%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU257+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n022.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 12:02:54 EDT 2023

% Result   : Theorem 48.62s 47.96s
% Output   : Proof 48.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU257+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 13:12:02 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 48.62/47.96  
% 48.62/47.96  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 48.62/47.96  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.62/47.96  %-----------------------------------------------------
% 48.62/47.96  ncf(matrix, plain, [(5188 ^ _488008) ^ [] : [well_ordering(relation_restriction(5182 ^ [], 5181 ^ []))], (5186 ^ _488008) ^ [] : [-(well_ordering(5182 ^ []))], (5184 ^ _488008) ^ [] : [-(relation(5182 ^ []))], !, (3469 ^ _308432) ^ [] : [empty(3467 ^ [])], (2665 ^ _308432) ^ [] : [true___, -(true___)], (428 ^ _308432) ^ [_322240, _322242] : [_322242 = _322240, -(succ(_322242) = succ(_322240))], (290 ^ _308432) ^ [_317483, _317485, _317487, _317489] : [-(subset(_317487, _317483)), subset(_317489, _317485), _317489 = _317487, _317485 = _317483], (2017 ^ _308432) ^ [_379623, _379625] : [_379623 = union(_379625), 2020 ^ _308432 : [(2030 ^ _308432) ^ [_380131] : [-(in(_380131, _379623)), 2031 ^ _308432 : [(2032 ^ _308432) ^ [_380229] : [in(_380131, _380229), in(_380229, _379625)]]], (2021 ^ _308432) ^ [_379804] : [in(_379804, _379623), 2025 ^ _308432 : [(2028 ^ _308432) ^ [] : [-(in(2024 ^ [_379623, _379625, _379804], _379625))], (2026 ^ _308432) ^ [] : [-(in(_379804, 2024 ^ [_379623, _379625, _379804]))]]]]], (3866 ^ _308432) ^ [_441186, _441188] : [relation(_441186), -(relation_restriction(_441186, _441188) = relation_dom_restriction(relation_rng_restriction(_441188, _441186), _441188))], (3452 ^ _308432) ^ [] : [-(epsilon_transitive(3442 ^ []))], (4056 ^ _308432) ^ [_447442, _447444] : [ordinal(_447442), in(_447444, _447442), -(ordinal(_447444))], (1799 ^ _308432) ^ [_371699] : [relation(_371699), 1802 ^ _308432 : [(1803 ^ _308432) ^ [_371896] : [is_well_founded_in(_371699, _371896), 1806 ^ _308432 : [(1807 ^ _308432) ^ [_372061] : [subset(_372061, _371896), -(_372061 = empty_set), 1815 ^ _308432 : [(1818 ^ _308432) ^ [] : [-(disjoint(fiber(_371699, 1814 ^ [_371699, _371896, _372061]), _372061))], (1816 ^ _308432) ^ [] : [-(in(1814 ^ [_371699, _371896, _372061], _372061))]]]]], (1820 ^ _308432) ^ [_372502] : [-(is_well_founded_in(_371699, _372502)), 1822 ^ _308432 : [(1827 ^ _308432) ^ [_372844] : [in(_372844, 1821 ^ [_371699, _372502]), disjoint(fiber(_371699, _372844), 1821 ^ [_371699, _372502])], (1825 ^ _308432) ^ [] : [1821 ^ [_371699, _372502] = empty_set], (1823 ^ _308432) ^ [] : [-(subset(1821 ^ [_371699, _372502], _372502))]]]]], (474 ^ _308432) ^ [_323938, _323940, _323942, _323944] : [-(meet_of_subsets(_323944, _323940) = meet_of_subsets(_323942, _323938)), _323944 = _323942, _323940 = _323938], (3177 ^ _308432) ^ [_417866, _417868] : [relation(_417866), -(subset(relation_dom(relation_rng_restriction(_417868, _417866)), relation_dom(_417866)))], (3381 ^ _308432) ^ [_425060, _425062, _425064] : [relation(_425060), function(_425060), 3388 ^ _308432 : [(3397 ^ _308432) ^ [] : [-(in(_425062, relation_dom(relation_dom_restriction(_425060, _425064)))), in(_425062, relation_dom(_425060)), in(_425062, _425064)], (3389 ^ _308432) ^ [] : [in(_425062, relation_dom(relation_dom_restriction(_425060, _425064))), 3392 ^ _308432 : [(3395 ^ _308432) ^ [] : [-(in(_425062, _425064))], (3393 ^ _308432) ^ [] : [-(in(_425062, relation_dom(_425060)))]]]]], (1427 ^ _308432) ^ [_358246, _358248] : [-(_358246 = powerset(_358248)), 1431 ^ _308432 : [(1434 ^ _308432) ^ [] : [subset(1428 ^ [_358246, _358248], _358248)], (1432 ^ _308432) ^ [] : [-(in(1428 ^ [_358246, _358248], _358246))]], 1435 ^ _308432 : [(1438 ^ _308432) ^ [] : [in(1428 ^ [_358246, _358248], _358246)], (1436 ^ _308432) ^ [] : [-(subset(1428 ^ [_358246, _358248], _358248))]]], (232 ^ _308432) ^ [_315682, _315684] : [-(one_to_one(_315682)), _315684 = _315682, one_to_one(_315684)], (2757 ^ _308432) ^ [] : [true___, -(true___)], (546 ^ _308432) ^ [_326528, _326530, _326532, _326534] : [-(set_intersection2(_326534, _326530) = set_intersection2(_326532, _326528)), _326534 = _326532, _326530 = _326528], (3617 ^ _308432) ^ [_432613, _432615] : [relation(_432613), -(subset(relation_rng_restriction(_432615, _432613), _432613))], (2243 ^ _308432) ^ [_387645] : [relation(_387645), 2246 ^ _308432 : [(2261 ^ _308432) ^ [_388290] : [-(well_orders(_387645, _388290)), is_reflexive_in(_387645, _388290), is_transitive_in(_387645, _388290), is_antisymmetric_in(_387645, _388290), is_connected_in(_387645, _388290), is_well_founded_in(_387645, _388290)], (2247 ^ _308432) ^ [_387829] : [well_orders(_387645, _387829), 2250 ^ _308432 : [(2251 ^ _308432) ^ [] : [-(is_reflexive_in(_387645, _387829))], (2255 ^ _308432) ^ [] : [-(is_antisymmetric_in(_387645, _387829))], (2259 ^ _308432) ^ [] : [-(is_well_founded_in(_387645, _387829))], (2257 ^ _308432) ^ [] : [-(is_connected_in(_387645, _387829))], (2253 ^ _308432) ^ [] : [-(is_transitive_in(_387645, _387829))]]]]], (3904 ^ _308432) ^ [_442557, _442559] : [in(_442559, _442557), -(element(_442559, _442557))], (3220 ^ _308432) ^ [_419439, _419441] : [in(_419441, _419439), -(subset(singleton(_419441), _419439))], (3157 ^ _308432) ^ [_417107] : [singleton(_417107) = empty_set], (3415 ^ _308432) ^ [] : [-(epsilon_connected(3411 ^ []))], (2235 ^ _308432) ^ [_387328, _387330] : [element(_387328, powerset(_387330)), -(subset_complement(_387330, _387328) = set_difference(_387330, _387328))], (3082 ^ _308432) ^ [_414551] : [empty(_414551), 3085 ^ _308432 : [(3088 ^ _308432) ^ [] : [-(relation(relation_dom(_414551)))], (3086 ^ _308432) ^ [] : [-(empty(relation_dom(_414551)))]]], (3439 ^ _308432) ^ [] : [-(empty(3435 ^ []))], (4380 ^ _308432) ^ [_458192, _458194, _458196] : [in(_458196, _458194), in(_458194, _458192), in(_458192, _458196)], (3114 ^ _308432) ^ [_415667, _415669] : [element(_415667, powerset(_415669)), -(subset_complement(_415669, subset_complement(_415669, _415667)) = _415667)], (3922 ^ _308432) ^ [_443157, _443159, _443161] : [relation(_443157), in(ordered_pair(_443161, _443159), _443157), 3929 ^ _308432 : [(3932 ^ _308432) ^ [] : [-(in(_443159, relation_rng(_443157)))], (3930 ^ _308432) ^ [] : [-(in(_443161, relation_dom(_443157)))]]], (4571 ^ _308432) ^ [_464528, _464530] : [element(_464528, powerset(powerset(_464530))), -(_464528 = empty_set), -(subset_difference(_464530, cast_to_subset(_464530), union_of_subsets(_464530, _464528)) = meet_of_subsets(_464530, complements_of_subsets(_464530, _464528)))], (706 ^ _308432) ^ [_332105, _332107] : [-(set_intersection2(_332107, _332105) = set_intersection2(_332105, _332107))], (2854 ^ _308432) ^ [_407531, _407533] : [2861 ^ _308432 : [(2864 ^ _308432) ^ [] : [-(relation(relation_composition(_407531, _407533)))], (2862 ^ _308432) ^ [] : [-(empty(relation_composition(_407531, _407533)))]], empty(_407533), relation(_407531)], (3629 ^ _308432) ^ [_433063, _433065, _433067] : [subset(_433067, _433065), 3632 ^ _308432 : [(3635 ^ _308432) ^ [] : [-(subset(cartesian_product2(_433063, _433067), cartesian_product2(_433063, _433065)))], (3633 ^ _308432) ^ [] : [-(subset(cartesian_product2(_433067, _433063), cartesian_product2(_433065, _433063)))]]], (2659 ^ _308432) ^ [] : [true___, -(true___)], (4501 ^ _308432) ^ [_462133] : [relation(_462133), 4504 ^ _308432 : [(4505 ^ _308432) ^ [_462270] : [relation(_462270), -(subset(relation_dom(relation_composition(_462133, _462270)), relation_dom(_462133)))]]], (3410 ^ _308432) ^ [] : [-(function(3406 ^ []))], (468 ^ _308432) ^ [_323692, _323694] : [_323694 = _323692, -(cast_to_subset(_323694) = cast_to_subset(_323692))], (1936 ^ _308432) ^ [_376422] : [relation(_376422), 1939 ^ _308432 : [(1940 ^ _308432) ^ [_376603] : [_376603 = relation_dom(_376422), 1943 ^ _308432 : [(1951 ^ _308432) ^ [_377027] : [1952 ^ _308432 : [(1953 ^ _308432) ^ [_377106] : [in(ordered_pair(_377027, _377106), _376422)]], -(in(_377027, _376603))], (1944 ^ _308432) ^ [_376783] : [in(_376783, _376603), -(in(ordered_pair(_376783, 1947 ^ [_376422, _376603, _376783]), _376422))]]], (1957 ^ _308432) ^ [_377234] : [-(_377234 = relation_dom(_376422)), 1961 ^ _308432 : [(1964 ^ _308432) ^ [_377497] : [in(ordered_pair(1958 ^ [_376422, _377234], _377497), _376422)], (1962 ^ _308432) ^ [] : [-(in(1958 ^ [_376422, _377234], _377234))]], 1966 ^ _308432 : [(1969 ^ _308432) ^ [] : [in(1958 ^ [_376422, _377234], _377234)], (1967 ^ _308432) ^ [] : [-(in(ordered_pair(1958 ^ [_376422, _377234], 1965 ^ [_376422, _377234]), _376422))]]]]], (180 ^ _308432) ^ [_314083, _314085, _314087, _314089] : [-(element(_314087, _314083)), element(_314089, _314085), _314089 = _314087, _314085 = _314083], (3880 ^ _308432) ^ [_441749, _441751, _441753] : [relation(_441749), in(_441753, relation_field(relation_restriction(_441749, _441751))), 3887 ^ _308432 : [(3890 ^ _308432) ^ [] : [-(in(_441753, _441751))], (3888 ^ _308432) ^ [] : [-(in(_441753, relation_field(_441749)))]]], (2787 ^ _308432) ^ [_405338, _405340] : [-(relation(relation_composition(_405340, _405338))), relation(_405340), relation(_405338)], (1223 ^ _308432) ^ [_350972] : [1225 ^ _308432 : [(1228 ^ _308432) ^ [_351209, _351211] : [1224 ^ [_350972] = ordered_pair(_351211, _351209)], (1226 ^ _308432) ^ [] : [-(in(1224 ^ [_350972], _350972))]], -(relation(_350972))], (4804 ^ _308432) ^ [] : [-(relation_rng(empty_set) = empty_set)], (2968 ^ _308432) ^ [_411033] : [2979 ^ _308432 : [(2982 ^ _308432) ^ [] : [-(function(relation_inverse(_411033)))], (2980 ^ _308432) ^ [] : [-(relation(relation_inverse(_411033)))]], relation(_411033), function(_411033), one_to_one(_411033)], (1533 ^ _308432) ^ [_361825, _361827, _361829] : [_361825 = unordered_pair(_361829, _361827), 1536 ^ _308432 : [(1537 ^ _308432) ^ [_362007] : [in(_362007, _361825), -(_362007 = _361829), -(_362007 = _361827)], (1547 ^ _308432) ^ [_362285] : [1548 ^ _308432 : [(1551 ^ _308432) ^ [] : [_362285 = _361827], (1549 ^ _308432) ^ [] : [_362285 = _361829]], -(in(_362285, _361825))]]], (520 ^ _308432) ^ [_325592, _325594, _325596, _325598] : [-(apply(_325598, _325594) = apply(_325596, _325592)), _325598 = _325596, _325594 = _325592], (3476 ^ _308432) ^ [] : [-(one_to_one(3470 ^ []))], (1835 ^ _308432) ^ [_373202, _373204, _373206] : [_373202 = set_intersection2(_373206, _373204), 1838 ^ _308432 : [(1847 ^ _308432) ^ [_373643] : [-(in(_373643, _373202)), in(_373643, _373206), in(_373643, _373204)], (1839 ^ _308432) ^ [_373384] : [in(_373384, _373202), 1842 ^ _308432 : [(1845 ^ _308432) ^ [] : [-(in(_373384, _373204))], (1843 ^ _308432) ^ [] : [-(in(_373384, _373206))]]]]], (1122 ^ _308432) ^ [_347512] : [relation(_347512), 1125 ^ _308432 : [(1132 ^ _308432) ^ [] : [is_connected_in(_347512, relation_field(_347512)), -(connected(_347512))], (1126 ^ _308432) ^ [] : [connected(_347512), -(is_connected_in(_347512, relation_field(_347512)))]]], (4848 ^ _308432) ^ [_473537] : [relation(_473537), 4851 ^ _308432 : [(4858 ^ _308432) ^ [] : [relation_rng(_473537) = empty_set, -(relation_dom(_473537) = empty_set)], (4852 ^ _308432) ^ [] : [relation_dom(_473537) = empty_set, -(relation_rng(_473537) = empty_set)]]], (4776 ^ _308432) ^ [_471459, _471461, _471463] : [in(_471463, _471461), element(_471461, powerset(_471459)), empty(_471459)], (2548 ^ _308432) ^ [_399093, _399095] : [element(_399093, powerset(powerset(_399095))), 2551 ^ _308432 : [(2552 ^ _308432) ^ [_399273] : [element(_399273, powerset(powerset(_399095))), 2555 ^ _308432 : [(2556 ^ _308432) ^ [] : [_399273 = complements_of_subsets(_399095, _399093), 2559 ^ _308432 : [(2560 ^ _308432) ^ [_399561] : [element(_399561, powerset(_399095)), 2563 ^ _308432 : [(2570 ^ _308432) ^ [] : [in(subset_complement(_399095, _399561), _399093), -(in(_399561, _399273))], (2564 ^ _308432) ^ [] : [in(_399561, _399273), -(in(subset_complement(_399095, _399561), _399093))]]]]], (2576 ^ _308432) ^ [] : [-(_399273 = complements_of_subsets(_399095, _399093)), 2578 ^ _308432 : [(2581 ^ _308432) ^ [] : [2582 ^ _308432 : [(2585 ^ _308432) ^ [] : [in(subset_complement(_399095, 2577 ^ [_399093, _399095, _399273]), _399093)], (2583 ^ _308432) ^ [] : [-(in(2577 ^ [_399093, _399095, _399273], _399273))]], 2586 ^ _308432 : [(2589 ^ _308432) ^ [] : [in(2577 ^ [_399093, _399095, _399273], _399273)], (2587 ^ _308432) ^ [] : [-(in(subset_complement(_399095, 2577 ^ [_399093, _399095, _399273]), _399093))]]], (2579 ^ _308432) ^ [] : [-(element(2577 ^ [_399093, _399095, _399273], powerset(_399095)))]]]]]]], (2349 ^ _308432) ^ [_391343] : [relation(_391343), 2352 ^ _308432 : [(2353 ^ _308432) ^ [_391503] : [relation(_391503), 2356 ^ _308432 : [(2357 ^ _308432) ^ [] : [_391503 = relation_inverse(_391343), 2360 ^ _308432 : [(2367 ^ _308432) ^ [_392002, _392004] : [in(ordered_pair(_392002, _392004), _391343), -(in(ordered_pair(_392004, _392002), _391503))], (2361 ^ _308432) ^ [_391812, _391814] : [in(ordered_pair(_391814, _391812), _391503), -(in(ordered_pair(_391812, _391814), _391343))]]], (2373 ^ _308432) ^ [] : [-(_391503 = relation_inverse(_391343)), 2378 ^ _308432 : [(2381 ^ _308432) ^ [] : [in(ordered_pair(2375 ^ [_391343, _391503], 2374 ^ [_391343, _391503]), _391343)], (2379 ^ _308432) ^ [] : [-(in(ordered_pair(2374 ^ [_391343, _391503], 2375 ^ [_391343, _391503]), _391503))]], 2382 ^ _308432 : [(2385 ^ _308432) ^ [] : [in(ordered_pair(2374 ^ [_391343, _391503], 2375 ^ [_391343, _391503]), _391503)], (2383 ^ _308432) ^ [] : [-(in(ordered_pair(2375 ^ [_391343, _391503], 2374 ^ [_391343, _391503]), _391343))]]]]]]], (3688 ^ _308432) ^ [_435270, _435272, _435274] : [relation(_435270), -(relation_dom_restriction(relation_rng_restriction(_435274, _435270), _435272) = relation_rng_restriction(_435274, relation_dom_restriction(_435270, _435272)))], (2593 ^ _308432) ^ [_400684, _400686] : [proper_subset(_400686, _400684), 2596 ^ _308432 : [(2599 ^ _308432) ^ [] : [_400686 = _400684], (2597 ^ _308432) ^ [] : [-(subset(_400686, _400684))]]], (5114 ^ _308432) ^ [_482246, _482248] : [relation(_482246), -(relation_dom(relation_dom_restriction(_482246, _482248)) = set_intersection2(relation_dom(_482246), _482248))], (2962 ^ _308432) ^ [_410831, _410833] : [-(empty(_410833)), empty(set_union2(_410833, _410831))], (3434 ^ _308432) ^ [] : [-(empty(3432 ^ []))], (3483 ^ _308432) ^ [] : [-(epsilon_connected(3477 ^ []))], (2938 ^ _308432) ^ [] : [-(function(empty_set))], (973 ^ _308432) ^ [_341667] : [relation(_341667), function(_341667), 980 ^ _308432 : [(981 ^ _308432) ^ [_341954, _341956] : [_341954 = relation_inverse_image(_341667, _341956), 984 ^ _308432 : [(993 ^ _308432) ^ [_342412] : [-(in(_342412, _341954)), in(_342412, relation_dom(_341667)), in(apply(_341667, _342412), _341956)], (985 ^ _308432) ^ [_342143] : [in(_342143, _341954), 988 ^ _308432 : [(991 ^ _308432) ^ [] : [-(in(apply(_341667, _342143), _341956))], (989 ^ _308432) ^ [] : [-(in(_342143, relation_dom(_341667)))]]]]], (1003 ^ _308432) ^ [_342706, _342708] : [-(_342706 = relation_inverse_image(_341667, _342708)), 1015 ^ _308432 : [(1020 ^ _308432) ^ [] : [in(1004 ^ [_341667, _342706, _342708], _342706)], (1018 ^ _308432) ^ [] : [-(in(apply(_341667, 1004 ^ [_341667, _342706, _342708]), _342708))], (1016 ^ _308432) ^ [] : [-(in(1004 ^ [_341667, _342706, _342708], relation_dom(_341667)))]], 1007 ^ _308432 : [(1010 ^ _308432) ^ [] : [in(1004 ^ [_341667, _342706, _342708], relation_dom(_341667)), in(apply(_341667, 1004 ^ [_341667, _342706, _342708]), _342708)], (1008 ^ _308432) ^ [] : [-(in(1004 ^ [_341667, _342706, _342708], _342706))]]]]], (3567 ^ _308432) ^ [_430945, _430947, _430949, _430951] : [-(in(ordered_pair(_430951, _430949), cartesian_product2(_430947, _430945))), in(_430951, _430947), in(_430949, _430945)], (3775 ^ _308432) ^ [_438178] : [relation(_438178), 3778 ^ _308432 : [(3779 ^ _308432) ^ [_438318] : [relation(_438318), -(relation_rng(relation_composition(_438178, _438318)) = relation_image(_438318, relation_rng(_438178)))]]], (3214 ^ _308432) ^ [_419273, _419275] : [subset(singleton(_419275), _419273), -(in(_419275, _419273))], (3589 ^ _308432) ^ [_431736, _431738, _431740] : [relation(_431736), 3592 ^ _308432 : [(3601 ^ _308432) ^ [] : [-(in(_431740, relation_rng(relation_rng_restriction(_431738, _431736)))), in(_431740, _431738), in(_431740, relation_rng(_431736))], (3593 ^ _308432) ^ [] : [in(_431740, relation_rng(relation_rng_restriction(_431738, _431736))), 3596 ^ _308432 : [(3599 ^ _308432) ^ [] : [-(in(_431740, relation_rng(_431736)))], (3597 ^ _308432) ^ [] : [-(in(_431740, _431738))]]]]], (276 ^ _308432) ^ [_317039, _317041, _317043, _317045] : [-(well_orders(_317043, _317039)), well_orders(_317045, _317041), _317045 = _317043, _317041 = _317039], (3134 ^ _308432) ^ [_416398] : [relation(_416398), 3137 ^ _308432 : [(3138 ^ _308432) ^ [] : [reflexive(_416398), 3141 ^ _308432 : [(3142 ^ _308432) ^ [_416642] : [in(_416642, relation_field(_416398)), -(in(ordered_pair(_416642, _416642), _416398))]]], (3148 ^ _308432) ^ [] : [3150 ^ _308432 : [(3153 ^ _308432) ^ [] : [in(ordered_pair(3149 ^ [_416398], 3149 ^ [_416398]), _416398)], (3151 ^ _308432) ^ [] : [-(in(3149 ^ [_416398], relation_field(_416398)))]], -(reflexive(_416398))]]], (3372 ^ _308432) ^ [_424687, _424689] : [3374 ^ _308432 : [(3377 ^ _308432) ^ [] : [in(3373 ^ [_424687, _424689], _424687)], (3375 ^ _308432) ^ [] : [-(in(3373 ^ [_424687, _424689], _424689))]], -(element(_424689, powerset(_424687)))], (2701 ^ _308432) ^ [_403197] : [2708 ^ _308432 : [(2711 ^ _308432) ^ [] : [-(function(function_inverse(_403197)))], (2709 ^ _308432) ^ [] : [-(relation(function_inverse(_403197)))]], relation(_403197), function(_403197)], (4527 ^ _308432) ^ [_463059] : [relation(_463059), 4530 ^ _308432 : [(4531 ^ _308432) ^ [_463206] : [relation(_463206), subset(relation_rng(_463059), relation_dom(_463206)), -(relation_dom(relation_composition(_463059, _463206)) = relation_dom(_463059))]]], (3723 ^ _308432) ^ [_436520, _436522] : [relation(_436520), -(subset(relation_image(_436520, _436522), relation_rng(_436520)))], (2942 ^ _308432) ^ [] : [-(empty(empty_set))], (702 ^ _308432) ^ [_331905, _331907] : [-(unordered_pair(_331907, _331905) = unordered_pair(_331905, _331907))], (3874 ^ _308432) ^ [_441509, _441511] : [relation(_441509), -(relation_restriction(_441509, _441511) = relation_rng_restriction(_441511, relation_dom_restriction(_441509, _441511)))], (242 ^ _308432) ^ [_316005, _316007, _316009, _316011] : [-(disjoint(_316009, _316005)), disjoint(_316011, _316007), _316011 = _316009, _316007 = _316005], (1555 ^ _308432) ^ [_362550, _362552, _362554] : [-(_362550 = unordered_pair(_362554, _362552)), 1559 ^ _308432 : [(1564 ^ _308432) ^ [] : [1556 ^ [_362550, _362552, _362554] = _362552], (1562 ^ _308432) ^ [] : [1556 ^ [_362550, _362552, _362554] = _362554], (1560 ^ _308432) ^ [] : [-(in(1556 ^ [_362550, _362552, _362554], _362550))]], 1565 ^ _308432 : [(1566 ^ _308432) ^ [] : [-(1556 ^ [_362550, _362552, _362554] = _362554), -(1556 ^ [_362550, _362552, _362554] = _362552)], (1572 ^ _308432) ^ [] : [in(1556 ^ [_362550, _362552, _362554], _362550)]]], (4925 ^ _308432) ^ [_476078, _476080] : [subset(singleton(_476080), singleton(_476078)), -(_476080 = _476078)], (2833 ^ _308432) ^ [_406959, _406961] : [relation(_406959), -(relation(relation_rng_restriction(_406961, _406959)))], (318 ^ _308432) ^ [_318371, _318373, _318375, _318377] : [-(in(_318375, _318371)), in(_318377, _318373), _318377 = _318375, _318373 = _318371], (5143 ^ _308432) ^ [_483458, _483460, _483462] : [-(in(_483458, 5139 ^ [_483462])), in(_483460, 5139 ^ [_483462]), subset(_483458, _483460)], (2401 ^ _308432) ^ [_393222] : [relation(_393222), function(_393222), 2408 ^ _308432 : [(2409 ^ _308432) ^ [] : [one_to_one(_393222), 2412 ^ _308432 : [(2413 ^ _308432) ^ [_393585, _393587] : [-(_393587 = _393585), in(_393587, relation_dom(_393222)), in(_393585, relation_dom(_393222)), apply(_393222, _393587) = apply(_393222, _393585)]]], (2427 ^ _308432) ^ [] : [2430 ^ _308432 : [(2433 ^ _308432) ^ [] : [-(in(2429 ^ [_393222], relation_dom(_393222)))], (2435 ^ _308432) ^ [] : [-(apply(_393222, 2428 ^ [_393222]) = apply(_393222, 2429 ^ [_393222]))], (2437 ^ _308432) ^ [] : [2428 ^ [_393222] = 2429 ^ [_393222]], (2431 ^ _308432) ^ [] : [-(in(2428 ^ [_393222], relation_dom(_393222)))]], -(one_to_one(_393222))]]], (218 ^ _308432) ^ [_315266, _315268, _315270, _315272] : [-(proper_subset(_315270, _315266)), proper_subset(_315272, _315268), _315272 = _315270, _315268 = _315266], (4206 ^ _308432) ^ [_452276, _452278] : [ordinal(_452276), subset(_452278, _452276), -(_452278 = empty_set), 4218 ^ _308432 : [(4223 ^ _308432) ^ [_452828] : [ordinal(_452828), in(_452828, _452278), -(ordinal_subset(4217 ^ [_452276, _452278], _452828))], (4221 ^ _308432) ^ [] : [-(in(4217 ^ [_452276, _452278], _452278))], (4219 ^ _308432) ^ [] : [-(ordinal(4217 ^ [_452276, _452278]))]]], (788 ^ _308432) ^ [_334812] : [relation(_334812), 791 ^ _308432 : [(792 ^ _308432) ^ [_334998, _335000] : [relation(_334998), 795 ^ _308432 : [(796 ^ _308432) ^ [] : [_334998 = relation_dom_restriction(_334812, _335000), 799 ^ _308432 : [(808 ^ _308432) ^ [_335602, _335604] : [-(in(ordered_pair(_335604, _335602), _334998)), in(_335604, _335000), in(ordered_pair(_335604, _335602), _334812)], (800 ^ _308432) ^ [_335323, _335325] : [in(ordered_pair(_335325, _335323), _334998), 803 ^ _308432 : [(806 ^ _308432) ^ [] : [-(in(ordered_pair(_335325, _335323), _334812))], (804 ^ _308432) ^ [] : [-(in(_335325, _335000))]]]]], (818 ^ _308432) ^ [] : [-(_334998 = relation_dom_restriction(_334812, _335000)), 831 ^ _308432 : [(836 ^ _308432) ^ [] : [in(ordered_pair(819 ^ [_334812, _334998, _335000], 820 ^ [_334812, _334998, _335000]), _334998)], (834 ^ _308432) ^ [] : [-(in(ordered_pair(819 ^ [_334812, _334998, _335000], 820 ^ [_334812, _334998, _335000]), _334812))], (832 ^ _308432) ^ [] : [-(in(819 ^ [_334812, _334998, _335000], _335000))]], 823 ^ _308432 : [(826 ^ _308432) ^ [] : [in(819 ^ [_334812, _334998, _335000], _335000), in(ordered_pair(819 ^ [_334812, _334998, _335000], 820 ^ [_334812, _334998, _335000]), _334812)], (824 ^ _308432) ^ [] : [-(in(ordered_pair(819 ^ [_334812, _334998, _335000], 820 ^ [_334812, _334998, _335000]), _334998))]]]]]]], (256 ^ _308432) ^ [_316421, _316423] : [-(empty(_316421)), _316423 = _316421, empty(_316423)], (3653 ^ _308432) ^ [_433967, _433969] : [subset(_433969, _433967), -(set_union2(_433969, _433967) = _433967)], (3183 ^ _308432) ^ [_418074] : [relation(_418074), 3186 ^ _308432 : [(3187 ^ _308432) ^ [] : [transitive(_418074), 3190 ^ _308432 : [(3191 ^ _308432) ^ [_418366, _418368, _418370] : [-(in(ordered_pair(_418370, _418366), _418074)), in(ordered_pair(_418370, _418368), _418074), in(ordered_pair(_418368, _418366), _418074)]]], (3201 ^ _308432) ^ [] : [3205 ^ _308432 : [(3210 ^ _308432) ^ [] : [in(ordered_pair(3202 ^ [_418074], 3204 ^ [_418074]), _418074)], (3208 ^ _308432) ^ [] : [-(in(ordered_pair(3203 ^ [_418074], 3204 ^ [_418074]), _418074))], (3206 ^ _308432) ^ [] : [-(in(ordered_pair(3202 ^ [_418074], 3203 ^ [_418074]), _418074))]], -(transitive(_418074))]]], (3461 ^ _308432) ^ [] : [-(relation(3457 ^ []))], (3424 ^ _308432) ^ [_426305] : [-(empty(_426305)), 3428 ^ _308432 : [(3431 ^ _308432) ^ [] : [empty(3427 ^ [_426305])], (3429 ^ _308432) ^ [] : [-(element(3427 ^ [_426305], powerset(_426305)))]]], (3226 ^ _308432) ^ [_419684, _419686] : [set_difference(_419686, _419684) = empty_set, -(subset(_419686, _419684))], (4593 ^ _308432) ^ [_465282] : [-(set_difference(empty_set, _465282) = empty_set)], (3497 ^ _308432) ^ [] : [-(function(3491 ^ []))], (4985 ^ _308432) ^ [_478043, _478045] : [in(_478045, _478043), empty(_478043)], (194 ^ _308432) ^ [_314499, _314501] : [-(well_founded_relation(_314499)), _314501 = _314499, well_founded_relation(_314501)], (3062 ^ _308432) ^ [_413997] : [empty(relation_dom(_413997)), -(empty(_413997)), relation(_413997)], (1576 ^ _308432) ^ [_363287] : [relation(_363287), 1579 ^ _308432 : [(1580 ^ _308432) ^ [] : [well_founded_relation(_363287), 1583 ^ _308432 : [(1584 ^ _308432) ^ [_363554] : [subset(_363554, relation_field(_363287)), -(_363554 = empty_set), 1592 ^ _308432 : [(1595 ^ _308432) ^ [] : [-(disjoint(fiber(_363287, 1591 ^ [_363287, _363554]), _363554))], (1593 ^ _308432) ^ [] : [-(in(1591 ^ [_363287, _363554], _363554))]]]]], (1597 ^ _308432) ^ [] : [-(well_founded_relation(_363287)), 1599 ^ _308432 : [(1604 ^ _308432) ^ [_364237] : [in(_364237, 1598 ^ [_363287]), disjoint(fiber(_363287, _364237), 1598 ^ [_363287])], (1602 ^ _308432) ^ [] : [1598 ^ [_363287] = empty_set], (1600 ^ _308432) ^ [] : [-(subset(1598 ^ [_363287], relation_field(_363287)))]]]]], (3112 ^ _308432) ^ [_415555, _415557] : [-(set_intersection2(_415557, _415557) = _415557)], (2827 ^ _308432) ^ [_406727, _406729] : [element(_406727, powerset(powerset(_406729))), -(element(complements_of_subsets(_406729, _406727), powerset(powerset(_406729))))], (1442 ^ _308432) ^ [_358797] : [epsilon_transitive(_358797), 1445 ^ _308432 : [(1446 ^ _308432) ^ [_358928] : [in(_358928, _358797), -(subset(_358928, _358797))]]], (4066 ^ _308432) ^ [_447737, _447739] : [relation(_447737), connected(_447737), -(connected(relation_restriction(_447737, _447739)))], (2892 ^ _308432) ^ [_408715, _408717] : [2907 ^ _308432 : [(2910 ^ _308432) ^ [] : [-(function(relation_composition(_408717, _408715)))], (2908 ^ _308432) ^ [] : [-(relation(relation_composition(_408717, _408715)))]], relation(_408717), function(_408717), relation(_408715), function(_408715)], (3920 ^ _308432) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (3553 ^ _308432) ^ [_430413, _430415] : [disjoint(_430415, _430413), -(disjoint(_430413, _430415))], (2745 ^ _308432) ^ [] : [true___, -(true___)], (4551 ^ _308432) ^ [_463849, _463851] : [in(_463851, _463849), -(set_union2(singleton(_463851), _463849) = _463849)], (444 ^ _308432) ^ [_322845, _322847, _322849, _322851] : [-(complements_of_subsets(_322851, _322847) = complements_of_subsets(_322849, _322845)), _322851 = _322849, _322847 = _322845], (4836 ^ _308432) ^ [_473184] : [relation(_473184), 4841 ^ _308432 : [(4844 ^ _308432) ^ [] : [relation_rng(_473184) = empty_set], (4842 ^ _308432) ^ [] : [relation_dom(_473184) = empty_set]], -(_473184 = empty_set)], (2845 ^ _308432) ^ [] : [true___, -(true___)], (5012 ^ _308432) ^ [_479075, _479077] : [set_difference(_479077, _479075) = _479077, -(disjoint(_479077, _479075))], (412 ^ _308432) ^ [_321691, _321693, _321695, _321697] : [-(fiber(_321697, _321693) = fiber(_321695, _321691)), _321697 = _321695, _321693 = _321691], (3990 ^ _308432) ^ [_445302] : [relation(_445302), -(subset(_445302, cartesian_product2(relation_dom(_445302), relation_rng(_445302))))], (4308 ^ _308432) ^ [_455675] : [relation(_455675), 4311 ^ _308432 : [(4314 ^ _308432) ^ [] : [-(relation_dom(_455675) = relation_rng(relation_inverse(_455675)))], (4312 ^ _308432) ^ [] : [-(relation_rng(_455675) = relation_dom(relation_inverse(_455675)))]]], (4370 ^ _308432) ^ [_457803, _457805] : [4371 ^ _308432 : [(4374 ^ _308432) ^ [] : [_457805 = singleton(_457803)], (4372 ^ _308432) ^ [] : [_457805 = empty_set]], -(subset(_457805, singleton(_457803)))], (4002 ^ _308432) ^ [_445764, _445766] : [relation(_445764), function(_445764), 4009 ^ _308432 : [(4010 ^ _308432) ^ [_446013] : [relation(_446013), function(_446013), in(_445766, relation_dom(relation_composition(_446013, _445764))), -(apply(relation_composition(_446013, _445764), _445766) = apply(_445764, apply(_446013, _445766)))]]], (2811 ^ _308432) ^ [_406186, _406188, _406190] : [-(element(subset_difference(_406190, _406188, _406186), powerset(_406190))), element(_406188, powerset(_406190)), element(_406186, powerset(_406190))], (3006 ^ _308432) ^ [_412175, _412177] : [empty(unordered_pair(_412177, _412175))], (2015 ^ _308432) ^ [_379485] : [-(cast_to_subset(_379485) = _379485)], (4947 ^ _308432) ^ [_476777] : [-(relation_rng(identity_relation(_476777)) = _476777)], (5040 ^ _308432) ^ [_479966, _479968] : [relation(_479966), -(subset(relation_dom_restriction(_479966, _479968), _479966))], (3755 ^ _308432) ^ [_437574] : [relation(_437574), -(relation_image(_437574, relation_dom(_437574)) = relation_rng(_437574))], (3521 ^ _308432) ^ [_429477, _429479] : [ordinal(_429479), ordinal(_429477), 3528 ^ _308432 : [(3535 ^ _308432) ^ [] : [subset(_429479, _429477), -(ordinal_subset(_429479, _429477))], (3529 ^ _308432) ^ [] : [ordinal_subset(_429479, _429477), -(subset(_429479, _429477))]]], (3577 ^ _308432) ^ [_431249] : [-(in(_431249, succ(_431249)))], (434 ^ _308432) ^ [_322486, _322488, _322490, _322492] : [-(union_of_subsets(_322492, _322488) = union_of_subsets(_322490, _322486)), _322492 = _322490, _322488 = _322486], (2499 ^ _308432) ^ [_397034] : [relation(_397034), 2502 ^ _308432 : [(2503 ^ _308432) ^ [_397248] : [is_transitive_in(_397034, _397248), 2506 ^ _308432 : [(2507 ^ _308432) ^ [_397458, _397460, _397462] : [-(in(ordered_pair(_397462, _397458), _397034)), in(_397462, _397248), in(_397460, _397248), in(_397458, _397248), in(ordered_pair(_397462, _397460), _397034), in(ordered_pair(_397460, _397458), _397034)]]], (2529 ^ _308432) ^ [_398069] : [2533 ^ _308432 : [(2536 ^ _308432) ^ [] : [-(in(2531 ^ [_397034, _398069], _398069))], (2534 ^ _308432) ^ [] : [-(in(2530 ^ [_397034, _398069], _398069))], (2544 ^ _308432) ^ [] : [in(ordered_pair(2530 ^ [_397034, _398069], 2532 ^ [_397034, _398069]), _397034)], (2540 ^ _308432) ^ [] : [-(in(ordered_pair(2530 ^ [_397034, _398069], 2531 ^ [_397034, _398069]), _397034))], (2542 ^ _308432) ^ [] : [-(in(ordered_pair(2531 ^ [_397034, _398069], 2532 ^ [_397034, _398069]), _397034))], (2538 ^ _308432) ^ [] : [-(in(2532 ^ [_397034, _398069], _398069))]], -(is_transitive_in(_397034, _398069))]]], (2876 ^ _308432) ^ [] : [-(relation(empty_set))], (3643 ^ _308432) ^ [_433636, _433638, _433640, _433642] : [-(subset(cartesian_product2(_433642, _433638), cartesian_product2(_433640, _433636))), subset(_433642, _433640), subset(_433638, _433636)], (4402 ^ _308432) ^ [_458931, _458933] : [-(disjoint(_458933, _458931)), 4406 ^ _308432 : [(4409 ^ _308432) ^ [] : [-(in(4405 ^ [_458931, _458933], _458931))], (4407 ^ _308432) ^ [] : [-(in(4405 ^ [_458931, _458933], _458933))]]], (1714 ^ _308432) ^ [_368615] : [epsilon_connected(_368615), 1717 ^ _308432 : [(1718 ^ _308432) ^ [_368791, _368793] : [in(_368793, _368615), in(_368791, _368615), -(in(_368793, _368791)), -(_368793 = _368791), -(in(_368791, _368793))]]], (4378 ^ _308432) ^ [_458068] : [-(set_difference(_458068, empty_set) = _458068)], (4870 ^ _308432) ^ [_474193, _474195] : [-(in(_474193, _474195)), -(set_difference(_474195, singleton(_474193)) = _474195)], (2641 ^ _308432) ^ [] : [true___, -(true___)], (4024 ^ _308432) ^ [_446458, _446460] : [relation(_446458), reflexive(_446458), -(reflexive(relation_restriction(_446458, _446460)))], (5126 ^ _308432) ^ [_482688, _482690] : [relation(_482688), -(relation_dom_restriction(_482688, _482690) = relation_composition(identity_relation(_482690), _482688))], (2283 ^ _308432) ^ [_388880] : [being_limit_ordinal(_388880), -(_388880 = union(_388880))], (4390 ^ _308432) ^ [_458529, _458531] : [element(_458531, powerset(_458529)), -(subset(_458531, _458529))], (3579 ^ _308432) ^ [_431386, _431388, _431390, _431392] : [unordered_pair(_431392, _431390) = unordered_pair(_431388, _431386), -(_431392 = _431388), -(_431392 = _431386)], (1517 ^ _308432) ^ [_361325, _361327] : [empty(_361327), 1520 ^ _308432 : [(1527 ^ _308432) ^ [] : [empty(_361325), -(element(_361325, _361327))], (1521 ^ _308432) ^ [] : [element(_361325, _361327), -(empty(_361325))]]], (957 ^ _308432) ^ [_341236] : [relation(_341236), 960 ^ _308432 : [(967 ^ _308432) ^ [] : [is_antisymmetric_in(_341236, relation_field(_341236)), -(antisymmetric(_341236))], (961 ^ _308432) ^ [] : [antisymmetric(_341236), -(is_antisymmetric_in(_341236, relation_field(_341236)))]]], (4595 ^ _308432) ^ [_465406, _465408, _465410] : [-(element(_465410, _465406)), in(_465410, _465408), element(_465408, powerset(_465406))], (1685 ^ _308432) ^ [_367352, _367354, _367356] : [-(_367352 = cartesian_product2(_367356, _367354)), 1703 ^ _308432 : [(1706 ^ _308432) ^ [] : [-(in(1702 ^ [_367352, _367354, _367356], _367354))], (1708 ^ _308432) ^ [] : [-(1686 ^ [_367352, _367354, _367356] = ordered_pair(1701 ^ [_367352, _367354, _367356], 1702 ^ [_367352, _367354, _367356]))], (1710 ^ _308432) ^ [] : [in(1686 ^ [_367352, _367354, _367356], _367352)], (1704 ^ _308432) ^ [] : [-(in(1701 ^ [_367352, _367354, _367356], _367356))]], 1689 ^ _308432 : [(1692 ^ _308432) ^ [_367690, _367692] : [in(_367692, _367356), in(_367690, _367354), 1686 ^ [_367352, _367354, _367356] = ordered_pair(_367692, _367690)], (1690 ^ _308432) ^ [] : [-(in(1686 ^ [_367352, _367354, _367356], _367352))]]], (3446 ^ _308432) ^ [] : [-(function(3442 ^ []))], (3420 ^ _308432) ^ [] : [-(empty(3418 ^ []))], (402 ^ _308432) ^ [_321332, _321334, _321336, _321338] : [-(cartesian_product2(_321338, _321334) = cartesian_product2(_321336, _321332)), _321338 = _321336, _321334 = _321332], (3340 ^ _308432) ^ [_423524, _423526] : [3341 ^ _308432 : [(3344 ^ _308432) ^ [] : [_423526 = singleton(_423524)], (3342 ^ _308432) ^ [] : [_423526 = empty_set]], -(subset(_423526, singleton(_423524)))], (840 ^ _308432) ^ [_336757] : [relation(_336757), function(_336757), 847 ^ _308432 : [(848 ^ _308432) ^ [_337055, _337057] : [_337055 = relation_image(_336757, _337057), 851 ^ _308432 : [(863 ^ _308432) ^ [_337710] : [-(in(_337710, _337055)), 864 ^ _308432 : [(865 ^ _308432) ^ [_337823] : [in(_337823, relation_dom(_336757)), in(_337823, _337057), _337710 = apply(_336757, _337823)]]], (852 ^ _308432) ^ [_337255] : [in(_337255, _337055), 856 ^ _308432 : [(861 ^ _308432) ^ [] : [-(_337255 = apply(_336757, 855 ^ [_336757, _337055, _337057, _337255]))], (859 ^ _308432) ^ [] : [-(in(855 ^ [_336757, _337055, _337057, _337255], _337057))], (857 ^ _308432) ^ [] : [-(in(855 ^ [_336757, _337055, _337057, _337255], relation_dom(_336757)))]]]]], (877 ^ _308432) ^ [_338183, _338185] : [-(_338183 = relation_image(_336757, _338185)), 894 ^ _308432 : [(897 ^ _308432) ^ [] : [-(in(893 ^ [_336757, _338183, _338185], _338185))], (899 ^ _308432) ^ [] : [-(878 ^ [_336757, _338183, _338185] = apply(_336757, 893 ^ [_336757, _338183, _338185]))], (901 ^ _308432) ^ [] : [in(878 ^ [_336757, _338183, _338185], _338183)], (895 ^ _308432) ^ [] : [-(in(893 ^ [_336757, _338183, _338185], relation_dom(_336757)))]], 881 ^ _308432 : [(884 ^ _308432) ^ [_338503] : [in(_338503, relation_dom(_336757)), in(_338503, _338185), 878 ^ [_336757, _338183, _338185] = apply(_336757, _338503)], (882 ^ _308432) ^ [] : [-(in(878 ^ [_336757, _338183, _338185], _338183))]]]]], (708 ^ _308432) ^ [_332220, _332222] : [ordinal(_332222), ordinal(_332220), -(ordinal_subset(_332222, _332220)), -(ordinal_subset(_332220, _332222))], (578 ^ _308432) ^ [_327682, _327684, _327686, _327688] : [-(relation_dom_restriction(_327688, _327684) = relation_dom_restriction(_327686, _327682)), _327688 = _327686, _327684 = _327682], (2936 ^ _308432) ^ [] : [-(relation_empty_yielding(empty_set))], (2924 ^ _308432) ^ [_409614] : [empty(powerset(_409614))], (3466 ^ _308432) ^ [_427636] : [-(empty(3462 ^ [_427636]))], (3036 ^ _308432) ^ [] : [-(empty(empty_set))], (2198 ^ _308432) ^ [_385873] : [relation(_385873), 2201 ^ _308432 : [(2202 ^ _308432) ^ [_386054] : [_386054 = relation_rng(_385873), 2205 ^ _308432 : [(2213 ^ _308432) ^ [_386478] : [2214 ^ _308432 : [(2215 ^ _308432) ^ [_386557] : [in(ordered_pair(_386557, _386478), _385873)]], -(in(_386478, _386054))], (2206 ^ _308432) ^ [_386234] : [in(_386234, _386054), -(in(ordered_pair(2209 ^ [_385873, _386054, _386234], _386234), _385873))]]], (2219 ^ _308432) ^ [_386685] : [-(_386685 = relation_rng(_385873)), 2223 ^ _308432 : [(2226 ^ _308432) ^ [_386948] : [in(ordered_pair(_386948, 2220 ^ [_385873, _386685]), _385873)], (2224 ^ _308432) ^ [] : [-(in(2220 ^ [_385873, _386685], _386685))]], 2228 ^ _308432 : [(2231 ^ _308432) ^ [] : [in(2220 ^ [_385873, _386685], _386685)], (2229 ^ _308432) ^ [] : [-(in(ordered_pair(2227 ^ [_385873, _386685], 2220 ^ [_385873, _386685]), _385873))]]]]], (4076 ^ _308432) ^ [_448022] : [ordinal(_448022), 4079 ^ _308432 : [(4080 ^ _308432) ^ [_448172] : [ordinal(_448172), -(in(_448022, _448172)), -(_448022 = _448172), -(in(_448172, _448022))]]], (2695 ^ _308432) ^ [] : [true___, -(true___)], (2719 ^ _308432) ^ [_403649] : [-(element(cast_to_subset(_403649), powerset(_403649)))], (1501 ^ _308432) ^ [_360912, _360914] : [-(empty(_360914)), 1504 ^ _308432 : [(1511 ^ _308432) ^ [] : [in(_360912, _360914), -(element(_360912, _360914))], (1505 ^ _308432) ^ [] : [element(_360912, _360914), -(in(_360912, _360914))]]], (422 ^ _308432) ^ [_322022, _322024] : [_322024 = _322022, -(relation_inverse(_322024) = relation_inverse(_322022))], (1918 ^ _308432) ^ [_375928] : [ordinal(_375928), 1921 ^ _308432 : [(1924 ^ _308432) ^ [] : [-(epsilon_connected(_375928))], (1922 ^ _308432) ^ [] : [-(epsilon_transitive(_375928))]]], (76 ^ _308432) ^ [_310956, _310958] : [-(epsilon_connected(_310956)), _310958 = _310956, epsilon_connected(_310958)], (3448 ^ _308432) ^ [] : [-(one_to_one(3442 ^ []))], (3481 ^ _308432) ^ [] : [-(epsilon_transitive(3477 ^ []))], (3694 ^ _308432) ^ [_435522, _435524, _435526] : [relation(_435522), 3697 ^ _308432 : [(3709 ^ _308432) ^ [] : [-(in(_435526, relation_image(_435522, _435524))), 3710 ^ _308432 : [(3711 ^ _308432) ^ [_436123] : [in(_436123, relation_dom(_435522)), in(ordered_pair(_436123, _435526), _435522), in(_436123, _435524)]]], (3698 ^ _308432) ^ [] : [in(_435526, relation_image(_435522, _435524)), 3702 ^ _308432 : [(3707 ^ _308432) ^ [] : [-(in(3701 ^ [_435522, _435524, _435526], _435524))], (3705 ^ _308432) ^ [] : [-(in(ordered_pair(3701 ^ [_435522, _435524, _435526], _435526), _435522))], (3703 ^ _308432) ^ [] : [-(in(3701 ^ [_435522, _435524, _435526], relation_dom(_435522)))]]]]], (622 ^ _308432) ^ [_329252, _329254, _329256, _329258] : [-(relation_restriction(_329258, _329254) = relation_restriction(_329256, _329252)), _329258 = _329256, _329254 = _329252], (3729 ^ _308432) ^ [_436738, _436740] : [-(subset(relation_image(_436738, relation_inverse_image(_436738, _436740)), _436740)), relation(_436738), function(_436738)], (1336 ^ _308432) ^ [_354990, _354992] : [-(_354990 = singleton(_354992)), 1340 ^ _308432 : [(1343 ^ _308432) ^ [] : [1337 ^ [_354990, _354992] = _354992], (1341 ^ _308432) ^ [] : [-(in(1337 ^ [_354990, _354992], _354990))]], 1344 ^ _308432 : [(1347 ^ _308432) ^ [] : [in(1337 ^ [_354990, _354992], _354990)], (1345 ^ _308432) ^ [] : [-(1337 ^ [_354990, _354992] = _354992)]]], (3232 ^ _308432) ^ [_419852, _419854] : [subset(_419854, _419852), -(set_difference(_419854, _419852) = empty_set)], (4 ^ _308432) ^ [_308663, _308665] : [_308665 = _308663, -(_308663 = _308665)], (1154 ^ _308432) ^ [_348445, _348447, _348449, _348451] : [_348445 = unordered_triple(_348451, _348449, _348447), 1157 ^ _308432 : [(1158 ^ _308432) ^ [_348647] : [in(_348647, _348445), -(_348647 = _348451), -(_348647 = _348449), -(_348647 = _348447)], (1172 ^ _308432) ^ [_349047] : [1173 ^ _308432 : [(1178 ^ _308432) ^ [] : [_349047 = _348447], (1176 ^ _308432) ^ [] : [_349047 = _348449], (1174 ^ _308432) ^ [] : [_349047 = _348451]], -(in(_349047, _348445))]]], (4154 ^ _308432) ^ [_450541, _450543] : [-(_450543 = _450541), 4158 ^ _308432 : [(4161 ^ _308432) ^ [] : [in(4155 ^ [_450541, _450543], _450541)], (4159 ^ _308432) ^ [] : [-(in(4155 ^ [_450541, _450543], _450543))]], 4162 ^ _308432 : [(4165 ^ _308432) ^ [] : [in(4155 ^ [_450541, _450543], _450543)], (4163 ^ _308432) ^ [] : [-(in(4155 ^ [_450541, _450543], _450541))]]], (2944 ^ _308432) ^ [] : [-(epsilon_transitive(empty_set))], (1320 ^ _308432) ^ [_354469, _354471] : [_354469 = singleton(_354471), 1323 ^ _308432 : [(1330 ^ _308432) ^ [_354811] : [_354811 = _354471, -(in(_354811, _354469))], (1324 ^ _308432) ^ [_354639] : [in(_354639, _354469), -(_354639 = _354471)]]], (3330 ^ _308432) ^ [_423264, _423266] : [subset(_423266, singleton(_423264)), -(_423266 = empty_set), -(_423266 = singleton(_423264))], (3660 ^ _308432) ^ [_434289] : [-(in(_434289, 3658 ^ [_434289]))], (5004 ^ _308432) ^ [_478766, _478768] : [-(subset(_478768, set_union2(_478768, _478766)))], (1304 ^ _308432) ^ [_353972, _353974] : [_353974 = empty_set, 1307 ^ _308432 : [(1314 ^ _308432) ^ [] : [_353972 = empty_set, -(_353972 = set_meet(_353974))], (1308 ^ _308432) ^ [] : [_353972 = set_meet(_353974), -(_353972 = empty_set)]]], (3456 ^ _308432) ^ [] : [-(ordinal(3442 ^ []))], (3422 ^ _308432) ^ [] : [-(relation(3418 ^ []))], (2930 ^ _308432) ^ [_409861] : [-(relation(identity_relation(_409861)))], (5166 ^ _308432) ^ [_484292, _484294] : [subset(_484292, 5139 ^ [_484294]), -(are_equipotent(_484292, 5139 ^ [_484294])), -(in(_484292, 5139 ^ [_484294]))], (3110 ^ _308432) ^ [_415458, _415460] : [-(set_union2(_415460, _415460) = _415460)], (3785 ^ _308432) ^ [_438567, _438569, _438571] : [relation(_438567), 3788 ^ _308432 : [(3800 ^ _308432) ^ [] : [-(in(_438571, relation_inverse_image(_438567, _438569))), 3801 ^ _308432 : [(3802 ^ _308432) ^ [_439168] : [in(_439168, relation_rng(_438567)), in(ordered_pair(_438571, _439168), _438567), in(_439168, _438569)]]], (3789 ^ _308432) ^ [] : [in(_438571, relation_inverse_image(_438567, _438569)), 3793 ^ _308432 : [(3798 ^ _308432) ^ [] : [-(in(3792 ^ [_438567, _438569, _438571], _438569))], (3796 ^ _308432) ^ [] : [-(in(ordered_pair(_438571, 3792 ^ [_438567, _438569, _438571]), _438567))], (3794 ^ _308432) ^ [] : [-(in(3792 ^ [_438567, _438569, _438571], relation_rng(_438567)))]]]]], (2880 ^ _308432) ^ [_408337, _408339] : [2887 ^ _308432 : [(2890 ^ _308432) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_408339, _408337)))], (2888 ^ _308432) ^ [] : [-(relation(relation_dom_restriction(_408339, _408337)))]], relation(_408339), relation_empty_yielding(_408339)], (1973 ^ _308432) ^ [_377863] : [relation(_377863), 1976 ^ _308432 : [(1977 ^ _308432) ^ [_378063] : [is_antisymmetric_in(_377863, _378063), 1980 ^ _308432 : [(1981 ^ _308432) ^ [_378245, _378247] : [-(_378247 = _378245), in(_378247, _378063), in(_378245, _378063), in(ordered_pair(_378247, _378245), _377863), in(ordered_pair(_378245, _378247), _377863)]]], (1999 ^ _308432) ^ [_378731] : [2002 ^ _308432 : [(2003 ^ _308432) ^ [] : [-(in(2000 ^ [_377863, _378731], _378731))], (2007 ^ _308432) ^ [] : [-(in(ordered_pair(2000 ^ [_377863, _378731], 2001 ^ [_377863, _378731]), _377863))], (2011 ^ _308432) ^ [] : [2000 ^ [_377863, _378731] = 2001 ^ [_377863, _378731]], (2009 ^ _308432) ^ [] : [-(in(ordered_pair(2001 ^ [_377863, _378731], 2000 ^ [_377863, _378731]), _377863))], (2005 ^ _308432) ^ [] : [-(in(2001 ^ [_377863, _378731], _378731))]], -(is_antisymmetric_in(_377863, _378731))]]], (352 ^ _308432) ^ [_319549, _319551, _319553, _319555, _319557, _319559] : [-(unordered_triple(_319559, _319555, _319551) = unordered_triple(_319557, _319553, _319549)), _319559 = _319557, _319555 = _319553, _319551 = _319549], (2874 ^ _308432) ^ [] : [-(empty(empty_set))], (4306 ^ _308432) ^ [_455577, _455579] : [-(subset(set_difference(_455579, _455577), _455579))], (2611 ^ _308432) ^ [_401212] : [relation(_401212), function(_401212), one_to_one(_401212), -(function_inverse(_401212) = relation_inverse(_401212))], (2996 ^ _308432) ^ [_411892, _411894] : [-(relation(set_difference(_411894, _411892))), relation(_411894), relation(_411892)], (4945 ^ _308432) ^ [_476729] : [-(relation_dom(identity_relation(_476729)) = _476729)], (3892 ^ _308432) ^ [_442161, _442163, _442165] : [-(subset(_442165, set_intersection2(_442163, _442161))), subset(_442165, _442163), subset(_442165, _442161)], (2948 ^ _308432) ^ [] : [-(ordinal(empty_set))], (3499 ^ _308432) ^ [_428676, _428678] : [element(_428676, powerset(powerset(_428678))), -(union_of_subsets(_428678, _428676) = union(_428676))], (638 ^ _308432) ^ [_329991, _329993] : [proper_subset(_329993, _329991), proper_subset(_329991, _329993)], (3485 ^ _308432) ^ [] : [-(ordinal(3477 ^ []))], (905 ^ _308432) ^ [_339313, _339315] : [relation(_339313), 908 ^ _308432 : [(909 ^ _308432) ^ [_339484] : [relation(_339484), 912 ^ _308432 : [(913 ^ _308432) ^ [] : [_339484 = relation_rng_restriction(_339315, _339313), 916 ^ _308432 : [(925 ^ _308432) ^ [_340090, _340092] : [-(in(ordered_pair(_340092, _340090), _339484)), in(_340090, _339315), in(ordered_pair(_340092, _340090), _339313)], (917 ^ _308432) ^ [_339811, _339813] : [in(ordered_pair(_339813, _339811), _339484), 920 ^ _308432 : [(923 ^ _308432) ^ [] : [-(in(ordered_pair(_339813, _339811), _339313))], (921 ^ _308432) ^ [] : [-(in(_339811, _339315))]]]]], (935 ^ _308432) ^ [] : [-(_339484 = relation_rng_restriction(_339315, _339313)), 948 ^ _308432 : [(953 ^ _308432) ^ [] : [in(ordered_pair(936 ^ [_339313, _339315, _339484], 937 ^ [_339313, _339315, _339484]), _339484)], (951 ^ _308432) ^ [] : [-(in(ordered_pair(936 ^ [_339313, _339315, _339484], 937 ^ [_339313, _339315, _339484]), _339313))], (949 ^ _308432) ^ [] : [-(in(937 ^ [_339313, _339315, _339484], _339315))]], 940 ^ _308432 : [(943 ^ _308432) ^ [] : [in(937 ^ [_339313, _339315, _339484], _339315), in(ordered_pair(936 ^ [_339313, _339315, _339484], 937 ^ [_339313, _339315, _339484]), _339313)], (941 ^ _308432) ^ [] : [-(in(ordered_pair(936 ^ [_339313, _339315, _339484], 937 ^ [_339313, _339315, _339484]), _339484))]]]]]]], (2713 ^ _308432) ^ [] : [true___, -(true___)], (3354 ^ _308432) ^ [_424089, _424091, _424093, _424095] : [in(ordered_pair(_424095, _424093), cartesian_product2(_424091, _424089)), 3357 ^ _308432 : [(3360 ^ _308432) ^ [] : [-(in(_424093, _424089))], (3358 ^ _308432) ^ [] : [-(in(_424095, _424091))]]], (4802 ^ _308432) ^ [] : [-(relation_dom(empty_set) = empty_set)], (3493 ^ _308432) ^ [] : [-(relation(3491 ^ []))], (510 ^ _308432) ^ [_325233, _325235, _325237, _325239] : [-(ordered_pair(_325239, _325235) = ordered_pair(_325237, _325233)), _325239 = _325237, _325235 = _325233], (4718 ^ _308432) ^ [_469684, _469686, _469688] : [element(_469684, powerset(_469688)), in(_469686, subset_complement(_469688, _469684)), in(_469686, _469684)], (4812 ^ _308432) ^ [_472503] : [relation(_472503), function(_472503), one_to_one(_472503), -(one_to_one(function_inverse(_472503)))], (2647 ^ _308432) ^ [] : [true___, -(true___)], (682 ^ _308432) ^ [_331310] : [-(ordinal(_331310)), epsilon_transitive(_331310), epsilon_connected(_331310)], (4728 ^ _308432) ^ [_469990] : [relation(_469990), function(_469990), one_to_one(_469990), 4739 ^ _308432 : [(4742 ^ _308432) ^ [] : [-(relation_dom(_469990) = relation_rng(function_inverse(_469990)))], (4740 ^ _308432) ^ [] : [-(relation_rng(_469990) = relation_dom(function_inverse(_469990)))]]], (2653 ^ _308432) ^ [] : [true___, -(true___)], (2852 ^ _308432) ^ [_407419] : [-(element(2850 ^ [_407419], _407419))], (3040 ^ _308432) ^ [_413327, _413329] : [empty(cartesian_product2(_413329, _413327)), -(empty(_413329)), -(empty(_413327))], (116 ^ _308432) ^ [_312136, _312138] : [-(connected(_312136)), _312138 = _312136, connected(_312138)], (612 ^ _308432) ^ [_328913, _328915, _328917, _328919] : [-(unordered_pair(_328919, _328915) = unordered_pair(_328917, _328913)), _328919 = _328917, _328915 = _328913], (484 ^ _308432) ^ [_324297, _324299, _324301, _324303] : [-(subset_complement(_324303, _324299) = subset_complement(_324301, _324297)), _324303 = _324301, _324299 = _324297], (778 ^ _308432) ^ [_334525, _334527] : [-(_334527 = _334525), subset(_334527, _334525), subset(_334525, _334527)], (3474 ^ _308432) ^ [] : [-(function(3470 ^ []))], (332 ^ _308432) ^ [_318787, _318789] : [-(relation(_318787)), _318789 = _318787, relation(_318789)], (3488 ^ _308432) ^ [] : [-(relation(3486 ^ []))], (2763 ^ _308432) ^ [] : [true___, -(true___)], (4183 ^ _308432) ^ [_451547] : [-(ordinal(_451547)), 4185 ^ _308432 : [(4188 ^ _308432) ^ [] : [ordinal(4184 ^ [_451547]), subset(4184 ^ [_451547], _451547)], (4186 ^ _308432) ^ [] : [-(in(4184 ^ [_451547], _451547))]]], (3132 ^ _308432) ^ [_416303, _416305] : [proper_subset(_416305, _416305)], (3072 ^ _308432) ^ [_414274] : [empty(relation_rng(_414274)), -(empty(_414274)), relation(_414274)], (2803 ^ _308432) ^ [_405836] : [-(relation(identity_relation(_405836)))], (5108 ^ _308432) ^ [_482020, _482022, _482024] : [singleton(_482024) = unordered_pair(_482022, _482020), -(_482024 = _482022)], (4744 ^ _308432) ^ [_470443] : [relation(_470443), -(in(ordered_pair(4749 ^ [_470443], 4750 ^ [_470443]), _470443)), -(_470443 = empty_set)], (722 ^ _308432) ^ [_332607, _332609] : [relation(_332607), 725 ^ _308432 : [(726 ^ _308432) ^ [] : [_332607 = identity_relation(_332609), 729 ^ _308432 : [(738 ^ _308432) ^ [_333180, _333182] : [-(in(ordered_pair(_333182, _333180), _332607)), in(_333182, _332609), _333182 = _333180], (730 ^ _308432) ^ [_332917, _332919] : [in(ordered_pair(_332919, _332917), _332607), 733 ^ _308432 : [(736 ^ _308432) ^ [] : [-(_332919 = _332917)], (734 ^ _308432) ^ [] : [-(in(_332919, _332609))]]]]], (748 ^ _308432) ^ [] : [-(_332607 = identity_relation(_332609)), 761 ^ _308432 : [(766 ^ _308432) ^ [] : [in(ordered_pair(749 ^ [_332607, _332609], 750 ^ [_332607, _332609]), _332607)], (764 ^ _308432) ^ [] : [-(749 ^ [_332607, _332609] = 750 ^ [_332607, _332609])], (762 ^ _308432) ^ [] : [-(in(749 ^ [_332607, _332609], _332609))]], 753 ^ _308432 : [(756 ^ _308432) ^ [] : [in(749 ^ [_332607, _332609], _332609), 749 ^ [_332607, _332609] = 750 ^ [_332607, _332609]], (754 ^ _308432) ^ [] : [-(in(ordered_pair(749 ^ [_332607, _332609], 750 ^ [_332607, _332609]), _332607))]]]]], (2926 ^ _308432) ^ [] : [-(empty(empty_set))], (5176 ^ _308432) ^ [_484626, _484628, _484630] : [singleton(_484630) = unordered_pair(_484628, _484626), -(_484628 = _484626)], (48 ^ _308432) ^ [_310096, _310098, _310100, _310102] : [-(is_transitive_in(_310100, _310096)), is_transitive_in(_310102, _310098), _310102 = _310100, _310098 = _310096], (2839 ^ _308432) ^ [] : [true___, -(true___)], (4963 ^ _308432) ^ [_477350, _477352, _477354, _477356] : [relation(_477350), 4966 ^ _308432 : [(4975 ^ _308432) ^ [] : [-(in(ordered_pair(_477356, _477354), relation_composition(identity_relation(_477352), _477350))), in(_477356, _477352), in(ordered_pair(_477356, _477354), _477350)], (4967 ^ _308432) ^ [] : [in(ordered_pair(_477356, _477354), relation_composition(identity_relation(_477352), _477350)), 4970 ^ _308432 : [(4973 ^ _308432) ^ [] : [-(in(ordered_pair(_477356, _477354), _477350))], (4971 ^ _308432) ^ [] : [-(in(_477356, _477352))]]]]], (5141 ^ _308432) ^ [_483346] : [-(in(_483346, 5139 ^ [_483346]))], (1780 ^ _308432) ^ [_371042, _371044] : [subset(_371044, _371042), 1783 ^ _308432 : [(1784 ^ _308432) ^ [_371179] : [in(_371179, _371044), -(in(_371179, _371042))]]], (1857 ^ _308432) ^ [_373927, _373929, _373931] : [-(_373927 = set_intersection2(_373931, _373929)), 1869 ^ _308432 : [(1874 ^ _308432) ^ [] : [in(1858 ^ [_373927, _373929, _373931], _373927)], (1872 ^ _308432) ^ [] : [-(in(1858 ^ [_373927, _373929, _373931], _373929))], (1870 ^ _308432) ^ [] : [-(in(1858 ^ [_373927, _373929, _373931], _373931))]], 1861 ^ _308432 : [(1864 ^ _308432) ^ [] : [in(1858 ^ [_373927, _373929, _373931], _373931), in(1858 ^ [_373927, _373929, _373931], _373929)], (1862 ^ _308432) ^ [] : [-(in(1858 ^ [_373927, _373929, _373931], _373927))]]], (4421 ^ _308432) ^ [_459594] : [subset(_459594, empty_set), -(_459594 = empty_set)], (4328 ^ _308432) ^ [_456418, _456420] : [subset(singleton(_456420), _456418), -(in(_456420, _456418))], (106 ^ _308432) ^ [_311841, _311843] : [-(reflexive(_311841)), _311843 = _311841, reflexive(_311843)], (2343 ^ _308432) ^ [_391115] : [relation(_391115), 2346 ^ _308432 : [(2347 ^ _308432) ^ [_391234] : [-(relation_restriction(_391115, _391234) = set_intersection2(_391115, cartesian_product2(_391234, _391234)))]]], (4142 ^ _308432) ^ [_450133] : [-(set_intersection2(_450133, empty_set) = empty_set)], (5082 ^ _308432) ^ [_481232] : [relation(_481232), 5085 ^ _308432 : [(5092 ^ _308432) ^ [] : [well_ordering(_481232), -(well_orders(_481232, relation_field(_481232)))], (5086 ^ _308432) ^ [] : [well_orders(_481232, relation_field(_481232)), -(well_ordering(_481232))]]], (588 ^ _308432) ^ [_328013, _328015] : [_328015 = _328013, -(relation_rng(_328015) = relation_rng(_328013))], (2912 ^ _308432) ^ [_409237] : [empty(succ(_409237))], (4233 ^ _308432) ^ [_453156] : [ordinal(_453156), 4236 ^ _308432 : [(4237 ^ _308432) ^ [_453294] : [ordinal(_453294), 4240 ^ _308432 : [(4247 ^ _308432) ^ [] : [ordinal_subset(succ(_453156), _453294), -(in(_453156, _453294))], (4241 ^ _308432) ^ [] : [in(_453156, _453294), -(ordinal_subset(succ(_453156), _453294))]]]]], (3417 ^ _308432) ^ [] : [-(ordinal(3411 ^ []))], (500 ^ _308432) ^ [_324874, _324876, _324878, _324880] : [-(set_difference(_324880, _324876) = set_difference(_324878, _324874)), _324880 = _324878, _324876 = _324874], (2102 ^ _308432) ^ [_382373, _382375, _382377] : [_382373 = set_difference(_382377, _382375), 2105 ^ _308432 : [(2114 ^ _308432) ^ [_382817] : [-(in(_382817, _382373)), in(_382817, _382377), -(in(_382817, _382375))], (2106 ^ _308432) ^ [_382557] : [in(_382557, _382373), 2109 ^ _308432 : [(2112 ^ _308432) ^ [] : [in(_382557, _382375)], (2110 ^ _308432) ^ [] : [-(in(_382557, _382377))]]]]], (34 ^ _308432) ^ [_309652, _309654, _309656, _309658] : [-(is_connected_in(_309656, _309652)), is_connected_in(_309658, _309654), _309658 = _309656, _309654 = _309652], (3479 ^ _308432) ^ [] : [empty(3477 ^ [])], (3820 ^ _308432) ^ [_439797, _439799, _439801] : [relation(_439797), 3823 ^ _308432 : [(3832 ^ _308432) ^ [] : [-(in(_439801, relation_restriction(_439797, _439799))), in(_439801, _439797), in(_439801, cartesian_product2(_439799, _439799))], (3824 ^ _308432) ^ [] : [in(_439801, relation_restriction(_439797, _439799)), 3827 ^ _308432 : [(3830 ^ _308432) ^ [] : [-(in(_439801, cartesian_product2(_439799, _439799)))], (3828 ^ _308432) ^ [] : [-(in(_439801, _439797))]]]]], (1351 ^ _308432) ^ [_355512] : [relation(_355512), 1354 ^ _308432 : [(1355 ^ _308432) ^ [_355716, _355718] : [_355716 = fiber(_355512, _355718), 1358 ^ _308432 : [(1367 ^ _308432) ^ [_356171] : [-(in(_356171, _355716)), -(_356171 = _355718), in(ordered_pair(_356171, _355718), _355512)], (1359 ^ _308432) ^ [_355905] : [in(_355905, _355716), 1362 ^ _308432 : [(1365 ^ _308432) ^ [] : [-(in(ordered_pair(_355905, _355718), _355512))], (1363 ^ _308432) ^ [] : [_355905 = _355718]]]]], (1377 ^ _308432) ^ [_356464, _356466] : [-(_356464 = fiber(_355512, _356466)), 1389 ^ _308432 : [(1394 ^ _308432) ^ [] : [in(1378 ^ [_355512, _356464, _356466], _356464)], (1392 ^ _308432) ^ [] : [-(in(ordered_pair(1378 ^ [_355512, _356464, _356466], _356466), _355512))], (1390 ^ _308432) ^ [] : [1378 ^ [_355512, _356464, _356466] = _356466]], 1381 ^ _308432 : [(1384 ^ _308432) ^ [] : [-(1378 ^ [_355512, _356464, _356466] = _356466), in(ordered_pair(1378 ^ [_355512, _356464, _356466], _356466), _355512)], (1382 ^ _308432) ^ [] : [-(in(1378 ^ [_355512, _356464, _356466], _356464))]]]]], (4605 ^ _308432) ^ [_465739, _465741] : [-(disjoint(_465741, _465739)), -(in(4608 ^ [_465739, _465741], set_intersection2(_465741, _465739)))], (4931 ^ _308432) ^ [_476310, _476312, _476314] : [relation(_476310), function(_476310), in(_476312, relation_dom(relation_dom_restriction(_476310, _476314))), -(apply(relation_dom_restriction(_476310, _476314), _476312) = apply(_476310, _476312))], (2878 ^ _308432) ^ [] : [-(relation_empty_yielding(empty_set))], (1411 ^ _308432) ^ [_357725, _357727] : [_357725 = powerset(_357727), 1414 ^ _308432 : [(1421 ^ _308432) ^ [_358067] : [subset(_358067, _357727), -(in(_358067, _357725))], (1415 ^ _308432) ^ [_357895] : [in(_357895, _357725), -(subset(_357895, _357727))]]], (2797 ^ _308432) ^ [_405637, _405639] : [element(_405637, powerset(powerset(_405639))), -(element(union_of_subsets(_405639, _405637), powerset(_405639)))], (3437 ^ _308432) ^ [] : [-(relation(3435 ^ []))], (650 ^ _308432) ^ [_330374] : [ordinal(_330374), 653 ^ _308432 : [(656 ^ _308432) ^ [] : [-(epsilon_connected(_330374))], (654 ^ _308432) ^ [] : [-(epsilon_transitive(_330374))]]], (20 ^ _308432) ^ [_309208, _309210, _309212, _309214] : [-(is_antisymmetric_in(_309212, _309208)), is_antisymmetric_in(_309214, _309210), _309214 = _309212, _309210 = _309208], (494 ^ _308432) ^ [_324628, _324630] : [_324630 = _324628, -(function_inverse(_324630) = function_inverse(_324628))], (1024 ^ _308432) ^ [_343474] : [relation(_343474), 1027 ^ _308432 : [(1028 ^ _308432) ^ [_343681, _343683] : [_343681 = relation_image(_343474, _343683), 1031 ^ _308432 : [(1041 ^ _308432) ^ [_344227] : [-(in(_344227, _343681)), 1042 ^ _308432 : [(1043 ^ _308432) ^ [_344332] : [in(ordered_pair(_344332, _344227), _343474), in(_344332, _343683)]]], (1032 ^ _308432) ^ [_343873] : [in(_343873, _343681), 1036 ^ _308432 : [(1039 ^ _308432) ^ [] : [-(in(1035 ^ [_343474, _343681, _343683, _343873], _343683))], (1037 ^ _308432) ^ [] : [-(in(ordered_pair(1035 ^ [_343474, _343681, _343683, _343873], _343873), _343474))]]]]], (1051 ^ _308432) ^ [_344587, _344589] : [-(_344587 = relation_image(_343474, _344589)), 1064 ^ _308432 : [(1069 ^ _308432) ^ [] : [in(1052 ^ [_343474, _344587, _344589], _344587)], (1067 ^ _308432) ^ [] : [-(in(1063 ^ [_343474, _344587, _344589], _344589))], (1065 ^ _308432) ^ [] : [-(in(ordered_pair(1063 ^ [_343474, _344587, _344589], 1052 ^ [_343474, _344587, _344589]), _343474))]], 1055 ^ _308432 : [(1058 ^ _308432) ^ [_344891] : [in(ordered_pair(_344891, 1052 ^ [_343474, _344587, _344589]), _343474), in(_344891, _344589)], (1056 ^ _308432) ^ [] : [-(in(1052 ^ [_343474, _344587, _344589], _344587))]]]]], (3098 ^ _308432) ^ [_415095, _415097] : [3105 ^ _308432 : [(3108 ^ _308432) ^ [] : [-(relation(relation_composition(_415097, _415095)))], (3106 ^ _308432) ^ [] : [-(empty(relation_composition(_415097, _415095)))]], empty(_415097), relation(_415095)], (5120 ^ _308432) ^ [_482474, _482476] : [in(_482476, _482474), -(subset(_482476, union(_482474)))], (2805 ^ _308432) ^ [_405944, _405946] : [element(_405944, powerset(powerset(_405946))), -(element(meet_of_subsets(_405946, _405944), powerset(_405946)))], (4253 ^ _308432) ^ [_453779, _453781, _453783] : [subset(_453783, _453781), -(subset(set_difference(_453783, _453779), set_difference(_453781, _453779)))], (10 ^ _308432) ^ [_308867, _308869, _308871] : [-(_308871 = _308867), _308871 = _308869, _308869 = _308867], (2769 ^ _308432) ^ [_404896] : [relation(_404896), -(relation(relation_inverse(_404896)))], (4429 ^ _308432) ^ [_459887] : [ordinal(_459887), 4432 ^ _308432 : [(4433 ^ _308432) ^ [] : [being_limit_ordinal(_459887), 4436 ^ _308432 : [(4437 ^ _308432) ^ [_460133] : [ordinal(_460133), in(_460133, _459887), -(in(succ(_460133), _459887))]]], (4447 ^ _308432) ^ [] : [4449 ^ _308432 : [(4454 ^ _308432) ^ [] : [in(succ(4448 ^ [_459887]), _459887)], (4452 ^ _308432) ^ [] : [-(in(4448 ^ [_459887], _459887))], (4450 ^ _308432) ^ [] : [-(ordinal(4448 ^ [_459887]))]], -(being_limit_ordinal(_459887))]]], (3472 ^ _308432) ^ [] : [-(relation(3470 ^ []))], (2781 ^ _308432) ^ [] : [true___, -(true___)], (4612 ^ _308432) ^ [_465974, _465976] : [4613 ^ _308432 : [(4614 ^ _308432) ^ [_466047] : [in(_466047, set_intersection2(_465976, _465974))]], disjoint(_465976, _465974)], (1926 ^ _308432) ^ [_376151] : [-(ordinal(_376151)), epsilon_transitive(_376151), epsilon_connected(_376151)], (4991 ^ _308432) ^ [_478250, _478252] : [in(_478252, _478250), 4995 ^ _308432 : [(4998 ^ _308432) ^ [_478541] : [in(_478541, _478250), in(_478541, 4994 ^ [_478250, _478252])], (4996 ^ _308432) ^ [] : [-(in(4994 ^ [_478250, _478252], _478250))]]], (536 ^ _308432) ^ [_326169, _326171, _326173, _326175] : [-(set_union2(_326175, _326171) = set_union2(_326173, _326169)), _326175 = _326173, _326171 = _326169], (4826 ^ _308432) ^ [_472889, _472891, _472893] : [-(disjoint(_472893, _472889)), subset(_472893, _472891), disjoint(_472891, _472889)], (3551 ^ _308432) ^ [_430304, _430306] : [-(subset(_430306, _430306))], (3120 ^ _308432) ^ [_415879] : [relation(_415879), -(relation_inverse(relation_inverse(_415879)) = _415879)], (4396 ^ _308432) ^ [_458695, _458697] : [subset(_458697, _458695), -(element(_458697, powerset(_458695)))], (658 ^ _308432) ^ [_330631] : [empty(_330631), -(relation(_330631))], (2689 ^ _308432) ^ [] : [true___, -(true___)], (4136 ^ _308432) ^ [_449946, _449948] : [subset(_449948, _449946), -(set_intersection2(_449948, _449946) = _449948)], (4171 ^ _308432) ^ [_451163, _451165, _451167] : [relation(_451163), in(ordered_pair(_451167, _451165), _451163), 4178 ^ _308432 : [(4181 ^ _308432) ^ [] : [-(in(_451165, relation_field(_451163)))], (4179 ^ _308432) ^ [] : [-(in(_451167, relation_field(_451163)))]]], (2775 ^ _308432) ^ [] : [true___, -(true___)], (3159 ^ _308432) ^ [_417216, _417218] : [in(_417218, _417216), -(set_union2(singleton(_417218), _417216) = _417216)], (1752 ^ _308432) ^ [_369959] : [relation(_369959), 1755 ^ _308432 : [(1756 ^ _308432) ^ [_370117] : [relation(_370117), 1759 ^ _308432 : [(1760 ^ _308432) ^ [] : [subset(_369959, _370117), 1763 ^ _308432 : [(1764 ^ _308432) ^ [_370393, _370395] : [in(ordered_pair(_370395, _370393), _369959), -(in(ordered_pair(_370395, _370393), _370117))]]], (1770 ^ _308432) ^ [] : [1773 ^ _308432 : [(1776 ^ _308432) ^ [] : [in(ordered_pair(1771 ^ [_369959, _370117], 1772 ^ [_369959, _370117]), _370117)], (1774 ^ _308432) ^ [] : [-(in(ordered_pair(1771 ^ [_369959, _370117], 1772 ^ [_369959, _370117]), _369959))]], -(subset(_369959, _370117))]]]]], (3678 ^ _308432) ^ [_434916, _434918] : [subset(_434916, 3658 ^ [_434918]), -(are_equipotent(_434916, 3658 ^ [_434918])), -(in(_434916, 3658 ^ [_434918]))], (2441 ^ _308432) ^ [_394532] : [relation(_394532), 2444 ^ _308432 : [(2445 ^ _308432) ^ [_394717] : [relation(_394717), 2448 ^ _308432 : [(2449 ^ _308432) ^ [_394898] : [relation(_394898), 2452 ^ _308432 : [(2453 ^ _308432) ^ [] : [_394898 = relation_composition(_394532, _394717), 2456 ^ _308432 : [(2466 ^ _308432) ^ [_395618, _395620] : [-(in(ordered_pair(_395620, _395618), _394898)), 2467 ^ _308432 : [(2468 ^ _308432) ^ [_395731] : [in(ordered_pair(_395620, _395731), _394532), in(ordered_pair(_395731, _395618), _394717)]]], (2457 ^ _308432) ^ [_395233, _395235] : [in(ordered_pair(_395235, _395233), _394898), 2461 ^ _308432 : [(2464 ^ _308432) ^ [] : [-(in(ordered_pair(2460 ^ [_394532, _394717, _394898, _395233, _395235], _395233), _394717))], (2462 ^ _308432) ^ [] : [-(in(ordered_pair(_395235, 2460 ^ [_394532, _394717, _394898, _395233, _395235]), _394532))]]]]], (2476 ^ _308432) ^ [] : [-(_394898 = relation_composition(_394532, _394717)), 2490 ^ _308432 : [(2495 ^ _308432) ^ [] : [in(ordered_pair(2477 ^ [_394532, _394717, _394898], 2478 ^ [_394532, _394717, _394898]), _394898)], (2493 ^ _308432) ^ [] : [-(in(ordered_pair(2489 ^ [_394532, _394717, _394898], 2478 ^ [_394532, _394717, _394898]), _394717))], (2491 ^ _308432) ^ [] : [-(in(ordered_pair(2477 ^ [_394532, _394717, _394898], 2489 ^ [_394532, _394717, _394898]), _394532))]], 2481 ^ _308432 : [(2484 ^ _308432) ^ [_396362] : [in(ordered_pair(2477 ^ [_394532, _394717, _394898], _396362), _394532), in(ordered_pair(_396362, 2478 ^ [_394532, _394717, _394898]), _394717)], (2482 ^ _308432) ^ [] : [-(in(ordered_pair(2477 ^ [_394532, _394717, _394898], 2478 ^ [_394532, _394717, _394898]), _394898))]]]]]]]]], (3902 ^ _308432) ^ [_442447] : [-(set_union2(_442447, empty_set) = _442447)], (3026 ^ _308432) ^ [_412866] : [ordinal(_412866), 3029 ^ _308432 : [(3034 ^ _308432) ^ [] : [-(ordinal(union(_412866)))], (3032 ^ _308432) ^ [] : [-(epsilon_connected(union(_412866)))], (3030 ^ _308432) ^ [] : [-(epsilon_transitive(union(_412866)))]]], (4411 ^ _308432) ^ [_459245, _459247] : [disjoint(_459247, _459245), 4412 ^ _308432 : [(4413 ^ _308432) ^ [_459337] : [in(_459337, _459247), in(_459337, _459245)]]], (5132 ^ _308432) ^ [_482912, _482914] : [relation(_482912), -(subset(relation_rng(relation_dom_restriction(_482912, _482914)), relation_rng(_482912)))], (126 ^ _308432) ^ [_312431, _312433] : [-(transitive(_312431)), _312433 = _312431, transitive(_312433)], (4169 ^ _308432) ^ [_451042] : [-(subset(empty_set, _451042))], (3126 ^ _308432) ^ [_416089, _416091] : [element(_416089, powerset(powerset(_416091))), -(complements_of_subsets(_416091, complements_of_subsets(_416091, _416089)) = _416089)], (136 ^ _308432) ^ [_312726, _312728] : [-(antisymmetric(_312726)), _312728 = _312726, antisymmetric(_312728)], (4864 ^ _308432) ^ [_474020, _474022] : [set_difference(_474022, singleton(_474020)) = _474022, in(_474020, _474022)], (2914 ^ _308432) ^ [_409345, _409347] : [-(relation(set_intersection2(_409347, _409345))), relation(_409347), relation(_409345)], (2040 ^ _308432) ^ [_380468, _380470] : [-(_380468 = union(_380470)), 2053 ^ _308432 : [(2058 ^ _308432) ^ [] : [in(2041 ^ [_380468, _380470], _380468)], (2056 ^ _308432) ^ [] : [-(in(2052 ^ [_380468, _380470], _380470))], (2054 ^ _308432) ^ [] : [-(in(2041 ^ [_380468, _380470], 2052 ^ [_380468, _380470]))]], 2044 ^ _308432 : [(2047 ^ _308432) ^ [_380751] : [in(2041 ^ [_380468, _380470], _380751), in(_380751, _380470)], (2045 ^ _308432) ^ [] : [-(in(2041 ^ [_380468, _380470], _380468))]]], (2928 ^ _308432) ^ [_409759, _409761] : [empty(ordered_pair(_409761, _409759))], (4511 ^ _308432) ^ [_462485] : [relation(_462485), 4514 ^ _308432 : [(4515 ^ _308432) ^ [_462622] : [relation(_462622), -(subset(relation_rng(relation_composition(_462485, _462622)), relation_rng(_462622)))]]], (4300 ^ _308432) ^ [_455372, _455374] : [in(_455372, _455374), -(apply(identity_relation(_455374), _455372) = _455372)], (4094 ^ _308432) ^ [_448575, _448577] : [relation(_448575), transitive(_448575), -(transitive(relation_restriction(_448575, _448577)))], (2289 ^ _308432) ^ [_389038] : [_389038 = union(_389038), -(being_limit_ordinal(_389038))], (382 ^ _308432) ^ [_320614, _320616, _320618, _320620] : [-(relation_inverse_image(_320620, _320616) = relation_inverse_image(_320618, _320614)), _320620 = _320618, _320616 = _320614], (2395 ^ _308432) ^ [_393018, _393020] : [set_intersection2(_393020, _393018) = empty_set, -(disjoint(_393020, _393018))], (2739 ^ _308432) ^ [] : [true___, -(true___)], (606 ^ _308432) ^ [_328667, _328669] : [_328669 = _328667, -(singleton(_328669) = singleton(_328667))], (3814 ^ _308432) ^ [_439565, _439567] : [relation(_439565), -(subset(relation_inverse_image(_439565, _439567), relation_dom(_439565)))], (2683 ^ _308432) ^ [] : [true___, -(true___)], (4427 ^ _308432) ^ [_459783, _459785] : [-(set_difference(set_union2(_459785, _459783), _459783) = set_difference(_459785, _459783))], (4144 ^ _308432) ^ [_450243, _450245] : [element(_450245, _450243), -(empty(_450243)), -(in(_450245, _450243))], (2960 ^ _308432) ^ [_410723] : [empty(singleton(_410723))], (692 ^ _308432) ^ [_331579] : [empty(_331579), 695 ^ _308432 : [(700 ^ _308432) ^ [] : [-(ordinal(_331579))], (698 ^ _308432) ^ [] : [-(epsilon_connected(_331579))], (696 ^ _308432) ^ [] : [-(epsilon_transitive(_331579))]]], (3362 ^ _308432) ^ [_424354, _424356, _424358, _424360] : [-(in(ordered_pair(_424360, _424358), cartesian_product2(_424356, _424354))), in(_424360, _424356), in(_424358, _424354)], (4360 ^ _308432) ^ [_457543, _457545] : [subset(_457545, singleton(_457543)), -(_457545 = empty_set), -(_457545 = singleton(_457543))], (3505 ^ _308432) ^ [_428904, _428906] : [element(_428904, powerset(powerset(_428906))), -(meet_of_subsets(_428906, _428904) = set_meet(_428904))], (3464 ^ _308432) ^ [_427585] : [-(element(3462 ^ [_427585], powerset(_427585)))], (562 ^ _308432) ^ [_327105, _327107, _327109, _327111] : [-(relation_composition(_327111, _327107) = relation_composition(_327109, _327105)), _327111 = _327109, _327107 = _327105], (4130 ^ _308432) ^ [_449718, _449720, _449722] : [subset(_449722, _449720), -(subset(set_intersection2(_449722, _449718), set_intersection2(_449720, _449718)))], (1182 ^ _308432) ^ [_349409, _349411, _349413, _349415] : [-(_349409 = unordered_triple(_349415, _349413, _349411)), 1186 ^ _308432 : [(1189 ^ _308432) ^ [] : [1183 ^ [_349409, _349411, _349413, _349415] = _349415], (1191 ^ _308432) ^ [] : [1183 ^ [_349409, _349411, _349413, _349415] = _349413], (1193 ^ _308432) ^ [] : [1183 ^ [_349409, _349411, _349413, _349415] = _349411], (1187 ^ _308432) ^ [] : [-(in(1183 ^ [_349409, _349411, _349413, _349415], _349409))]], 1194 ^ _308432 : [(1195 ^ _308432) ^ [] : [-(1183 ^ [_349409, _349411, _349413, _349415] = _349415), -(1183 ^ [_349409, _349411, _349413, _349415] = _349413), -(1183 ^ [_349409, _349411, _349413, _349415] = _349411)], (1205 ^ _308432) ^ [] : [in(1183 ^ [_349409, _349411, _349413, _349415], _349409)]]], (4322 ^ _308432) ^ [_456171, _456173] : [subset(_456173, _456171), -(set_difference(_456173, _456171) = empty_set)], (3441 ^ _308432) ^ [] : [-(function(3435 ^ []))], (3278 ^ _308432) ^ [_421472, _421474, _421476] : [subset(_421476, _421474), -(in(_421472, _421476)), -(subset(_421476, set_difference(_421474, singleton(_421472))))], (3014 ^ _308432) ^ [_412502, _412504] : [3021 ^ _308432 : [(3024 ^ _308432) ^ [] : [-(function(relation_dom_restriction(_412504, _412502)))], (3022 ^ _308432) ^ [] : [-(relation(relation_dom_restriction(_412504, _412502)))]], relation(_412504), function(_412504)], (3942 ^ _308432) ^ [_443862, _443864] : [relation(_443862), function(_443862), 3949 ^ _308432 : [(3950 ^ _308432) ^ [_444112] : [relation(_444112), function(_444112), 3957 ^ _308432 : [(3966 ^ _308432) ^ [] : [-(in(_443864, relation_dom(relation_composition(_444112, _443862)))), in(_443864, relation_dom(_444112)), in(apply(_444112, _443864), relation_dom(_443862))], (3958 ^ _308432) ^ [] : [in(_443864, relation_dom(relation_composition(_444112, _443862))), 3961 ^ _308432 : [(3964 ^ _308432) ^ [] : [-(in(apply(_444112, _443864), relation_dom(_443862)))], (3962 ^ _308432) ^ [] : [-(in(_443864, relation_dom(_444112)))]]]]]]], (3745 ^ _308432) ^ [_437275, _437277] : [relation(_437275), subset(_437277, relation_dom(_437275)), -(subset(_437277, relation_inverse_image(_437275, relation_image(_437275, _437277))))], (530 ^ _308432) ^ [_325923, _325925] : [_325925 = _325923, -(relation_field(_325925) = relation_field(_325923))], (632 ^ _308432) ^ [_329780, _329782] : [in(_329782, _329780), in(_329780, _329782)], (4316 ^ _308432) ^ [_456003, _456005] : [set_difference(_456005, _456003) = empty_set, -(subset(_456005, _456003))], (3444 ^ _308432) ^ [] : [-(relation(3442 ^ []))], (3459 ^ _308432) ^ [] : [empty(3457 ^ [])], (1736 ^ _308432) ^ [_369253] : [1739 ^ _308432 : [(1740 ^ _308432) ^ [] : [-(in(1737 ^ [_369253], _369253))], (1744 ^ _308432) ^ [] : [in(1737 ^ [_369253], 1738 ^ [_369253])], (1748 ^ _308432) ^ [] : [in(1738 ^ [_369253], 1737 ^ [_369253])], (1746 ^ _308432) ^ [] : [1737 ^ [_369253] = 1738 ^ [_369253]], (1742 ^ _308432) ^ [] : [-(in(1738 ^ [_369253], _369253))]], -(epsilon_connected(_369253))], (3842 ^ _308432) ^ [_440453, _440455] : [relation(_440453), -(_440455 = empty_set), subset(_440455, relation_rng(_440453)), relation_inverse_image(_440453, _440455) = empty_set], (2940 ^ _308432) ^ [] : [-(one_to_one(empty_set))], (3408 ^ _308432) ^ [] : [-(relation(3406 ^ []))], (3165 ^ _308432) ^ [_417436, _417438] : [disjoint(singleton(_417438), _417436), in(_417438, _417436)], (2984 ^ _308432) ^ [_411464] : [ordinal(_411464), 2987 ^ _308432 : [(2990 ^ _308432) ^ [] : [-(epsilon_transitive(succ(_411464)))], (2992 ^ _308432) ^ [] : [-(epsilon_connected(succ(_411464)))], (2994 ^ _308432) ^ [] : [-(ordinal(succ(_411464)))], (2988 ^ _308432) ^ [] : [empty(succ(_411464))]]], (2124 ^ _308432) ^ [_383104, _383106, _383108] : [-(_383104 = set_difference(_383108, _383106)), 2136 ^ _308432 : [(2141 ^ _308432) ^ [] : [in(2125 ^ [_383104, _383106, _383108], _383104)], (2139 ^ _308432) ^ [] : [in(2125 ^ [_383104, _383106, _383108], _383106)], (2137 ^ _308432) ^ [] : [-(in(2125 ^ [_383104, _383106, _383108], _383108))]], 2128 ^ _308432 : [(2131 ^ _308432) ^ [] : [in(2125 ^ [_383104, _383106, _383108], _383108), -(in(2125 ^ [_383104, _383106, _383108], _383106))], (2129 ^ _308432) ^ [] : [-(in(2125 ^ [_383104, _383106, _383108], _383104))]]], (1655 ^ _308432) ^ [_366095, _366097, _366099] : [_366095 = cartesian_product2(_366099, _366097), 1658 ^ _308432 : [(1671 ^ _308432) ^ [_366856] : [-(in(_366856, _366095)), 1672 ^ _308432 : [(1673 ^ _308432) ^ [_366986, _366988] : [in(_366988, _366099), in(_366986, _366097), _366856 = ordered_pair(_366988, _366986)]]], (1659 ^ _308432) ^ [_366296] : [in(_366296, _366095), 1664 ^ _308432 : [(1669 ^ _308432) ^ [] : [-(_366296 = ordered_pair(1662 ^ [_366095, _366097, _366099, _366296], 1663 ^ [_366095, _366097, _366099, _366296]))], (1667 ^ _308432) ^ [] : [-(in(1663 ^ [_366095, _366097, _366099, _366296], _366097))], (1665 ^ _308432) ^ [] : [-(in(1662 ^ [_366095, _366097, _366099, _366296], _366099))]]]]], (1255 ^ _308432) ^ [_352265, _352267] : [-(_352267 = empty_set), 1258 ^ _308432 : [(1259 ^ _308432) ^ [] : [_352265 = set_meet(_352267), 1262 ^ _308432 : [(1263 ^ _308432) ^ [_352563] : [in(_352563, _352265), 1266 ^ _308432 : [(1267 ^ _308432) ^ [_352708] : [in(_352708, _352267), -(in(_352563, _352708))]]], (1273 ^ _308432) ^ [_352893] : [1275 ^ _308432 : [(1278 ^ _308432) ^ [] : [in(_352893, 1274 ^ [_352265, _352267, _352893])], (1276 ^ _308432) ^ [] : [-(in(1274 ^ [_352265, _352267, _352893], _352267))]], -(in(_352893, _352265))]]], (1282 ^ _308432) ^ [] : [-(_352265 = set_meet(_352267)), 1286 ^ _308432 : [(1292 ^ _308432) ^ [] : [in(1283 ^ [_352265, _352267], 1288 ^ [_352265, _352267])], (1290 ^ _308432) ^ [] : [-(in(1288 ^ [_352265, _352267], _352267))], (1287 ^ _308432) ^ [] : [-(in(1283 ^ [_352265, _352267], _352265))]], 1293 ^ _308432 : [(1294 ^ _308432) ^ [_353667] : [in(_353667, _352267), -(in(1283 ^ [_352265, _352267], _353667))], (1300 ^ _308432) ^ [] : [in(1283 ^ [_352265, _352267], _352265)]]]]], (2866 ^ _308432) ^ [_407895] : [empty(_407895), 2869 ^ _308432 : [(2872 ^ _308432) ^ [] : [-(relation(relation_inverse(_407895)))], (2870 ^ _308432) ^ [] : [-(empty(relation_inverse(_407895)))]]], (3611 ^ _308432) ^ [_432395, _432397] : [relation(_432395), -(subset(relation_rng(relation_rng_restriction(_432397, _432395)), _432397))], (366 ^ _308432) ^ [_320009, _320011] : [_320011 = _320009, -(set_meet(_320011) = set_meet(_320009))], (4348 ^ _308432) ^ [_457094, _457096, _457098] : [-(subset(unordered_pair(_457098, _457096), _457094)), in(_457098, _457094), in(_457096, _457094)], (4806 ^ _308432) ^ [_472308, _472310] : [subset(_472310, _472308), proper_subset(_472308, _472310)], (3976 ^ _308432) ^ [_444876] : [epsilon_transitive(_444876), 3979 ^ _308432 : [(3980 ^ _308432) ^ [_445012] : [ordinal(_445012), proper_subset(_444876, _445012), -(in(_444876, _445012))]]], (3348 ^ _308432) ^ [_423818, _423820] : [in(_423820, _423818), -(subset(_423820, union(_423818)))], (3171 ^ _308432) ^ [_417649, _417651] : [-(in(_417651, _417649)), -(disjoint(singleton(_417651), _417649))], (2751 ^ _308432) ^ [_404448, _404450] : [element(_404448, powerset(_404450)), -(element(subset_complement(_404450, _404448), powerset(_404450)))], (3739 ^ _308432) ^ [_437045, _437047] : [relation(_437045), -(relation_image(_437045, _437047) = relation_image(_437045, set_intersection2(relation_dom(_437045), _437047)))], (146 ^ _308432) ^ [_313049, _313051, _313053, _313055] : [-(ordinal_subset(_313053, _313049)), ordinal_subset(_313055, _313051), _313055 = _313053, _313051 = _313049], (1461 ^ _308432) ^ [_359422] : [relation(_359422), 1464 ^ _308432 : [(1465 ^ _308432) ^ [_359580] : [relation(_359580), 1468 ^ _308432 : [(1469 ^ _308432) ^ [] : [_359422 = _359580, 1472 ^ _308432 : [(1479 ^ _308432) ^ [_360075, _360077] : [in(ordered_pair(_360077, _360075), _359580), -(in(ordered_pair(_360077, _360075), _359422))], (1473 ^ _308432) ^ [_359885, _359887] : [in(ordered_pair(_359887, _359885), _359422), -(in(ordered_pair(_359887, _359885), _359580))]]], (1485 ^ _308432) ^ [] : [-(_359422 = _359580), 1490 ^ _308432 : [(1493 ^ _308432) ^ [] : [in(ordered_pair(1486 ^ [_359422, _359580], 1487 ^ [_359422, _359580]), _359580)], (1491 ^ _308432) ^ [] : [-(in(ordered_pair(1486 ^ [_359422, _359580], 1487 ^ [_359422, _359580]), _359422))]], 1494 ^ _308432 : [(1497 ^ _308432) ^ [] : [in(ordered_pair(1486 ^ [_359422, _359580], 1487 ^ [_359422, _359580]), _359422)], (1495 ^ _308432) ^ [] : [-(in(ordered_pair(1486 ^ [_359422, _359580], 1487 ^ [_359422, _359580]), _359580))]]]]]]], (3490 ^ _308432) ^ [] : [-(relation_empty_yielding(3486 ^ []))], (664 ^ _308432) ^ [_330817] : [675 ^ _308432 : [(680 ^ _308432) ^ [] : [-(one_to_one(_330817))], (678 ^ _308432) ^ [] : [-(function(_330817))], (676 ^ _308432) ^ [] : [-(relation(_330817))]], relation(_330817), empty(_330817), function(_330817)], (4334 ^ _308432) ^ [_456584, _456586] : [in(_456586, _456584), -(subset(singleton(_456586), _456584))], (170 ^ _308432) ^ [_313760, _313762] : [-(being_limit_ordinal(_313760)), _313762 = _313760, being_limit_ordinal(_313762)], (3856 ^ _308432) ^ [_440867, _440869, _440871] : [relation(_440867), subset(_440871, _440869), -(subset(relation_inverse_image(_440867, _440871), relation_inverse_image(_440867, _440869)))], (2934 ^ _308432) ^ [] : [-(relation(empty_set))], (4120 ^ _308432) ^ [_449405, _449407] : [relation(_449405), antisymmetric(_449405), -(antisymmetric(relation_restriction(_449405, _449407)))], (2389 ^ _308432) ^ [_392850, _392852] : [disjoint(_392852, _392850), -(set_intersection2(_392852, _392850) = empty_set)], (266 ^ _308432) ^ [_316716, _316718] : [-(function(_316716)), _316718 = _316716, function(_316718)], (342 ^ _308432) ^ [_319062, _319064] : [-(well_ordering(_319062)), _319064 = _319062, well_ordering(_319064)], (1138 ^ _308432) ^ [_347943] : [relation(_347943), 1141 ^ _308432 : [(1148 ^ _308432) ^ [] : [is_transitive_in(_347943, relation_field(_347943)), -(transitive(_347943))], (1142 ^ _308432) ^ [] : [transitive(_347943), -(is_transitive_in(_347943, relation_field(_347943)))]]], (3541 ^ _308432) ^ [_430024, _430026] : [-(ordinal_subset(_430026, _430026)), ordinal(_430026), ordinal(_430024)], (1209 ^ _308432) ^ [_350382] : [-(succ(_350382) = set_union2(_350382, singleton(_350382)))], (4591 ^ _308432) ^ [_465193, _465195] : [-(set_difference(_465195, set_difference(_465195, _465193)) = set_intersection2(_465195, _465193))], (5006 ^ _308432) ^ [_478907, _478909] : [disjoint(_478909, _478907), -(set_difference(_478909, _478907) = _478909)], (96 ^ _308432) ^ [_311546, _311548] : [-(epsilon_transitive(_311546)), _311548 = _311546, epsilon_transitive(_311548)], (86 ^ _308432) ^ [_311251, _311253] : [-(relation_empty_yielding(_311251)), _311253 = _311251, relation_empty_yielding(_311253)], (160 ^ _308432) ^ [_313465, _313467] : [-(ordinal(_313465)), _313467 = _313465, ordinal(_313467)], (3872 ^ _308432) ^ [_441397, _441399] : [-(subset(set_intersection2(_441399, _441397), _441399))], (3238 ^ _308432) ^ [_420070, _420072] : [element(_420070, powerset(_420072)), 3241 ^ _308432 : [(3242 ^ _308432) ^ [_420211] : [in(_420211, _420070), -(in(_420211, _420072))]]], (2733 ^ _308432) ^ [] : [true___, -(true___)], (2821 ^ _308432) ^ [_406515, _406517] : [relation(_406517), -(relation(relation_dom_restriction(_406517, _406515)))], (1404 ^ _308432) ^ [_357434] : [-(in(1405 ^ [_357434], _357434)), -(_357434 = empty_set)], (1452 ^ _308432) ^ [_359097] : [1454 ^ _308432 : [(1457 ^ _308432) ^ [] : [subset(1453 ^ [_359097], _359097)], (1455 ^ _308432) ^ [] : [-(in(1453 ^ [_359097], _359097))]], -(epsilon_transitive(_359097))], (4618 ^ _308432) ^ [_466199] : [-(_466199 = empty_set), 4621 ^ _308432 : [(4622 ^ _308432) ^ [_466359] : [element(_466359, powerset(_466199)), 4625 ^ _308432 : [(4626 ^ _308432) ^ [_466513] : [element(_466513, _466199), -(in(_466513, _466359)), -(in(_466513, subset_complement(_466199, _466359)))]]]]], (5018 ^ _308432) ^ [_479307, _479309, _479311] : [relation(_479307), 5021 ^ _308432 : [(5030 ^ _308432) ^ [] : [-(in(_479311, relation_dom(relation_dom_restriction(_479307, _479309)))), in(_479311, _479309), in(_479311, relation_dom(_479307))], (5022 ^ _308432) ^ [] : [in(_479311, relation_dom(relation_dom_restriction(_479307, _479309))), 5025 ^ _308432 : [(5028 ^ _308432) ^ [] : [-(in(_479311, relation_dom(_479307)))], (5026 ^ _308432) ^ [] : [-(in(_479311, _479309))]]]]], (2727 ^ _308432) ^ [_403879, _403881] : [relation(_403881), -(relation(relation_restriction(_403881, _403879)))], (5138 ^ _308432) ^ [_483105] : [-(union(powerset(_483105)) = _483105)], (704 ^ _308432) ^ [_332005, _332007] : [-(set_union2(_332007, _332005) = set_union2(_332005, _332007))], (3511 ^ _308432) ^ [_429146, _429148, _429150] : [-(subset_difference(_429150, _429148, _429146) = set_difference(_429148, _429146)), element(_429148, powerset(_429150)), element(_429146, powerset(_429150))], (1232 ^ _308432) ^ [_351366] : [relation(_351366), 1235 ^ _308432 : [(1236 ^ _308432) ^ [_351540] : [is_reflexive_in(_351366, _351540), 1239 ^ _308432 : [(1240 ^ _308432) ^ [_351682] : [in(_351682, _351540), -(in(ordered_pair(_351682, _351682), _351366))]]], (1246 ^ _308432) ^ [_351865] : [1248 ^ _308432 : [(1251 ^ _308432) ^ [] : [in(ordered_pair(1247 ^ [_351366, _351865], 1247 ^ [_351366, _351865]), _351366)], (1249 ^ _308432) ^ [] : [-(in(1247 ^ [_351366, _351865], _351865))]], -(is_reflexive_in(_351366, _351865))]]], (4876 ^ _308432) ^ [_474418, _474420] : [relation(_474418), function(_474418), 4883 ^ _308432 : [(4884 ^ _308432) ^ [_474685] : [relation(_474685), function(_474685), 4891 ^ _308432 : [(4904 ^ _308432) ^ [] : [-(_474418 = relation_dom_restriction(_474685, _474420)), relation_dom(_474418) = set_intersection2(relation_dom(_474685), _474420), 4910 ^ _308432 : [(4913 ^ _308432) ^ [] : [apply(_474418, 4909 ^ [_474418, _474420, _474685]) = apply(_474685, 4909 ^ [_474418, _474420, _474685])], (4911 ^ _308432) ^ [] : [-(in(4909 ^ [_474418, _474420, _474685], relation_dom(_474418)))]]], (4892 ^ _308432) ^ [] : [_474418 = relation_dom_restriction(_474685, _474420), 4895 ^ _308432 : [(4898 ^ _308432) ^ [_475139] : [in(_475139, relation_dom(_474418)), -(apply(_474418, _475139) = apply(_474685, _475139))], (4896 ^ _308432) ^ [] : [-(relation_dom(_474418) = set_intersection2(relation_dom(_474685), _474420))]]]]]]], (2062 ^ _308432) ^ [_381301] : [relation(_381301), 2065 ^ _308432 : [(2080 ^ _308432) ^ [] : [-(well_ordering(_381301)), reflexive(_381301), transitive(_381301), antisymmetric(_381301), connected(_381301), well_founded_relation(_381301)], (2066 ^ _308432) ^ [] : [well_ordering(_381301), 2069 ^ _308432 : [(2070 ^ _308432) ^ [] : [-(reflexive(_381301))], (2074 ^ _308432) ^ [] : [-(antisymmetric(_381301))], (2078 ^ _308432) ^ [] : [-(well_founded_relation(_381301))], (2076 ^ _308432) ^ [] : [-(connected(_381301))], (2072 ^ _308432) ^ [] : [-(transitive(_381301))]]]]], (5153 ^ _308432) ^ [_483773, _483775] : [in(_483773, 5139 ^ [_483775]), 5157 ^ _308432 : [(5160 ^ _308432) ^ [_484085] : [subset(_484085, _483773), -(in(_484085, 5156 ^ [_483773, _483775]))], (5158 ^ _308432) ^ [] : [-(in(5156 ^ [_483773, _483775], 5139 ^ [_483775]))]]], (2241 ^ _308432) ^ [_387539, _387541] : [-(ordered_pair(_387541, _387539) = unordered_pair(unordered_pair(_387541, _387539), singleton(_387541)))], (3623 ^ _308432) ^ [_432827, _432829] : [relation(_432827), -(subset(relation_rng(relation_rng_restriction(_432829, _432827)), relation_rng(_432827)))], (594 ^ _308432) ^ [_328231, _328233] : [_328233 = _328231, -(union(_328233) = union(_328231))], (2625 ^ _308432) ^ [_401576] : [relation(_401576), 2628 ^ _308432 : [(2635 ^ _308432) ^ [] : [is_reflexive_in(_401576, relation_field(_401576)), -(reflexive(_401576))], (2629 ^ _308432) ^ [] : [reflexive(_401576), -(is_reflexive_in(_401576, relation_field(_401576)))]]], (4259 ^ _308432) ^ [_454035, _454037, _454039, _454041] : [ordered_pair(_454041, _454039) = ordered_pair(_454037, _454035), 4262 ^ _308432 : [(4265 ^ _308432) ^ [] : [-(_454039 = _454035)], (4263 ^ _308432) ^ [] : [-(_454041 = _454037)]]], (1612 ^ _308432) ^ [_364576, _364578, _364580] : [_364576 = set_union2(_364580, _364578), 1615 ^ _308432 : [(1616 ^ _308432) ^ [_364758] : [in(_364758, _364576), -(in(_364758, _364580)), -(in(_364758, _364578))], (1626 ^ _308432) ^ [_365036] : [1627 ^ _308432 : [(1630 ^ _308432) ^ [] : [in(_365036, _364578)], (1628 ^ _308432) ^ [] : [in(_365036, _364580)]], -(in(_365036, _364576))]]], (4636 ^ _308432) ^ [_466831] : [relation(_466831), function(_466831), one_to_one(_466831), 4647 ^ _308432 : [(4648 ^ _308432) ^ [_467218] : [relation(_467218), function(_467218), 4655 ^ _308432 : [(4656 ^ _308432) ^ [] : [_467218 = function_inverse(_466831), 4659 ^ _308432 : [(4674 ^ _308432) ^ [_468109, _468111] : [4681 ^ _308432 : [(4684 ^ _308432) ^ [] : [-(_468109 = apply(_467218, _468111))], (4682 ^ _308432) ^ [] : [-(in(_468111, relation_rng(_466831)))]], in(_468109, relation_dom(_466831)), _468111 = apply(_466831, _468109)], (4662 ^ _308432) ^ [_467735, _467737] : [4669 ^ _308432 : [(4672 ^ _308432) ^ [] : [-(_467737 = apply(_466831, _467735))], (4670 ^ _308432) ^ [] : [-(in(_467735, relation_dom(_466831)))]], in(_467737, relation_rng(_466831)), _467735 = apply(_467218, _467737)], (4660 ^ _308432) ^ [] : [-(relation_dom(_467218) = relation_rng(_466831))]]], (4686 ^ _308432) ^ [] : [-(_467218 = function_inverse(_466831)), relation_dom(_467218) = relation_rng(_466831), 4695 ^ _308432 : [(4700 ^ _308432) ^ [] : [in(4692 ^ [_466831, _467218], relation_dom(_466831)), 4691 ^ [_466831, _467218] = apply(_466831, 4692 ^ [_466831, _467218])], (4698 ^ _308432) ^ [] : [-(4692 ^ [_466831, _467218] = apply(_467218, 4691 ^ [_466831, _467218]))], (4696 ^ _308432) ^ [] : [-(in(4691 ^ [_466831, _467218], relation_rng(_466831)))]], 4705 ^ _308432 : [(4710 ^ _308432) ^ [] : [in(4691 ^ [_466831, _467218], relation_rng(_466831)), 4692 ^ [_466831, _467218] = apply(_467218, 4691 ^ [_466831, _467218])], (4708 ^ _308432) ^ [] : [-(4691 ^ [_466831, _467218] = apply(_466831, 4692 ^ [_466831, _467218]))], (4706 ^ _308432) ^ [] : [-(in(4692 ^ [_466831, _467218], relation_dom(_466831)))]]]]]]], (4557 ^ _308432) ^ [_464055] : [relation(_464055), 4560 ^ _308432 : [(4561 ^ _308432) ^ [_464202] : [relation(_464202), subset(relation_dom(_464055), relation_rng(_464202)), -(relation_rng(relation_composition(_464202, _464055)) = relation_rng(_464055))]]], (1211 ^ _308432) ^ [_350511] : [relation(_350511), 1214 ^ _308432 : [(1215 ^ _308432) ^ [_350659] : [in(_350659, _350511), -(_350659 = ordered_pair(1218 ^ [_350511, _350659], 1219 ^ [_350511, _350659]))]]], (3761 ^ _308432) ^ [_437790, _437792] : [relation(_437790), function(_437790), subset(_437792, relation_rng(_437790)), -(relation_image(_437790, relation_inverse_image(_437790, _437792)) = _437792)], (556 ^ _308432) ^ [_326859, _326861] : [_326861 = _326859, -(relation_dom(_326861) = relation_dom(_326859))], (3454 ^ _308432) ^ [] : [-(epsilon_connected(3442 ^ []))], (4581 ^ _308432) ^ [_464868, _464870] : [element(_464868, powerset(powerset(_464870))), -(_464868 = empty_set), -(union_of_subsets(_464870, complements_of_subsets(_464870, _464868)) = subset_difference(_464870, cast_to_subset(_464870), meet_of_subsets(_464870, _464868)))], (3090 ^ _308432) ^ [_414816] : [empty(_414816), 3093 ^ _308432 : [(3096 ^ _308432) ^ [] : [-(relation(relation_rng(_414816)))], (3094 ^ _308432) ^ [] : [-(empty(relation_rng(_414816)))]]], (3559 ^ _308432) ^ [_430680, _430682, _430684, _430686] : [in(ordered_pair(_430686, _430684), cartesian_product2(_430682, _430680)), 3562 ^ _308432 : [(3565 ^ _308432) ^ [] : [-(in(_430684, _430680))], (3563 ^ _308432) ^ [] : [-(in(_430686, _430682))]]], (204 ^ _308432) ^ [_314822, _314824, _314826, _314828] : [-(is_well_founded_in(_314826, _314822)), is_well_founded_in(_314828, _314824), _314828 = _314826, _314824 = _314822], (2677 ^ _308432) ^ [] : [true___, -(true___)], (304 ^ _308432) ^ [_317927, _317929, _317931, _317933] : [-(are_equipotent(_317931, _317927)), are_equipotent(_317933, _317929), _317933 = _317931, _317929 = _317927], (3008 ^ _308432) ^ [_412286, _412288] : [-(empty(_412288)), empty(set_union2(_412286, _412288))], (1073 ^ _308432) ^ [_345493] : [relation(_345493), 1076 ^ _308432 : [(1077 ^ _308432) ^ [_345700, _345702] : [_345700 = relation_inverse_image(_345493, _345702), 1080 ^ _308432 : [(1090 ^ _308432) ^ [_346246] : [-(in(_346246, _345700)), 1091 ^ _308432 : [(1092 ^ _308432) ^ [_346351] : [in(ordered_pair(_346246, _346351), _345493), in(_346351, _345702)]]], (1081 ^ _308432) ^ [_345892] : [in(_345892, _345700), 1085 ^ _308432 : [(1088 ^ _308432) ^ [] : [-(in(1084 ^ [_345493, _345700, _345702, _345892], _345702))], (1086 ^ _308432) ^ [] : [-(in(ordered_pair(_345892, 1084 ^ [_345493, _345700, _345702, _345892]), _345493))]]]]], (1100 ^ _308432) ^ [_346606, _346608] : [-(_346606 = relation_inverse_image(_345493, _346608)), 1113 ^ _308432 : [(1118 ^ _308432) ^ [] : [in(1101 ^ [_345493, _346606, _346608], _346606)], (1116 ^ _308432) ^ [] : [-(in(1112 ^ [_345493, _346606, _346608], _346608))], (1114 ^ _308432) ^ [] : [-(in(ordered_pair(1101 ^ [_345493, _346606, _346608], 1112 ^ [_345493, _346606, _346608]), _345493))]], 1104 ^ _308432 : [(1107 ^ _308432) ^ [_346910] : [in(ordered_pair(1101 ^ [_345493, _346606, _346608], _346910), _345493), in(_346910, _346608)], (1105 ^ _308432) ^ [] : [-(in(1101 ^ [_345493, _346606, _346608], _346606))]]]]], (2946 ^ _308432) ^ [] : [-(epsilon_connected(empty_set))], (4786 ^ _308432) ^ [_471755] : [relation(_471755), 4789 ^ _308432 : [(4796 ^ _308432) ^ [] : [is_well_founded_in(_471755, relation_field(_471755)), -(well_founded_relation(_471755))], (4790 ^ _308432) ^ [] : [well_founded_relation(_471755), -(is_well_founded_in(_471755, relation_field(_471755)))]]], (1790 ^ _308432) ^ [_371356, _371358] : [1792 ^ _308432 : [(1795 ^ _308432) ^ [] : [in(1791 ^ [_371356, _371358], _371356)], (1793 ^ _308432) ^ [] : [-(in(1791 ^ [_371356, _371358], _371358))]], -(subset(_371358, _371356))], (2 ^ _308432) ^ [_308556] : [-(_308556 = _308556)], (600 ^ _308432) ^ [_328449, _328451] : [_328451 = _328449, -(powerset(_328451) = powerset(_328449))], (3038 ^ _308432) ^ [] : [-(relation(empty_set))], (4267 ^ _308432) ^ [_454348, _454350] : [relation(_454348), function(_454348), 4274 ^ _308432 : [(4287 ^ _308432) ^ [] : [-(_454348 = identity_relation(_454350)), relation_dom(_454348) = _454350, 4293 ^ _308432 : [(4296 ^ _308432) ^ [] : [apply(_454348, 4292 ^ [_454348, _454350]) = 4292 ^ [_454348, _454350]], (4294 ^ _308432) ^ [] : [-(in(4292 ^ [_454348, _454350], _454350))]]], (4275 ^ _308432) ^ [] : [_454348 = identity_relation(_454350), 4278 ^ _308432 : [(4281 ^ _308432) ^ [_454767] : [in(_454767, _454350), -(apply(_454348, _454767) = _454767)], (4279 ^ _308432) ^ [] : [-(relation_dom(_454348) = _454350)]]]]], (372 ^ _308432) ^ [_320255, _320257, _320259, _320261] : [-(relation_image(_320261, _320257) = relation_image(_320259, _320255)), _320261 = _320259, _320257 = _320255], (2601 ^ _308432) ^ [_400922, _400924] : [-(proper_subset(_400924, _400922)), subset(_400924, _400922), -(_400924 = _400922)], (5056 ^ _308432) ^ [_480491, _480493, _480495] : [relation(_480491), function(_480491), 5063 ^ _308432 : [(5072 ^ _308432) ^ [] : [-(in(ordered_pair(_480495, _480493), _480491)), in(_480495, relation_dom(_480491)), _480493 = apply(_480491, _480495)], (5064 ^ _308432) ^ [] : [in(ordered_pair(_480495, _480493), _480491), 5067 ^ _308432 : [(5070 ^ _308432) ^ [] : [-(_480493 = apply(_480491, _480495))], (5068 ^ _308432) ^ [] : [-(in(_480495, relation_dom(_480491)))]]]]], (2145 ^ _308432) ^ [_383847] : [relation(_383847), function(_383847), 2152 ^ _308432 : [(2153 ^ _308432) ^ [_384119] : [_384119 = relation_rng(_383847), 2156 ^ _308432 : [(2166 ^ _308432) ^ [_384649] : [-(in(_384649, _384119)), 2167 ^ _308432 : [(2168 ^ _308432) ^ [_384752] : [in(_384752, relation_dom(_383847)), _384649 = apply(_383847, _384752)]]], (2157 ^ _308432) ^ [_384307] : [in(_384307, _384119), 2161 ^ _308432 : [(2164 ^ _308432) ^ [] : [-(_384307 = apply(_383847, 2160 ^ [_383847, _384119, _384307]))], (2162 ^ _308432) ^ [] : [-(in(2160 ^ [_383847, _384119, _384307], relation_dom(_383847)))]]]]], (2176 ^ _308432) ^ [_385001] : [-(_385001 = relation_rng(_383847)), 2189 ^ _308432 : [(2194 ^ _308432) ^ [] : [in(2177 ^ [_383847, _385001], _385001)], (2192 ^ _308432) ^ [] : [-(2177 ^ [_383847, _385001] = apply(_383847, 2188 ^ [_383847, _385001]))], (2190 ^ _308432) ^ [] : [-(in(2188 ^ [_383847, _385001], relation_dom(_383847)))]], 2180 ^ _308432 : [(2183 ^ _308432) ^ [_385296] : [in(_385296, relation_dom(_383847)), 2177 ^ [_383847, _385001] = apply(_383847, _385296)], (2181 ^ _308432) ^ [] : [-(in(2177 ^ [_383847, _385001], _385001))]]]]], (3934 ^ _308432) ^ [_443555, _443557] : [relation(_443555), 3937 ^ _308432 : [(3940 ^ _308432) ^ [] : [-(subset(relation_field(relation_restriction(_443555, _443557)), _443557))], (3938 ^ _308432) ^ [] : [-(subset(relation_field(relation_restriction(_443555, _443557)), relation_field(_443555)))]]], (4917 ^ _308432) ^ [_475778] : [-(unordered_pair(_475778, _475778) = singleton(_475778))], (644 ^ _308432) ^ [_330188] : [empty(_330188), -(function(_330188))], (3637 ^ _308432) ^ [_433380, _433382] : [relation(_433380), -(relation_rng(relation_rng_restriction(_433382, _433380)) = set_intersection2(relation_rng(_433380), _433382))], (1878 ^ _308432) ^ [_374666] : [relation(_374666), function(_374666), 1885 ^ _308432 : [(1902 ^ _308432) ^ [_375410, _375412] : [-(in(_375412, relation_dom(_374666))), 1905 ^ _308432 : [(1912 ^ _308432) ^ [] : [_375410 = empty_set, -(_375410 = apply(_374666, _375412))], (1906 ^ _308432) ^ [] : [_375410 = apply(_374666, _375412), -(_375410 = empty_set)]]], (1886 ^ _308432) ^ [_374958, _374960] : [in(_374960, relation_dom(_374666)), 1889 ^ _308432 : [(1896 ^ _308432) ^ [] : [in(ordered_pair(_374960, _374958), _374666), -(_374958 = apply(_374666, _374960))], (1890 ^ _308432) ^ [] : [_374958 = apply(_374666, _374960), -(in(ordered_pair(_374960, _374958), _374666))]]]]], (3050 ^ _308432) ^ [_413633, _413635] : [3057 ^ _308432 : [(3060 ^ _308432) ^ [] : [-(function(relation_rng_restriction(_413635, _413633)))], (3058 ^ _308432) ^ [] : [-(relation(relation_rng_restriction(_413635, _413633)))]], relation(_413633), function(_413633)], (3910 ^ _308432) ^ [_442781, _442783, _442785] : [-(subset(_442785, _442781)), subset(_442785, _442783), subset(_442783, _442781)], (3996 ^ _308432) ^ [_445532, _445534, _445536] : [relation(_445532), -(subset(fiber(relation_restriction(_445532, _445536), _445534), fiber(_445532, _445534)))], (4919 ^ _308432) ^ [_475876] : [empty(_475876), -(_475876 = empty_set)], (4756 ^ _308432) ^ [_470861, _470863] : [relation(_470861), function(_470861), 4771 ^ _308432 : [(4774 ^ _308432) ^ [] : [-(_470863 = apply(relation_composition(function_inverse(_470861), _470861), _470863))], (4772 ^ _308432) ^ [] : [-(_470863 = apply(_470861, apply(function_inverse(_470861), _470863)))]], one_to_one(_470861), in(_470863, relation_rng(_470861))], (1634 ^ _308432) ^ [_365301, _365303, _365305] : [-(_365301 = set_union2(_365305, _365303)), 1638 ^ _308432 : [(1643 ^ _308432) ^ [] : [in(1635 ^ [_365301, _365303, _365305], _365303)], (1641 ^ _308432) ^ [] : [in(1635 ^ [_365301, _365303, _365305], _365305)], (1639 ^ _308432) ^ [] : [-(in(1635 ^ [_365301, _365303, _365305], _365301))]], 1644 ^ _308432 : [(1645 ^ _308432) ^ [] : [-(in(1635 ^ [_365301, _365303, _365305], _365305)), -(in(1635 ^ [_365301, _365303, _365305], _365303))], (1651 ^ _308432) ^ [] : [in(1635 ^ [_365301, _365303, _365305], _365301)]]], (4481 ^ _308432) ^ [_461497, _461499] : [element(_461497, powerset(_461499)), 4484 ^ _308432 : [(4485 ^ _308432) ^ [_461649] : [element(_461649, powerset(_461499)), 4488 ^ _308432 : [(4495 ^ _308432) ^ [] : [subset(_461497, subset_complement(_461499, _461649)), -(disjoint(_461497, _461649))], (4489 ^ _308432) ^ [] : [disjoint(_461497, _461649), -(subset(_461497, subset_complement(_461499, _461649)))]]]]], (2932 ^ _308432) ^ [_409906] : [-(function(identity_relation(_409906)))], (4358 ^ _308432) ^ [_457396, _457398] : [-(set_union2(_457398, set_difference(_457396, _457398)) = set_union2(_457398, _457396))], (2950 ^ _308432) ^ [_410454, _410456] : [-(relation(set_union2(_410456, _410454))), relation(_410456), relation(_410454)], (4521 ^ _308432) ^ [_462851, _462853] : [subset(_462853, _462851), -(_462851 = set_union2(_462853, set_difference(_462851, _462853)))], (3288 ^ _308432) ^ [_421778] : [relation(_421778), 3291 ^ _308432 : [(3292 ^ _308432) ^ [] : [connected(_421778), 3295 ^ _308432 : [(3296 ^ _308432) ^ [_422072, _422074] : [in(_422074, relation_field(_421778)), in(_422072, relation_field(_421778)), -(_422074 = _422072), -(in(ordered_pair(_422074, _422072), _421778)), -(in(ordered_pair(_422072, _422074), _421778))]]], (3314 ^ _308432) ^ [] : [3317 ^ _308432 : [(3318 ^ _308432) ^ [] : [-(in(3315 ^ [_421778], relation_field(_421778)))], (3322 ^ _308432) ^ [] : [3315 ^ [_421778] = 3316 ^ [_421778]], (3326 ^ _308432) ^ [] : [in(ordered_pair(3316 ^ [_421778], 3315 ^ [_421778]), _421778)], (3324 ^ _308432) ^ [] : [in(ordered_pair(3315 ^ [_421778], 3316 ^ [_421778]), _421778)], (3320 ^ _308432) ^ [] : [-(in(3316 ^ [_421778], relation_field(_421778)))]], -(connected(_421778))]]], (392 ^ _308432) ^ [_320973, _320975, _320977, _320979] : [-(relation_rng_restriction(_320979, _320975) = relation_rng_restriction(_320977, _320973)), _320979 = _320977, _320975 = _320973], (4196 ^ _308432) ^ [_451977, _451979] : [relation(_451977), well_founded_relation(_451977), -(well_founded_relation(relation_restriction(_451977, _451979)))], (4034 ^ _308432) ^ [_446757, _446759] : [relation(_446757), function(_446757), 4041 ^ _308432 : [(4042 ^ _308432) ^ [_447003] : [relation(_447003), function(_447003), in(_446759, relation_dom(_446757)), -(apply(relation_composition(_446757, _447003), _446759) = apply(_447003, apply(_446757, _446759)))]]], (2301 ^ _308432) ^ [_389438] : [relation(_389438), 2304 ^ _308432 : [(2305 ^ _308432) ^ [_389646] : [is_connected_in(_389438, _389646), 2308 ^ _308432 : [(2309 ^ _308432) ^ [_389836, _389838] : [in(_389838, _389646), in(_389836, _389646), -(_389838 = _389836), -(in(ordered_pair(_389838, _389836), _389438)), -(in(ordered_pair(_389836, _389838), _389438))]]], (2327 ^ _308432) ^ [_390330] : [2330 ^ _308432 : [(2331 ^ _308432) ^ [] : [-(in(2328 ^ [_389438, _390330], _390330))], (2335 ^ _308432) ^ [] : [2328 ^ [_389438, _390330] = 2329 ^ [_389438, _390330]], (2339 ^ _308432) ^ [] : [in(ordered_pair(2329 ^ [_389438, _390330], 2328 ^ [_389438, _390330]), _389438)], (2337 ^ _308432) ^ [] : [in(ordered_pair(2328 ^ [_389438, _390330], 2329 ^ [_389438, _390330]), _389438)], (2333 ^ _308432) ^ [] : [-(in(2329 ^ [_389438, _390330], _390330))]], -(is_connected_in(_389438, _390330))]]], (3672 ^ _308432) ^ [_434716, _434718] : [in(_434716, 3658 ^ [_434718]), -(in(powerset(_434716), 3658 ^ [_434718]))], (4340 ^ _308432) ^ [_456843, _456845, _456847] : [subset(unordered_pair(_456847, _456845), _456843), 4343 ^ _308432 : [(4346 ^ _308432) ^ [] : [-(in(_456845, _456843))], (4344 ^ _308432) ^ [] : [-(in(_456847, _456843))]]], (3495 ^ _308432) ^ [] : [-(relation_empty_yielding(3491 ^ []))], (5046 ^ _308432) ^ [_480180, _480182] : [empty(_480182), -(_480182 = _480180), empty(_480180)], (3662 ^ _308432) ^ [_434401, _434403, _434405] : [-(in(_434401, 3658 ^ [_434405])), in(_434403, 3658 ^ [_434405]), subset(_434401, _434403)], (3450 ^ _308432) ^ [] : [-(empty(3442 ^ []))], (770 ^ _308432) ^ [_334288, _334290] : [_334290 = _334288, 773 ^ _308432 : [(776 ^ _308432) ^ [] : [-(subset(_334288, _334290))], (774 ^ _308432) ^ [] : [-(subset(_334290, _334288))]]], (1398 ^ _308432) ^ [_357255] : [_357255 = empty_set, 1401 ^ _308432 : [(1402 ^ _308432) ^ [_357368] : [in(_357368, _357255)]]], (572 ^ _308432) ^ [_327436, _327438] : [_327438 = _327436, -(identity_relation(_327438) = identity_relation(_327436))], (4541 ^ _308432) ^ [_463532, _463534] : [element(_463532, powerset(powerset(_463534))), -(_463532 = empty_set), complements_of_subsets(_463534, _463532) = empty_set], (2671 ^ _308432) ^ [] : [true___, -(true___)], (2721 ^ _308432) ^ [] : [true___, -(true___)], (4949 ^ _308432) ^ [_476904, _476906, _476908] : [relation(_476904), function(_476904), in(_476906, _476908), -(apply(relation_dom_restriction(_476904, _476908), _476906) = apply(_476904, _476906))], (5098 ^ _308432) ^ [_481691, _481693, _481695] : [-(subset(set_union2(_481695, _481691), _481693)), subset(_481695, _481693), subset(_481691, _481693)], (4458 ^ _308432) ^ [_460759] : [ordinal(_460759), 4461 ^ _308432 : [(4471 ^ _308432) ^ [] : [being_limit_ordinal(_460759), 4472 ^ _308432 : [(4473 ^ _308432) ^ [_461230] : [ordinal(_461230), _460759 = succ(_461230)]]], (4462 ^ _308432) ^ [] : [-(being_limit_ordinal(_460759)), 4466 ^ _308432 : [(4469 ^ _308432) ^ [] : [-(_460759 = succ(4465 ^ [_460759]))], (4467 ^ _308432) ^ [] : [-(ordinal(4465 ^ [_460759]))]]]]], (4104 ^ _308432) ^ [_448860] : [relation(_448860), 4107 ^ _308432 : [(4108 ^ _308432) ^ [_449010] : [relation(_449010), subset(_448860, _449010), 4115 ^ _308432 : [(4118 ^ _308432) ^ [] : [-(subset(relation_rng(_448860), relation_rng(_449010)))], (4116 ^ _308432) ^ [] : [-(subset(relation_dom(_448860), relation_dom(_449010)))]]]]], (62 ^ _308432) ^ [_310540, _310542, _310544, _310546] : [-(is_reflexive_in(_310544, _310540)), is_reflexive_in(_310546, _310542), _310546 = _310544, _310542 = _310540], (454 ^ _308432) ^ [_323232, _323234, _323236, _323238, _323240, _323242] : [-(subset_difference(_323242, _323238, _323234) = subset_difference(_323240, _323236, _323232)), _323242 = _323240, _323238 = _323236, _323234 = _323232], (3413 ^ _308432) ^ [] : [-(epsilon_transitive(3411 ^ []))], (2295 ^ _308432) ^ [_389232] : [relation(_389232), -(relation_field(_389232) = set_union2(relation_dom(_389232), relation_rng(_389232)))], (3248 ^ _308432) ^ [_420422] : [relation(_420422), 3251 ^ _308432 : [(3252 ^ _308432) ^ [] : [antisymmetric(_420422), 3255 ^ _308432 : [(3256 ^ _308432) ^ [_420692, _420694] : [-(_420694 = _420692), in(ordered_pair(_420694, _420692), _420422), in(ordered_pair(_420692, _420694), _420422)]]], (3266 ^ _308432) ^ [] : [3269 ^ _308432 : [(3274 ^ _308432) ^ [] : [3267 ^ [_420422] = 3268 ^ [_420422]], (3272 ^ _308432) ^ [] : [-(in(ordered_pair(3268 ^ [_420422], 3267 ^ [_420422]), _420422))], (3270 ^ _308432) ^ [] : [-(in(ordered_pair(3267 ^ [_420422], 3268 ^ [_420422]), _420422))]], -(antisymmetric(_420422))]]]], input).
% 48.62/47.96  ncf('1',plain,[well_ordering(relation_restriction(5182 ^ [], 5181 ^ []))],start(5188 ^ 0)).
% 48.62/47.96  ncf('1.1',plain,[-(well_ordering(relation_restriction(5182 ^ [], 5181 ^ []))), 2080 : reflexive(relation_restriction(5182 ^ [], 5181 ^ [])), 2080 : transitive(relation_restriction(5182 ^ [], 5181 ^ [])), 2080 : antisymmetric(relation_restriction(5182 ^ [], 5181 ^ [])), 2080 : connected(relation_restriction(5182 ^ [], 5181 ^ [])), 2080 : well_founded_relation(relation_restriction(5182 ^ [], 5181 ^ [])), 2080 : relation(relation_restriction(5182 ^ [], 5181 ^ []))],extension(2062 ^ 1,bind([[_381301], [relation_restriction(5182 ^ [], 5181 ^ [])]]))).
% 48.62/47.96  ncf('1.1.1',plain,[-(reflexive(relation_restriction(5182 ^ [], 5181 ^ []))), relation(5182 ^ []), reflexive(5182 ^ [])],extension(4024 ^ 4,bind([[_446458, _446460], [5182 ^ [], 5181 ^ []]]))).
% 48.62/47.96  ncf('1.1.1.1',plain,[-(relation(5182 ^ []))],extension(5184 ^ 5)).
% 48.62/47.96  ncf('1.1.1.2',plain,[-(reflexive(5182 ^ [])), 2066 : well_ordering(5182 ^ []), 2066 : relation(5182 ^ [])],extension(2062 ^ 5,bind([[_381301], [5182 ^ []]]))).
% 48.62/47.96  ncf('1.1.1.2.1',plain,[-(well_ordering(5182 ^ []))],extension(5186 ^ 8)).
% 48.62/47.96  ncf('1.1.1.2.2',plain,[-(relation(5182 ^ []))],lemmata('[1, 1].x')).
% 48.62/47.96  ncf('1.1.2',plain,[-(transitive(relation_restriction(5182 ^ [], 5181 ^ []))), relation(5182 ^ []), transitive(5182 ^ [])],extension(4094 ^ 4,bind([[_448575, _448577], [5182 ^ [], 5181 ^ []]]))).
% 48.62/47.96  ncf('1.1.2.1',plain,[-(relation(5182 ^ []))],extension(5184 ^ 5)).
% 48.62/47.96  ncf('1.1.2.2',plain,[-(transitive(5182 ^ [])), 2066 : well_ordering(5182 ^ []), 2066 : relation(5182 ^ [])],extension(2062 ^ 5,bind([[_381301], [5182 ^ []]]))).
% 48.62/47.96  ncf('1.1.2.2.1',plain,[-(well_ordering(5182 ^ []))],extension(5186 ^ 8)).
% 48.62/47.96  ncf('1.1.2.2.2',plain,[-(relation(5182 ^ []))],lemmata('[1, 1].x')).
% 48.62/47.96  ncf('1.1.3',plain,[-(antisymmetric(relation_restriction(5182 ^ [], 5181 ^ []))), relation(5182 ^ []), antisymmetric(5182 ^ [])],extension(4120 ^ 4,bind([[_449405, _449407], [5182 ^ [], 5181 ^ []]]))).
% 48.62/47.96  ncf('1.1.3.1',plain,[-(relation(5182 ^ []))],extension(5184 ^ 5)).
% 48.62/47.96  ncf('1.1.3.2',plain,[-(antisymmetric(5182 ^ [])), 2066 : well_ordering(5182 ^ []), 2066 : relation(5182 ^ [])],extension(2062 ^ 5,bind([[_381301], [5182 ^ []]]))).
% 48.62/47.96  ncf('1.1.3.2.1',plain,[-(well_ordering(5182 ^ []))],extension(5186 ^ 8)).
% 48.62/47.96  ncf('1.1.3.2.2',plain,[-(relation(5182 ^ []))],lemmata('[1, 1].x')).
% 48.62/47.96  ncf('1.1.4',plain,[-(connected(relation_restriction(5182 ^ [], 5181 ^ []))), relation(5182 ^ []), connected(5182 ^ [])],extension(4066 ^ 4,bind([[_447737, _447739], [5182 ^ [], 5181 ^ []]]))).
% 48.62/47.96  ncf('1.1.4.1',plain,[-(relation(5182 ^ []))],extension(5184 ^ 5)).
% 48.62/47.96  ncf('1.1.4.2',plain,[-(connected(5182 ^ [])), 2066 : well_ordering(5182 ^ []), 2066 : relation(5182 ^ [])],extension(2062 ^ 5,bind([[_381301], [5182 ^ []]]))).
% 48.62/47.96  ncf('1.1.4.2.1',plain,[-(well_ordering(5182 ^ []))],extension(5186 ^ 8)).
% 48.62/47.96  ncf('1.1.4.2.2',plain,[-(relation(5182 ^ []))],lemmata('[1, 1].x')).
% 48.62/47.96  ncf('1.1.5',plain,[-(well_founded_relation(relation_restriction(5182 ^ [], 5181 ^ []))), relation(5182 ^ []), well_founded_relation(5182 ^ [])],extension(4196 ^ 4,bind([[_451977, _451979], [5182 ^ [], 5181 ^ []]]))).
% 48.62/47.96  ncf('1.1.5.1',plain,[-(relation(5182 ^ []))],extension(5184 ^ 5)).
% 48.62/47.96  ncf('1.1.5.2',plain,[-(well_founded_relation(5182 ^ [])), 2066 : well_ordering(5182 ^ []), 2066 : relation(5182 ^ [])],extension(2062 ^ 5,bind([[_381301], [5182 ^ []]]))).
% 48.62/47.96  ncf('1.1.5.2.1',plain,[-(well_ordering(5182 ^ []))],extension(5186 ^ 8)).
% 48.62/47.96  ncf('1.1.5.2.2',plain,[-(relation(5182 ^ []))],lemmata('[1, 1].x')).
% 48.62/47.96  ncf('1.1.6',plain,[-(relation(relation_restriction(5182 ^ [], 5181 ^ []))), relation(5182 ^ [])],extension(2727 ^ 2,bind([[_403879, _403881], [5181 ^ [], 5182 ^ []]]))).
% 48.62/47.96  ncf('1.1.6.1',plain,[-(relation(5182 ^ []))],extension(5184 ^ 3)).
% 48.62/47.96  %-----------------------------------------------------
% 48.62/47.96  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------