, _436889] : [4570 ^ _280972 : [(4573 ^ _280972) ^ [] : [-(_436887 = apply(_435996, _436889))], (4571 ^ _280972) ^ [] : [-(in(_436889, relation_rng(_435609)))]], in(_436887, relation_dom(_435609)), _436889 = apply(_435609, _436887)], (4551 ^ _280972) ^ [_436513, _436515] : [4558 ^ _280972 : [(4561 ^ _280972) ^ [] : [-(_436515 = apply(_435609, _436513))], (4559 ^ _280972) ^ [] : [-(in(_436513, relation_dom(_435609)))]], in(_436515, relation_rng(_435609)), _436513 = apply(_435996, _436515)], (4549 ^ _280972) ^ [] : [-(relation_dom(_435996) = relation_rng(_435609))]]], (4575 ^ _280972) ^ [] : [-(_435996 = function_inverse(_435609)), relation_dom(_435996) = relation_rng(_435609), 4584 ^ _280972 : [(4589 ^ _280972) ^ [] : [in(4581 ^ [_435609, _435996], relation_dom(_435609)), 4580 ^ [_435609, _435996] = apply(_435609, 4581 ^ [_435609, _435996])], (4587 ^ _280972) ^ [] : [-(4581 ^ [_435609, _435996] = apply(_435996, 4580 ^ [_435609, _435996]))], (4585 ^ _280972) ^ [] : [-(in(4580 ^ [_435609, _435996], relation_rng(_435609)))]], 4594 ^ _280972 : [(4599 ^ _280972) ^ [] : [in(4580 ^ [_435609, _435996], relation_rng(_435609)), 4581 ^ [_435609, _435996] = apply(_435996, 4580 ^ [_435609, _435996])], (4597 ^ _280972) ^ [] : [-(4580 ^ [_435609, _435996] = apply(_435609, 4581 ^ [_435609, _435996]))], (4595 ^ _280972) ^ [] : [-(in(4581 ^ [_435609, _435996], relation_dom(_435609)))]]]]]]], (3366 ^ _280972) ^ [] : [-(epsilon_transitive(3364 ^ []))], (2807 ^ _280972) ^ [_378357, _378359] : [2814 ^ _280972 : [(2817 ^ _280972) ^ [] : [-(relation(relation_composition(_378357, _378359)))], (2815 ^ _280972) ^ [] : [-(empty(relation_composition(_378357, _378359)))]], empty(_378359), relation(_378357)], (3375 ^ _280972) ^ [] : [-(relation(3371 ^ []))], (638 ^ _280972) ^ [_302531, _302533] : [proper_subset(_302533, _302531), proper_subset(_302531, _302533)], (3025 ^ _280972) ^ [_385100] : [empty(relation_rng(_385100)), -(empty(_385100)), relation(_385100)], (3738 ^ _280972) ^ [_409393, _409395, _409397] : [relation(_409393), 3741 ^ _280972 : [(3753 ^ _280972) ^ [] : [-(in(_409397, relation_inverse_image(_409393, _409395))), 3754 ^ _280972 : [(3755 ^ _280972) ^ [_409994] : [in(_409994, relation_rng(_409393)), in(ordered_pair(_409397, _409994), _409393), in(_409994, _409395)]]], (3742 ^ _280972) ^ [] : [in(_409397, relation_inverse_image(_409393, _409395)), 3746 ^ _280972 : [(3751 ^ _280972) ^ [] : [-(in(3745 ^ [_409393, _409395, _409397], _409395))], (3749 ^ _280972) ^ [] : [-(in(ordered_pair(_409397, 3745 ^ [_409393, _409395, _409397]), _409393))], (3747 ^ _280972) ^ [] : [-(in(3745 ^ [_409393, _409395, _409397], relation_rng(_409393)))]]]]], (2716 ^ _280972) ^ [] : [true___, -(true___)], (600 ^ _280972) ^ [_300989, _300991] : [_300991 = _300989, -(singleton(_300991) = singleton(_300989))], (3051 ^ _280972) ^ [_385921, _385923] : [3058 ^ _280972 : [(3061 ^ _280972) ^ [] : [-(relation(relation_composition(_385923, _385921)))], (3059 ^ _280972) ^ [] : [-(empty(relation_composition(_385923, _385921)))]], empty(_385923), relation(_385921)], (3073 ^ _280972) ^ [_386705] : [relation(_386705), -(relation_inverse(relation_inverse(_386705)) = _386705)], (338 ^ _280972) ^ [_291481, _291483, _291485, _291487] : [-(subset(_291485, _291481)), subset(_291487, _291483), _291487 = _291485, _291483 = _291481], (1705 ^ _280972) ^ [_340785] : [relation(_340785), 1708 ^ _280972 : [(1709 ^ _280972) ^ [_340943] : [relation(_340943), 1712 ^ _280972 : [(1713 ^ _280972) ^ [] : [subset(_340785, _340943), 1716 ^ _280972 : [(1717 ^ _280972) ^ [_341219, _341221] : [in(ordered_pair(_341221, _341219), _340785), -(in(ordered_pair(_341221, _341219), _340943))]]], (1723 ^ _280972) ^ [] : [1726 ^ _280972 : [(1729 ^ _280972) ^ [] : [in(ordered_pair(1724 ^ [_340785, _340943], 1725 ^ [_340785, _340943]), _340943)], (1727 ^ _280972) ^ [] : [-(in(ordered_pair(1724 ^ [_340785, _340943], 1725 ^ [_340785, _340943]), _340785))]], -(subset(_340785, _340943))]]]]], (4759 ^ _280972) ^ [_442971, _442973] : [-(in(_442971, _442973)), -(set_difference(_442973, singleton(_442971)) = _442973)], (10 ^ _280972) ^ [_281407, _281409, _281411] : [-(_281411 = _281407), _281411 = _281409, _281409 = _281407], (4971 ^ _280972) ^ [_450010] : [relation(_450010), 4974 ^ _280972 : [(4981 ^ _280972) ^ [] : [well_ordering(_450010), -(well_orders(_450010, relation_field(_450010)))], (4975 ^ _280972) ^ [] : [well_orders(_450010, relation_field(_450010)), -(well_ordering(_450010))]]], (3542 ^ _280972) ^ [_402562, _402564, _402566] : [relation(_402562), 3545 ^ _280972 : [(3554 ^ _280972) ^ [] : [-(in(_402566, relation_rng(relation_rng_restriction(_402564, _402562)))), in(_402566, _402564), in(_402566, relation_rng(_402562))], (3546 ^ _280972) ^ [] : [in(_402566, relation_rng(relation_rng_restriction(_402564, _402562))), 3549 ^ _280972 : [(3552 ^ _280972) ^ [] : [-(in(_402566, relation_rng(_402562)))], (3550 ^ _280972) ^ [] : [-(in(_402566, _402564))]]]]], (1395 ^ _280972) ^ [_329623] : [epsilon_transitive(_329623), 1398 ^ _280972 : [(1399 ^ _280972) ^ [_329754] : [in(_329754, _329623), -(subset(_329754, _329623))]]], (4041 ^ _280972) ^ [_419210] : [-(set_intersection2(_419210, empty_set) = empty_set)], (3409 ^ _280972) ^ [] : [-(ordinal(3395 ^ []))], (2452 ^ _280972) ^ [_367860] : [relation(_367860), 2455 ^ _280972 : [(2456 ^ _280972) ^ [_368074] : [is_transitive_in(_367860, _368074), 2459 ^ _280972 : [(2460 ^ _280972) ^ [_368284, _368286, _368288] : [-(in(ordered_pair(_368288, _368284), _367860)), in(_368288, _368074), in(_368286, _368074), in(_368284, _368074), in(ordered_pair(_368288, _368286), _367860), in(ordered_pair(_368286, _368284), _367860)]]], (2482 ^ _280972) ^ [_368895] : [2486 ^ _280972 : [(2489 ^ _280972) ^ [] : [-(in(2484 ^ [_367860, _368895], _368895))], (2487 ^ _280972) ^ [] : [-(in(2483 ^ [_367860, _368895], _368895))], (2497 ^ _280972) ^ [] : [in(ordered_pair(2483 ^ [_367860, _368895], 2485 ^ [_367860, _368895]), _367860)], (2493 ^ _280972) ^ [] : [-(in(ordered_pair(2483 ^ [_367860, _368895], 2484 ^ [_367860, _368895]), _367860))], (2495 ^ _280972) ^ [] : [-(in(ordered_pair(2484 ^ [_367860, _368895], 2485 ^ [_367860, _368895]), _367860))], (2491 ^ _280972) ^ [] : [-(in(2485 ^ [_367860, _368895], _368895))]], -(is_transitive_in(_367860, _368895))]]], (3458 ^ _280972) ^ [_399730, _399732] : [element(_399730, powerset(powerset(_399732))), -(meet_of_subsets(_399732, _399730) = set_meet(_399730))], (3370 ^ _280972) ^ [] : [-(ordinal(3364 ^ []))], (4122 ^ _280972) ^ [_421934] : [ordinal(_421934), 4125 ^ _280972 : [(4126 ^ _280972) ^ [_422072] : [ordinal(_422072), 4129 ^ _280972 : [(4136 ^ _280972) ^ [] : [ordinal_subset(succ(_421934), _422072), -(in(_421934, _422072))], (4130 ^ _280972) ^ [] : [in(_421934, _422072), -(ordinal_subset(succ(_421934), _422072))]]]]], (194 ^ _280972) ^ [_287039, _287041] : [-(well_founded_relation(_287039)), _287041 = _287039, well_founded_relation(_287041)], (3863 ^ _280972) ^ [_413607, _413609, _413611] : [-(subset(_413611, _413607)), subset(_413611, _413609), subset(_413609, _413607)], (588 ^ _280972) ^ [_300553, _300555] : [_300555 = _300553, -(union(_300555) = union(_300553))], (4617 ^ _280972) ^ [_438768] : [relation(_438768), function(_438768), one_to_one(_438768), 4628 ^ _280972 : [(4631 ^ _280972) ^ [] : [-(relation_dom(_438768) = relation_rng(function_inverse(_438768)))], (4629 ^ _280972) ^ [] : [-(relation_rng(_438768) = relation_dom(function_inverse(_438768)))]]], (106 ^ _280972) ^ [_284381, _284383] : [-(connected(_284381)), _284383 = _284381, connected(_284383)], (1470 ^ _280972) ^ [_332151, _332153] : [empty(_332153), 1473 ^ _280972 : [(1480 ^ _280972) ^ [] : [empty(_332151), -(element(_332151, _332153))], (1474 ^ _280972) ^ [] : [element(_332151, _332153), -(empty(_332151))]]], (556 ^ _280972) ^ [_299427, _299429, _299431, _299433] : [-(relation_composition(_299433, _299429) = relation_composition(_299431, _299427)), _299433 = _299431, _299429 = _299427], (4997 ^ _280972) ^ [_450798, _450800, _450802] : [singleton(_450802) = unordered_pair(_450800, _450798), -(_450802 = _450800)], (616 ^ _280972) ^ [_301566, _301568] : [_301568 = _301566, -(relation_field(_301568) = relation_field(_301566))], (3570 ^ _280972) ^ [_403439, _403441] : [relation(_403439), -(subset(relation_rng_restriction(_403441, _403439), _403439))], (494 ^ _280972) ^ [_297168, _297170] : [_297170 = _297168, -(function_inverse(_297170) = function_inverse(_297168))], (1154 ^ _280972) ^ [_320985, _320987, _320989, _320991] : [_320985 = unordered_triple(_320991, _320989, _320987), 1157 ^ _280972 : [(1158 ^ _280972) ^ [_321187] : [in(_321187, _320985), -(_321187 = _320991), -(_321187 = _320989), -(_321187 = _320987)], (1172 ^ _280972) ^ [_321587] : [1173 ^ _280972 : [(1178 ^ _280972) ^ [] : [_321587 = _320987], (1176 ^ _280972) ^ [] : [_321587 = _320989], (1174 ^ _280972) ^ [] : [_321587 = _320991]], -(in(_321587, _320985))]]], (2921 ^ _280972) ^ [_381859] : [2932 ^ _280972 : [(2935 ^ _280972) ^ [] : [-(function(relation_inverse(_381859)))], (2933 ^ _280972) ^ [] : [-(relation(relation_inverse(_381859)))]], relation(_381859), function(_381859), one_to_one(_381859)], (3334 ^ _280972) ^ [_395886, _395888, _395890] : [relation(_395886), function(_395886), 3341 ^ _280972 : [(3350 ^ _280972) ^ [] : [-(in(_395888, relation_dom(relation_dom_restriction(_395886, _395890)))), in(_395888, relation_dom(_395886)), in(_395888, _395890)], (3342 ^ _280972) ^ [] : [in(_395888, relation_dom(relation_dom_restriction(_395886, _395890))), 3345 ^ _280972 : [(3348 ^ _280972) ^ [] : [-(in(_395888, _395890))], (3346 ^ _280972) ^ [] : [-(in(_395888, relation_dom(_395886)))]]]]], (4753 ^ _280972) ^ [_442798, _442800] : [set_difference(_442800, singleton(_442798)) = _442800, in(_442798, _442800)], (3845 ^ _280972) ^ [_412987, _412989, _412991] : [-(subset(_412991, set_intersection2(_412989, _412987))), subset(_412991, _412989), subset(_412991, _412987)], (3873 ^ _280972) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (3124 ^ _280972) ^ [_388475, _388477] : [-(in(_388477, _388475)), -(disjoint(singleton(_388477), _388475))], (3403 ^ _280972) ^ [] : [-(empty(3395 ^ []))], (5009 ^ _280972) ^ [_451252, _451254] : [in(_451254, _451252), -(subset(_451254, union(_451252)))], (314 ^ _280972) ^ [_290762, _290764, _290766, _290768] : [-(in(_290766, _290762)), in(_290768, _290764), _290768 = _290766, _290764 = _290762], (1968 ^ _280972) ^ [_350311] : [-(cast_to_subset(_350311) = _350311)], (3417 ^ _280972) ^ [_398411] : [-(element(3415 ^ [_398411], powerset(_398411)))], (2881 ^ _280972) ^ [_380585, _380587] : [empty(ordered_pair(_380587, _380585))], (4693 ^ _280972) ^ [] : [-(relation_rng(empty_set) = empty_set)], (3241 ^ _280972) ^ [_392604] : [relation(_392604), 3244 ^ _280972 : [(3245 ^ _280972) ^ [] : [connected(_392604), 3248 ^ _280972 : [(3249 ^ _280972) ^ [_392898, _392900] : [in(_392900, relation_field(_392604)), in(_392898, relation_field(_392604)), -(_392900 = _392898), -(in(ordered_pair(_392900, _392898), _392604)), -(in(ordered_pair(_392898, _392900), _392604))]]], (3267 ^ _280972) ^ [] : [3270 ^ _280972 : [(3271 ^ _280972) ^ [] : [-(in(3268 ^ [_392604], relation_field(_392604)))], (3275 ^ _280972) ^ [] : [3268 ^ [_392604] = 3269 ^ [_392604]], (3279 ^ _280972) ^ [] : [in(ordered_pair(3269 ^ [_392604], 3268 ^ [_392604]), _392604)], (3277 ^ _280972) ^ [] : [in(ordered_pair(3268 ^ [_392604], 3269 ^ [_392604]), _392604)], (3273 ^ _280972) ^ [] : [-(in(3269 ^ [_392604], relation_field(_392604)))]], -(connected(_392604))]]], (3035 ^ _280972) ^ [_385377] : [empty(_385377), 3038 ^ _280972 : [(3041 ^ _280972) ^ [] : [-(relation(relation_dom(_385377)))], (3039 ^ _280972) ^ [] : [-(empty(relation_dom(_385377)))]]], (3590 ^ _280972) ^ [_404206, _404208] : [relation(_404206), -(relation_rng(relation_rng_restriction(_404208, _404206)) = set_intersection2(relation_rng(_404206), _404208))], (3231 ^ _280972) ^ [_392298, _392300, _392302] : [subset(_392302, _392300), -(in(_392298, _392302)), -(subset(_392302, set_difference(_392300, singleton(_392298))))], (4507 ^ _280972) ^ [_434977] : [-(_434977 = empty_set), 4510 ^ _280972 : [(4511 ^ _280972) ^ [_435137] : [element(_435137, powerset(_434977)), 4514 ^ _280972 : [(4515 ^ _280972) ^ [_435291] : [element(_435291, _434977), -(in(_435291, _435137)), -(in(_435291, subset_complement(_434977, _435137)))]]]]], (4370 ^ _280972) ^ [_430275, _430277] : [element(_430275, powerset(_430277)), 4373 ^ _280972 : [(4374 ^ _280972) ^ [_430427] : [element(_430427, powerset(_430277)), 4377 ^ _280972 : [(4384 ^ _280972) ^ [] : [subset(_430275, subset_complement(_430277, _430427)), -(disjoint(_430275, _430427))], (4378 ^ _280972) ^ [] : [disjoint(_430275, _430427), -(subset(_430275, subset_complement(_430277, _430427)))]]]]], (4501 ^ _280972) ^ [_434752, _434754] : [4502 ^ _280972 : [(4503 ^ _280972) ^ [_434825] : [in(_434825, set_intersection2(_434754, _434752))]], disjoint(_434754, _434752)], (4156 ^ _280972) ^ [_423126, _423128] : [relation(_423126), function(_423126), 4163 ^ _280972 : [(4176 ^ _280972) ^ [] : [-(_423126 = identity_relation(_423128)), relation_dom(_423126) = _423128, 4182 ^ _280972 : [(4185 ^ _280972) ^ [] : [apply(_423126, 4181 ^ [_423126, _423128]) = 4181 ^ [_423126, _423128]], (4183 ^ _280972) ^ [] : [-(in(4181 ^ [_423126, _423128], _423128))]]], (4164 ^ _280972) ^ [] : [_423126 = identity_relation(_423128), 4167 ^ _280972 : [(4170 ^ _280972) ^ [_423545] : [in(_423545, _423128), -(apply(_423126, _423545) = _423545)], (4168 ^ _280972) ^ [] : [-(relation_dom(_423126) = _423128)]]]]], (1211 ^ _280972) ^ [_323051] : [relation(_323051), 1214 ^ _280972 : [(1215 ^ _280972) ^ [_323199] : [in(_323199, _323051), -(_323199 = ordered_pair(1218 ^ [_323051, _323199], 1219 ^ [_323051, _323199]))]]], (4269 ^ _280972) ^ [_426970, _426972, _426974] : [in(_426974, _426972), in(_426972, _426970), in(_426970, _426974)], (2242 ^ _280972) ^ [_359864] : [_359864 = union(_359864), -(being_limit_ordinal(_359864))], (722 ^ _280972) ^ [_305147, _305149] : [relation(_305147), 725 ^ _280972 : [(726 ^ _280972) ^ [] : [_305147 = identity_relation(_305149), 729 ^ _280972 : [(738 ^ _280972) ^ [_305720, _305722] : [-(in(ordered_pair(_305722, _305720), _305147)), in(_305722, _305149), _305722 = _305720], (730 ^ _280972) ^ [_305457, _305459] : [in(ordered_pair(_305459, _305457), _305147), 733 ^ _280972 : [(736 ^ _280972) ^ [] : [-(_305459 = _305457)], (734 ^ _280972) ^ [] : [-(in(_305459, _305149))]]]]], (748 ^ _280972) ^ [] : [-(_305147 = identity_relation(_305149)), 761 ^ _280972 : [(766 ^ _280972) ^ [] : [in(ordered_pair(749 ^ [_305147, _305149], 750 ^ [_305147, _305149]), _305147)], (764 ^ _280972) ^ [] : [-(749 ^ [_305147, _305149] = 750 ^ [_305147, _305149])], (762 ^ _280972) ^ [] : [-(in(749 ^ [_305147, _305149], _305149))]], 753 ^ _280972 : [(756 ^ _280972) ^ [] : [in(749 ^ [_305147, _305149], _305149), 749 ^ [_305147, _305149] = 750 ^ [_305147, _305149]], (754 ^ _280972) ^ [] : [-(in(ordered_pair(749 ^ [_305147, _305149], 750 ^ [_305147, _305149]), _305147))]]]]], (1733 ^ _280972) ^ [_341868, _341870] : [subset(_341870, _341868), 1736 ^ _280972 : [(1737 ^ _280972) ^ [_342005] : [in(_342005, _341870), -(in(_342005, _341868))]]], (2236 ^ _280972) ^ [_359706] : [being_limit_ordinal(_359706), -(_359706 = union(_359706))], (3576 ^ _280972) ^ [_403653, _403655] : [relation(_403653), -(subset(relation_rng(relation_rng_restriction(_403655, _403653)), relation_rng(_403653)))], (3613 ^ _280972) ^ [_405115] : [-(in(_405115, 3611 ^ [_405115]))], (204 ^ _280972) ^ [_287362, _287364, _287366, _287368] : [-(is_well_founded_in(_287366, _287362)), is_well_founded_in(_287368, _287364), _287368 = _287366, _287364 = _287362], (3921 ^ _280972) ^ [_415395] : [epsilon_transitive(_415395), 3924 ^ _280972 : [(3925 ^ _280972) ^ [_415531] : [ordinal(_415531), proper_subset(_415395, _415531), -(in(_415395, _415531))]]], (3401 ^ _280972) ^ [] : [-(one_to_one(3395 ^ []))], (2885 ^ _280972) ^ [_380732] : [-(function(identity_relation(_380732)))], (706 ^ _280972) ^ [_304645, _304647] : [-(set_intersection2(_304647, _304645) = set_intersection2(_304645, _304647))], (34 ^ _280972) ^ [_282192, _282194, _282196, _282198] : [-(is_connected_in(_282196, _282192)), is_connected_in(_282198, _282194), _282198 = _282196, _282194 = _282192], (2805 ^ _280972) ^ [_378245] : [-(element(2803 ^ [_378245], _378245))], (2654 ^ _280972) ^ [_374023] : [2661 ^ _280972 : [(2664 ^ _280972) ^ [] : [-(function(function_inverse(_374023)))], (2662 ^ _280972) ^ [] : [-(relation(function_inverse(_374023)))]], relation(_374023), function(_374023)], (4880 ^ _280972) ^ [_447028, _447030] : [in(_447030, _447028), 4884 ^ _280972 : [(4887 ^ _280972) ^ [_447319] : [in(_447319, _447028), in(_447319, 4883 ^ [_447028, _447030])], (4885 ^ _280972) ^ [] : [-(in(4883 ^ [_447028, _447030], _447028))]]], (1638 ^ _280972) ^ [_338178, _338180, _338182] : [-(_338178 = cartesian_product2(_338182, _338180)), 1656 ^ _280972 : [(1659 ^ _280972) ^ [] : [-(in(1655 ^ [_338178, _338180, _338182], _338180))], (1661 ^ _280972) ^ [] : [-(1639 ^ [_338178, _338180, _338182] = ordered_pair(1654 ^ [_338178, _338180, _338182], 1655 ^ [_338178, _338180, _338182]))], (1663 ^ _280972) ^ [] : [in(1639 ^ [_338178, _338180, _338182], _338178)], (1657 ^ _280972) ^ [] : [-(in(1654 ^ [_338178, _338180, _338182], _338182))]], 1642 ^ _280972 : [(1645 ^ _280972) ^ [_338516, _338518] : [in(_338518, _338182), in(_338516, _338180), 1639 ^ [_338178, _338180, _338182] = ordered_pair(_338518, _338516)], (1643 ^ _280972) ^ [] : [-(in(1639 ^ [_338178, _338180, _338182], _338178))]]], (2564 ^ _280972) ^ [_372038] : [relation(_372038), function(_372038), one_to_one(_372038), -(function_inverse(_372038) = relation_inverse(_372038))], (3427 ^ _280972) ^ [] : [-(function(3423 ^ []))], (692 ^ _280972) ^ [_304119] : [empty(_304119), 695 ^ _280972 : [(700 ^ _280972) ^ [] : [-(ordinal(_304119))], (698 ^ _280972) ^ [] : [-(epsilon_connected(_304119))], (696 ^ _280972) ^ [] : [-(epsilon_transitive(_304119))]]], (2348 ^ _280972) ^ [_363844, _363846] : [set_intersection2(_363846, _363844) = empty_set, -(disjoint(_363846, _363844))], (2798 ^ _280972) ^ [] : [true___, -(true___)], (412 ^ _280972) ^ [_294231, _294233, _294235, _294237] : [-(cartesian_product2(_294237, _294233) = cartesian_product2(_294235, _294231)), _294237 = _294235, _294233 = _294231], (3714 ^ _280972) ^ [_408616, _408618] : [relation(_408616), function(_408616), subset(_408618, relation_rng(_408616)), -(relation_image(_408616, relation_inverse_image(_408616, _408618)) = _408618)], (1788 ^ _280972) ^ [_344028, _344030, _344032] : [_344028 = set_intersection2(_344032, _344030), 1791 ^ _280972 : [(1800 ^ _280972) ^ [_344469] : [-(in(_344469, _344028)), in(_344469, _344032), in(_344469, _344030)], (1792 ^ _280972) ^ [_344210] : [in(_344210, _344028), 1795 ^ _280972 : [(1798 ^ _280972) ^ [] : [-(in(_344210, _344030))], (1796 ^ _280972) ^ [] : [-(in(_344210, _344032))]]]]], (2903 ^ _280972) ^ [_381280, _381282] : [-(relation(set_union2(_381282, _381280))), relation(_381282), relation(_381280)], (550 ^ _280972) ^ [_299181, _299183] : [_299183 = _299181, -(relation_dom(_299183) = relation_dom(_299181))], (3728 ^ _280972) ^ [_409004] : [relation(_409004), 3731 ^ _280972 : [(3732 ^ _280972) ^ [_409144] : [relation(_409144), -(relation_rng(relation_composition(_409004, _409144)) = relation_image(_409144, relation_rng(_409004)))]]], (4482 ^ _280972) ^ [_434060] : [-(set_difference(empty_set, _434060) = empty_set)], (3377 ^ _280972) ^ [_397131] : [-(empty(_397131)), 3381 ^ _280972 : [(3384 ^ _280972) ^ [] : [empty(3380 ^ [_397131])], (3382 ^ _280972) ^ [] : [-(element(3380 ^ [_397131], powerset(_397131)))]]], (3464 ^ _280972) ^ [_399972, _399974, _399976] : [-(subset_difference(_399976, _399974, _399972) = set_difference(_399974, _399972)), element(_399974, powerset(_399976)), element(_399972, powerset(_399976))], (474 ^ _280972) ^ [_296478, _296480, _296482, _296484] : [-(meet_of_subsets(_296484, _296480) = meet_of_subsets(_296482, _296478)), _296484 = _296482, _296480 = _296478], (2594 ^ _280972) ^ [] : [true___, -(true___)], (1926 ^ _280972) ^ [_348689] : [relation(_348689), 1929 ^ _280972 : [(1930 ^ _280972) ^ [_348889] : [is_antisymmetric_in(_348689, _348889), 1933 ^ _280972 : [(1934 ^ _280972) ^ [_349071, _349073] : [-(_349073 = _349071), in(_349073, _348889), in(_349071, _348889), in(ordered_pair(_349073, _349071), _348689), in(ordered_pair(_349071, _349073), _348689)]]], (1952 ^ _280972) ^ [_349557] : [1955 ^ _280972 : [(1956 ^ _280972) ^ [] : [-(in(1953 ^ [_348689, _349557], _349557))], (1960 ^ _280972) ^ [] : [-(in(ordered_pair(1953 ^ [_348689, _349557], 1954 ^ [_348689, _349557]), _348689))], (1964 ^ _280972) ^ [] : [1953 ^ [_348689, _349557] = 1954 ^ [_348689, _349557]], (1962 ^ _280972) ^ [] : [-(in(ordered_pair(1954 ^ [_348689, _349557], 1953 ^ [_348689, _349557]), _348689))], (1958 ^ _280972) ^ [] : [-(in(1954 ^ [_348689, _349557], _349557))]], -(is_antisymmetric_in(_348689, _349557))]]], (3625 ^ _280972) ^ [_405542, _405544] : [in(_405542, 3611 ^ [_405544]), -(in(powerset(_405542), 3611 ^ [_405544]))], (2780 ^ _280972) ^ [_377553, _377555] : [element(_377553, powerset(powerset(_377555))), -(element(complements_of_subsets(_377555, _377553), powerset(powerset(_377555))))], (3079 ^ _280972) ^ [_386915, _386917] : [element(_386915, powerset(powerset(_386917))), -(complements_of_subsets(_386917, complements_of_subsets(_386917, _386915)) = _386915)], (2993 ^ _280972) ^ [_384153, _384155] : [empty(cartesian_product2(_384155, _384153)), -(empty(_384155)), -(empty(_384153))], (3631 ^ _280972) ^ [_405742, _405744] : [subset(_405742, 3611 ^ [_405744]), -(are_equipotent(_405742, 3611 ^ [_405744])), -(in(_405742, 3611 ^ [_405744]))], (256 ^ _280972) ^ [_288961, _288963] : [-(empty(_288961)), _288963 = _288961, empty(_288963)], (2989 ^ _280972) ^ [] : [-(empty(empty_set))], (2196 ^ _280972) ^ [_358471] : [relation(_358471), 2199 ^ _280972 : [(2214 ^ _280972) ^ [_359116] : [-(well_orders(_358471, _359116)), is_reflexive_in(_358471, _359116), is_transitive_in(_358471, _359116), is_antisymmetric_in(_358471, _359116), is_connected_in(_358471, _359116), is_well_founded_in(_358471, _359116)], (2200 ^ _280972) ^ [_358655] : [well_orders(_358471, _358655), 2203 ^ _280972 : [(2204 ^ _280972) ^ [] : [-(is_reflexive_in(_358471, _358655))], (2208 ^ _280972) ^ [] : [-(is_antisymmetric_in(_358471, _358655))], (2212 ^ _280972) ^ [] : [-(is_well_founded_in(_358471, _358655))], (2210 ^ _280972) ^ [] : [-(is_connected_in(_358471, _358655))], (2206 ^ _280972) ^ [] : [-(is_transitive_in(_358471, _358655))]]]]], (4197 ^ _280972) ^ [_424453] : [relation(_424453), 4200 ^ _280972 : [(4203 ^ _280972) ^ [] : [-(relation_dom(_424453) = relation_rng(relation_inverse(_424453)))], (4201 ^ _280972) ^ [] : [-(relation_rng(_424453) = relation_dom(relation_inverse(_424453)))]]], (3407 ^ _280972) ^ [] : [-(epsilon_connected(3395 ^ []))], (232 ^ _280972) ^ [_288222, _288224] : [-(one_to_one(_288222)), _288224 = _288222, one_to_one(_288224)], (3995 ^ _280972) ^ [_417697] : [ordinal(_417697), 3998 ^ _280972 : [(3999 ^ _280972) ^ [_417847] : [ordinal(_417847), -(in(_417697, _417847)), -(_417697 = _417847), -(in(_417847, _417697))]]], (4834 ^ _280972) ^ [_445507] : [-(relation_dom(identity_relation(_445507)) = _445507)], (1364 ^ _280972) ^ [_328551, _328553] : [_328551 = powerset(_328553), 1367 ^ _280972 : [(1374 ^ _280972) ^ [_328893] : [subset(_328893, _328553), -(in(_328893, _328551))], (1368 ^ _280972) ^ [_328721] : [in(_328721, _328551), -(subset(_328721, _328553))]]], (664 ^ _280972) ^ [_303357] : [675 ^ _280972 : [(680 ^ _280972) ^ [] : [-(one_to_one(_303357))], (678 ^ _280972) ^ [] : [-(function(_303357))], (676 ^ _280972) ^ [] : [-(relation(_303357))]], relation(_303357), empty(_303357), function(_303357)], (2680 ^ _280972) ^ [_374705, _374707] : [relation(_374707), -(relation(relation_restriction(_374707, _374705)))], (4217 ^ _280972) ^ [_425196, _425198] : [subset(singleton(_425198), _425196), -(in(_425198, _425196))], (1304 ^ _280972) ^ [_326512, _326514] : [_326514 = empty_set, 1307 ^ _280972 : [(1314 ^ _280972) ^ [] : [_326512 = empty_set, -(_326512 = set_meet(_326514))], (1308 ^ _280972) ^ [] : [_326512 = set_meet(_326514), -(_326512 = empty_set)]]], (1232 ^ _280972) ^ [_323906] : [relation(_323906), 1235 ^ _280972 : [(1236 ^ _280972) ^ [_324080] : [is_reflexive_in(_323906, _324080), 1239 ^ _280972 : [(1240 ^ _280972) ^ [_324222] : [in(_324222, _324080), -(in(ordered_pair(_324222, _324222), _323906))]]], (1246 ^ _280972) ^ [_324405] : [1248 ^ _280972 : [(1251 ^ _280972) ^ [] : [in(ordered_pair(1247 ^ [_323906, _324405], 1247 ^ [_323906, _324405]), _323906)], (1249 ^ _280972) ^ [] : [-(in(1247 ^ [_323906, _324405], _324405))]], -(is_reflexive_in(_323906, _324405))]]], (2501 ^ _280972) ^ [_369919, _369921] : [element(_369919, powerset(powerset(_369921))), 2504 ^ _280972 : [(2505 ^ _280972) ^ [_370099] : [element(_370099, powerset(powerset(_369921))), 2508 ^ _280972 : [(2509 ^ _280972) ^ [] : [_370099 = complements_of_subsets(_369921, _369919), 2512 ^ _280972 : [(2513 ^ _280972) ^ [_370387] : [element(_370387, powerset(_369921)), 2516 ^ _280972 : [(2523 ^ _280972) ^ [] : [in(subset_complement(_369921, _370387), _369919), -(in(_370387, _370099))], (2517 ^ _280972) ^ [] : [in(_370387, _370099), -(in(subset_complement(_369921, _370387), _369919))]]]]], (2529 ^ _280972) ^ [] : [-(_370099 = complements_of_subsets(_369921, _369919)), 2531 ^ _280972 : [(2534 ^ _280972) ^ [] : [2535 ^ _280972 : [(2538 ^ _280972) ^ [] : [in(subset_complement(_369921, 2530 ^ [_369919, _369921, _370099]), _369919)], (2536 ^ _280972) ^ [] : [-(in(2530 ^ [_369919, _369921, _370099], _370099))]], 2539 ^ _280972 : [(2542 ^ _280972) ^ [] : [in(2530 ^ [_369919, _369921, _370099], _370099)], (2540 ^ _280972) ^ [] : [-(in(subset_complement(_369921, 2530 ^ [_369919, _369921, _370099]), _369919))]]], (2532 ^ _280972) ^ [] : [-(element(2530 ^ [_369919, _369921, _370099], powerset(_369921)))]]]]]]], (1752 ^ _280972) ^ [_342525] : [relation(_342525), 1755 ^ _280972 : [(1756 ^ _280972) ^ [_342722] : [is_well_founded_in(_342525, _342722), 1759 ^ _280972 : [(1760 ^ _280972) ^ [_342887] : [subset(_342887, _342722), -(_342887 = empty_set), 1768 ^ _280972 : [(1771 ^ _280972) ^ [] : [-(disjoint(fiber(_342525, 1767 ^ [_342525, _342722, _342887]), _342887))], (1769 ^ _280972) ^ [] : [-(in(1767 ^ [_342525, _342722, _342887], _342887))]]]]], (1773 ^ _280972) ^ [_343328] : [-(is_well_founded_in(_342525, _343328)), 1775 ^ _280972 : [(1780 ^ _280972) ^ [_343670] : [in(_343670, 1774 ^ [_342525, _343328]), disjoint(fiber(_342525, _343670), 1774 ^ [_342525, _343328])], (1778 ^ _280972) ^ [] : [1774 ^ [_342525, _343328] = empty_set], (1776 ^ _280972) ^ [] : [-(subset(1774 ^ [_342525, _343328], _343328))]]]]], (1073 ^ _280972) ^ [_318033] : [relation(_318033), 1076 ^ _280972 : [(1077 ^ _280972) ^ [_318240, _318242] : [_318240 = relation_inverse_image(_318033, _318242), 1080 ^ _280972 : [(1090 ^ _280972) ^ [_318786] : [-(in(_318786, _318240)), 1091 ^ _280972 : [(1092 ^ _280972) ^ [_318891] : [in(ordered_pair(_318786, _318891), _318033), in(_318891, _318242)]]], (1081 ^ _280972) ^ [_318432] : [in(_318432, _318240), 1085 ^ _280972 : [(1088 ^ _280972) ^ [] : [-(in(1084 ^ [_318033, _318240, _318242, _318432], _318242))], (1086 ^ _280972) ^ [] : [-(in(ordered_pair(_318432, 1084 ^ [_318033, _318240, _318242, _318432]), _318033))]]]]], (1100 ^ _280972) ^ [_319146, _319148] : [-(_319146 = relation_inverse_image(_318033, _319148)), 1113 ^ _280972 : [(1118 ^ _280972) ^ [] : [in(1101 ^ [_318033, _319146, _319148], _319146)], (1116 ^ _280972) ^ [] : [-(in(1112 ^ [_318033, _319146, _319148], _319148))], (1114 ^ _280972) ^ [] : [-(in(ordered_pair(1101 ^ [_318033, _319146, _319148], 1112 ^ [_318033, _319146, _319148]), _318033))]], 1104 ^ _280972 : [(1107 ^ _280972) ^ [_319450] : [in(ordered_pair(1101 ^ [_318033, _319146, _319148], _319450), _318033), in(_319450, _319148)], (1105 ^ _280972) ^ [] : [-(in(1101 ^ [_318033, _319146, _319148], _319146))]]]]], (376 ^ _280972) ^ [_292908, _292910] : [_292910 = _292908, -(set_meet(_292910) = set_meet(_292908))], (2636 ^ _280972) ^ [] : [true___, -(true___)], (2786 ^ _280972) ^ [_377785, _377787] : [relation(_377785), -(relation(relation_rng_restriction(_377787, _377785)))], (4725 ^ _280972) ^ [_441962] : [relation(_441962), 4730 ^ _280972 : [(4733 ^ _280972) ^ [] : [relation_rng(_441962) = empty_set], (4731 ^ _280972) ^ [] : [relation_dom(_441962) = empty_set]], -(_441962 = empty_set)], (5015 ^ _280972) ^ [_451466, _451468] : [relation(_451466), -(relation_dom_restriction(_451466, _451468) = relation_composition(identity_relation(_451468), _451466))], (778 ^ _280972) ^ [_307065, _307067] : [-(_307067 = _307065), subset(_307067, _307065), subset(_307065, _307067)], (2302 ^ _280972) ^ [_362169] : [relation(_362169), 2305 ^ _280972 : [(2306 ^ _280972) ^ [_362329] : [relation(_362329), 2309 ^ _280972 : [(2310 ^ _280972) ^ [] : [_362329 = relation_inverse(_362169), 2313 ^ _280972 : [(2320 ^ _280972) ^ [_362828, _362830] : [in(ordered_pair(_362828, _362830), _362169), -(in(ordered_pair(_362830, _362828), _362329))], (2314 ^ _280972) ^ [_362638, _362640] : [in(ordered_pair(_362640, _362638), _362329), -(in(ordered_pair(_362638, _362640), _362169))]]], (2326 ^ _280972) ^ [] : [-(_362329 = relation_inverse(_362169)), 2331 ^ _280972 : [(2334 ^ _280972) ^ [] : [in(ordered_pair(2328 ^ [_362169, _362329], 2327 ^ [_362169, _362329]), _362169)], (2332 ^ _280972) ^ [] : [-(in(ordered_pair(2327 ^ [_362169, _362329], 2328 ^ [_362169, _362329]), _362329))]], 2335 ^ _280972 : [(2338 ^ _280972) ^ [] : [in(ordered_pair(2327 ^ [_362169, _362329], 2328 ^ [_362169, _362329]), _362329)], (2336 ^ _280972) ^ [] : [-(in(ordered_pair(2328 ^ [_362169, _362329], 2327 ^ [_362169, _362329]), _362169))]]]]]]], (1320 ^ _280972) ^ [_327009, _327011] : [_327009 = singleton(_327011), 1323 ^ _280972 : [(1330 ^ _280972) ^ [_327351] : [_327351 = _327011, -(in(_327351, _327009))], (1324 ^ _280972) ^ [_327179] : [in(_327179, _327009), -(_327179 = _327011)]]], (4987 ^ _280972) ^ [_450469, _450471, _450473] : [-(subset(set_union2(_450473, _450469), _450471)), subset(_450473, _450471), subset(_450469, _450471)], (3325 ^ _280972) ^ [_395513, _395515] : [3327 ^ _280972 : [(3330 ^ _280972) ^ [] : [in(3326 ^ [_395513, _395515], _395513)], (3328 ^ _280972) ^ [] : [-(in(3326 ^ [_395513, _395515], _395515))]], -(element(_395515, powerset(_395513)))], (146 ^ _280972) ^ [_285589, _285591, _285593, _285595] : [-(ordinal_subset(_285593, _285589)), ordinal_subset(_285595, _285591), _285595 = _285593, _285591 = _285589], (4633 ^ _280972) ^ [_439221] : [relation(_439221), -(in(ordered_pair(4638 ^ [_439221], 4639 ^ [_439221]), _439221)), -(_439221 = empty_set)], (2865 ^ _280972) ^ [_380063] : [empty(succ(_380063))], (3676 ^ _280972) ^ [_407346, _407348] : [relation(_407346), -(subset(relation_image(_407346, _407348), relation_rng(_407346)))], (2961 ^ _280972) ^ [_383112, _383114] : [-(empty(_383114)), empty(set_union2(_383112, _383114))], (3434 ^ _280972) ^ [] : [-(epsilon_transitive(3430 ^ []))], (5021 ^ _280972) ^ [_451690, _451692] : [relation(_451690), -(subset(relation_rng(relation_dom_restriction(_451690, _451692)), relation_rng(_451690)))], (2949 ^ _280972) ^ [_382718, _382720] : [-(relation(set_difference(_382720, _382718))), relation(_382720), relation(_382718)], (1608 ^ _280972) ^ [_336921, _336923, _336925] : [_336921 = cartesian_product2(_336925, _336923), 1611 ^ _280972 : [(1624 ^ _280972) ^ [_337682] : [-(in(_337682, _336921)), 1625 ^ _280972 : [(1626 ^ _280972) ^ [_337812, _337814] : [in(_337814, _336925), in(_337812, _336923), _337682 = ordered_pair(_337814, _337812)]]], (1612 ^ _280972) ^ [_337122] : [in(_337122, _336921), 1617 ^ _280972 : [(1622 ^ _280972) ^ [] : [-(_337122 = ordered_pair(1615 ^ [_336921, _336923, _336925, _337122], 1616 ^ [_336921, _336923, _336925, _337122]))], (1620 ^ _280972) ^ [] : [-(in(1616 ^ [_336921, _336923, _336925, _337122], _336923))], (1618 ^ _280972) ^ [] : [-(in(1615 ^ [_336921, _336923, _336925, _337122], _336925))]]]]], (3443 ^ _280972) ^ [] : [-(relation_empty_yielding(3439 ^ []))], (3419 ^ _280972) ^ [_398462] : [-(empty(3415 ^ [_398462]))], (632 ^ _280972) ^ [_302320, _302322] : [in(_302322, _302320), in(_302320, _302322)], (4237 ^ _280972) ^ [_425872, _425874, _425876] : [-(subset(unordered_pair(_425876, _425874), _425872)), in(_425876, _425872), in(_425874, _425872)], (2831 ^ _280972) ^ [] : [-(relation_empty_yielding(empty_set))], (136 ^ _280972) ^ [_285266, _285268] : [-(epsilon_transitive(_285266)), _285268 = _285266, epsilon_transitive(_285268)], (3833 ^ _280972) ^ [_412575, _412577, _412579] : [relation(_412575), in(_412579, relation_field(relation_restriction(_412575, _412577))), 3840 ^ _280972 : [(3843 ^ _280972) ^ [] : [-(in(_412579, _412577))], (3841 ^ _280972) ^ [] : [-(in(_412579, relation_field(_412575)))]]], (3429 ^ _280972) ^ [] : [-(one_to_one(3423 ^ []))], (402 ^ _280972) ^ [_293872, _293874, _293876, _293878] : [-(relation_rng_restriction(_293878, _293874) = relation_rng_restriction(_293876, _293872)), _293878 = _293876, _293874 = _293872], (3436 ^ _280972) ^ [] : [-(epsilon_connected(3430 ^ []))], (1993 ^ _280972) ^ [_351294, _351296] : [-(_351294 = union(_351296)), 2006 ^ _280972 : [(2011 ^ _280972) ^ [] : [in(1994 ^ [_351294, _351296], _351294)], (2009 ^ _280972) ^ [] : [-(in(2005 ^ [_351294, _351296], _351296))], (2007 ^ _280972) ^ [] : [-(in(1994 ^ [_351294, _351296], 2005 ^ [_351294, _351296]))]], 1997 ^ _280972 : [(2000 ^ _280972) ^ [_351577] : [in(1994 ^ [_351294, _351296], _351577), in(_351577, _351296)], (1998 ^ _280972) ^ [] : [-(in(1994 ^ [_351294, _351296], _351294))]]], (86 ^ _280972) ^ [_283791, _283793] : [-(transitive(_283791)), _283793 = _283791, transitive(_283793)], (4806 ^ _280972) ^ [_444556] : [-(unordered_pair(_444556, _444556) = singleton(_444556))], (5003 ^ _280972) ^ [_451024, _451026] : [relation(_451024), -(relation_dom(relation_dom_restriction(_451024, _451026)) = set_intersection2(relation_dom(_451024), _451026))], (2756 ^ _280972) ^ [_376662] : [-(relation(identity_relation(_376662)))], (4446 ^ _280972) ^ [_432833] : [relation(_432833), 4449 ^ _280972 : [(4450 ^ _280972) ^ [_432980] : [relation(_432980), subset(relation_dom(_432833), relation_rng(_432980)), -(relation_rng(relation_composition(_432980, _432833)) = relation_rng(_432833))]]], (5065 ^ _280972) ^ [_453404, _453406, _453408] : [singleton(_453408) = unordered_pair(_453406, _453404), -(_453406 = _453404)], (2774 ^ _280972) ^ [_377341, _377343] : [relation(_377343), -(relation(relation_dom_restriction(_377343, _377341)))], (3596 ^ _280972) ^ [_404462, _404464, _404466, _404468] : [-(subset(cartesian_product2(_404468, _404464), cartesian_product2(_404466, _404462))), subset(_404468, _404466), subset(_404464, _404462)], (3963 ^ _280972) ^ [_416731, _416733] : [relation(_416731), function(_416731), 3970 ^ _280972 : [(3971 ^ _280972) ^ [_416977] : [relation(_416977), function(_416977), in(_416733, relation_dom(_416731)), -(apply(relation_composition(_416731, _416977), _416733) = apply(_416977, apply(_416731, _416733)))]]], (3173 ^ _280972) ^ [_390265, _390267] : [in(_390267, _390265), -(subset(singleton(_390267), _390265))], (4082 ^ _280972) ^ [_420624] : [-(ordinal(_420624)), 4084 ^ _280972 : [(4087 ^ _280972) ^ [] : [ordinal(4083 ^ [_420624]), subset(4083 ^ [_420624], _420624)], (4085 ^ _280972) ^ [] : [-(in(4083 ^ [_420624], _420624))]]], (3606 ^ _280972) ^ [_404793, _404795] : [subset(_404795, _404793), -(set_union2(_404795, _404793) = _404793)], (770 ^ _280972) ^ [_306828, _306830] : [_306830 = _306828, 773 ^ _280972 : [(776 ^ _280972) ^ [] : [-(subset(_306828, _306830))], (774 ^ _280972) ^ [] : [-(subset(_306830, _306828))]]], (2897 ^ _280972) ^ [] : [-(epsilon_transitive(empty_set))], (2764 ^ _280972) ^ [_377012, _377014, _377016] : [-(element(subset_difference(_377016, _377014, _377012), powerset(_377016))), element(_377014, powerset(_377016)), element(_377012, powerset(_377016))], (4852 ^ _280972) ^ [_446128, _446130, _446132, _446134] : [relation(_446128), 4855 ^ _280972 : [(4864 ^ _280972) ^ [] : [-(in(ordered_pair(_446134, _446132), relation_composition(identity_relation(_446130), _446128))), in(_446134, _446130), in(ordered_pair(_446134, _446132), _446128)], (4856 ^ _280972) ^ [] : [in(ordered_pair(_446134, _446132), relation_composition(identity_relation(_446130), _446128)), 4859 ^ _280972 : [(4862 ^ _280972) ^ [] : [-(in(ordered_pair(_446134, _446132), _446128))], (4860 ^ _280972) ^ [] : [-(in(_446134, _446130))]]]]], (2194 ^ _280972) ^ [_358365, _358367] : [-(ordered_pair(_358367, _358365) = unordered_pair(unordered_pair(_358367, _358365), singleton(_358367)))], (2893 ^ _280972) ^ [] : [-(one_to_one(empty_set))], (2792 ^ _280972) ^ [] : [true___, -(true___)], (4318 ^ _280972) ^ [_428665] : [ordinal(_428665), 4321 ^ _280972 : [(4322 ^ _280972) ^ [] : [being_limit_ordinal(_428665), 4325 ^ _280972 : [(4326 ^ _280972) ^ [_428911] : [ordinal(_428911), in(_428911, _428665), -(in(succ(_428911), _428665))]]], (4336 ^ _280972) ^ [] : [4338 ^ _280972 : [(4343 ^ _280972) ^ [] : [in(succ(4337 ^ [_428665]), _428665)], (4341 ^ _280972) ^ [] : [-(in(4337 ^ [_428665], _428665))], (4339 ^ _280972) ^ [] : [-(ordinal(4337 ^ [_428665]))]], -(being_limit_ordinal(_428665))]]], (2618 ^ _280972) ^ [] : [true___, -(true___)], (422 ^ _280972) ^ [_294562, _294564] : [_294564 = _294562, -(relation_inverse(_294564) = relation_inverse(_294562))], (3474 ^ _280972) ^ [_400303, _400305] : [ordinal(_400305), ordinal(_400303), 3481 ^ _280972 : [(3488 ^ _280972) ^ [] : [subset(_400305, _400303), -(ordinal_subset(_400305, _400303))], (3482 ^ _280972) ^ [] : [ordinal_subset(_400305, _400303), -(subset(_400305, _400303))]]], (4400 ^ _280972) ^ [_431263] : [relation(_431263), 4403 ^ _280972 : [(4404 ^ _280972) ^ [_431400] : [relation(_431400), -(subset(relation_rng(relation_composition(_431263, _431400)), relation_rng(_431400)))]]], (1529 ^ _280972) ^ [_334113] : [relation(_334113), 1532 ^ _280972 : [(1533 ^ _280972) ^ [] : [well_founded_relation(_334113), 1536 ^ _280972 : [(1537 ^ _280972) ^ [_334380] : [subset(_334380, relation_field(_334113)), -(_334380 = empty_set), 1545 ^ _280972 : [(1548 ^ _280972) ^ [] : [-(disjoint(fiber(_334113, 1544 ^ [_334113, _334380]), _334380))], (1546 ^ _280972) ^ [] : [-(in(1544 ^ [_334113, _334380], _334380))]]]]], (1550 ^ _280972) ^ [] : [-(well_founded_relation(_334113)), 1552 ^ _280972 : [(1557 ^ _280972) ^ [_335063] : [in(_335063, 1551 ^ [_334113]), disjoint(fiber(_334113, _335063), 1551 ^ [_334113])], (1555 ^ _280972) ^ [] : [1551 ^ [_334113] = empty_set], (1553 ^ _280972) ^ [] : [-(subset(1551 ^ [_334113], relation_field(_334113)))]]]]], (2600 ^ _280972) ^ [] : [true___, -(true___)], (3520 ^ _280972) ^ [_401771, _401773, _401775, _401777] : [-(in(ordered_pair(_401777, _401775), cartesian_product2(_401773, _401771))), in(_401777, _401773), in(_401775, _401771)], (1743 ^ _280972) ^ [_342182, _342184] : [1745 ^ _280972 : [(1748 ^ _280972) ^ [] : [in(1744 ^ [_342182, _342184], _342182)], (1746 ^ _280972) ^ [] : [-(in(1744 ^ [_342182, _342184], _342184))]], -(subset(_342184, _342182))], (2891 ^ _280972) ^ [] : [-(function(empty_set))], (468 ^ _280972) ^ [_296232, _296234] : [_296234 = _296232, -(cast_to_subset(_296234) = cast_to_subset(_296232))], (3390 ^ _280972) ^ [] : [-(relation(3388 ^ []))], (1414 ^ _280972) ^ [_330248] : [relation(_330248), 1417 ^ _280972 : [(1418 ^ _280972) ^ [_330406] : [relation(_330406), 1421 ^ _280972 : [(1422 ^ _280972) ^ [] : [_330248 = _330406, 1425 ^ _280972 : [(1432 ^ _280972) ^ [_330901, _330903] : [in(ordered_pair(_330903, _330901), _330406), -(in(ordered_pair(_330903, _330901), _330248))], (1426 ^ _280972) ^ [_330711, _330713] : [in(ordered_pair(_330713, _330711), _330248), -(in(ordered_pair(_330713, _330711), _330406))]]], (1438 ^ _280972) ^ [] : [-(_330248 = _330406), 1443 ^ _280972 : [(1446 ^ _280972) ^ [] : [in(ordered_pair(1439 ^ [_330248, _330406], 1440 ^ [_330248, _330406]), _330406)], (1444 ^ _280972) ^ [] : [-(in(ordered_pair(1439 ^ [_330248, _330406], 1440 ^ [_330248, _330406]), _330248))]], 1447 ^ _280972 : [(1450 ^ _280972) ^ [] : [in(ordered_pair(1439 ^ [_330248, _330406], 1440 ^ [_330248, _330406]), _330248)], (1448 ^ _280972) ^ [] : [-(in(ordered_pair(1439 ^ [_330248, _330406], 1440 ^ [_330248, _330406]), _330406))]]]]]]], (572 ^ _280972) ^ [_300004, _300006, _300008, _300010] : [-(relation_dom_restriction(_300010, _300006) = relation_dom_restriction(_300008, _300004)), _300010 = _300008, _300006 = _300004], (4484 ^ _280972) ^ [_434184, _434186, _434188] : [-(element(_434188, _434184)), in(_434188, _434186), element(_434186, powerset(_434184))], (3641 ^ _280972) ^ [_406096, _406098, _406100] : [relation(_406096), -(relation_dom_restriction(relation_rng_restriction(_406100, _406096), _406098) = relation_rng_restriction(_406100, relation_dom_restriction(_406096, _406098)))], (4249 ^ _280972) ^ [_426321, _426323] : [subset(_426323, singleton(_426321)), -(_426323 = empty_set), -(_426323 = singleton(_426321))], (5055 ^ _280972) ^ [_453070, _453072] : [subset(_453070, 5028 ^ [_453072]), -(are_equipotent(_453070, 5028 ^ [_453072])), -(in(_453070, 5028 ^ [_453072]))], (454 ^ _280972) ^ [_295772, _295774, _295776, _295778, _295780, _295782] : [-(subset_difference(_295782, _295778, _295774) = subset_difference(_295780, _295776, _295772)), _295782 = _295780, _295778 = _295776, _295774 = _295772], (2833 ^ _280972) ^ [_379163, _379165] : [2840 ^ _280972 : [(2843 ^ _280972) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_379165, _379163)))], (2841 ^ _280972) ^ [] : [-(relation(relation_dom_restriction(_379165, _379163)))]], relation(_379165), relation_empty_yielding(_379165)], (2546 ^ _280972) ^ [_371510, _371512] : [proper_subset(_371512, _371510), 2549 ^ _280972 : [(2552 ^ _280972) ^ [] : [_371512 = _371510], (2550 ^ _280972) ^ [] : [-(subset(_371512, _371510))]]], (444 ^ _280972) ^ [_295385, _295387, _295389, _295391] : [-(complements_of_subsets(_295391, _295387) = complements_of_subsets(_295389, _295385)), _295391 = _295389, _295387 = _295385], (4247 ^ _280972) ^ [_426174, _426176] : [-(set_union2(_426176, set_difference(_426174, _426176)) = set_union2(_426176, _426174))], (4945 ^ _280972) ^ [_449269, _449271, _449273] : [relation(_449269), function(_449269), 4952 ^ _280972 : [(4961 ^ _280972) ^ [] : [-(in(ordered_pair(_449273, _449271), _449269)), in(_449273, relation_dom(_449269)), _449271 = apply(_449269, _449273)], (4953 ^ _280972) ^ [] : [in(ordered_pair(_449273, _449271), _449269), 4956 ^ _280972 : [(4959 ^ _280972) ^ [] : [-(_449271 = apply(_449269, _449273))], (4957 ^ _280972) ^ [] : [-(in(_449273, relation_dom(_449269)))]]]]], (3448 ^ _280972) ^ [] : [-(relation_empty_yielding(3444 ^ []))], (4013 ^ _280972) ^ [_418236] : [relation(_418236), 4016 ^ _280972 : [(4017 ^ _280972) ^ [_418386] : [relation(_418386), subset(_418236, _418386), 4024 ^ _280972 : [(4027 ^ _280972) ^ [] : [-(subset(relation_rng(_418236), relation_rng(_418386)))], (4025 ^ _280972) ^ [] : [-(subset(relation_dom(_418236), relation_dom(_418386)))]]]]], (266 ^ _280972) ^ [_289256, _289258] : [-(function(_289256)), _289258 = _289256, function(_289258)], (3067 ^ _280972) ^ [_386493, _386495] : [element(_386493, powerset(_386495)), -(subset_complement(_386495, subset_complement(_386495, _386493)) = _386493)], (290 ^ _280972) ^ [_289995, _289997] : [-(well_ordering(_289995)), _289997 = _289995, well_ordering(_289997)], (3494 ^ _280972) ^ [_400850, _400852] : [-(ordinal_subset(_400852, _400852)), ordinal(_400852), ordinal(_400850)], (3201 ^ _280972) ^ [_391248] : [relation(_391248), 3204 ^ _280972 : [(3205 ^ _280972) ^ [] : [antisymmetric(_391248), 3208 ^ _280972 : [(3209 ^ _280972) ^ [_391518, _391520] : [-(_391520 = _391518), in(ordered_pair(_391520, _391518), _391248), in(ordered_pair(_391518, _391520), _391248)]]], (3219 ^ _280972) ^ [] : [3222 ^ _280972 : [(3227 ^ _280972) ^ [] : [3220 ^ [_391248] = 3221 ^ [_391248]], (3225 ^ _280972) ^ [] : [-(in(ordered_pair(3221 ^ [_391248], 3220 ^ [_391248]), _391248))], (3223 ^ _280972) ^ [] : [-(in(ordered_pair(3220 ^ [_391248], 3221 ^ [_391248]), _391248))]], -(antisymmetric(_391248))]]], (2 ^ _280972) ^ [_281096] : [-(_281096 = _281096)], (530 ^ _280972) ^ [_298491, _298493, _298495, _298497] : [-(set_union2(_298497, _298493) = set_union2(_298495, _298491)), _298497 = _298495, _298493 = _298491], (1336 ^ _280972) ^ [_327530, _327532] : [-(_327530 = singleton(_327532)), 1340 ^ _280972 : [(1343 ^ _280972) ^ [] : [1337 ^ [_327530, _327532] = _327532], (1341 ^ _280972) ^ [] : [-(in(1337 ^ [_327530, _327532], _327530))]], 1344 ^ _280972 : [(1347 ^ _280972) ^ [] : [in(1337 ^ [_327530, _327532], _327530)], (1345 ^ _280972) ^ [] : [-(1337 ^ [_327530, _327532] = _327532)]]], (4310 ^ _280972) ^ [_428372] : [subset(_428372, empty_set), -(_428372 = empty_set)], (2704 ^ _280972) ^ [_375274, _375276] : [element(_375274, powerset(_375276)), -(element(subset_complement(_375276, _375274), powerset(_375276)))], (2883 ^ _280972) ^ [_380687] : [-(relation(identity_relation(_380687)))], (1209 ^ _280972) ^ [_322922] : [-(succ(_322922) = set_union2(_322922, singleton(_322922)))], (4029 ^ _280972) ^ [_418795, _418797, _418799] : [subset(_418799, _418797), -(subset(set_intersection2(_418799, _418795), set_intersection2(_418797, _418795)))], (2624 ^ _280972) ^ [] : [true___, -(true___)], (4480 ^ _280972) ^ [_433971, _433973] : [-(set_difference(_433973, set_difference(_433973, _433971)) = set_intersection2(_433973, _433971))], (4907 ^ _280972) ^ [_448085, _448087, _448089] : [relation(_448085), 4910 ^ _280972 : [(4919 ^ _280972) ^ [] : [-(in(_448089, relation_dom(relation_dom_restriction(_448085, _448087)))), in(_448089, _448087), in(_448089, relation_dom(_448085))], (4911 ^ _280972) ^ [] : [in(_448089, relation_dom(relation_dom_restriction(_448085, _448087))), 4914 ^ _280972 : [(4917 ^ _280972) ^ [] : [-(in(_448089, relation_dom(_448085)))], (4915 ^ _280972) ^ [] : [-(in(_448089, _448087))]]]]], (3085 ^ _280972) ^ [_387129, _387131] : [proper_subset(_387131, _387131)], (4195 ^ _280972) ^ [_424355, _424357] : [-(subset(set_difference(_424357, _424355), _424357))], (2648 ^ _280972) ^ [] : [true___, -(true___)], (1138 ^ _280972) ^ [_320483] : [relation(_320483), 1141 ^ _280972 : [(1148 ^ _280972) ^ [] : [is_transitive_in(_320483, relation_field(_320483)), -(transitive(_320483))], (1142 ^ _280972) ^ [] : [transitive(_320483), -(is_transitive_in(_320483, relation_field(_320483)))]]], (3438 ^ _280972) ^ [] : [-(ordinal(3430 ^ []))], (3441 ^ _280972) ^ [] : [-(relation(3439 ^ []))], (1831 ^ _280972) ^ [_345492] : [relation(_345492), function(_345492), 1838 ^ _280972 : [(1855 ^ _280972) ^ [_346236, _346238] : [-(in(_346238, relation_dom(_345492))), 1858 ^ _280972 : [(1865 ^ _280972) ^ [] : [_346236 = empty_set, -(_346236 = apply(_345492, _346238))], (1859 ^ _280972) ^ [] : [_346236 = apply(_345492, _346238), -(_346236 = empty_set)]]], (1839 ^ _280972) ^ [_345784, _345786] : [in(_345786, relation_dom(_345492)), 1842 ^ _280972 : [(1849 ^ _280972) ^ [] : [in(ordered_pair(_345786, _345784), _345492), -(_345784 = apply(_345492, _345786))], (1843 ^ _280972) ^ [] : [_345784 = apply(_345492, _345786), -(in(ordered_pair(_345786, _345784), _345492))]]]]], (3647 ^ _280972) ^ [_406348, _406350, _406352] : [relation(_406348), 3650 ^ _280972 : [(3662 ^ _280972) ^ [] : [-(in(_406352, relation_image(_406348, _406350))), 3663 ^ _280972 : [(3664 ^ _280972) ^ [_406949] : [in(_406949, relation_dom(_406348)), in(ordered_pair(_406949, _406352), _406348), in(_406949, _406350)]]], (3651 ^ _280972) ^ [] : [in(_406352, relation_image(_406348, _406350)), 3655 ^ _280972 : [(3660 ^ _280972) ^ [] : [-(in(3654 ^ [_406348, _406350, _406352], _406350))], (3658 ^ _280972) ^ [] : [-(in(ordered_pair(3654 ^ [_406348, _406350, _406352], _406352), _406348))], (3656 ^ _280972) ^ [] : [-(in(3654 ^ [_406348, _406350, _406352], relation_dom(_406348)))]]]]], (1351 ^ _280972) ^ [_328081] : [_328081 = empty_set, 1354 ^ _280972 : [(1355 ^ _280972) ^ [_328194] : [in(_328194, _328081)]]], (1357 ^ _280972) ^ [_328260] : [-(in(1358 ^ [_328260], _328260)), -(_328260 = empty_set)], (4440 ^ _280972) ^ [_432627, _432629] : [in(_432629, _432627), -(set_union2(singleton(_432629), _432627) = _432627)], (2937 ^ _280972) ^ [_382290] : [ordinal(_382290), 2940 ^ _280972 : [(2943 ^ _280972) ^ [] : [-(epsilon_transitive(succ(_382290)))], (2945 ^ _280972) ^ [] : [-(epsilon_connected(succ(_382290)))], (2947 ^ _280972) ^ [] : [-(ordinal(succ(_382290)))], (2941 ^ _280972) ^ [] : [empty(succ(_382290))]]], (4410 ^ _280972) ^ [_431629, _431631] : [subset(_431631, _431629), -(_431629 = set_union2(_431631, set_difference(_431629, _431631)))], (126 ^ _280972) ^ [_284971, _284973] : [-(relation_empty_yielding(_284971)), _284973 = _284971, relation_empty_yielding(_284973)], (4901 ^ _280972) ^ [_447853, _447855] : [set_difference(_447855, _447853) = _447855, -(disjoint(_447855, _447853))], (2829 ^ _280972) ^ [] : [-(relation(empty_set))], (4205 ^ _280972) ^ [_424781, _424783] : [set_difference(_424783, _424781) = empty_set, -(subset(_424783, _424781))], (5027 ^ _280972) ^ [_451883] : [-(union(powerset(_451883)) = _451883)], (4895 ^ _280972) ^ [_447685, _447687] : [disjoint(_447687, _447685), -(set_difference(_447687, _447685) = _447687)], (566 ^ _280972) ^ [_299758, _299760] : [_299760 = _299758, -(identity_relation(_299760) = identity_relation(_299758))], (3015 ^ _280972) ^ [_384823] : [empty(relation_dom(_384823)), -(empty(_384823)), relation(_384823)], (1182 ^ _280972) ^ [_321949, _321951, _321953, _321955] : [-(_321949 = unordered_triple(_321955, _321953, _321951)), 1186 ^ _280972 : [(1189 ^ _280972) ^ [] : [1183 ^ [_321949, _321951, _321953, _321955] = _321955], (1191 ^ _280972) ^ [] : [1183 ^ [_321949, _321951, _321953, _321955] = _321953], (1193 ^ _280972) ^ [] : [1183 ^ [_321949, _321951, _321953, _321955] = _321951], (1187 ^ _280972) ^ [] : [-(in(1183 ^ [_321949, _321951, _321953, _321955], _321949))]], 1194 ^ _280972 : [(1195 ^ _280972) ^ [] : [-(1183 ^ [_321949, _321951, _321953, _321955] = _321955), -(1183 ^ [_321949, _321951, _321953, _321955] = _321953), -(1183 ^ [_321949, _321951, _321953, _321955] = _321951)], (1205 ^ _280972) ^ [] : [in(1183 ^ [_321949, _321951, _321953, _321955], _321949)]]], (3825 ^ _280972) ^ [_412223, _412225] : [-(subset(set_intersection2(_412225, _412223), _412225))], (3857 ^ _280972) ^ [_413383, _413385] : [in(_413385, _413383), -(element(_413385, _413383))], (4095 ^ _280972) ^ [_421054, _421056] : [ordinal(_421054), subset(_421056, _421054), -(_421056 = empty_set), 4107 ^ _280972 : [(4112 ^ _280972) ^ [_421606] : [ordinal(_421606), in(_421606, _421056), -(ordinal_subset(4106 ^ [_421054, _421056], _421606))], (4110 ^ _280972) ^ [] : [-(in(4106 ^ [_421054, _421056], _421056))], (4108 ^ _280972) ^ [] : [-(ordinal(4106 ^ [_421054, _421056]))]]], (1889 ^ _280972) ^ [_347248] : [relation(_347248), 1892 ^ _280972 : [(1893 ^ _280972) ^ [_347429] : [_347429 = relation_dom(_347248), 1896 ^ _280972 : [(1904 ^ _280972) ^ [_347853] : [1905 ^ _280972 : [(1906 ^ _280972) ^ [_347932] : [in(ordered_pair(_347853, _347932), _347248)]], -(in(_347853, _347429))], (1897 ^ _280972) ^ [_347609] : [in(_347609, _347429), -(in(ordered_pair(_347609, 1900 ^ [_347248, _347429, _347609]), _347248))]]], (1910 ^ _280972) ^ [_348060] : [-(_348060 = relation_dom(_347248)), 1914 ^ _280972 : [(1917 ^ _280972) ^ [_348323] : [in(ordered_pair(1911 ^ [_347248, _348060], _348323), _347248)], (1915 ^ _280972) ^ [] : [-(in(1911 ^ [_347248, _348060], _348060))]], 1919 ^ _280972 : [(1922 ^ _280972) ^ [] : [in(1911 ^ [_347248, _348060], _348060)], (1920 ^ _280972) ^ [] : [-(in(ordered_pair(1911 ^ [_347248, _348060], 1918 ^ [_347248, _348060]), _347248))]]]]], (4701 ^ _280972) ^ [_441281] : [relation(_441281), function(_441281), one_to_one(_441281), -(one_to_one(function_inverse(_441281)))], (3692 ^ _280972) ^ [_407871, _407873] : [relation(_407871), -(relation_image(_407871, _407873) = relation_image(_407871, set_intersection2(relation_dom(_407871), _407873)))], (4211 ^ _280972) ^ [_424949, _424951] : [subset(_424951, _424949), -(set_difference(_424951, _424949) = empty_set)], (3506 ^ _280972) ^ [_401239, _401241] : [disjoint(_401241, _401239), -(disjoint(_401239, _401241))], (2728 ^ _280972) ^ [] : [true___, -(true___)], (1454 ^ _280972) ^ [_331738, _331740] : [-(empty(_331740)), 1457 ^ _280972 : [(1464 ^ _280972) ^ [] : [in(_331738, _331740), -(element(_331738, _331740))], (1458 ^ _280972) ^ [] : [element(_331738, _331740), -(in(_331738, _331740))]]], (2750 ^ _280972) ^ [_376463, _376465] : [element(_376463, powerset(powerset(_376465))), -(element(union_of_subsets(_376465, _376463), powerset(_376465)))], (4390 ^ _280972) ^ [_430911] : [relation(_430911), 4393 ^ _280972 : [(4394 ^ _280972) ^ [_431048] : [relation(_431048), -(subset(relation_dom(relation_composition(_430911, _431048)), relation_dom(_430911)))]]], (4043 ^ _280972) ^ [_419320, _419322] : [element(_419322, _419320), -(empty(_419320)), -(in(_419322, _419320))], (2889 ^ _280972) ^ [] : [-(relation_empty_yielding(empty_set))], (594 ^ _280972) ^ [_300771, _300773] : [_300773 = _300771, -(powerset(_300773) = powerset(_300771))], (3809 ^ _280972) ^ [_411693, _411695, _411697] : [relation(_411693), subset(_411697, _411695), -(subset(relation_inverse_image(_411693, _411697), relation_inverse_image(_411693, _411695)))], (4148 ^ _280972) ^ [_422813, _422815, _422817, _422819] : [ordered_pair(_422819, _422817) = ordered_pair(_422815, _422813), 4151 ^ _280972 : [(4154 ^ _280972) ^ [] : [-(_422817 = _422813)], (4152 ^ _280972) ^ [] : [-(_422819 = _422815)]]], (658 ^ _280972) ^ [_303171] : [empty(_303171), -(relation(_303171))], (3827 ^ _280972) ^ [_412335, _412337] : [relation(_412335), -(relation_restriction(_412335, _412337) = relation_rng_restriction(_412337, relation_dom_restriction(_412335, _412337)))]], input).
% 64.78/63.47  ncf('1',plain,[subset(relation_field(relation_restriction(5071 ^ [], 5070 ^ [])), relation_field(5071 ^ [])), subset(relation_field(relation_restriction(5071 ^ [], 5070 ^ [])), 5070 ^ [])],start(5075 ^ 0)).
% 64.78/63.47  ncf('1.1',plain,[-(subset(relation_field(relation_restriction(5071 ^ [], 5070 ^ [])), relation_field(5071 ^ []))), 1748 : in(1744 ^ [relation_field(5071 ^ []), relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], relation_field(5071 ^ []))],extension(1743 ^ 1,bind([[_342182, _342184], [relation_field(5071 ^ []), relation_field(relation_restriction(5071 ^ [], 5070 ^ []))]]))).
% 64.78/63.47  ncf('1.1.1',plain,[-(in(1744 ^ [relation_field(5071 ^ []), relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], relation_field(5071 ^ []))), relation(5071 ^ []), in(1744 ^ [relation_field(5071 ^ []), relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], relation_field(relation_restriction(5071 ^ [], 5070 ^ [])))],extension(3833 ^ 4,bind([[_412575, _412577, _412579], [5071 ^ [], 5070 ^ [], 1744 ^ [relation_field(5071 ^ []), relation_field(relation_restriction(5071 ^ [], 5070 ^ []))]]]))).
% 64.78/63.47  ncf('1.1.1.1',plain,[-(relation(5071 ^ []))],extension(5073 ^ 5)).
% 64.78/63.47  ncf('1.1.1.2',plain,[-(in(1744 ^ [relation_field(5071 ^ []), relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))))],extension(1746 ^ 5)).
% 64.78/63.47  ncf('1.2',plain,[-(subset(relation_field(relation_restriction(5071 ^ [], 5070 ^ [])), 5070 ^ [])), 1748 : in(1744 ^ [5070 ^ [], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], 5070 ^ [])],extension(1743 ^ 1,bind([[_342182, _342184], [5070 ^ [], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))]]))).
% 64.78/63.47  ncf('1.2.1',plain,[-(in(1744 ^ [5070 ^ [], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], 5070 ^ [])), relation(5071 ^ []), in(1744 ^ [5070 ^ [], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], relation_field(relation_restriction(5071 ^ [], 5070 ^ [])))],extension(3833 ^ 4,bind([[_412575, _412577, _412579], [5071 ^ [], 5070 ^ [], 1744 ^ [5070 ^ [], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))]]]))).
% 64.78/63.47  ncf('1.2.1.1',plain,[-(relation(5071 ^ []))],extension(5073 ^ 5)).
% 64.78/63.47  ncf('1.2.1.2',plain,[-(in(1744 ^ [5070 ^ [], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))], relation_field(relation_restriction(5071 ^ [], 5070 ^ []))))],extension(1746 ^ 5)).
% 64.78/63.47  %-----------------------------------------------------
% 64.78/63.47  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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