%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU204+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.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 12:02:38 EDT 2023

% Result   : Theorem 69.63s 67.72s
% Output   : Proof 69.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU204+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 13:18:20 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 69.63/67.72  
% 69.63/67.72  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 69.63/67.72  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.63/67.72  %-----------------------------------------------------
% 69.63/67.72  ncf(matrix, plain, [(2721 ^ _488355) ^ [] : [subset(relation_image(2717 ^ [], 2716 ^ []), relation_rng(2717 ^ []))], (2719 ^ _488355) ^ [] : [-(relation(2717 ^ []))], !, (322 ^ _391403) ^ [_402578, _402580, _402582, _402584] : [-(relation_image(_402584, _402580) = relation_image(_402582, _402578)), _402584 = _402582, _402580 = _402578], (2203 ^ _391403) ^ [_469060, _469062] : [in(_469062, _469060), -(subset(singleton(_469062), _469060))], (1823 ^ _391403) ^ [] : [-(relation(1819 ^ []))], (2453 ^ _391403) ^ [_477723] : [relation(_477723), -(in(ordered_pair(2458 ^ [_477723], 2459 ^ [_477723]), _477723)), -(_477723 = empty_set)], (2062 ^ _391403) ^ [_464121, _464123, _464125] : [-(subset(_464125, _464121)), subset(_464125, _464123), subset(_464123, _464121)], (1856 ^ _391403) ^ [_456696, _456698] : [element(_456696, powerset(powerset(_456698))), -(meet_of_subsets(_456698, _456696) = set_meet(_456696))], (1850 ^ _391403) ^ [_456468, _456470] : [element(_456468, powerset(powerset(_456470))), -(union_of_subsets(_456470, _456468) = union(_456468))], (1779 ^ _391403) ^ [_453935, _453937] : [1780 ^ _391403 : [(1783 ^ _391403) ^ [] : [_453937 = singleton(_453935)], (1781 ^ _391403) ^ [] : [_453937 = empty_set]], -(subset(_453937, singleton(_453935)))], (1737 ^ _391403) ^ [_452560, _452562] : [set_difference(_452562, _452560) = empty_set, -(subset(_452562, _452560))], (1591 ^ _391403) ^ [_447561, _447563] : [empty(ordered_pair(_447563, _447561))], (344 ^ _391403) ^ [_403432, _403434] : [proper_subset(_403434, _403432), proper_subset(_403432, _403434)], (602 ^ _391403) ^ [_413153, _413155] : [-(_413155 = empty_set), 605 ^ _391403 : [(606 ^ _391403) ^ [] : [_413153 = set_meet(_413155), 609 ^ _391403 : [(610 ^ _391403) ^ [_413451] : [in(_413451, _413153), 613 ^ _391403 : [(614 ^ _391403) ^ [_413596] : [in(_413596, _413155), -(in(_413451, _413596))]]], (620 ^ _391403) ^ [_413781] : [622 ^ _391403 : [(625 ^ _391403) ^ [] : [in(_413781, 621 ^ [_413153, _413155, _413781])], (623 ^ _391403) ^ [] : [-(in(621 ^ [_413153, _413155, _413781], _413155))]], -(in(_413781, _413153))]]], (629 ^ _391403) ^ [] : [-(_413153 = set_meet(_413155)), 633 ^ _391403 : [(639 ^ _391403) ^ [] : [in(630 ^ [_413153, _413155], 635 ^ [_413153, _413155])], (637 ^ _391403) ^ [] : [-(in(635 ^ [_413153, _413155], _413155))], (634 ^ _391403) ^ [] : [-(in(630 ^ [_413153, _413155], _413153))]], 640 ^ _391403 : [(641 ^ _391403) ^ [_414555] : [in(_414555, _413155), -(in(630 ^ [_413153, _413155], _414555))], (647 ^ _391403) ^ [] : [in(630 ^ [_413153, _413155], _413153)]]]]], (1991 ^ _391403) ^ [_461586, _461588] : [in(_461586, 1977 ^ [_461588]), -(in(powerset(_461586), 1977 ^ [_461588]))], (1619 ^ _391403) ^ [] : [-(empty(empty_set))], (1633 ^ _391403) ^ [_448976] : [empty(relation_dom(_448976)), -(empty(_448976)), relation(_448976)], (683 ^ _391403) ^ [_415878, _415880] : [-(_415878 = singleton(_415880)), 687 ^ _391403 : [(690 ^ _391403) ^ [] : [684 ^ [_415878, _415880] = _415880], (688 ^ _391403) ^ [] : [-(in(684 ^ [_415878, _415880], _415878))]], 691 ^ _391403 : [(694 ^ _391403) ^ [] : [in(684 ^ [_415878, _415880], _415878)], (692 ^ _391403) ^ [] : [-(684 ^ [_415878, _415880] = _415880)]]], (2209 ^ _391403) ^ [_469319, _469321, _469323] : [subset(unordered_pair(_469323, _469321), _469319), 2212 ^ _391403 : [(2215 ^ _391403) ^ [] : [-(in(_469321, _469319))], (2213 ^ _391403) ^ [] : [-(in(_469323, _469319))]]], (1948 ^ _391403) ^ [_459933, _459935, _459937] : [subset(_459937, _459935), 1951 ^ _391403 : [(1954 ^ _391403) ^ [] : [-(subset(cartesian_product2(_459933, _459937), cartesian_product2(_459933, _459935)))], (1952 ^ _391403) ^ [] : [-(subset(cartesian_product2(_459937, _459933), cartesian_product2(_459935, _459933)))]]], (360 ^ _391403) ^ [_404014, _404016] : [-(set_intersection2(_404016, _404014) = set_intersection2(_404014, _404016))], (879 ^ _391403) ^ [_422589, _422591, _422593] : [-(_422589 = set_union2(_422593, _422591)), 883 ^ _391403 : [(888 ^ _391403) ^ [] : [in(880 ^ [_422589, _422591, _422593], _422591)], (886 ^ _391403) ^ [] : [in(880 ^ [_422589, _422591, _422593], _422593)], (884 ^ _391403) ^ [] : [-(in(880 ^ [_422589, _422591, _422593], _422589))]], 889 ^ _391403 : [(890 ^ _391403) ^ [] : [-(in(880 ^ [_422589, _422591, _422593], _422593)), -(in(880 ^ [_422589, _422591, _422593], _422591))], (896 ^ _391403) ^ [] : [in(880 ^ [_422589, _422591, _422593], _422589)]]], (62 ^ _391403) ^ [_393483, _393485] : [-(empty(_393483)), _393485 = _393483, empty(_393485)], (704 ^ _391403) ^ [_416608] : [-(in(705 ^ [_416608], _416608)), -(_416608 = empty_set)], (1556 ^ _391403) ^ [] : [true___, -(true___)], (1681 ^ _391403) ^ [_450437, _450439] : [-(set_union2(_450439, _450439) = _450439)], (1930 ^ _391403) ^ [_459265, _459267] : [relation(_459265), -(subset(relation_rng(relation_rng_restriction(_459267, _459265)), _459267))], (2661 ^ _391403) ^ [_484601, _484603] : [relation(_484601), -(relation_dom_restriction(_484601, _484603) = relation_composition(identity_relation(_484603), _484601))], (1400 ^ _391403) ^ [] : [true___, -(true___)], (1801 ^ _391403) ^ [_454765, _454767, _454769, _454771] : [-(in(ordered_pair(_454771, _454769), cartesian_product2(_454767, _454765))), in(_454771, _454767), in(_454769, _454765)], (2308 ^ _391403) ^ [_472691] : [relation(_472691), 2311 ^ _391403 : [(2312 ^ _391403) ^ [_472828] : [relation(_472828), -(subset(relation_dom(relation_composition(_472691, _472828)), relation_dom(_472691)))]]], (2378 ^ _391403) ^ [_475086, _475088] : [element(_475086, powerset(powerset(_475088))), -(_475086 = empty_set), -(subset_difference(_475088, cast_to_subset(_475088), union_of_subsets(_475088, _475086)) = meet_of_subsets(_475088, complements_of_subsets(_475088, _475086)))], (2286 ^ _391403) ^ [_471937, _471939] : [-(set_difference(set_union2(_471939, _471937), _471937) = set_difference(_471939, _471937))], (100 ^ _391403) ^ [_394666, _394668] : [-(relation(_394666)), _394668 = _394666, relation(_394668)], (2249 ^ _391403) ^ [_470683, _470685] : [element(_470685, powerset(_470683)), -(subset(_470685, _470683))], (130 ^ _391403) ^ [_395651, _395653, _395655, _395657] : [-(relation_rng_restriction(_395657, _395653) = relation_rng_restriction(_395655, _395651)), _395657 = _395655, _395653 = _395651], (2553 ^ _391403) ^ [_480994, _480996, _480998, _481000] : [relation(_480994), 2556 ^ _391403 : [(2565 ^ _391403) ^ [] : [-(in(ordered_pair(_481000, _480998), relation_composition(identity_relation(_480996), _480994))), in(_481000, _480996), in(ordered_pair(_481000, _480998), _480994)], (2557 ^ _391403) ^ [] : [in(ordered_pair(_481000, _480998), relation_composition(identity_relation(_480996), _480994)), 2560 ^ _391403 : [(2563 ^ _391403) ^ [] : [-(in(ordered_pair(_481000, _480998), _480994))], (2561 ^ _391403) ^ [] : [-(in(_481000, _480996))]]]]], (1589 ^ _391403) ^ [] : [-(empty(empty_set))], (2255 ^ _391403) ^ [_470849, _470851] : [subset(_470851, _470849), -(element(_470851, powerset(_470849)))], (2543 ^ _391403) ^ [_480596, _480598] : [subset(singleton(_480598), singleton(_480596)), -(_480598 = _480596)], (1516 ^ _391403) ^ [_445182, _445184] : [element(_445182, powerset(powerset(_445184))), -(element(meet_of_subsets(_445184, _445182), powerset(_445184)))], (1605 ^ _391403) ^ [_448049, _448051] : [-(empty(_448051)), empty(set_union2(_448051, _448049))], (2108 ^ _391403) ^ [_465642, _465644, _465646] : [subset(_465646, _465644), -(subset(set_intersection2(_465646, _465642), set_intersection2(_465644, _465642)))], (1532 ^ _391403) ^ [_445753, _445755] : [relation(_445755), -(relation(relation_dom_restriction(_445755, _445753)))], (1593 ^ _391403) ^ [_447672, _447674] : [-(relation(set_union2(_447674, _447672))), relation(_447674), relation(_447672)], (1769 ^ _391403) ^ [_453675, _453677] : [subset(_453677, singleton(_453675)), -(_453677 = empty_set), -(_453677 = singleton(_453675))], (150 ^ _391403) ^ [_396341, _396343] : [_396343 = _396341, -(relation_field(_396343) = relation_field(_396341))], (1942 ^ _391403) ^ [_459697, _459699] : [relation(_459697), -(subset(relation_rng(relation_rng_restriction(_459699, _459697)), relation_rng(_459697)))], (2523 ^ _391403) ^ [_479927, _479929] : [set_difference(_479929, singleton(_479927)) = _479929, in(_479927, _479929)], (2 ^ _391403) ^ [_391527] : [-(_391527 = _391527)], (1972 ^ _391403) ^ [_460837, _460839] : [subset(_460839, _460837), -(set_union2(_460839, _460837) = _460837)], (2191 ^ _391403) ^ [_468647, _468649] : [subset(_468649, _468647), -(set_difference(_468649, _468647) = empty_set)], (2711 ^ _391403) ^ [_486539, _486541, _486543] : [singleton(_486543) = unordered_pair(_486541, _486539), -(_486541 = _486539)], (930 ^ _391403) ^ [_424640, _424642, _424644] : [-(_424640 = cartesian_product2(_424644, _424642)), 948 ^ _391403 : [(951 ^ _391403) ^ [] : [-(in(947 ^ [_424640, _424642, _424644], _424642))], (953 ^ _391403) ^ [] : [-(931 ^ [_424640, _424642, _424644] = ordered_pair(946 ^ [_424640, _424642, _424644], 947 ^ [_424640, _424642, _424644]))], (955 ^ _391403) ^ [] : [in(931 ^ [_424640, _424642, _424644], _424640)], (949 ^ _391403) ^ [] : [-(in(946 ^ [_424640, _424642, _424644], _424644))]], 934 ^ _391403 : [(937 ^ _391403) ^ [_424978, _424980] : [in(_424980, _424644), in(_424978, _424642), 931 ^ [_424640, _424642, _424644] = ordered_pair(_424980, _424978)], (935 ^ _391403) ^ [] : [-(in(931 ^ [_424640, _424642, _424644], _424640))]]], (2589 ^ _391403) ^ [_482188, _482190] : [set_difference(_482190, _482188) = _482190, -(disjoint(_482190, _482188))], (2177 ^ _391403) ^ [_468151] : [relation(_468151), 2180 ^ _391403 : [(2183 ^ _391403) ^ [] : [-(relation_dom(_468151) = relation_rng(relation_inverse(_468151)))], (2181 ^ _391403) ^ [] : [-(relation_rng(_468151) = relation_dom(relation_inverse(_468151)))]]], (1713 ^ _391403) ^ [_451690, _451692] : [disjoint(singleton(_451692), _451690), in(_451692, _451690)], (1028 ^ _391403) ^ [_428396, _428398, _428400] : [-(_428396 = set_intersection2(_428400, _428398)), 1040 ^ _391403 : [(1045 ^ _391403) ^ [] : [in(1029 ^ [_428396, _428398, _428400], _428396)], (1043 ^ _391403) ^ [] : [-(in(1029 ^ [_428396, _428398, _428400], _428398))], (1041 ^ _391403) ^ [] : [-(in(1029 ^ [_428396, _428398, _428400], _428400))]], 1032 ^ _391403 : [(1035 ^ _391403) ^ [] : [in(1029 ^ [_428396, _428398, _428400], _428400), in(1029 ^ [_428396, _428398, _428400], _428398)], (1033 ^ _391403) ^ [] : [-(in(1029 ^ [_428396, _428398, _428400], _428396))]]], (2623 ^ _391403) ^ [_483293, _483295] : [empty(_483295), -(_483295 = _483293), empty(_483293)], (900 ^ _391403) ^ [_423383, _423385, _423387] : [_423383 = cartesian_product2(_423387, _423385), 903 ^ _391403 : [(916 ^ _391403) ^ [_424144] : [-(in(_424144, _423383)), 917 ^ _391403 : [(918 ^ _391403) ^ [_424274, _424276] : [in(_424276, _423387), in(_424274, _423385), _424144 = ordered_pair(_424276, _424274)]]], (904 ^ _391403) ^ [_423584] : [in(_423584, _423383), 909 ^ _391403 : [(914 ^ _391403) ^ [] : [-(_423584 = ordered_pair(907 ^ [_423383, _423385, _423387, _423584], 908 ^ [_423383, _423385, _423387, _423584]))], (912 ^ _391403) ^ [] : [-(in(908 ^ [_423383, _423385, _423387, _423584], _423385))], (910 ^ _391403) ^ [] : [-(in(907 ^ [_423383, _423385, _423387, _423584], _423387))]]]]], (1508 ^ _391403) ^ [_444875, _444877] : [element(_444875, powerset(powerset(_444877))), -(element(union_of_subsets(_444877, _444875), powerset(_444877)))], (2649 ^ _391403) ^ [_484159, _484161] : [relation(_484159), -(relation_dom(relation_dom_restriction(_484159, _484161)) = set_intersection2(relation_dom(_484159), _484161))], (2147 ^ _391403) ^ [_466966] : [-(subset(empty_set, _466966))], (1811 ^ _391403) ^ [_455098, _455100] : [1813 ^ _391403 : [(1816 ^ _391403) ^ [] : [in(1812 ^ [_455098, _455100], _455098)], (1814 ^ _391403) ^ [] : [-(in(1812 ^ [_455098, _455100], _455100))]], -(element(_455100, powerset(_455098)))], (2595 ^ _391403) ^ [_482420, _482422, _482424] : [relation(_482420), 2598 ^ _391403 : [(2607 ^ _391403) ^ [] : [-(in(_482424, relation_dom(relation_dom_restriction(_482420, _482422)))), in(_482424, _482422), in(_482424, relation_dom(_482420))], (2599 ^ _391403) ^ [] : [in(_482424, relation_dom(relation_dom_restriction(_482420, _482422))), 2602 ^ _391403 : [(2605 ^ _391403) ^ [] : [-(in(_482424, relation_dom(_482420)))], (2603 ^ _391403) ^ [] : [-(in(_482424, _482422))]]]]], (857 ^ _391403) ^ [_421864, _421866, _421868] : [_421864 = set_union2(_421868, _421866), 860 ^ _391403 : [(861 ^ _391403) ^ [_422046] : [in(_422046, _421864), -(in(_422046, _421868)), -(in(_422046, _421866))], (871 ^ _391403) ^ [_422324] : [872 ^ _391403 : [(875 ^ _391403) ^ [] : [in(_422324, _421866)], (873 ^ _391403) ^ [] : [in(_422324, _421868)]], -(in(_422324, _421864))]]], (1845 ^ _391403) ^ [_456265] : [-(empty(1841 ^ [_456265]))], (1444 ^ _391403) ^ [] : [true___, -(true___)], (2583 ^ _391403) ^ [_482020, _482022] : [disjoint(_482022, _482020), -(set_difference(_482022, _482020) = _482022)], (1898 ^ _391403) ^ [_458256, _458258, _458260, _458262] : [unordered_pair(_458262, _458260) = unordered_pair(_458258, _458256), -(_458262 = _458258), -(_458262 = _458256)], (1643 ^ _391403) ^ [_449253] : [empty(relation_rng(_449253)), -(empty(_449253)), relation(_449253)], (2167 ^ _391403) ^ [_467755, _467757, _467759, _467761] : [ordered_pair(_467761, _467759) = ordered_pair(_467757, _467755), 2170 ^ _391403 : [(2173 ^ _391403) ^ [] : [-(_467759 = _467755)], (2171 ^ _391403) ^ [] : [-(_467761 = _467757)]]], (2334 ^ _391403) ^ [_473617] : [relation(_473617), 2337 ^ _391403 : [(2338 ^ _391403) ^ [_473764] : [relation(_473764), subset(relation_rng(_473617), relation_dom(_473764)), -(relation_dom(relation_composition(_473617, _473764)) = relation_dom(_473617))]]], (2535 ^ _391403) ^ [_480296] : [-(unordered_pair(_480296, _480296) = singleton(_480296))], (667 ^ _391403) ^ [_415357, _415359] : [_415357 = singleton(_415359), 670 ^ _391403 : [(677 ^ _391403) ^ [_415699] : [_415699 = _415359, -(in(_415699, _415357))], (671 ^ _391403) ^ [_415527] : [in(_415527, _415357), -(_415527 = _415359)]]], (2633 ^ _391403) ^ [_483604, _483606, _483608] : [-(subset(set_union2(_483608, _483604), _483606)), subset(_483608, _483606), subset(_483604, _483606)], (418 ^ _391403) ^ [_406047, _406049] : [-(_406049 = _406047), subset(_406049, _406047), subset(_406047, _406049)], (140 ^ _391403) ^ [_396010, _396012, _396014, _396016] : [-(cartesian_product2(_396016, _396012) = cartesian_product2(_396014, _396010)), _396016 = _396014, _396012 = _396010], (698 ^ _391403) ^ [_416429] : [_416429 = empty_set, 701 ^ _391403 : [(702 ^ _391403) ^ [_416542] : [in(_416542, _416429)]]], (2042 ^ _391403) ^ [_463375, _463377] : [-(subset(set_intersection2(_463377, _463375), _463377))], (727 ^ _391403) ^ [_417420, _417422] : [-(_417420 = powerset(_417422)), 731 ^ _391403 : [(734 ^ _391403) ^ [] : [subset(728 ^ [_417420, _417422], _417422)], (732 ^ _391403) ^ [] : [-(in(728 ^ [_417420, _417422], _417420))]], 735 ^ _391403 : [(738 ^ _391403) ^ [] : [in(728 ^ [_417420, _417422], _417420)], (736 ^ _391403) ^ [] : [-(subset(728 ^ [_417420, _417422], _417422))]]], (1653 ^ _391403) ^ [_449530] : [empty(_449530), 1656 ^ _391403 : [(1659 ^ _391403) ^ [] : [-(relation(relation_dom(_449530)))], (1657 ^ _391403) ^ [] : [-(empty(relation_dom(_449530)))]]], (2507 ^ _391403) ^ [_479444] : [relation(_479444), 2510 ^ _391403 : [(2517 ^ _391403) ^ [] : [relation_rng(_479444) = empty_set, -(relation_dom(_479444) = empty_set)], (2511 ^ _391403) ^ [] : [relation_dom(_479444) = empty_set, -(relation_rng(_479444) = empty_set)]]], (278 ^ _391403) ^ [_400960, _400962] : [_400962 = _400960, -(identity_relation(_400962) = identity_relation(_400960))], (1390 ^ _391403) ^ [_442110, _442112] : [-(proper_subset(_442112, _442110)), subset(_442112, _442110), -(_442112 = _442110)], (1450 ^ _391403) ^ [] : [true___, -(true___)], (2239 ^ _391403) ^ [_470279, _470281] : [2240 ^ _391403 : [(2243 ^ _391403) ^ [] : [_470281 = singleton(_470279)], (2241 ^ _391403) ^ [] : [_470281 = empty_set]], -(subset(_470281, singleton(_470279)))], (156 ^ _391403) ^ [_396559, _396561] : [_396561 = _396559, -(relation_inverse(_396561) = relation_inverse(_396559))], (294 ^ _391403) ^ [_401537, _401539] : [_401539 = _401537, -(union(_401539) = union(_401537))], (1997 ^ _391403) ^ [_461786, _461788] : [subset(_461786, 1977 ^ [_461788]), -(are_equipotent(_461786, 1977 ^ [_461788])), -(in(_461786, 1977 ^ [_461788]))], (2485 ^ _391403) ^ [_478796, _478798, _478800] : [-(disjoint(_478800, _478796)), subset(_478800, _478798), disjoint(_478798, _478796)], (2358 ^ _391403) ^ [_474407, _474409] : [in(_474409, _474407), -(set_union2(singleton(_474409), _474407) = _474407)], (1486 ^ _391403) ^ [] : [true___, -(true___)], (2701 ^ _391403) ^ [_486205, _486207] : [subset(_486205, 2674 ^ [_486207]), -(are_equipotent(_486205, 2674 ^ [_486207])), -(in(_486205, 2674 ^ [_486207]))], (1213 ^ _391403) ^ [_435363, _435365] : [element(_435363, powerset(_435365)), -(subset_complement(_435365, _435363) = set_difference(_435365, _435363))], (711 ^ _391403) ^ [_416899, _416901] : [_416899 = powerset(_416901), 714 ^ _391403 : [(721 ^ _391403) ^ [_417241] : [subset(_417241, _416901), -(in(_417241, _416899))], (715 ^ _391403) ^ [_417069] : [in(_417069, _416899), -(subset(_417069, _416901))]]], (1279 ^ _391403) ^ [_437765] : [relation(_437765), 1282 ^ _391403 : [(1283 ^ _391403) ^ [_437950] : [relation(_437950), 1286 ^ _391403 : [(1287 ^ _391403) ^ [_438131] : [relation(_438131), 1290 ^ _391403 : [(1291 ^ _391403) ^ [] : [_438131 = relation_composition(_437765, _437950), 1294 ^ _391403 : [(1304 ^ _391403) ^ [_438851, _438853] : [-(in(ordered_pair(_438853, _438851), _438131)), 1305 ^ _391403 : [(1306 ^ _391403) ^ [_438964] : [in(ordered_pair(_438853, _438964), _437765), in(ordered_pair(_438964, _438851), _437950)]]], (1295 ^ _391403) ^ [_438466, _438468] : [in(ordered_pair(_438468, _438466), _438131), 1299 ^ _391403 : [(1302 ^ _391403) ^ [] : [-(in(ordered_pair(1298 ^ [_437765, _437950, _438131, _438466, _438468], _438466), _437950))], (1300 ^ _391403) ^ [] : [-(in(ordered_pair(_438468, 1298 ^ [_437765, _437950, _438131, _438466, _438468]), _437765))]]]]], (1314 ^ _391403) ^ [] : [-(_438131 = relation_composition(_437765, _437950)), 1328 ^ _391403 : [(1333 ^ _391403) ^ [] : [in(ordered_pair(1315 ^ [_437765, _437950, _438131], 1316 ^ [_437765, _437950, _438131]), _438131)], (1331 ^ _391403) ^ [] : [-(in(ordered_pair(1327 ^ [_437765, _437950, _438131], 1316 ^ [_437765, _437950, _438131]), _437950))], (1329 ^ _391403) ^ [] : [-(in(ordered_pair(1315 ^ [_437765, _437950, _438131], 1327 ^ [_437765, _437950, _438131]), _437765))]], 1319 ^ _391403 : [(1322 ^ _391403) ^ [_439595] : [in(ordered_pair(1315 ^ [_437765, _437950, _438131], _439595), _437765), in(ordered_pair(_439595, 1316 ^ [_437765, _437950, _438131]), _437950)], (1320 ^ _391403) ^ [] : [-(in(ordered_pair(1315 ^ [_437765, _437950, _438131], 1316 ^ [_437765, _437950, _438131]), _438131))]]]]]]]]], (1843 ^ _391403) ^ [_456214] : [-(element(1841 ^ [_456214], powerset(_456214)))], (1759 ^ _391403) ^ [_453326, _453328, _453330] : [subset(_453330, _453328), -(in(_453326, _453330)), -(subset(_453330, set_difference(_453328, singleton(_453326))))], (1936 ^ _391403) ^ [_459483, _459485] : [relation(_459483), -(subset(relation_rng_restriction(_459485, _459483), _459483))], (4 ^ _391403) ^ [_391634, _391636] : [_391636 = _391634, -(_391634 = _391636)], (2581 ^ _391403) ^ [_481879, _481881] : [-(subset(_481881, set_union2(_481881, _481879)))], (2495 ^ _391403) ^ [_479091] : [relation(_479091), 2500 ^ _391403 : [(2503 ^ _391403) ^ [] : [relation_rng(_479091) = empty_set], (2501 ^ _391403) ^ [] : [relation_dom(_479091) = empty_set]], -(_479091 = empty_set)], (332 ^ _391403) ^ [_402889, _402891] : [_402891 = _402889, -(relation_rng(_402891) = relation_rng(_402889))], (10 ^ _391403) ^ [_391838, _391840, _391842] : [-(_391842 = _391838), _391842 = _391840, _391840 = _391838], (1623 ^ _391403) ^ [_448684, _448686] : [empty(cartesian_product2(_448686, _448684)), -(empty(_448686)), -(empty(_448684))], (2667 ^ _391403) ^ [_484825, _484827] : [relation(_484825), -(subset(relation_rng(relation_dom_restriction(_484825, _484827)), relation_rng(_484825)))], (1382 ^ _391403) ^ [_441872, _441874] : [proper_subset(_441874, _441872), 1385 ^ _391403 : [(1388 ^ _391403) ^ [] : [_441874 = _441872], (1386 ^ _391403) ^ [] : [-(subset(_441874, _441872))]]], (2247 ^ _391403) ^ [_470544] : [-(set_difference(_470544, empty_set) = _470544)], (2122 ^ _391403) ^ [_466167, _466169] : [element(_466169, _466167), -(empty(_466167)), -(in(_466169, _466167))], (1587 ^ _391403) ^ [_447416] : [empty(powerset(_447416))], (2364 ^ _391403) ^ [_474613] : [relation(_474613), 2367 ^ _391403 : [(2368 ^ _391403) ^ [_474760] : [relation(_474760), subset(relation_dom(_474613), relation_rng(_474760)), -(relation_rng(relation_composition(_474760, _474613)) = relation_rng(_474613))]]], (2217 ^ _391403) ^ [_469570, _469572, _469574] : [-(subset(unordered_pair(_469574, _469572), _469570)), in(_469574, _469570), in(_469572, _469570)], (1743 ^ _391403) ^ [_452728, _452730] : [subset(_452730, _452728), -(set_difference(_452730, _452728) = empty_set)], (2475 ^ _391403) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2185 ^ _391403) ^ [_468479, _468481] : [set_difference(_468481, _468479) = empty_set, -(subset(_468481, _468479))], (2419 ^ _391403) ^ [_476532, _476534] : [2420 ^ _391403 : [(2421 ^ _391403) ^ [_476605] : [in(_476605, set_intersection2(_476534, _476532))]], disjoint(_476534, _476532)], (2056 ^ _391403) ^ [_463897, _463899] : [in(_463899, _463897), -(element(_463899, _463897))], (2537 ^ _391403) ^ [_480394] : [empty(_480394), -(_480394 = empty_set)], (997 ^ _391403) ^ [_427271, _427273] : [999 ^ _391403 : [(1002 ^ _391403) ^ [] : [in(998 ^ [_427271, _427273], _427271)], (1000 ^ _391403) ^ [] : [-(in(998 ^ [_427271, _427273], _427273))]], -(subset(_427273, _427271))], (1406 ^ _391403) ^ [] : [true___, -(true___)], (2643 ^ _391403) ^ [_483933, _483935, _483937] : [singleton(_483937) = unordered_pair(_483935, _483933), -(_483937 = _483935)], (2092 ^ _391403) ^ [_465083] : [relation(_465083), 2095 ^ _391403 : [(2096 ^ _391403) ^ [_465233] : [relation(_465233), subset(_465083, _465233), 2103 ^ _391403 : [(2106 ^ _391403) ^ [] : [-(subset(relation_rng(_465083), relation_rng(_465233)))], (2104 ^ _391403) ^ [] : [-(subset(relation_dom(_465083), relation_dom(_465233)))]]]]], (1962 ^ _391403) ^ [_460506, _460508, _460510, _460512] : [-(subset(cartesian_product2(_460512, _460508), cartesian_product2(_460510, _460506))), subset(_460512, _460510), subset(_460508, _460506)], (162 ^ _391403) ^ [_396805, _396807, _396809, _396811] : [-(union_of_subsets(_396811, _396807) = union_of_subsets(_396809, _396805)), _396811 = _396809, _396807 = _396805], (252 ^ _391403) ^ [_400052, _400054, _400056, _400058] : [-(set_intersection2(_400058, _400054) = set_intersection2(_400056, _400052)), _400058 = _400056, _400054 = _400052], (1133 ^ _391403) ^ [_432434, _432436, _432438] : [_432434 = set_difference(_432438, _432436), 1136 ^ _391403 : [(1145 ^ _391403) ^ [_432878] : [-(in(_432878, _432434)), in(_432878, _432438), -(in(_432878, _432436))], (1137 ^ _391403) ^ [_432618] : [in(_432618, _432434), 1140 ^ _391403 : [(1143 ^ _391403) ^ [] : [in(_432618, _432436)], (1141 ^ _391403) ^ [] : [-(in(_432618, _432438))]]]]], (2676 ^ _391403) ^ [_485259] : [-(in(_485259, 2674 ^ [_485259]))], (362 ^ _391403) ^ [_404129, _404131] : [relation(_404129), 365 ^ _391403 : [(366 ^ _391403) ^ [] : [_404129 = identity_relation(_404131), 369 ^ _391403 : [(378 ^ _391403) ^ [_404702, _404704] : [-(in(ordered_pair(_404704, _404702), _404129)), in(_404704, _404131), _404704 = _404702], (370 ^ _391403) ^ [_404439, _404441] : [in(ordered_pair(_404441, _404439), _404129), 373 ^ _391403 : [(376 ^ _391403) ^ [] : [-(_404441 = _404439)], (374 ^ _391403) ^ [] : [-(in(_404441, _404131))]]]]], (388 ^ _391403) ^ [] : [-(_404129 = identity_relation(_404131)), 401 ^ _391403 : [(406 ^ _391403) ^ [] : [in(ordered_pair(389 ^ [_404129, _404131], 390 ^ [_404129, _404131]), _404129)], (404 ^ _391403) ^ [] : [-(389 ^ [_404129, _404131] = 390 ^ [_404129, _404131])], (402 ^ _391403) ^ [] : [-(in(389 ^ [_404129, _404131], _404131))]], 393 ^ _391403 : [(396 ^ _391403) ^ [] : [in(389 ^ [_404129, _404131], _404131), 389 ^ [_404129, _404131] = 390 ^ [_404129, _404131]], (394 ^ _391403) ^ [] : [-(in(ordered_pair(389 ^ [_404129, _404131], 390 ^ [_404129, _404131]), _404129))]]]]], (1825 ^ _391403) ^ [_455592] : [-(empty(_455592)), 1829 ^ _391403 : [(1832 ^ _391403) ^ [] : [empty(1828 ^ [_455592])], (1830 ^ _391403) ^ [] : [-(element(1828 ^ [_455592], powerset(_455592)))]]], (2197 ^ _391403) ^ [_468894, _468896] : [subset(singleton(_468896), _468894), -(in(_468896, _468894))], (356 ^ _391403) ^ [_403814, _403816] : [-(unordered_pair(_403816, _403814) = unordered_pair(_403814, _403816))], (358 ^ _391403) ^ [_403914, _403916] : [-(set_union2(_403916, _403914) = set_union2(_403914, _403916))], (1577 ^ _391403) ^ [_447147, _447149] : [-(relation(set_intersection2(_447149, _447147))), relation(_447149), relation(_447147)], (2132 ^ _391403) ^ [_466465, _466467] : [-(_466467 = _466465), 2136 ^ _391403 : [(2139 ^ _391403) ^ [] : [in(2133 ^ [_466465, _466467], _466465)], (2137 ^ _391403) ^ [] : [-(in(2133 ^ [_466465, _466467], _466467))]], 2140 ^ _391403 : [(2143 ^ _391403) ^ [] : [in(2133 ^ [_466465, _466467], _466467)], (2141 ^ _391403) ^ [] : [-(in(2133 ^ [_466465, _466467], _466465))]]], (1456 ^ _391403) ^ [] : [true___, -(true___)], (2149 ^ _391403) ^ [_467087, _467089, _467091] : [relation(_467087), in(ordered_pair(_467091, _467089), _467087), 2156 ^ _391403 : [(2159 ^ _391403) ^ [] : [-(in(_467089, relation_field(_467087)))], (2157 ^ _391403) ^ [] : [-(in(_467091, relation_field(_467087)))]]], (2400 ^ _391403) ^ [_475840] : [-(set_difference(empty_set, _475840) = empty_set)], (2270 ^ _391403) ^ [_471399, _471401] : [disjoint(_471401, _471399), 2271 ^ _391403 : [(2272 ^ _391403) ^ [_471491] : [in(_471491, _471401), in(_471491, _471399)]]], (410 ^ _391403) ^ [_405810, _405812] : [_405812 = _405810, 413 ^ _391403 : [(416 ^ _391403) ^ [] : [-(subset(_405810, _405812))], (414 ^ _391403) ^ [] : [-(subset(_405812, _405810))]]], (1550 ^ _391403) ^ [] : [true___, -(true___)], (1111 ^ _391403) ^ [_431544, _431546] : [-(_431544 = union(_431546)), 1124 ^ _391403 : [(1129 ^ _391403) ^ [] : [in(1112 ^ [_431544, _431546], _431544)], (1127 ^ _391403) ^ [] : [-(in(1123 ^ [_431544, _431546], _431546))], (1125 ^ _391403) ^ [] : [-(in(1112 ^ [_431544, _431546], 1123 ^ [_431544, _431546]))]], 1115 ^ _391403 : [(1118 ^ _391403) ^ [_431827] : [in(1112 ^ [_431544, _431546], _431827), in(_431827, _431546)], (1116 ^ _391403) ^ [] : [-(in(1112 ^ [_431544, _431546], _431544))]]], (814 ^ _391403) ^ [_420345, _420347, _420349] : [_420345 = unordered_pair(_420349, _420347), 817 ^ _391403 : [(818 ^ _391403) ^ [_420527] : [in(_420527, _420345), -(_420527 = _420349), -(_420527 = _420347)], (828 ^ _391403) ^ [_420805] : [829 ^ _391403 : [(832 ^ _391403) ^ [] : [_420805 = _420347], (830 ^ _391403) ^ [] : [_420805 = _420349]], -(in(_420805, _420345))]]], (1862 ^ _391403) ^ [_456938, _456940, _456942] : [-(subset_difference(_456942, _456940, _456938) = set_difference(_456940, _456938)), element(_456940, powerset(_456942)), element(_456938, powerset(_456942))], (34 ^ _391403) ^ [_392623, _392625, _392627, _392629] : [-(proper_subset(_392627, _392623)), proper_subset(_392629, _392625), _392629 = _392627, _392625 = _392623], (593 ^ _391403) ^ [_412725] : [595 ^ _391403 : [(598 ^ _391403) ^ [_412962, _412964] : [594 ^ [_412725] = ordered_pair(_412964, _412962)], (596 ^ _391403) ^ [] : [-(in(594 ^ [_412725], _412725))]], -(relation(_412725))], (1683 ^ _391403) ^ [_450534, _450536] : [-(set_intersection2(_450536, _450536) = _450536)], (1221 ^ _391403) ^ [_435680] : [relation(_435680), -(relation_field(_435680) = set_union2(relation_dom(_435680), relation_rng(_435680)))], (581 ^ _391403) ^ [_412264] : [relation(_412264), 584 ^ _391403 : [(585 ^ _391403) ^ [_412412] : [in(_412412, _412264), -(_412412 = ordered_pair(588 ^ [_412264, _412412], 589 ^ [_412264, _412412]))]]], (1731 ^ _391403) ^ [_452315, _452317] : [in(_452317, _452315), -(subset(singleton(_452317), _452315))], (1661 ^ _391403) ^ [_449795] : [empty(_449795), 1664 ^ _391403 : [(1667 ^ _391403) ^ [] : [-(relation(relation_rng(_449795)))], (1665 ^ _391403) ^ [] : [-(empty(relation_rng(_449795)))]]], (350 ^ _391403) ^ [_403629] : [empty(_403629), -(relation(_403629))], (1438 ^ _391403) ^ [] : [true___, -(true___)], (2655 ^ _391403) ^ [_484387, _484389] : [in(_484389, _484387), -(subset(_484389, union(_484387)))], (1462 ^ _391403) ^ [_443686, _443688] : [element(_443686, powerset(_443688)), -(element(subset_complement(_443688, _443686), powerset(_443688)))], (1474 ^ _391403) ^ [] : [true___, -(true___)], (2074 ^ _391403) ^ [_464497, _464499, _464501] : [relation(_464497), in(ordered_pair(_464501, _464499), _464497), 2081 ^ _391403 : [(2084 ^ _391403) ^ [] : [-(in(_464499, relation_rng(_464497)))], (2082 ^ _391403) ^ [] : [-(in(_464501, relation_dom(_464497)))]]], (1337 ^ _391403) ^ [_440281, _440283] : [element(_440281, powerset(powerset(_440283))), 1340 ^ _391403 : [(1341 ^ _391403) ^ [_440461] : [element(_440461, powerset(powerset(_440283))), 1344 ^ _391403 : [(1345 ^ _391403) ^ [] : [_440461 = complements_of_subsets(_440283, _440281), 1348 ^ _391403 : [(1349 ^ _391403) ^ [_440749] : [element(_440749, powerset(_440283)), 1352 ^ _391403 : [(1359 ^ _391403) ^ [] : [in(subset_complement(_440283, _440749), _440281), -(in(_440749, _440461))], (1353 ^ _391403) ^ [] : [in(_440749, _440461), -(in(subset_complement(_440283, _440749), _440281))]]]]], (1365 ^ _391403) ^ [] : [-(_440461 = complements_of_subsets(_440283, _440281)), 1367 ^ _391403 : [(1370 ^ _391403) ^ [] : [1371 ^ _391403 : [(1374 ^ _391403) ^ [] : [in(subset_complement(_440283, 1366 ^ [_440281, _440283, _440461]), _440281)], (1372 ^ _391403) ^ [] : [-(in(1366 ^ [_440281, _440283, _440461], _440461))]], 1375 ^ _391403 : [(1378 ^ _391403) ^ [] : [in(1366 ^ [_440281, _440283, _440461], _440461)], (1376 ^ _391403) ^ [] : [-(in(subset_complement(_440283, 1366 ^ [_440281, _440283, _440461]), _440281))]]], (1368 ^ _391403) ^ [] : [-(element(1366 ^ [_440281, _440283, _440461], powerset(_440283)))]]]]]]], (1908 ^ _391403) ^ [_458606, _458608, _458610] : [relation(_458606), 1911 ^ _391403 : [(1920 ^ _391403) ^ [] : [-(in(_458610, relation_rng(relation_rng_restriction(_458608, _458606)))), in(_458610, _458608), in(_458610, relation_rng(_458606))], (1912 ^ _391403) ^ [] : [in(_458610, relation_rng(relation_rng_restriction(_458608, _458606))), 1915 ^ _391403 : [(1918 ^ _391403) ^ [] : [-(in(_458610, relation_rng(_458606)))], (1916 ^ _391403) ^ [] : [-(in(_458610, _458608))]]]]], (1725 ^ _391403) ^ [_452149, _452151] : [subset(singleton(_452151), _452149), -(in(_452151, _452149))], (1707 ^ _391403) ^ [_451470, _451472] : [in(_451472, _451470), -(set_union2(singleton(_451472), _451470) = _451470)], (1492 ^ _391403) ^ [] : [true___, -(true___)], (2007 ^ _391403) ^ [_462140, _462142, _462144] : [relation(_462140), -(relation_dom_restriction(relation_rng_restriction(_462144, _462140), _462142) = relation_rng_restriction(_462144, relation_dom_restriction(_462140, _462142)))], (1874 ^ _391403) ^ [_457363, _457365] : [disjoint(_457365, _457363), -(disjoint(_457363, _457365))], (2678 ^ _391403) ^ [_485371, _485373, _485375] : [-(in(_485371, 2674 ^ [_485375])), in(_485373, 2674 ^ [_485375]), subset(_485371, _485373)], (1888 ^ _391403) ^ [_457895, _457897, _457899, _457901] : [-(in(ordered_pair(_457901, _457899), cartesian_product2(_457897, _457895))), in(_457901, _457897), in(_457899, _457895)], (1430 ^ _391403) ^ [] : [true___, -(true___)], (172 ^ _391403) ^ [_397164, _397166, _397168, _397170] : [-(complements_of_subsets(_397170, _397166) = complements_of_subsets(_397168, _397164)), _397170 = _397168, _397166 = _397164], (86 ^ _391403) ^ [_394250, _394252, _394254, _394256] : [-(in(_394254, _394250)), in(_394256, _394252), _394256 = _394254, _394252 = _394250], (1436 ^ _391403) ^ [_443099] : [-(element(cast_to_subset(_443099), powerset(_443099)))], (2328 ^ _391403) ^ [_473409, _473411] : [subset(_473411, _473409), -(_473409 = set_union2(_473411, set_difference(_473409, _473411)))], (1603 ^ _391403) ^ [_447941] : [empty(singleton(_447941))], (1821 ^ _391403) ^ [] : [-(empty(1819 ^ []))], (2402 ^ _391403) ^ [_475964, _475966, _475968] : [-(element(_475968, _475964)), in(_475968, _475966), element(_475966, powerset(_475964))], (2479 ^ _391403) ^ [_478573, _478575] : [subset(_478575, _478573), proper_subset(_478573, _478575)], (2175 ^ _391403) ^ [_468053, _468055] : [-(subset(set_difference(_468055, _468053), _468055))], (959 ^ _391403) ^ [_425874] : [relation(_425874), 962 ^ _391403 : [(963 ^ _391403) ^ [_426032] : [relation(_426032), 966 ^ _391403 : [(967 ^ _391403) ^ [] : [subset(_425874, _426032), 970 ^ _391403 : [(971 ^ _391403) ^ [_426308, _426310] : [in(ordered_pair(_426310, _426308), _425874), -(in(ordered_pair(_426310, _426308), _426032))]]], (977 ^ _391403) ^ [] : [980 ^ _391403 : [(983 ^ _391403) ^ [] : [in(ordered_pair(978 ^ [_425874, _426032], 979 ^ [_425874, _426032]), _426032)], (981 ^ _391403) ^ [] : [-(in(ordered_pair(978 ^ [_425874, _426032], 979 ^ [_425874, _426032]), _425874))]], -(subset(_425874, _426032))]]]]], (1691 ^ _391403) ^ [_450858] : [relation(_450858), -(relation_inverse(relation_inverse(_450858)) = _450858)], (2477 ^ _391403) ^ [] : [-(relation_rng(empty_set) = empty_set)], (1981 ^ _391403) ^ [_461271, _461273, _461275] : [-(in(_461271, 1977 ^ [_461275])), in(_461273, 1977 ^ [_461275]), subset(_461271, _461273)], (202 ^ _391403) ^ [_398257, _398259, _398261, _398263] : [-(meet_of_subsets(_398263, _398259) = meet_of_subsets(_398261, _398257)), _398263 = _398261, _398259 = _398257], (1840 ^ _391403) ^ [] : [-(relation(1836 ^ []))], (2318 ^ _391403) ^ [_473043] : [relation(_473043), 2321 ^ _391403 : [(2322 ^ _391403) ^ [_473180] : [relation(_473180), -(subset(relation_rng(relation_composition(_473043, _473180)), relation_rng(_473180)))]]], (2072 ^ _391403) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (20 ^ _391403) ^ [_392179, _392181, _392183, _392185] : [-(element(_392183, _392179)), element(_392185, _392181), _392185 = _392183, _392181 = _392179], (110 ^ _391403) ^ [_394969, _394971, _394973, _394975] : [-(subset(_394973, _394969)), subset(_394975, _394971), _394975 = _394973, _394971 = _394969], (1522 ^ _391403) ^ [_445424, _445426, _445428] : [-(element(subset_difference(_445428, _445426, _445424), powerset(_445428))), element(_445426, powerset(_445428)), element(_445424, powerset(_445428))], (1227 ^ _391403) ^ [_435886] : [relation(_435886), 1230 ^ _391403 : [(1231 ^ _391403) ^ [_436046] : [relation(_436046), 1234 ^ _391403 : [(1235 ^ _391403) ^ [] : [_436046 = relation_inverse(_435886), 1238 ^ _391403 : [(1245 ^ _391403) ^ [_436545, _436547] : [in(ordered_pair(_436545, _436547), _435886), -(in(ordered_pair(_436547, _436545), _436046))], (1239 ^ _391403) ^ [_436355, _436357] : [in(ordered_pair(_436357, _436355), _436046), -(in(ordered_pair(_436355, _436357), _435886))]]], (1251 ^ _391403) ^ [] : [-(_436046 = relation_inverse(_435886)), 1256 ^ _391403 : [(1259 ^ _391403) ^ [] : [in(ordered_pair(1253 ^ [_435886, _436046], 1252 ^ [_435886, _436046]), _435886)], (1257 ^ _391403) ^ [] : [-(in(ordered_pair(1252 ^ [_435886, _436046], 1253 ^ [_435886, _436046]), _436046))]], 1260 ^ _391403 : [(1263 ^ _391403) ^ [] : [in(ordered_pair(1252 ^ [_435886, _436046], 1253 ^ [_435886, _436046]), _436046)], (1261 ^ _391403) ^ [] : [-(in(ordered_pair(1253 ^ [_435886, _436046], 1252 ^ [_435886, _436046]), _435886))]]]]]]], (1880 ^ _391403) ^ [_457630, _457632, _457634, _457636] : [in(ordered_pair(_457636, _457634), cartesian_product2(_457632, _457630)), 1883 ^ _391403 : [(1886 ^ _391403) ^ [] : [-(in(_457634, _457630))], (1884 ^ _391403) ^ [] : [-(in(_457636, _457632))]]], (1621 ^ _391403) ^ [] : [-(relation(empty_set))], (1267 ^ _391403) ^ [_437393, _437395] : [disjoint(_437395, _437393), -(set_intersection2(_437395, _437393) = empty_set)], (480 ^ _391403) ^ [_408293, _408295] : [relation(_408293), 483 ^ _391403 : [(484 ^ _391403) ^ [_408464] : [relation(_408464), 487 ^ _391403 : [(488 ^ _391403) ^ [] : [_408464 = relation_rng_restriction(_408295, _408293), 491 ^ _391403 : [(500 ^ _391403) ^ [_409070, _409072] : [-(in(ordered_pair(_409072, _409070), _408464)), in(_409070, _408295), in(ordered_pair(_409072, _409070), _408293)], (492 ^ _391403) ^ [_408791, _408793] : [in(ordered_pair(_408793, _408791), _408464), 495 ^ _391403 : [(498 ^ _391403) ^ [] : [-(in(ordered_pair(_408793, _408791), _408293))], (496 ^ _391403) ^ [] : [-(in(_408791, _408295))]]]]], (510 ^ _391403) ^ [] : [-(_408464 = relation_rng_restriction(_408295, _408293)), 523 ^ _391403 : [(528 ^ _391403) ^ [] : [in(ordered_pair(511 ^ [_408293, _408295, _408464], 512 ^ [_408293, _408295, _408464]), _408464)], (526 ^ _391403) ^ [] : [-(in(ordered_pair(511 ^ [_408293, _408295, _408464], 512 ^ [_408293, _408295, _408464]), _408293))], (524 ^ _391403) ^ [] : [-(in(512 ^ [_408293, _408295, _408464], _408295))]], 515 ^ _391403 : [(518 ^ _391403) ^ [] : [in(512 ^ [_408293, _408295, _408464], _408295), in(ordered_pair(511 ^ [_408293, _408295, _408464], 512 ^ [_408293, _408295, _408464]), _408293)], (516 ^ _391403) ^ [] : [-(in(ordered_pair(511 ^ [_408293, _408295, _408464], 512 ^ [_408293, _408295, _408464]), _408464))]]]]]]], (1049 ^ _391403) ^ [_429135] : [relation(_429135), 1052 ^ _391403 : [(1053 ^ _391403) ^ [_429316] : [_429316 = relation_dom(_429135), 1056 ^ _391403 : [(1064 ^ _391403) ^ [_429740] : [1065 ^ _391403 : [(1066 ^ _391403) ^ [_429819] : [in(ordered_pair(_429740, _429819), _429135)]], -(in(_429740, _429316))], (1057 ^ _391403) ^ [_429496] : [in(_429496, _429316), -(in(ordered_pair(_429496, 1060 ^ [_429135, _429316, _429496]), _429135))]]], (1070 ^ _391403) ^ [_429947] : [-(_429947 = relation_dom(_429135)), 1074 ^ _391403 : [(1077 ^ _391403) ^ [_430210] : [in(ordered_pair(1071 ^ [_429135, _429947], _430210), _429135)], (1075 ^ _391403) ^ [] : [-(in(1071 ^ [_429135, _429947], _429947))]], 1079 ^ _391403 : [(1082 ^ _391403) ^ [] : [in(1071 ^ [_429135, _429947], _429947)], (1080 ^ _391403) ^ [] : [-(in(ordered_pair(1071 ^ [_429135, _429947], 1078 ^ [_429135, _429947]), _429135))]]]]], (428 ^ _391403) ^ [_406334] : [relation(_406334), 431 ^ _391403 : [(432 ^ _391403) ^ [_406520, _406522] : [relation(_406520), 435 ^ _391403 : [(436 ^ _391403) ^ [] : [_406520 = relation_dom_restriction(_406334, _406522), 439 ^ _391403 : [(448 ^ _391403) ^ [_407124, _407126] : [-(in(ordered_pair(_407126, _407124), _406520)), in(_407126, _406522), in(ordered_pair(_407126, _407124), _406334)], (440 ^ _391403) ^ [_406845, _406847] : [in(ordered_pair(_406847, _406845), _406520), 443 ^ _391403 : [(446 ^ _391403) ^ [] : [-(in(ordered_pair(_406847, _406845), _406334))], (444 ^ _391403) ^ [] : [-(in(_406847, _406522))]]]]], (458 ^ _391403) ^ [] : [-(_406520 = relation_dom_restriction(_406334, _406522)), 471 ^ _391403 : [(476 ^ _391403) ^ [] : [in(ordered_pair(459 ^ [_406334, _406520, _406522], 460 ^ [_406334, _406520, _406522]), _406520)], (474 ^ _391403) ^ [] : [-(in(ordered_pair(459 ^ [_406334, _406520, _406522], 460 ^ [_406334, _406520, _406522]), _406334))], (472 ^ _391403) ^ [] : [-(in(459 ^ [_406334, _406520, _406522], _406522))]], 463 ^ _391403 : [(466 ^ _391403) ^ [] : [in(459 ^ [_406334, _406520, _406522], _406522), in(ordered_pair(459 ^ [_406334, _406520, _406522], 460 ^ [_406334, _406520, _406522]), _406334)], (464 ^ _391403) ^ [] : [-(in(ordered_pair(459 ^ [_406334, _406520, _406522], 460 ^ [_406334, _406520, _406522]), _406520))]]]]]]], (284 ^ _391403) ^ [_401206, _401208, _401210, _401212] : [-(relation_dom_restriction(_401212, _401208) = relation_dom_restriction(_401210, _401206)), _401212 = _401210, _401208 = _401206], (1563 ^ _391403) ^ [_446657] : [-(element(1561 ^ [_446657], _446657))], (1669 ^ _391403) ^ [_450074, _450076] : [1676 ^ _391403 : [(1679 ^ _391403) ^ [] : [-(relation(relation_composition(_450076, _450074)))], (1677 ^ _391403) ^ [] : [-(empty(relation_composition(_450076, _450074)))]], empty(_450076), relation(_450074)], (1697 ^ _391403) ^ [_451068, _451070] : [element(_451068, powerset(powerset(_451070))), -(complements_of_subsets(_451070, complements_of_subsets(_451070, _451068)) = _451068)], (196 ^ _391403) ^ [_398011, _398013] : [_398013 = _398011, -(cast_to_subset(_398013) = cast_to_subset(_398011))], (532 ^ _391403) ^ [_410216] : [relation(_410216), 535 ^ _391403 : [(536 ^ _391403) ^ [_410423, _410425] : [_410423 = relation_image(_410216, _410425), 539 ^ _391403 : [(549 ^ _391403) ^ [_410969] : [-(in(_410969, _410423)), 550 ^ _391403 : [(551 ^ _391403) ^ [_411074] : [in(ordered_pair(_411074, _410969), _410216), in(_411074, _410425)]]], (540 ^ _391403) ^ [_410615] : [in(_410615, _410423), 544 ^ _391403 : [(547 ^ _391403) ^ [] : [-(in(543 ^ [_410216, _410423, _410425, _410615], _410425))], (545 ^ _391403) ^ [] : [-(in(ordered_pair(543 ^ [_410216, _410423, _410425, _410615], _410615), _410216))]]]]], (559 ^ _391403) ^ [_411329, _411331] : [-(_411329 = relation_image(_410216, _411331)), 572 ^ _391403 : [(577 ^ _391403) ^ [] : [in(560 ^ [_410216, _411329, _411331], _411329)], (575 ^ _391403) ^ [] : [-(in(571 ^ [_410216, _411329, _411331], _411331))], (573 ^ _391403) ^ [] : [-(in(ordered_pair(571 ^ [_410216, _411329, _411331], 560 ^ [_410216, _411329, _411331]), _410216))]], 563 ^ _391403 : [(566 ^ _391403) ^ [_411633] : [in(ordered_pair(_411633, 560 ^ [_410216, _411329, _411331]), _410216), in(_411633, _411331)], (564 ^ _391403) ^ [] : [-(in(560 ^ [_410216, _411329, _411331], _411329))]]]]], (2161 ^ _391403) ^ [_467499, _467501, _467503] : [subset(_467503, _467501), -(subset(set_difference(_467503, _467499), set_difference(_467501, _467499)))], (1219 ^ _391403) ^ [_435574, _435576] : [-(ordered_pair(_435576, _435574) = unordered_pair(unordered_pair(_435576, _435574), singleton(_435576)))], (2425 ^ _391403) ^ [_476757] : [-(_476757 = empty_set), 2428 ^ _391403 : [(2429 ^ _391403) ^ [_476917] : [element(_476917, powerset(_476757)), 2432 ^ _391403 : [(2433 ^ _391403) ^ [_477071] : [element(_477071, _476757), -(in(_477071, _476917)), -(in(_477071, subset_complement(_476757, _476917)))]]]]], (2529 ^ _391403) ^ [_480100, _480102] : [-(in(_480100, _480102)), -(set_difference(_480102, singleton(_480100)) = _480102)], (798 ^ _391403) ^ [_419845, _419847] : [empty(_419847), 801 ^ _391403 : [(808 ^ _391403) ^ [] : [empty(_419845), -(element(_419845, _419847))], (802 ^ _391403) ^ [] : [element(_419845, _419847), -(empty(_419845))]]], (2280 ^ _391403) ^ [_471748] : [subset(_471748, empty_set), -(_471748 = empty_set)], (1749 ^ _391403) ^ [_452946, _452948] : [element(_452946, powerset(_452948)), 1752 ^ _391403 : [(1753 ^ _391403) ^ [_453087] : [in(_453087, _452946), -(in(_453087, _452948))]]], (2398 ^ _391403) ^ [_475751, _475753] : [-(set_difference(_475753, set_difference(_475753, _475751)) = set_intersection2(_475753, _475751))], (2575 ^ _391403) ^ [_481687, _481689] : [in(_481689, _481687), empty(_481687)], (48 ^ _391403) ^ [_393067, _393069, _393071, _393073] : [-(disjoint(_393071, _393067)), disjoint(_393073, _393069), _393073 = _393071, _393069 = _393067], (1705 ^ _391403) ^ [_451361] : [singleton(_451361) = empty_set], (1703 ^ _391403) ^ [_451282, _451284] : [proper_subset(_451284, _451284)], (1155 ^ _391403) ^ [_433165, _433167, _433169] : [-(_433165 = set_difference(_433169, _433167)), 1167 ^ _391403 : [(1172 ^ _391403) ^ [] : [in(1156 ^ [_433165, _433167, _433169], _433165)], (1170 ^ _391403) ^ [] : [in(1156 ^ [_433165, _433167, _433169], _433167)], (1168 ^ _391403) ^ [] : [-(in(1156 ^ [_433165, _433167, _433169], _433169))]], 1159 ^ _391403 : [(1162 ^ _391403) ^ [] : [in(1156 ^ [_433165, _433167, _433169], _433169), -(in(1156 ^ [_433165, _433167, _433169], _433167))], (1160 ^ _391403) ^ [] : [-(in(1156 ^ [_433165, _433167, _433169], _433165))]]], (836 ^ _391403) ^ [_421070, _421072, _421074] : [-(_421070 = unordered_pair(_421074, _421072)), 840 ^ _391403 : [(845 ^ _391403) ^ [] : [837 ^ [_421070, _421072, _421074] = _421072], (843 ^ _391403) ^ [] : [837 ^ [_421070, _421072, _421074] = _421074], (841 ^ _391403) ^ [] : [-(in(837 ^ [_421070, _421072, _421074], _421070))]], 846 ^ _391403 : [(847 ^ _391403) ^ [] : [-(837 ^ [_421070, _421072, _421074] = _421074), -(837 ^ [_421070, _421072, _421074] = _421072)], (853 ^ _391403) ^ [] : [in(837 ^ [_421070, _421072, _421074], _421070)]]], (2465 ^ _391403) ^ [_478155, _478157, _478159] : [in(_478159, _478157), element(_478157, powerset(_478155)), empty(_478155)], (2261 ^ _391403) ^ [_471085, _471087] : [-(disjoint(_471087, _471085)), 2265 ^ _391403 : [(2268 ^ _391403) ^ [] : [-(in(2264 ^ [_471085, _471087], _471085))], (2266 ^ _391403) ^ [] : [-(in(2264 ^ [_471085, _471087], _471087))]]], (2688 ^ _391403) ^ [_485686, _485688] : [in(_485686, 2674 ^ [_485688]), 2692 ^ _391403 : [(2695 ^ _391403) ^ [_485998] : [subset(_485998, _485686), -(in(_485998, 2691 ^ [_485686, _485688]))], (2693 ^ _391403) ^ [] : [-(in(2691 ^ [_485686, _485688], 2674 ^ [_485688]))]]], (312 ^ _391403) ^ [_402219, _402221, _402223, _402225] : [-(unordered_pair(_402225, _402221) = unordered_pair(_402223, _402219)), _402225 = _402223, _402221 = _402219], (242 ^ _391403) ^ [_399693, _399695, _399697, _399699] : [-(set_union2(_399699, _399695) = set_union2(_399697, _399693)), _399699 = _399697, _399695 = _399693], (1544 ^ _391403) ^ [_446197, _446199] : [relation(_446197), -(relation(relation_rng_restriction(_446199, _446197)))], (1835 ^ _391403) ^ [] : [-(empty(1833 ^ []))], (1086 ^ _391403) ^ [_430561] : [-(cast_to_subset(_430561) = _430561)], (1787 ^ _391403) ^ [_454229, _454231] : [in(_454231, _454229), -(subset(_454231, union(_454229)))], (306 ^ _391403) ^ [_401973, _401975] : [_401975 = _401973, -(singleton(_401975) = singleton(_401973))], (2617 ^ _391403) ^ [_483079, _483081] : [relation(_483079), -(subset(relation_dom_restriction(_483079, _483081), _483079))], (1006 ^ _391403) ^ [_427671, _427673, _427675] : [_427671 = set_intersection2(_427675, _427673), 1009 ^ _391403 : [(1018 ^ _391403) ^ [_428112] : [-(in(_428112, _427671)), in(_428112, _427675), in(_428112, _427673)], (1010 ^ _391403) ^ [_427853] : [in(_427853, _427671), 1013 ^ _391403 : [(1016 ^ _391403) ^ [] : [-(in(_427853, _427673))], (1014 ^ _391403) ^ [] : [-(in(_427853, _427675))]]]]], (1685 ^ _391403) ^ [_450646, _450648] : [element(_450646, powerset(_450648)), -(subset_complement(_450648, subset_complement(_450648, _450646)) = _450646)], (1611 ^ _391403) ^ [_448249, _448251] : [empty(unordered_pair(_448251, _448249))], (300 ^ _391403) ^ [_401755, _401757] : [_401757 = _401755, -(powerset(_401757) = powerset(_401755))], (2388 ^ _391403) ^ [_475426, _475428] : [element(_475426, powerset(powerset(_475428))), -(_475426 = empty_set), -(union_of_subsets(_475428, complements_of_subsets(_475428, _475426)) = subset_difference(_475428, cast_to_subset(_475428), meet_of_subsets(_475428, _475426)))], (651 ^ _391403) ^ [_414860, _414862] : [_414862 = empty_set, 654 ^ _391403 : [(661 ^ _391403) ^ [] : [_414860 = empty_set, -(_414860 = set_meet(_414862))], (655 ^ _391403) ^ [] : [_414860 = set_meet(_414862), -(_414860 = empty_set)]]], (1848 ^ _391403) ^ [] : [empty(1846 ^ [])], (1088 ^ _391403) ^ [_430699, _430701] : [_430699 = union(_430701), 1091 ^ _391403 : [(1101 ^ _391403) ^ [_431207] : [-(in(_431207, _430699)), 1102 ^ _391403 : [(1103 ^ _391403) ^ [_431305] : [in(_431207, _431305), in(_431305, _430701)]]], (1092 ^ _391403) ^ [_430880] : [in(_430880, _430699), 1096 ^ _391403 : [(1099 ^ _391403) ^ [] : [-(in(1095 ^ [_430699, _430701, _430880], _430701))], (1097 ^ _391403) ^ [] : [-(in(_430880, 1095 ^ [_430699, _430701, _430880]))]]]]], (1514 ^ _391403) ^ [_445074] : [-(relation(identity_relation(_445074)))], (1979 ^ _391403) ^ [_461159] : [-(in(_461159, 1977 ^ [_461159]))], (2443 ^ _391403) ^ [_477417, _477419, _477421] : [element(_477417, powerset(_477421)), in(_477419, subset_complement(_477421, _477417)), in(_477419, _477417)], (1273 ^ _391403) ^ [_437561, _437563] : [set_intersection2(_437563, _437561) = empty_set, -(disjoint(_437563, _437561))], (1418 ^ _391403) ^ [] : [true___, -(true___)], (1613 ^ _391403) ^ [_448360, _448362] : [-(empty(_448362)), empty(set_union2(_448360, _448362))], (2412 ^ _391403) ^ [_476297, _476299] : [-(disjoint(_476299, _476297)), -(in(2415 ^ [_476297, _476299], set_intersection2(_476299, _476297)))], (2120 ^ _391403) ^ [_466057] : [-(set_intersection2(_466057, empty_set) = empty_set)], (2549 ^ _391403) ^ [_480805] : [-(relation_dom(identity_relation(_480805)) = _480805)], (1956 ^ _391403) ^ [_460250, _460252] : [relation(_460250), -(relation_rng(relation_rng_restriction(_460252, _460250)) = set_intersection2(relation_rng(_460250), _460252))], (1793 ^ _391403) ^ [_454500, _454502, _454504, _454506] : [in(ordered_pair(_454506, _454504), cartesian_product2(_454502, _454500)), 1796 ^ _391403 : [(1799 ^ _391403) ^ [] : [-(in(_454504, _454500))], (1797 ^ _391403) ^ [] : [-(in(_454506, _454502))]]], (1468 ^ _391403) ^ [] : [true___, -(true___)], (182 ^ _391403) ^ [_397551, _397553, _397555, _397557, _397559, _397561] : [-(subset_difference(_397561, _397557, _397553) = subset_difference(_397559, _397555, _397551)), _397561 = _397559, _397557 = _397555, _397553 = _397551], (232 ^ _391403) ^ [_399334, _399336, _399338, _399340] : [-(set_difference(_399340, _399336) = set_difference(_399338, _399334)), _399340 = _399338, _399336 = _399334], (1424 ^ _391403) ^ [] : [true___, -(true___)], (1538 ^ _391403) ^ [_445965, _445967] : [element(_445965, powerset(powerset(_445967))), -(element(complements_of_subsets(_445967, _445965), powerset(powerset(_445967))))], (1480 ^ _391403) ^ [_444134] : [relation(_444134), -(relation(relation_inverse(_444134)))], (1412 ^ _391403) ^ [] : [true___, -(true___)], (782 ^ _391403) ^ [_419432, _419434] : [-(empty(_419434)), 785 ^ _391403 : [(792 ^ _391403) ^ [] : [in(_419432, _419434), -(element(_419432, _419434))], (786 ^ _391403) ^ [] : [element(_419432, _419434), -(in(_419432, _419434))]]], (2054 ^ _391403) ^ [_463787] : [-(set_union2(_463787, empty_set) = _463787)], (2086 ^ _391403) ^ [_464881] : [relation(_464881), -(subset(_464881, cartesian_product2(relation_dom(_464881), relation_rng(_464881))))], (1565 ^ _391403) ^ [_446769, _446771] : [1572 ^ _391403 : [(1575 ^ _391403) ^ [] : [-(relation(relation_composition(_446769, _446771)))], (1573 ^ _391403) ^ [] : [-(empty(relation_composition(_446769, _446771)))]], empty(_446771), relation(_446769)], (742 ^ _391403) ^ [_417942] : [relation(_417942), 745 ^ _391403 : [(746 ^ _391403) ^ [_418100] : [relation(_418100), 749 ^ _391403 : [(750 ^ _391403) ^ [] : [_417942 = _418100, 753 ^ _391403 : [(760 ^ _391403) ^ [_418595, _418597] : [in(ordered_pair(_418597, _418595), _418100), -(in(ordered_pair(_418597, _418595), _417942))], (754 ^ _391403) ^ [_418405, _418407] : [in(ordered_pair(_418407, _418405), _417942), -(in(ordered_pair(_418407, _418405), _418100))]]], (766 ^ _391403) ^ [] : [-(_417942 = _418100), 771 ^ _391403 : [(774 ^ _391403) ^ [] : [in(ordered_pair(767 ^ [_417942, _418100], 768 ^ [_417942, _418100]), _418100)], (772 ^ _391403) ^ [] : [-(in(ordered_pair(767 ^ [_417942, _418100], 768 ^ [_417942, _418100]), _417942))]], 775 ^ _391403 : [(778 ^ _391403) ^ [] : [in(ordered_pair(767 ^ [_417942, _418100], 768 ^ [_417942, _418100]), _417942)], (776 ^ _391403) ^ [] : [-(in(ordered_pair(767 ^ [_417942, _418100], 768 ^ [_417942, _418100]), _418100))]]]]]]], (2227 ^ _391403) ^ [_469872, _469874] : [-(set_union2(_469874, set_difference(_469872, _469874)) = set_union2(_469874, _469872))], (1719 ^ _391403) ^ [_451903, _451905] : [-(in(_451905, _451903)), -(disjoint(singleton(_451905), _451903))], (2114 ^ _391403) ^ [_465870, _465872] : [subset(_465872, _465870), -(set_intersection2(_465872, _465870) = _465872)], (268 ^ _391403) ^ [_400629, _400631, _400633, _400635] : [-(relation_composition(_400635, _400631) = relation_composition(_400633, _400629)), _400635 = _400633, _400631 = _400629], (1176 ^ _391403) ^ [_433908] : [relation(_433908), 1179 ^ _391403 : [(1180 ^ _391403) ^ [_434089] : [_434089 = relation_rng(_433908), 1183 ^ _391403 : [(1191 ^ _391403) ^ [_434513] : [1192 ^ _391403 : [(1193 ^ _391403) ^ [_434592] : [in(ordered_pair(_434592, _434513), _433908)]], -(in(_434513, _434089))], (1184 ^ _391403) ^ [_434269] : [in(_434269, _434089), -(in(ordered_pair(1187 ^ [_433908, _434089, _434269], _434269), _433908))]]], (1197 ^ _391403) ^ [_434720] : [-(_434720 = relation_rng(_433908)), 1201 ^ _391403 : [(1204 ^ _391403) ^ [_434983] : [in(ordered_pair(_434983, 1198 ^ [_433908, _434720]), _433908)], (1202 ^ _391403) ^ [] : [-(in(1198 ^ [_433908, _434720], _434720))]], 1206 ^ _391403 : [(1209 ^ _391403) ^ [] : [in(1198 ^ [_433908, _434720], _434720)], (1207 ^ _391403) ^ [] : [-(in(ordered_pair(1205 ^ [_433908, _434720], 1198 ^ [_433908, _434720]), _433908))]]]]], (2348 ^ _391403) ^ [_474090, _474092] : [element(_474090, powerset(powerset(_474092))), -(_474090 = empty_set), complements_of_subsets(_474092, _474090) = empty_set], (2673 ^ _391403) ^ [_485018] : [-(union(powerset(_485018)) = _485018)], (2551 ^ _391403) ^ [_480853] : [-(relation_rng(identity_relation(_480853)) = _480853)], (2229 ^ _391403) ^ [_470019, _470021] : [subset(_470021, singleton(_470019)), -(_470021 = empty_set), -(_470021 = singleton(_470019))], (222 ^ _391403) ^ [_398975, _398977, _398979, _398981] : [-(ordered_pair(_398981, _398977) = ordered_pair(_398979, _398975)), _398981 = _398979, _398977 = _398975], (2013 ^ _391403) ^ [_462392, _462394, _462396] : [relation(_462392), 2016 ^ _391403 : [(2028 ^ _391403) ^ [] : [-(in(_462396, relation_image(_462392, _462394))), 2029 ^ _391403 : [(2030 ^ _391403) ^ [_462993] : [in(_462993, relation_dom(_462392)), in(ordered_pair(_462993, _462396), _462392), in(_462993, _462394)]]], (2017 ^ _391403) ^ [] : [in(_462396, relation_image(_462392, _462394)), 2021 ^ _391403 : [(2026 ^ _391403) ^ [] : [-(in(2020 ^ [_462392, _462394, _462396], _462394))], (2024 ^ _391403) ^ [] : [-(in(ordered_pair(2020 ^ [_462392, _462394, _462396], _462396), _462392))], (2022 ^ _391403) ^ [] : [-(in(2020 ^ [_462392, _462394, _462396], relation_dom(_462392)))]]]]], (72 ^ _391403) ^ [_393806, _393808, _393810, _393812] : [-(are_equipotent(_393810, _393806)), are_equipotent(_393812, _393808), _393812 = _393810, _393808 = _393806], (124 ^ _391403) ^ [_395405, _395407] : [_395407 = _395405, -(set_meet(_395407) = set_meet(_395405))], (2288 ^ _391403) ^ [_472055, _472057] : [element(_472055, powerset(_472057)), 2291 ^ _391403 : [(2292 ^ _391403) ^ [_472207] : [element(_472207, powerset(_472057)), 2295 ^ _391403 : [(2302 ^ _391403) ^ [] : [subset(_472055, subset_complement(_472057, _472207)), -(disjoint(_472055, _472207))], (2296 ^ _391403) ^ [] : [disjoint(_472055, _472207), -(subset(_472055, subset_complement(_472057, _472207)))]]]]], (1872 ^ _391403) ^ [_457254, _457256] : [-(subset(_457256, _457256))], (1498 ^ _391403) ^ [_444576, _444578] : [-(relation(relation_composition(_444578, _444576))), relation(_444578), relation(_444576)], (987 ^ _391403) ^ [_426957, _426959] : [subset(_426959, _426957), 990 ^ _391403 : [(991 ^ _391403) ^ [_427094] : [in(_427094, _426959), -(in(_427094, _426957))]]], (338 ^ _391403) ^ [_403221, _403223] : [in(_403223, _403221), in(_403221, _403223)], (262 ^ _391403) ^ [_400383, _400385] : [_400385 = _400383, -(relation_dom(_400385) = relation_dom(_400383))], (2044 ^ _391403) ^ [_463501, _463503, _463505] : [-(subset(_463505, set_intersection2(_463503, _463501))), subset(_463505, _463503), subset(_463505, _463501)], (1838 ^ _391403) ^ [] : [empty(1836 ^ [])], (212 ^ _391403) ^ [_398616, _398618, _398620, _398622] : [-(subset_complement(_398622, _398618) = subset_complement(_398620, _398616)), _398622 = _398620, _398618 = _398616]], input).
% 69.63/67.72  ncf('1',plain,[-(relation(2717 ^ []))],start(2719 ^ 0)).
% 69.63/67.72  ncf('1.1',plain,[relation(2717 ^ []), in(ordered_pair(2020 ^ [2717 ^ [], 2716 ^ [], 998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]], 998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]), 2717 ^ []), 2084 : -(in(998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])], relation_rng(2717 ^ [])))],extension(2074 ^ 1,bind([[_464497, _464499, _464501], [2717 ^ [], 998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])], 2020 ^ [2717 ^ [], 2716 ^ [], 998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]]]]))).
% 69.63/67.72  ncf('1.1.1',plain,[-(in(ordered_pair(2020 ^ [2717 ^ [], 2716 ^ [], 998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]], 998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]), 2717 ^ [])), 2017 : in(998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])], relation_image(2717 ^ [], 2716 ^ [])), 2017 : relation(2717 ^ [])],extension(2013 ^ 2,bind([[_462392, _462394, _462396], [2717 ^ [], 2716 ^ [], 998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]]]))).
% 69.63/67.72  ncf('1.1.1.1',plain,[-(in(998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])], relation_image(2717 ^ [], 2716 ^ []))), -(subset(relation_image(2717 ^ [], 2716 ^ []), relation_rng(2717 ^ [])))],extension(997 ^ 5,bind([[_427271, _427273], [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]]))).
% 69.63/67.72  ncf('1.1.1.1.1',plain,[subset(relation_image(2717 ^ [], 2716 ^ []), relation_rng(2717 ^ []))],extension(2721 ^ 6)).
% 69.63/67.72  ncf('1.1.1.2',plain,[-(relation(2717 ^ []))],reduction('1')).
% 69.63/67.72  ncf('1.1.2',plain,[in(998 ^ [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])], relation_rng(2717 ^ [])), -(subset(relation_image(2717 ^ [], 2716 ^ []), relation_rng(2717 ^ [])))],extension(997 ^ 4,bind([[_427271, _427273], [relation_rng(2717 ^ []), relation_image(2717 ^ [], 2716 ^ [])]]))).
% 69.63/67.72  ncf('1.1.2.1',plain,[subset(relation_image(2717 ^ [], 2716 ^ []), relation_rng(2717 ^ []))],extension(2721 ^ 5)).
% 69.63/67.72  %-----------------------------------------------------
% 69.63/67.72  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------