%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU189+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n017.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 12:02:35 EDT 2023

% Result   : Theorem 55.40s 54.10s
% Output   : Proof 55.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SEU189+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n017.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May 18 12:28:00 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 55.40/54.10  
% 55.40/54.10  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 55.40/54.10  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.40/54.10  %-----------------------------------------------------
% 55.40/54.10  ncf(matrix, plain, [(2192 ^ _403744) ^ [] : [2193 ^ _403744 : [(2196 ^ _403744) ^ [] : [relation_rng(2188 ^ []) = empty_set], (2194 ^ _403744) ^ [] : [-(relation_dom(2188 ^ []) = empty_set)]], 2197 ^ _403744 : [(2200 ^ _403744) ^ [] : [relation_dom(2188 ^ []) = empty_set], (2198 ^ _403744) ^ [] : [-(relation_rng(2188 ^ []) = empty_set)]]], (2190 ^ _403744) ^ [] : [-(relation(2188 ^ []))], !, (232 ^ _325847) ^ [_333778, _333780, _333782, _333784] : [-(ordered_pair(_333784, _333780) = ordered_pair(_333782, _333778)), _333784 = _333782, _333780 = _333778], (1622 ^ _325847) ^ [_382705, _382707, _382709] : [-(subset(_382709, _382705)), subset(_382709, _382707), subset(_382707, _382705)], (62 ^ _325847) ^ [_327927, _327929] : [-(empty(_327927)), _327929 = _327927, empty(_327929)], (1888 ^ _325847) ^ [_391993, _391995] : [subset(_391995, _391993), -(_391993 = set_union2(_391995, set_difference(_391993, _391995)))], (130 ^ _325847) ^ [_330095, _330097, _330099, _330101] : [-(cartesian_product2(_330101, _330097) = cartesian_product2(_330099, _330095)), _330101 = _330099, _330097 = _330095], (1674 ^ _325847) ^ [_384454, _384456] : [subset(_384456, _384454), -(set_intersection2(_384456, _384454) = _384456)], (962 ^ _325847) ^ [_360473, _360475] : [disjoint(_360475, _360473), -(set_intersection2(_360475, _360473) = empty_set)], (701 ^ _325847) ^ [_350751, _350753, _350755] : [_350751 = set_intersection2(_350755, _350753), 704 ^ _325847 : [(713 ^ _325847) ^ [_351192] : [-(in(_351192, _350751)), in(_351192, _350755), in(_351192, _350753)], (705 ^ _325847) ^ [_350933] : [in(_350933, _350751), 708 ^ _325847 : [(711 ^ _325847) ^ [] : [-(in(_350933, _350753))], (709 ^ _325847) ^ [] : [-(in(_350933, _350755))]]]]], (1486 ^ _325847) ^ [_377668] : [-(empty(1482 ^ [_377668]))], (1442 ^ _325847) ^ [_376168, _376170, _376172, _376174] : [-(in(ordered_pair(_376174, _376172), cartesian_product2(_376170, _376168))), in(_376174, _376170), in(_376172, _376168)], (414 ^ _325847) ^ [_340436, _340438] : [_340438 = empty_set, 417 ^ _325847 : [(424 ^ _325847) ^ [] : [_340436 = empty_set, -(_340436 = set_meet(_340438))], (418 ^ _325847) ^ [] : [_340436 = set_meet(_340438), -(_340436 = empty_set)]]], (974 ^ _325847) ^ [_360845] : [relation(_360845), 977 ^ _325847 : [(978 ^ _325847) ^ [_361030] : [relation(_361030), 981 ^ _325847 : [(982 ^ _325847) ^ [_361211] : [relation(_361211), 985 ^ _325847 : [(986 ^ _325847) ^ [] : [_361211 = relation_composition(_360845, _361030), 989 ^ _325847 : [(999 ^ _325847) ^ [_361931, _361933] : [-(in(ordered_pair(_361933, _361931), _361211)), 1000 ^ _325847 : [(1001 ^ _325847) ^ [_362044] : [in(ordered_pair(_361933, _362044), _360845), in(ordered_pair(_362044, _361931), _361030)]]], (990 ^ _325847) ^ [_361546, _361548] : [in(ordered_pair(_361548, _361546), _361211), 994 ^ _325847 : [(997 ^ _325847) ^ [] : [-(in(ordered_pair(993 ^ [_360845, _361030, _361211, _361546, _361548], _361546), _361030))], (995 ^ _325847) ^ [] : [-(in(ordered_pair(_361548, 993 ^ [_360845, _361030, _361211, _361546, _361548]), _360845))]]]]], (1009 ^ _325847) ^ [] : [-(_361211 = relation_composition(_360845, _361030)), 1023 ^ _325847 : [(1028 ^ _325847) ^ [] : [in(ordered_pair(1010 ^ [_360845, _361030, _361211], 1011 ^ [_360845, _361030, _361211]), _361211)], (1026 ^ _325847) ^ [] : [-(in(ordered_pair(1022 ^ [_360845, _361030, _361211], 1011 ^ [_360845, _361030, _361211]), _361030))], (1024 ^ _325847) ^ [] : [-(in(ordered_pair(1010 ^ [_360845, _361030, _361211], 1022 ^ [_360845, _361030, _361211]), _360845))]], 1014 ^ _325847 : [(1017 ^ _325847) ^ [_362675] : [in(ordered_pair(1010 ^ [_360845, _361030, _361211], _362675), _360845), in(ordered_pair(_362675, 1011 ^ [_360845, _361030, _361211]), _361030)], (1015 ^ _325847) ^ [] : [-(in(ordered_pair(1010 ^ [_360845, _361030, _361211], 1011 ^ [_360845, _361030, _361211]), _361211))]]]]]]]]], (1296 ^ _325847) ^ [_371034] : [empty(relation_rng(_371034)), -(empty(_371034)), relation(_371034)], (744 ^ _325847) ^ [_352215] : [relation(_352215), 747 ^ _325847 : [(748 ^ _325847) ^ [_352396] : [_352396 = relation_dom(_352215), 751 ^ _325847 : [(759 ^ _325847) ^ [_352820] : [760 ^ _325847 : [(761 ^ _325847) ^ [_352899] : [in(ordered_pair(_352820, _352899), _352215)]], -(in(_352820, _352396))], (752 ^ _325847) ^ [_352576] : [in(_352576, _352396), -(in(ordered_pair(_352576, 755 ^ [_352215, _352396, _352576]), _352215))]]], (765 ^ _325847) ^ [_353027] : [-(_353027 = relation_dom(_352215)), 769 ^ _325847 : [(772 ^ _325847) ^ [_353290] : [in(ordered_pair(766 ^ [_352215, _353027], _353290), _352215)], (770 ^ _325847) ^ [] : [-(in(766 ^ [_352215, _353027], _353027))]], 774 ^ _325847 : [(777 ^ _325847) ^ [] : [in(766 ^ [_352215, _353027], _353027)], (775 ^ _325847) ^ [] : [-(in(ordered_pair(766 ^ [_352215, _353027], 773 ^ [_352215, _353027]), _352215))]]]]], (86 ^ _325847) ^ [_328694, _328696, _328698, _328700] : [-(are_equipotent(_328698, _328694)), are_equipotent(_328700, _328696), _328700 = _328698, _328696 = _328694], (1274 ^ _325847) ^ [] : [-(relation(empty_set))], (1139 ^ _325847) ^ [] : [true___, -(true___)], (2055 ^ _325847) ^ [_397675] : [relation(_397675), 2060 ^ _325847 : [(2063 ^ _325847) ^ [] : [relation_rng(_397675) = empty_set], (2061 ^ _325847) ^ [] : [relation_dom(_397675) = empty_set]], -(_397675 = empty_set)], (1787 ^ _325847) ^ [_388456, _388458] : [-(set_union2(_388458, set_difference(_388456, _388458)) = set_union2(_388458, _388456))], (2099 ^ _325847) ^ [_399150, _399152] : [-(subset(_399152, set_union2(_399152, _399150)))], (1557 ^ _325847) ^ [_380354, _380356, _380358, _380360] : [-(subset(cartesian_product2(_380360, _380356), cartesian_product2(_380358, _380354))), subset(_380360, _380358), subset(_380356, _380354)], (1489 ^ _325847) ^ [] : [empty(1487 ^ [])], (1751 ^ _325847) ^ [_387231, _387233] : [subset(_387233, _387231), -(set_difference(_387233, _387231) = empty_set)], (1491 ^ _325847) ^ [_377871, _377873] : [element(_377871, powerset(powerset(_377873))), -(union_of_subsets(_377873, _377871) = union(_377871))], (344 ^ _325847) ^ [_337840] : [relation(_337840), 347 ^ _325847 : [(348 ^ _325847) ^ [_337988] : [in(_337988, _337840), -(_337988 = ordered_pair(351 ^ [_337840, _337988], 352 ^ [_337840, _337988]))]]], (1789 ^ _325847) ^ [_388603, _388605] : [subset(_388605, singleton(_388603)), -(_388605 = empty_set), -(_388605 = singleton(_388603))], (1830 ^ _325847) ^ [_389983, _389985] : [disjoint(_389985, _389983), 1831 ^ _325847 : [(1832 ^ _325847) ^ [_390075] : [in(_390075, _389985), in(_390075, _389983)]]], (1592 ^ _325847) ^ [_381634, _381636] : [subset(_381634, 1572 ^ [_381636]), -(are_equipotent(_381634, 1572 ^ [_381636])), -(in(_381634, 1572 ^ [_381636]))], (268 ^ _325847) ^ [_335045, _335047] : [_335047 = _335045, -(powerset(_335047) = powerset(_335045))], (1908 ^ _325847) ^ [_392674, _392676] : [element(_392674, powerset(powerset(_392676))), -(_392674 = empty_set), complements_of_subsets(_392676, _392674) = empty_set], (1256 ^ _325847) ^ [_369722] : [empty(singleton(_369722))], (2079 ^ _325847) ^ [_398440] : [-(unordered_pair(_398440, _398440) = singleton(_398440))], (114 ^ _325847) ^ [_329534, _329536] : [-(relation(_329534)), _329536 = _329534, relation(_329536)], (1479 ^ _325847) ^ [] : [empty(1477 ^ [])], (1258 ^ _325847) ^ [_369830, _369832] : [-(empty(_369832)), empty(set_union2(_369832, _369830))], (326 ^ _325847) ^ [_337287, _337289] : [_337289 = _337287, 329 ^ _325847 : [(332 ^ _325847) ^ [] : [-(subset(_337287, _337289))], (330 ^ _325847) ^ [] : [-(subset(_337289, _337287))]]], (1549 ^ _325847) ^ [_380009, _380011, _380013] : [subset(_380013, _380011), 1552 ^ _325847 : [(1555 ^ _325847) ^ [] : [-(subset(cartesian_product2(_380009, _380013), cartesian_product2(_380009, _380011)))], (1553 ^ _325847) ^ [] : [-(subset(cartesian_product2(_380013, _380009), cartesian_product2(_380011, _380009)))]]], (1727 ^ _325847) ^ [_386339, _386341, _386343, _386345] : [ordered_pair(_386345, _386343) = ordered_pair(_386341, _386339), 1730 ^ _325847 : [(1733 ^ _325847) ^ [] : [-(_386343 = _386339)], (1731 ^ _325847) ^ [] : [-(_386345 = _386341)]]], (2067 ^ _325847) ^ [_398071, _398073] : [set_difference(_398073, singleton(_398071)) = _398073, in(_398071, _398073)], (1032 ^ _325847) ^ [_363361, _363363] : [element(_363361, powerset(powerset(_363363))), 1035 ^ _325847 : [(1036 ^ _325847) ^ [_363541] : [element(_363541, powerset(powerset(_363363))), 1039 ^ _325847 : [(1040 ^ _325847) ^ [] : [_363541 = complements_of_subsets(_363363, _363361), 1043 ^ _325847 : [(1044 ^ _325847) ^ [_363829] : [element(_363829, powerset(_363363)), 1047 ^ _325847 : [(1054 ^ _325847) ^ [] : [in(subset_complement(_363363, _363829), _363361), -(in(_363829, _363541))], (1048 ^ _325847) ^ [] : [in(_363829, _363541), -(in(subset_complement(_363363, _363829), _363361))]]]]], (1060 ^ _325847) ^ [] : [-(_363541 = complements_of_subsets(_363363, _363361)), 1062 ^ _325847 : [(1065 ^ _325847) ^ [] : [1066 ^ _325847 : [(1069 ^ _325847) ^ [] : [in(subset_complement(_363363, 1061 ^ [_363361, _363363, _363541]), _363361)], (1067 ^ _325847) ^ [] : [-(in(1061 ^ [_363361, _363363, _363541], _363541))]], 1070 ^ _325847 : [(1073 ^ _325847) ^ [] : [in(1061 ^ [_363361, _363363, _363541], _363541)], (1071 ^ _325847) ^ [] : [-(in(subset_complement(_363363, 1061 ^ [_363361, _363363, _363541]), _363361))]]], (1063 ^ _325847) ^ [] : [-(element(1061 ^ [_363361, _363363, _363541], powerset(_363363)))]]]]]]], (1193 ^ _325847) ^ [_367656, _367658] : [-(relation(relation_composition(_367658, _367656))), relation(_367658), relation(_367656)], (1878 ^ _325847) ^ [_391627] : [relation(_391627), 1881 ^ _325847 : [(1882 ^ _325847) ^ [_391764] : [relation(_391764), -(subset(relation_rng(relation_composition(_391627, _391764)), relation_rng(_391764)))]]], (1326 ^ _325847) ^ [_372049, _372051] : [element(_372049, powerset(_372051)), -(subset_complement(_372051, subset_complement(_372051, _372049)) = _372049)], (1616 ^ _325847) ^ [_382481, _382483] : [in(_382483, _382481), -(element(_382483, _382481))], (559 ^ _325847) ^ [_345190, _345192, _345194] : [-(_345190 = unordered_pair(_345194, _345192)), 563 ^ _325847 : [(568 ^ _325847) ^ [] : [560 ^ [_345190, _345192, _345194] = _345192], (566 ^ _325847) ^ [] : [560 ^ [_345190, _345192, _345194] = _345194], (564 ^ _325847) ^ [] : [-(in(560 ^ [_345190, _345192, _345194], _345190))]], 569 ^ _325847 : [(570 ^ _325847) ^ [] : [-(560 ^ [_345190, _345192, _345194] = _345194), -(560 ^ [_345190, _345192, _345194] = _345192)], (576 ^ _325847) ^ [] : [in(560 ^ [_345190, _345192, _345194], _345190)]]], (1634 ^ _325847) ^ [_383081, _383083, _383085] : [relation(_383081), in(ordered_pair(_383085, _383083), _383081), 1641 ^ _325847 : [(1644 ^ _325847) ^ [] : [-(in(_383083, relation_rng(_383081)))], (1642 ^ _325847) ^ [] : [-(in(_383085, relation_dom(_383081)))]]], (1246 ^ _325847) ^ [_369453, _369455] : [-(relation(set_union2(_369455, _369453))), relation(_369455), relation(_369453)], (1344 ^ _325847) ^ [_372685, _372687] : [proper_subset(_372687, _372687)], (1840 ^ _325847) ^ [_390332] : [subset(_390332, empty_set), -(_390332 = empty_set)], (580 ^ _325847) ^ [_345984, _345986, _345988] : [_345984 = set_union2(_345988, _345986), 583 ^ _325847 : [(584 ^ _325847) ^ [_346166] : [in(_346166, _345984), -(in(_346166, _345988)), -(in(_346166, _345986))], (594 ^ _325847) ^ [_346444] : [595 ^ _325847 : [(598 ^ _325847) ^ [] : [in(_346444, _345986)], (596 ^ _325847) ^ [] : [in(_346444, _345988)]], -(in(_346444, _345984))]]], (1286 ^ _325847) ^ [_370757] : [empty(relation_dom(_370757)), -(empty(_370757)), relation(_370757)], (1745 ^ _325847) ^ [_387063, _387065] : [set_difference(_387065, _387063) = empty_set, -(subset(_387065, _387063))], (806 ^ _325847) ^ [_354624, _354626] : [-(_354624 = union(_354626)), 819 ^ _325847 : [(824 ^ _325847) ^ [] : [in(807 ^ [_354624, _354626], _354624)], (822 ^ _325847) ^ [] : [-(in(818 ^ [_354624, _354626], _354626))], (820 ^ _325847) ^ [] : [-(in(807 ^ [_354624, _354626], 818 ^ [_354624, _354626]))]], 810 ^ _325847 : [(813 ^ _325847) ^ [_354907] : [in(807 ^ [_354624, _354626], _354907), in(_354907, _354626)], (811 ^ _325847) ^ [] : [-(in(807 ^ [_354624, _354626], _354624))]]], (1938 ^ _325847) ^ [_393670, _393672] : [element(_393670, powerset(powerset(_393672))), -(_393670 = empty_set), -(subset_difference(_393672, cast_to_subset(_393672), union_of_subsets(_393672, _393670)) = meet_of_subsets(_393672, complements_of_subsets(_393672, _393670)))], (34 ^ _325847) ^ [_327067, _327069, _327071, _327073] : [-(proper_subset(_327071, _327067)), proper_subset(_327073, _327069), _327073 = _327071, _327069 = _327067], (1131 ^ _325847) ^ [_366179] : [-(element(cast_to_subset(_366179), powerset(_366179)))], (1721 ^ _325847) ^ [_386083, _386085, _386087] : [subset(_386087, _386085), -(subset(set_difference(_386087, _386083), set_difference(_386085, _386083)))], (723 ^ _325847) ^ [_351476, _351478, _351480] : [-(_351476 = set_intersection2(_351480, _351478)), 735 ^ _325847 : [(740 ^ _325847) ^ [] : [in(724 ^ [_351476, _351478, _351480], _351476)], (738 ^ _325847) ^ [] : [-(in(724 ^ [_351476, _351478, _351480], _351478))], (736 ^ _325847) ^ [] : [-(in(724 ^ [_351476, _351478, _351480], _351480))]], 727 ^ _325847 : [(730 ^ _325847) ^ [] : [in(724 ^ [_351476, _351478, _351480], _351480), in(724 ^ [_351476, _351478, _351480], _351478)], (728 ^ _325847) ^ [] : [-(in(724 ^ [_351476, _351478, _351480], _351476))]]], (1574 ^ _325847) ^ [_381007] : [-(in(_381007, 1572 ^ [_381007]))], (461 ^ _325847) ^ [_342005] : [_342005 = empty_set, 464 ^ _325847 : [(465 ^ _325847) ^ [_342118] : [in(_342118, _342005)]]], (1692 ^ _325847) ^ [_385049, _385051] : [-(_385051 = _385049), 1696 ^ _325847 : [(1699 ^ _325847) ^ [] : [in(1693 ^ [_385049, _385051], _385049)], (1697 ^ _325847) ^ [] : [-(in(1693 ^ [_385049, _385051], _385051))]], 1700 ^ _325847 : [(1703 ^ _325847) ^ [] : [in(1693 ^ [_385049, _385051], _385051)], (1701 ^ _325847) ^ [] : [-(in(1693 ^ [_385049, _385051], _385049))]]], (2087 ^ _325847) ^ [_398740, _398742] : [subset(singleton(_398742), singleton(_398740)), -(_398742 = _398740)], (1757 ^ _325847) ^ [_387478, _387480] : [subset(singleton(_387480), _387478), -(in(_387480, _387478))], (1848 ^ _325847) ^ [_390639, _390641] : [element(_390639, powerset(_390641)), 1851 ^ _325847 : [(1852 ^ _325847) ^ [_390791] : [element(_390791, powerset(_390641)), 1855 ^ _325847 : [(1862 ^ _325847) ^ [] : [subset(_390639, subset_complement(_390641, _390791)), -(disjoint(_390639, _390791))], (1856 ^ _325847) ^ [] : [disjoint(_390639, _390791), -(subset(_390639, subset_complement(_390641, _390791)))]]]]], (222 ^ _325847) ^ [_333419, _333421, _333423, _333425] : [-(subset_complement(_333425, _333421) = subset_complement(_333423, _333419)), _333425 = _333423, _333421 = _333419], (623 ^ _325847) ^ [_347503, _347505, _347507] : [_347503 = cartesian_product2(_347507, _347505), 626 ^ _325847 : [(639 ^ _325847) ^ [_348264] : [-(in(_348264, _347503)), 640 ^ _325847 : [(641 ^ _325847) ^ [_348394, _348396] : [in(_348396, _347507), in(_348394, _347505), _348264 = ordered_pair(_348396, _348394)]]], (627 ^ _325847) ^ [_347704] : [in(_347704, _347503), 632 ^ _325847 : [(637 ^ _325847) ^ [] : [-(_347704 = ordered_pair(630 ^ [_347503, _347505, _347507, _347704], 631 ^ [_347503, _347505, _347507, _347704]))], (635 ^ _325847) ^ [] : [-(in(631 ^ [_347503, _347505, _347507, _347704], _347505))], (633 ^ _325847) ^ [] : [-(in(630 ^ [_347503, _347505, _347507, _347704], _347507))]]]]], (1244 ^ _325847) ^ [_369342, _369344] : [empty(ordered_pair(_369344, _369342))], (202 ^ _325847) ^ [_332701, _332703, _332705, _332707] : [-(meet_of_subsets(_332707, _332703) = meet_of_subsets(_332705, _332701)), _332707 = _332705, _332703 = _332701], (1314 ^ _325847) ^ [_371576] : [empty(_371576), 1317 ^ _325847 : [(1320 ^ _325847) ^ [] : [-(relation(relation_rng(_371576)))], (1318 ^ _325847) ^ [] : [-(empty(relation_rng(_371576)))]]], (1225 ^ _325847) ^ [_368754, _368756] : [element(_368754, powerset(powerset(_368756))), -(element(complements_of_subsets(_368756, _368754), powerset(powerset(_368756))))], (1133 ^ _325847) ^ [] : [true___, -(true___)], (1539 ^ _325847) ^ [_379659, _379661, _379663, _379665] : [unordered_pair(_379665, _379663) = unordered_pair(_379661, _379659), -(_379665 = _379661), -(_379665 = _379659)], (1434 ^ _325847) ^ [_375903, _375905, _375907, _375909] : [in(ordered_pair(_375909, _375907), cartesian_product2(_375905, _375903)), 1437 ^ _325847 : [(1440 ^ _325847) ^ [] : [-(in(_375907, _375903))], (1438 ^ _325847) ^ [] : [-(in(_375909, _375905))]]], (2173 ^ _325847) ^ [_401915, _401917] : [subset(_401915, 2146 ^ [_401917]), -(are_equipotent(_401915, 2146 ^ [_401917])), -(in(_401915, 2146 ^ [_401917]))], (1231 ^ _325847) ^ [] : [true___, -(true___)], (1125 ^ _325847) ^ [] : [true___, -(true___)], (320 ^ _325847) ^ [_336943, _336945] : [-(unordered_pair(_336945, _336943) = unordered_pair(_336943, _336945))], (1466 ^ _325847) ^ [_376995] : [-(empty(_376995)), 1470 ^ _325847 : [(1473 ^ _325847) ^ [] : [empty(1469 ^ [_376995])], (1471 ^ _325847) ^ [] : [-(element(1469 ^ [_376995], powerset(_376995)))]]], (2133 ^ _325847) ^ [_400317, _400319, _400321] : [singleton(_400321) = unordered_pair(_400319, _400317), -(_400321 = _400319)], (1924 ^ _325847) ^ [_393197] : [relation(_393197), 1927 ^ _325847 : [(1928 ^ _325847) ^ [_393344] : [relation(_393344), subset(relation_dom(_393197), relation_rng(_393344)), -(relation_rng(relation_composition(_393344, _393197)) = relation_rng(_393197))]]], (2123 ^ _325847) ^ [_399988, _399990, _399992] : [-(subset(set_union2(_399992, _399988), _399990)), subset(_399992, _399990), subset(_399988, _399990)], (1113 ^ _325847) ^ [] : [true___, -(true___)], (1777 ^ _325847) ^ [_388154, _388156, _388158] : [-(subset(unordered_pair(_388158, _388156), _388154)), in(_388158, _388154), in(_388156, _388154)], (1576 ^ _325847) ^ [_381119, _381121, _381123] : [-(in(_381119, 1572 ^ [_381123])), in(_381121, 1572 ^ [_381123]), subset(_381119, _381121)], (1085 ^ _325847) ^ [_365190, _365192] : [-(proper_subset(_365192, _365190)), subset(_365192, _365190), -(_365192 = _365190)], (1400 ^ _325847) ^ [_374729, _374731, _374733] : [subset(_374733, _374731), -(in(_374729, _374733)), -(subset(_374733, set_difference(_374731, singleton(_374729))))], (692 ^ _325847) ^ [_350351, _350353] : [694 ^ _325847 : [(697 ^ _325847) ^ [] : [in(693 ^ [_350351, _350353], _350351)], (695 ^ _325847) ^ [] : [-(in(693 ^ [_350351, _350353], _350353))]], -(subset(_350353, _350351))], (1390 ^ _325847) ^ [_374349, _374351] : [element(_374349, powerset(_374351)), 1393 ^ _325847 : [(1394 ^ _325847) ^ [_374490] : [in(_374490, _374349), -(in(_374490, _374351))]]], (2039 ^ _325847) ^ [_397157, _397159] : [subset(_397159, _397157), proper_subset(_397157, _397159)], (968 ^ _325847) ^ [_360641, _360643] : [set_intersection2(_360643, _360641) = empty_set, -(disjoint(_360643, _360641))], (1918 ^ _325847) ^ [_392991, _392993] : [in(_392993, _392991), -(set_union2(singleton(_392993), _392991) = _392991)], (262 ^ _325847) ^ [_334827, _334829] : [_334829 = _334827, -(union(_334829) = union(_334827))], (324 ^ _325847) ^ [_337143, _337145] : [-(set_intersection2(_337145, _337143) = set_intersection2(_337143, _337145))], (1428 ^ _325847) ^ [_375632, _375634] : [in(_375634, _375632), -(subset(_375634, union(_375632)))], (1378 ^ _325847) ^ [_373963, _373965] : [set_difference(_373965, _373963) = empty_set, -(subset(_373965, _373963))], (274 ^ _325847) ^ [_335263, _335265] : [_335265 = _335263, -(singleton(_335265) = singleton(_335263))], (871 ^ _325847) ^ [_356988] : [relation(_356988), 874 ^ _325847 : [(875 ^ _325847) ^ [_357169] : [_357169 = relation_rng(_356988), 878 ^ _325847 : [(886 ^ _325847) ^ [_357593] : [887 ^ _325847 : [(888 ^ _325847) ^ [_357672] : [in(ordered_pair(_357672, _357593), _356988)]], -(in(_357593, _357169))], (879 ^ _325847) ^ [_357349] : [in(_357349, _357169), -(in(ordered_pair(882 ^ [_356988, _357169, _357349], _357349), _356988))]]], (892 ^ _325847) ^ [_357800] : [-(_357800 = relation_rng(_356988)), 896 ^ _325847 : [(899 ^ _325847) ^ [_358063] : [in(ordered_pair(_358063, 893 ^ [_356988, _357800]), _356988)], (897 ^ _325847) ^ [] : [-(in(893 ^ [_356988, _357800], _357800))]], 901 ^ _325847 : [(904 ^ _325847) ^ [] : [in(893 ^ [_356988, _357800], _357800)], (902 ^ _325847) ^ [] : [-(in(ordered_pair(900 ^ [_356988, _357800], 893 ^ [_356988, _357800]), _356988))]]]]], (1348 ^ _325847) ^ [_372873, _372875] : [in(_372875, _372873), -(set_union2(singleton(_372875), _372873) = _372873)], (2145 ^ _325847) ^ [_400728] : [-(union(powerset(_400728)) = _400728)], (2113 ^ _325847) ^ [_399677, _399679] : [empty(_399679), -(_399679 = _399677), empty(_399677)], (1322 ^ _325847) ^ [_371840, _371842] : [-(set_union2(_371842, _371842) = _371842)], (781 ^ _325847) ^ [_353641] : [-(cast_to_subset(_353641) = _353641)], (1175 ^ _325847) ^ [_367214] : [relation(_367214), -(relation(relation_inverse(_367214)))], (1979 ^ _325847) ^ [_395116, _395118] : [1980 ^ _325847 : [(1981 ^ _325847) ^ [_395189] : [in(_395189, set_intersection2(_395118, _395116))]], disjoint(_395118, _395116)], (1763 ^ _325847) ^ [_387644, _387646] : [in(_387646, _387644), -(subset(singleton(_387646), _387644))], (1586 ^ _325847) ^ [_381434, _381436] : [in(_381434, 1572 ^ [_381436]), -(in(powerset(_381434), 1572 ^ [_381436]))], (1962 ^ _325847) ^ [_394548, _394550, _394552] : [-(element(_394552, _394548)), in(_394552, _394550), element(_394550, powerset(_394548))], (1503 ^ _325847) ^ [_378341, _378343, _378345] : [-(subset_difference(_378345, _378343, _378341) = set_difference(_378343, _378341)), element(_378343, powerset(_378345)), element(_378341, powerset(_378345))], (1682 ^ _325847) ^ [_384751, _384753] : [element(_384753, _384751), -(empty(_384751)), -(in(_384753, _384751))], (2045 ^ _325847) ^ [_397380, _397382, _397384] : [-(disjoint(_397384, _397380)), subset(_397384, _397382), disjoint(_397382, _397380)], (1815 ^ _325847) ^ [_389433, _389435] : [subset(_389435, _389433), -(element(_389435, powerset(_389433)))], (4 ^ _325847) ^ [_326078, _326080] : [_326080 = _326078, -(_326078 = _326080)], (322 ^ _325847) ^ [_337043, _337045] : [-(set_union2(_337045, _337043) = set_union2(_337043, _337045))], (1101 ^ _325847) ^ [] : [true___, -(true___)], (1481 ^ _325847) ^ [] : [-(relation(1477 ^ []))], (2139 ^ _325847) ^ [_400543, _400545] : [in(_400545, _400543), -(subset(_400545, union(_400543)))], (1306 ^ _325847) ^ [_371311] : [empty(_371311), 1309 ^ _325847 : [(1312 ^ _325847) ^ [] : [-(relation(relation_dom(_371311)))], (1310 ^ _325847) ^ [] : [-(empty(relation_dom(_371311)))]]], (1346 ^ _325847) ^ [_372764] : [singleton(_372764) = empty_set], (2037 ^ _325847) ^ [] : [-(relation_rng(empty_set) = empty_set)], (10 ^ _325847) ^ [_326282, _326284, _326286] : [-(_326286 = _326282), _326286 = _326284, _326284 = _326282], (1652 ^ _325847) ^ [_383667] : [relation(_383667), 1655 ^ _325847 : [(1656 ^ _325847) ^ [_383817] : [relation(_383817), subset(_383667, _383817), 1663 ^ _325847 : [(1666 ^ _325847) ^ [] : [-(subset(relation_rng(_383667), relation_rng(_383817)))], (1664 ^ _325847) ^ [] : [-(subset(relation_dom(_383667), relation_dom(_383817)))]]]]], (1366 ^ _325847) ^ [_373552, _373554] : [subset(singleton(_373554), _373552), -(in(_373554, _373552))], (2013 ^ _325847) ^ [_396307] : [relation(_396307), -(in(ordered_pair(2018 ^ [_396307], 2019 ^ [_396307]), _396307)), -(_396307 = empty_set)], (1181 ^ _325847) ^ [] : [true___, -(true___)], (1238 ^ _325847) ^ [_369115] : [-(element(1236 ^ [_369115], _369115))], (48 ^ _325847) ^ [_327511, _327513, _327515, _327517] : [-(disjoint(_327515, _327511)), disjoint(_327517, _327513), _327517 = _327515, _327513 = _327511], (182 ^ _325847) ^ [_331995, _331997, _331999, _332001, _332003, _332005] : [-(subset_difference(_332005, _332001, _331997) = subset_difference(_332003, _331999, _331995)), _332005 = _332003, _332001 = _331999, _331997 = _331995], (490 ^ _325847) ^ [_342996, _342998] : [-(_342996 = powerset(_342998)), 494 ^ _325847 : [(497 ^ _325847) ^ [] : [subset(491 ^ [_342996, _342998], _342998)], (495 ^ _325847) ^ [] : [-(in(491 ^ [_342996, _342998], _342996))]], 498 ^ _325847 : [(501 ^ _325847) ^ [] : [in(491 ^ [_342996, _342998], _342996)], (499 ^ _325847) ^ [] : [-(subset(491 ^ [_342996, _342998], _342998))]]], (1151 ^ _325847) ^ [] : [true___, -(true___)], (2025 ^ _325847) ^ [_396739, _396741, _396743] : [in(_396743, _396741), element(_396741, powerset(_396739)), empty(_396739)], (1735 ^ _325847) ^ [_386637, _386639] : [-(subset(set_difference(_386639, _386637), _386639))], (1332 ^ _325847) ^ [_372261] : [relation(_372261), -(relation_inverse(relation_inverse(_372261)) = _372261)], (152 ^ _325847) ^ [_330890, _330892, _330894, _330896] : [-(relation_composition(_330896, _330892) = relation_composition(_330894, _330890)), _330896 = _330894, _330892 = _330890], (1338 ^ _325847) ^ [_372471, _372473] : [element(_372471, powerset(powerset(_372473))), -(complements_of_subsets(_372473, complements_of_subsets(_372473, _372471)) = _372471)], (20 ^ _325847) ^ [_326623, _326625, _326627, _326629] : [-(element(_326627, _326623)), element(_326629, _326625), _326629 = _326627, _326625 = _326623], (1242 ^ _325847) ^ [] : [-(empty(empty_set))], (308 ^ _325847) ^ [_336561, _336563] : [proper_subset(_336563, _336561), proper_subset(_336561, _336563)], (1452 ^ _325847) ^ [_376501, _376503] : [1454 ^ _325847 : [(1457 ^ _325847) ^ [] : [in(1453 ^ [_376501, _376503], _376501)], (1455 ^ _325847) ^ [] : [-(in(1453 ^ [_376501, _376503], _376503))]], -(element(_376503, powerset(_376501)))], (602 ^ _325847) ^ [_346709, _346711, _346713] : [-(_346709 = set_union2(_346713, _346711)), 606 ^ _325847 : [(611 ^ _325847) ^ [] : [in(603 ^ [_346709, _346711, _346713], _346711)], (609 ^ _325847) ^ [] : [in(603 ^ [_346709, _346711, _346713], _346713)], (607 ^ _325847) ^ [] : [-(in(603 ^ [_346709, _346711, _346713], _346709))]], 612 ^ _325847 : [(613 ^ _325847) ^ [] : [-(in(603 ^ [_346709, _346711, _346713], _346713)), -(in(603 ^ [_346709, _346711, _346713], _346711))], (619 ^ _325847) ^ [] : [in(603 ^ [_346709, _346711, _346713], _346709)]]], (1709 ^ _325847) ^ [_385671, _385673, _385675] : [relation(_385671), in(ordered_pair(_385675, _385673), _385671), 1716 ^ _325847 : [(1719 ^ _325847) ^ [] : [-(in(_385673, relation_field(_385671)))], (1717 ^ _325847) ^ [] : [-(in(_385675, relation_field(_385671)))]]], (1476 ^ _325847) ^ [] : [-(empty(1474 ^ []))], (2148 ^ _325847) ^ [_400969] : [-(in(_400969, 2146 ^ [_400969]))], (1266 ^ _325847) ^ [_370141, _370143] : [-(empty(_370143)), empty(set_union2(_370141, _370143))], (1264 ^ _325847) ^ [_370030, _370032] : [empty(unordered_pair(_370032, _370030))], (1567 ^ _325847) ^ [_380685, _380687] : [subset(_380687, _380685), -(set_union2(_380687, _380685) = _380685)], (922 ^ _325847) ^ [_358966] : [relation(_358966), 925 ^ _325847 : [(926 ^ _325847) ^ [_359126] : [relation(_359126), 929 ^ _325847 : [(930 ^ _325847) ^ [] : [_359126 = relation_inverse(_358966), 933 ^ _325847 : [(940 ^ _325847) ^ [_359625, _359627] : [in(ordered_pair(_359625, _359627), _358966), -(in(ordered_pair(_359627, _359625), _359126))], (934 ^ _325847) ^ [_359435, _359437] : [in(ordered_pair(_359437, _359435), _359126), -(in(ordered_pair(_359435, _359437), _358966))]]], (946 ^ _325847) ^ [] : [-(_359126 = relation_inverse(_358966)), 951 ^ _325847 : [(954 ^ _325847) ^ [] : [in(ordered_pair(948 ^ [_358966, _359126], 947 ^ [_358966, _359126]), _358966)], (952 ^ _325847) ^ [] : [-(in(ordered_pair(947 ^ [_358966, _359126], 948 ^ [_358966, _359126]), _359126))]], 955 ^ _325847 : [(958 ^ _325847) ^ [] : [in(ordered_pair(947 ^ [_358966, _359126], 948 ^ [_358966, _359126]), _359126)], (956 ^ _325847) ^ [] : [-(in(ordered_pair(948 ^ [_358966, _359126], 947 ^ [_358966, _359126]), _358966))]]]]]]], (682 ^ _325847) ^ [_350037, _350039] : [subset(_350039, _350037), 685 ^ _325847 : [(686 ^ _325847) ^ [_350174] : [in(_350174, _350039), -(in(_350174, _350037))]]], (1821 ^ _325847) ^ [_389669, _389671] : [-(disjoint(_389671, _389669)), 1825 ^ _325847 : [(1828 ^ _325847) ^ [] : [-(in(1824 ^ [_389669, _389671], _389669))], (1826 ^ _325847) ^ [] : [-(in(1824 ^ [_389669, _389671], _389671))]]], (1515 ^ _325847) ^ [_378766, _378768] : [disjoint(_378768, _378766), -(disjoint(_378766, _378768))], (2035 ^ _325847) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2073 ^ _325847) ^ [_398244, _398246] : [-(in(_398244, _398246)), -(set_difference(_398246, singleton(_398244)) = _398246)], (242 ^ _325847) ^ [_334137, _334139, _334141, _334143] : [-(set_difference(_334143, _334139) = set_difference(_334141, _334137)), _334143 = _334141, _334139 = _334137], (1948 ^ _325847) ^ [_394010, _394012] : [element(_394010, powerset(powerset(_394012))), -(_394010 = empty_set), -(union_of_subsets(_394012, complements_of_subsets(_394012, _394010)) = subset_difference(_394012, cast_to_subset(_394012), meet_of_subsets(_394012, _394010)))], (124 ^ _325847) ^ [_329849, _329851] : [_329851 = _329849, -(set_meet(_329851) = set_meet(_329849))], (356 ^ _325847) ^ [_338301] : [358 ^ _325847 : [(361 ^ _325847) ^ [_338538, _338540] : [357 ^ [_338301] = ordered_pair(_338540, _338538)], (359 ^ _325847) ^ [] : [-(in(357 ^ [_338301], _338301))]], -(relation(_338301))], (908 ^ _325847) ^ [_358443, _358445] : [element(_358443, powerset(_358445)), -(subset_complement(_358445, _358443) = set_difference(_358445, _358443))], (2101 ^ _325847) ^ [_399291, _399293] : [disjoint(_399293, _399291), -(set_difference(_399293, _399291) = _399293)], (1384 ^ _325847) ^ [_374131, _374133] : [subset(_374133, _374131), -(set_difference(_374133, _374131) = empty_set)], (1354 ^ _325847) ^ [_373093, _373095] : [disjoint(singleton(_373095), _373093), in(_373095, _373093)], (2107 ^ _325847) ^ [_399459, _399461] : [set_difference(_399461, _399459) = _399461, -(disjoint(_399461, _399459))], (1163 ^ _325847) ^ [] : [true___, -(true___)], (1960 ^ _325847) ^ [_394424] : [-(set_difference(empty_set, _394424) = empty_set)], (1095 ^ _325847) ^ [] : [true___, -(true___)], (1497 ^ _325847) ^ [_378099, _378101] : [element(_378099, powerset(powerset(_378101))), -(meet_of_subsets(_378101, _378099) = set_meet(_378099))], (72 ^ _325847) ^ [_328250, _328252, _328254, _328256] : [-(subset(_328254, _328250)), subset(_328256, _328252), _328256 = _328254, _328252 = _328250], (334 ^ _325847) ^ [_337524, _337526] : [-(_337526 = _337524), subset(_337526, _337524), subset(_337524, _337526)], (2160 ^ _325847) ^ [_401396, _401398] : [in(_401396, 2146 ^ [_401398]), 2164 ^ _325847 : [(2167 ^ _325847) ^ [_401708] : [subset(_401708, _401396), -(in(_401708, 2163 ^ [_401396, _401398]))], (2165 ^ _325847) ^ [] : [-(in(2163 ^ [_401396, _401398], 2146 ^ [_401398]))]]], (1614 ^ _325847) ^ [_382371] : [-(set_union2(_382371, empty_set) = _382371)], (537 ^ _325847) ^ [_344465, _344467, _344469] : [_344465 = unordered_pair(_344469, _344467), 540 ^ _325847 : [(541 ^ _325847) ^ [_344647] : [in(_344647, _344465), -(_344647 = _344469), -(_344647 = _344467)], (551 ^ _325847) ^ [_344925] : [552 ^ _325847 : [(555 ^ _325847) ^ [] : [_344925 = _344467], (553 ^ _325847) ^ [] : [_344925 = _344469]], -(in(_344925, _344465))]]], (140 ^ _325847) ^ [_330426, _330428] : [_330428 = _330426, -(relation_field(_330428) = relation_field(_330426))], (1169 ^ _325847) ^ [] : [true___, -(true___)], (474 ^ _325847) ^ [_342475, _342477] : [_342475 = powerset(_342477), 477 ^ _325847 : [(484 ^ _325847) ^ [_342817] : [subset(_342817, _342477), -(in(_342817, _342475))], (478 ^ _325847) ^ [_342645] : [in(_342645, _342475), -(subset(_342645, _342477))]]], (146 ^ _325847) ^ [_330644, _330646] : [_330646 = _330644, -(relation_inverse(_330646) = relation_inverse(_330644))], (1985 ^ _325847) ^ [_395341] : [-(_395341 = empty_set), 1988 ^ _325847 : [(1989 ^ _325847) ^ [_395501] : [element(_395501, powerset(_395341)), 1992 ^ _325847 : [(1993 ^ _325847) ^ [_395655] : [element(_395655, _395341), -(in(_395655, _395501)), -(in(_395655, subset_complement(_395341, _395501)))]]]]], (1604 ^ _325847) ^ [_382085, _382087, _382089] : [-(subset(_382089, set_intersection2(_382087, _382085))), subset(_382089, _382087), subset(_382089, _382085)], (1632 ^ _325847) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (1958 ^ _325847) ^ [_394335, _394337] : [-(set_difference(_394337, set_difference(_394337, _394335)) = set_intersection2(_394337, _394335))], (172 ^ _325847) ^ [_331608, _331610, _331612, _331614] : [-(complements_of_subsets(_331614, _331610) = complements_of_subsets(_331612, _331608)), _331614 = _331612, _331610 = _331608], (1157 ^ _325847) ^ [_366766, _366768] : [element(_366766, powerset(_366768)), -(element(subset_complement(_366768, _366766), powerset(_366768)))], (1807 ^ _325847) ^ [_389128] : [-(set_difference(_389128, empty_set) = _389128)], (302 ^ _325847) ^ [_336350, _336352] : [in(_336352, _336350), in(_336350, _336352)], (1209 ^ _325847) ^ [_368183, _368185] : [element(_368183, powerset(powerset(_368185))), -(element(meet_of_subsets(_368185, _368183), powerset(_368185)))], (1145 ^ _325847) ^ [] : [true___, -(true___)], (2003 ^ _325847) ^ [_396001, _396003, _396005] : [element(_396001, powerset(_396005)), in(_396003, subset_complement(_396005, _396001)), in(_396003, _396001)], (1894 ^ _325847) ^ [_392201] : [relation(_392201), 1897 ^ _325847 : [(1898 ^ _325847) ^ [_392348] : [relation(_392348), subset(relation_rng(_392201), relation_dom(_392348)), -(relation_dom(relation_composition(_392201, _392348)) = relation_dom(_392201))]]], (2 ^ _325847) ^ [_325971] : [-(_325971 = _325971)], (1799 ^ _325847) ^ [_388863, _388865] : [1800 ^ _325847 : [(1803 ^ _325847) ^ [] : [_388865 = singleton(_388863)], (1801 ^ _325847) ^ [] : [_388865 = empty_set]], -(subset(_388865, singleton(_388863)))], (783 ^ _325847) ^ [_353779, _353781] : [_353779 = union(_353781), 786 ^ _325847 : [(796 ^ _325847) ^ [_354287] : [-(in(_354287, _353779)), 797 ^ _325847 : [(798 ^ _325847) ^ [_354385] : [in(_354287, _354385), in(_354385, _353781)]]], (787 ^ _325847) ^ [_353960] : [in(_353960, _353779), 791 ^ _325847 : [(794 ^ _325847) ^ [] : [-(in(790 ^ [_353779, _353781, _353960], _353781))], (792 ^ _325847) ^ [] : [-(in(_353960, 790 ^ [_353779, _353781, _353960]))]]]]], (1462 ^ _325847) ^ [] : [-(empty(1460 ^ []))], (1513 ^ _325847) ^ [_378657, _378659] : [-(subset(_378659, _378659))], (1464 ^ _325847) ^ [] : [-(relation(1460 ^ []))], (1846 ^ _325847) ^ [_390521, _390523] : [-(set_difference(set_union2(_390523, _390521), _390521) = set_difference(_390523, _390521))], (2183 ^ _325847) ^ [_402249, _402251, _402253] : [singleton(_402253) = unordered_pair(_402251, _402249), -(_402251 = _402249)], (1420 ^ _325847) ^ [_375338, _375340] : [1421 ^ _325847 : [(1424 ^ _325847) ^ [] : [_375340 = singleton(_375338)], (1422 ^ _325847) ^ [] : [_375340 = empty_set]], -(subset(_375340, singleton(_375338)))], (521 ^ _325847) ^ [_343965, _343967] : [empty(_343967), 524 ^ _325847 : [(531 ^ _325847) ^ [] : [empty(_343965), -(element(_343965, _343967))], (525 ^ _325847) ^ [] : [element(_343965, _343967), -(empty(_343965))]]], (162 ^ _325847) ^ [_331249, _331251, _331253, _331255] : [-(union_of_subsets(_331255, _331251) = union_of_subsets(_331253, _331249)), _331255 = _331253, _331251 = _331249], (1529 ^ _325847) ^ [_379298, _379300, _379302, _379304] : [-(in(ordered_pair(_379304, _379302), cartesian_product2(_379300, _379298))), in(_379304, _379300), in(_379302, _379298)], (1187 ^ _325847) ^ [] : [true___, -(true___)], (1602 ^ _325847) ^ [_381959, _381961] : [-(subset(set_intersection2(_381961, _381959), _381961))], (1077 ^ _325847) ^ [_364952, _364954] : [proper_subset(_364954, _364952), 1080 ^ _325847 : [(1083 ^ _325847) ^ [] : [_364954 = _364952], (1081 ^ _325847) ^ [] : [-(subset(_364954, _364952))]]], (1737 ^ _325847) ^ [_386735] : [relation(_386735), 1740 ^ _325847 : [(1743 ^ _325847) ^ [] : [-(relation_dom(_386735) = relation_rng(relation_inverse(_386735)))], (1741 ^ _325847) ^ [] : [-(relation_rng(_386735) = relation_dom(relation_inverse(_386735)))]]], (1868 ^ _325847) ^ [_391275] : [relation(_391275), 1871 ^ _325847 : [(1872 ^ _325847) ^ [_391412] : [relation(_391412), -(subset(relation_dom(relation_composition(_391275, _391412)), relation_dom(_391275)))]]], (1119 ^ _325847) ^ [] : [true___, -(true___)], (850 ^ _325847) ^ [_356245, _356247, _356249] : [-(_356245 = set_difference(_356249, _356247)), 862 ^ _325847 : [(867 ^ _325847) ^ [] : [in(851 ^ [_356245, _356247, _356249], _356245)], (865 ^ _325847) ^ [] : [in(851 ^ [_356245, _356247, _356249], _356247)], (863 ^ _325847) ^ [] : [-(in(851 ^ [_356245, _356247, _356249], _356249))]], 854 ^ _325847 : [(857 ^ _325847) ^ [] : [in(851 ^ [_356245, _356247, _356249], _356249), -(in(851 ^ [_356245, _356247, _356249], _356247))], (855 ^ _325847) ^ [] : [-(in(851 ^ [_356245, _356247, _356249], _356245))]]], (2081 ^ _325847) ^ [_398538] : [empty(_398538), -(_398538 = empty_set)], (196 ^ _325847) ^ [_332455, _332457] : [_332457 = _332455, -(cast_to_subset(_332457) = cast_to_subset(_332455))], (212 ^ _325847) ^ [_333060, _333062, _333064, _333066] : [-(set_intersection2(_333066, _333062) = set_intersection2(_333064, _333060)), _333066 = _333064, _333062 = _333060], (653 ^ _325847) ^ [_348760, _348762, _348764] : [-(_348760 = cartesian_product2(_348764, _348762)), 671 ^ _325847 : [(674 ^ _325847) ^ [] : [-(in(670 ^ [_348760, _348762, _348764], _348762))], (676 ^ _325847) ^ [] : [-(654 ^ [_348760, _348762, _348764] = ordered_pair(669 ^ [_348760, _348762, _348764], 670 ^ [_348760, _348762, _348764]))], (678 ^ _325847) ^ [] : [in(654 ^ [_348760, _348762, _348764], _348760)], (672 ^ _325847) ^ [] : [-(in(669 ^ [_348760, _348762, _348764], _348764))]], 657 ^ _325847 : [(660 ^ _325847) ^ [_349098, _349100] : [in(_349100, _348764), in(_349098, _348762), 654 ^ [_348760, _348762, _348764] = ordered_pair(_349100, _349098)], (658 ^ _325847) ^ [] : [-(in(654 ^ [_348760, _348762, _348764], _348760))]]], (314 ^ _325847) ^ [_336758] : [empty(_336758), -(relation(_336758))], (1215 ^ _325847) ^ [_368425, _368427, _368429] : [-(element(subset_difference(_368429, _368427, _368425), powerset(_368429))), element(_368427, powerset(_368429)), element(_368425, powerset(_368429))], (430 ^ _325847) ^ [_340933, _340935] : [_340933 = singleton(_340935), 433 ^ _325847 : [(440 ^ _325847) ^ [_341275] : [_341275 = _340935, -(in(_341275, _340933))], (434 ^ _325847) ^ [_341103] : [in(_341103, _340933), -(_341103 = _340935)]]], (505 ^ _325847) ^ [_343552, _343554] : [-(empty(_343554)), 508 ^ _325847 : [(515 ^ _325847) ^ [] : [in(_343552, _343554), -(element(_343552, _343554))], (509 ^ _325847) ^ [] : [element(_343552, _343554), -(in(_343552, _343554))]]], (1809 ^ _325847) ^ [_389267, _389269] : [element(_389269, powerset(_389267)), -(subset(_389269, _389267))], (1360 ^ _325847) ^ [_373306, _373308] : [-(in(_373308, _373306)), -(disjoint(singleton(_373308), _373306))], (1680 ^ _325847) ^ [_384641] : [-(set_intersection2(_384641, empty_set) = empty_set)], (2093 ^ _325847) ^ [_398958, _398960] : [in(_398960, _398958), empty(_398958)], (1521 ^ _325847) ^ [_379033, _379035, _379037, _379039] : [in(ordered_pair(_379039, _379037), cartesian_product2(_379035, _379033)), 1524 ^ _325847 : [(1527 ^ _325847) ^ [] : [-(in(_379037, _379033))], (1525 ^ _325847) ^ [] : [-(in(_379039, _379035))]]], (1410 ^ _325847) ^ [_375078, _375080] : [subset(_375080, singleton(_375078)), -(_375080 = empty_set), -(_375080 = singleton(_375078))], (1668 ^ _325847) ^ [_384226, _384228, _384230] : [subset(_384230, _384228), -(subset(set_intersection2(_384230, _384226), set_intersection2(_384228, _384226)))], (914 ^ _325847) ^ [_358654, _358656] : [-(ordered_pair(_358656, _358654) = unordered_pair(unordered_pair(_358656, _358654), singleton(_358656)))], (1240 ^ _325847) ^ [_369197] : [empty(powerset(_369197))], (446 ^ _325847) ^ [_341454, _341456] : [-(_341454 = singleton(_341456)), 450 ^ _325847 : [(453 ^ _325847) ^ [] : [447 ^ [_341454, _341456] = _341456], (451 ^ _325847) ^ [] : [-(in(447 ^ [_341454, _341456], _341454))]], 454 ^ _325847 : [(457 ^ _325847) ^ [] : [in(447 ^ [_341454, _341456], _341454)], (455 ^ _325847) ^ [] : [-(447 ^ [_341454, _341456] = _341456)]]], (1203 ^ _325847) ^ [_367955, _367957] : [element(_367955, powerset(powerset(_367957))), -(element(union_of_subsets(_367957, _367955), powerset(_367957)))], (290 ^ _325847) ^ [_335840, _335842] : [_335842 = _335840, -(relation_dom(_335842) = relation_dom(_335840))], (828 ^ _325847) ^ [_355514, _355516, _355518] : [_355514 = set_difference(_355518, _355516), 831 ^ _325847 : [(840 ^ _325847) ^ [_355958] : [-(in(_355958, _355514)), in(_355958, _355518), -(in(_355958, _355516))], (832 ^ _325847) ^ [_355698] : [in(_355698, _355514), 835 ^ _325847 : [(838 ^ _325847) ^ [] : [in(_355698, _355516)], (836 ^ _325847) ^ [] : [-(in(_355698, _355518))]]]]], (1707 ^ _325847) ^ [_385550] : [-(subset(empty_set, _385550))], (1276 ^ _325847) ^ [_370465, _370467] : [empty(cartesian_product2(_370467, _370465)), -(empty(_370467)), -(empty(_370465))], (252 ^ _325847) ^ [_334496, _334498, _334500, _334502] : [-(set_union2(_334502, _334498) = set_union2(_334500, _334496)), _334502 = _334500, _334498 = _334496], (2150 ^ _325847) ^ [_401081, _401083, _401085] : [-(in(_401081, 2146 ^ [_401085])), in(_401083, 2146 ^ [_401085]), subset(_401081, _401083)], (1372 ^ _325847) ^ [_373718, _373720] : [in(_373720, _373718), -(subset(singleton(_373720), _373718))], (365 ^ _325847) ^ [_338729, _338731] : [-(_338731 = empty_set), 368 ^ _325847 : [(369 ^ _325847) ^ [] : [_338729 = set_meet(_338731), 372 ^ _325847 : [(373 ^ _325847) ^ [_339027] : [in(_339027, _338729), 376 ^ _325847 : [(377 ^ _325847) ^ [_339172] : [in(_339172, _338731), -(in(_339027, _339172))]]], (383 ^ _325847) ^ [_339357] : [385 ^ _325847 : [(388 ^ _325847) ^ [] : [in(_339357, 384 ^ [_338729, _338731, _339357])], (386 ^ _325847) ^ [] : [-(in(384 ^ [_338729, _338731, _339357], _338731))]], -(in(_339357, _338729))]]], (392 ^ _325847) ^ [] : [-(_338729 = set_meet(_338731)), 396 ^ _325847 : [(402 ^ _325847) ^ [] : [in(393 ^ [_338729, _338731], 398 ^ [_338729, _338731])], (400 ^ _325847) ^ [] : [-(in(398 ^ [_338729, _338731], _338731))], (397 ^ _325847) ^ [] : [-(in(393 ^ [_338729, _338731], _338729))]], 403 ^ _325847 : [(404 ^ _325847) ^ [_340131] : [in(_340131, _338731), -(in(393 ^ [_338729, _338731], _340131))], (410 ^ _325847) ^ [] : [in(393 ^ [_338729, _338731], _338729)]]]]], (467 ^ _325847) ^ [_342184] : [-(in(468 ^ [_342184], _342184)), -(_342184 = empty_set)], (296 ^ _325847) ^ [_336038, _336040] : [_336040 = _336038, -(relation_rng(_336040) = relation_rng(_336038))], (1272 ^ _325847) ^ [] : [-(empty(empty_set))], (1769 ^ _325847) ^ [_387903, _387905, _387907] : [subset(unordered_pair(_387907, _387905), _387903), 1772 ^ _325847 : [(1775 ^ _325847) ^ [] : [-(in(_387905, _387903))], (1773 ^ _325847) ^ [] : [-(in(_387907, _387903))]]], (100 ^ _325847) ^ [_329138, _329140, _329142, _329144] : [-(in(_329142, _329138)), in(_329144, _329140), _329144 = _329142, _329140 = _329138], (1972 ^ _325847) ^ [_394881, _394883] : [-(disjoint(_394883, _394881)), -(in(1975 ^ [_394881, _394883], set_intersection2(_394883, _394881)))], (280 ^ _325847) ^ [_335509, _335511, _335513, _335515] : [-(unordered_pair(_335515, _335511) = unordered_pair(_335513, _335509)), _335515 = _335513, _335511 = _335509], (1107 ^ _325847) ^ [] : [true___, -(true___)], (1646 ^ _325847) ^ [_383465] : [relation(_383465), -(subset(_383465, cartesian_product2(relation_dom(_383465), relation_rng(_383465))))], (1484 ^ _325847) ^ [_377617] : [-(element(1482 ^ [_377617], powerset(_377617)))], (1324 ^ _325847) ^ [_371937, _371939] : [-(set_intersection2(_371939, _371939) = _371939)], (916 ^ _325847) ^ [_358760] : [relation(_358760), -(relation_field(_358760) = set_union2(relation_dom(_358760), relation_rng(_358760)))]], input).
% 55.40/54.10  ncf('1',plain,[2194 : -(relation_dom(2188 ^ []) = empty_set), 2198 : -(relation_rng(2188 ^ []) = empty_set)],start(2192 ^ 0)).
% 55.40/54.10  ncf('1.1',plain,[relation_dom(2188 ^ []) = empty_set, relation(2188 ^ []), -(2188 ^ [] = empty_set)],extension(2055 ^ 3,bind([[_397675], [2188 ^ []]]))).
% 55.40/54.10  ncf('1.1.1',plain,[-(relation(2188 ^ []))],extension(2190 ^ 4)).
% 55.40/54.10  ncf('1.1.2',plain,[2188 ^ [] = empty_set, -(relation_rng(2188 ^ []) = relation_rng(empty_set))],extension(296 ^ 4,bind([[_336038, _336040], [empty_set, 2188 ^ []]]))).
% 55.40/54.10  ncf('1.1.2.1',plain,[relation_rng(2188 ^ []) = relation_rng(empty_set), -(relation_rng(2188 ^ []) = empty_set), relation_rng(empty_set) = empty_set],extension(10 ^ 5,bind([[_326282, _326284, _326286], [empty_set, relation_rng(empty_set), relation_rng(2188 ^ [])]]))).
% 55.40/54.10  ncf('1.1.2.1.1',plain,[relation_rng(2188 ^ []) = empty_set],extension(2196 ^ 6)).
% 55.40/54.10  ncf('1.1.2.1.2',plain,[-(relation_rng(empty_set) = empty_set)],extension(2037 ^ 6)).
% 55.40/54.10  ncf('1.2',plain,[relation_rng(2188 ^ []) = empty_set, relation(2188 ^ []), -(2188 ^ [] = empty_set)],extension(2055 ^ 3,bind([[_397675], [2188 ^ []]]))).
% 55.40/54.10  ncf('1.2.1',plain,[-(relation(2188 ^ []))],extension(2190 ^ 4)).
% 55.40/54.10  ncf('1.2.2',plain,[2188 ^ [] = empty_set, -(relation_dom(2188 ^ []) = relation_dom(empty_set))],extension(290 ^ 4,bind([[_335840, _335842], [empty_set, 2188 ^ []]]))).
% 55.40/54.10  ncf('1.2.2.1',plain,[relation_dom(2188 ^ []) = relation_dom(empty_set), -(relation_dom(2188 ^ []) = empty_set), relation_dom(empty_set) = empty_set],extension(10 ^ 5,bind([[_326282, _326284, _326286], [empty_set, relation_dom(empty_set), relation_dom(2188 ^ [])]]))).
% 55.40/54.10  ncf('1.2.2.1.1',plain,[relation_dom(2188 ^ []) = empty_set],extension(2200 ^ 6)).
% 55.40/54.10  ncf('1.2.2.1.2',plain,[-(relation_dom(empty_set) = empty_set)],extension(2035 ^ 6)).
% 55.40/54.10  %-----------------------------------------------------
% 55.40/54.10  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------