%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU203+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 63.32s 61.45s
% Output   : Proof 63.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU203+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 13:36:14 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 63.32/61.45  
% 63.32/61.45  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 63.32/61.45  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.32/61.45  %-----------------------------------------------------
% 63.32/61.45  ncf(matrix, plain, [(2693 ^ _58803) ^ [] : [2707 ^ _58803 : [(2710 ^ _58803) ^ [] : [-(in(ordered_pair(2706 ^ [], 2687 ^ []), 2689 ^ []))], (2712 ^ _58803) ^ [] : [-(in(2706 ^ [], 2688 ^ []))], (2714 ^ _58803) ^ [] : [in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ []))], (2708 ^ _58803) ^ [] : [-(in(2706 ^ [], relation_dom(2689 ^ [])))]], 2694 ^ _58803 : [(2697 ^ _58803) ^ [_58876] : [in(_58876, relation_dom(2689 ^ [])), in(ordered_pair(_58876, 2687 ^ []), 2689 ^ []), in(_58876, 2688 ^ [])], (2695 ^ _58803) ^ [] : [-(in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ [])))]]], (2691 ^ _58803) ^ [] : [-(relation(2689 ^ []))], !, (1779 ^ _17227) ^ [_44562, _44564] : [1780 ^ _17227 : [(1783 ^ _17227) ^ [] : [_44564 = singleton(_44562)], (1781 ^ _17227) ^ [] : [_44564 = empty_set]], -(subset(_44564, singleton(_44562)))], (1749 ^ _17227) ^ [_44201, _44203] : [element(_44201, powerset(_44203)), 1752 ^ _17227 : [(1753 ^ _17227) ^ [_44268] : [in(_44268, _44201), -(in(_44268, _44203))]]], (1563 ^ _17227) ^ [_41749] : [-(element(1561 ^ [_41749], _41749))], (2174 ^ _17227) ^ [_50267, _50269] : [in(_50269, _50267), -(subset(singleton(_50269), _50267))], (1267 ^ _17227) ^ [_37473, _37475] : [disjoint(_37475, _37473), -(set_intersection2(_37475, _37473) = empty_set)], (1643 ^ _17227) ^ [_42756] : [empty(relation_rng(_42756)), -(empty(_42756)), relation(_42756)], (2522 ^ _17227) ^ [_55065] : [-(relation_rng(identity_relation(_55065)) = _55065)], (2500 ^ _17227) ^ [_54814, _54816] : [-(in(_54814, _54816)), -(set_difference(_54816, singleton(_54814)) = _54816)], (2632 ^ _17227) ^ [_56619, _56621] : [relation(_56619), -(relation_dom_restriction(_56619, _56621) = relation_composition(identity_relation(_56621), _56619))], (358 ^ _17227) ^ [_22402, _22404] : [-(set_union2(_22404, _22402) = set_union2(_22402, _22404))], (2279 ^ _17227) ^ [_51738] : [relation(_51738), 2282 ^ _17227 : [(2283 ^ _17227) ^ [_51803] : [relation(_51803), -(subset(relation_dom(relation_composition(_51738, _51803)), relation_dom(_51738)))]]], (1133 ^ _17227) ^ [_35162, _35164, _35166] : [_35162 = set_difference(_35166, _35164), 1136 ^ _17227 : [(1145 ^ _17227) ^ [_35364] : [-(in(_35364, _35162)), in(_35364, _35166), -(in(_35364, _35164))], (1137 ^ _17227) ^ [_35253] : [in(_35253, _35162), 1140 ^ _17227 : [(1143 ^ _17227) ^ [] : [in(_35253, _35164)], (1141 ^ _17227) ^ [] : [-(in(_35253, _35166))]]]]], (2198 ^ _17227) ^ [_50616, _50618] : [-(set_union2(_50618, set_difference(_50616, _50618)) = set_union2(_50618, _50616))], (2349 ^ _17227) ^ [_52833, _52835] : [element(_52833, powerset(powerset(_52835))), -(_52833 = empty_set), -(subset_difference(_52835, cast_to_subset(_52835), union_of_subsets(_52835, _52833)) = meet_of_subsets(_52835, complements_of_subsets(_52835, _52833)))], (2552 ^ _17227) ^ [_55494, _55496] : [-(subset(_55496, set_union2(_55496, _55494)))], (140 ^ _17227) ^ [_19145, _19147, _19149, _19151] : [-(cartesian_product2(_19151, _19147) = cartesian_product2(_19149, _19145)), _19151 = _19149, _19147 = _19145], (1731 ^ _17227) ^ [_43939, _43941] : [in(_43941, _43939), -(subset(singleton(_43941), _43939))], (2093 ^ _17227) ^ [_49117, _49119] : [element(_49119, _49117), -(empty(_49117)), -(in(_49119, _49117))], (1683 ^ _17227) ^ [_43276, _43278] : [-(set_intersection2(_43278, _43278) = _43278)], (2079 ^ _17227) ^ [_48917, _48919, _48921] : [subset(_48921, _48919), -(subset(set_intersection2(_48921, _48917), set_intersection2(_48919, _48917)))], (196 ^ _17227) ^ [_19983, _19985] : [_19985 = _19983, -(cast_to_subset(_19985) = cast_to_subset(_19983))], (312 ^ _17227) ^ [_21685, _21687, _21689, _21691] : [-(relation_image(_21691, _21687) = relation_image(_21689, _21685)), _21691 = _21689, _21687 = _21685], (2414 ^ _17227) ^ [_53703, _53705, _53707] : [element(_53703, powerset(_53707)), in(_53705, subset_complement(_53707, _53703)), in(_53705, _53703)], (2146 ^ _17227) ^ [_49845, _49847] : [-(subset(set_difference(_49847, _49845), _49847))], (1848 ^ _17227) ^ [] : [empty(1846 ^ [])], (1825 ^ _17227) ^ [_45239] : [-(empty(_45239)), 1829 ^ _17227 : [(1832 ^ _17227) ^ [] : [empty(1828 ^ [_45239])], (1830 ^ _17227) ^ [] : [-(element(1828 ^ [_45239], powerset(_45239)))]]], (1705 ^ _17227) ^ [_43621] : [singleton(_43621) = empty_set], (1438 ^ _17227) ^ [] : [true___, -(true___)], (1972 ^ _17227) ^ [_47311, _47313] : [subset(_47313, _47311), -(set_union2(_47313, _47311) = _47311)], (1874 ^ _17227) ^ [_45903, _45905] : [disjoint(_45905, _45903), -(disjoint(_45903, _45905))], (1936 ^ _17227) ^ [_46768, _46770] : [relation(_46768), -(subset(relation_rng_restriction(_46770, _46768), _46768))], (62 ^ _17227) ^ [_18066, _18068] : [-(empty(_18066)), _18068 = _18066, empty(_18068)], (1468 ^ _17227) ^ [] : [true___, -(true___)], (1619 ^ _17227) ^ [] : [-(empty(empty_set))], (2682 ^ _17227) ^ [_57482, _57484, _57486] : [singleton(_57486) = unordered_pair(_57484, _57482), -(_57484 = _57482)], (1835 ^ _17227) ^ [] : [-(empty(1833 ^ []))], (1430 ^ _17227) ^ [] : [true___, -(true___)], (683 ^ _17227) ^ [_27916, _27918] : [-(_27916 = singleton(_27918)), 687 ^ _17227 : [(690 ^ _17227) ^ [] : [684 ^ [_27916, _27918] = _27918], (688 ^ _17227) ^ [] : [-(in(684 ^ [_27916, _27918], _27916))]], 691 ^ _17227 : [(694 ^ _17227) ^ [] : [in(684 ^ [_27916, _27918], _27916)], (692 ^ _17227) ^ [] : [-(684 ^ [_27916, _27918] = _27918)]]], (1962 ^ _17227) ^ [_47162, _47164, _47166, _47168] : [-(subset(cartesian_product2(_47168, _47164), cartesian_product2(_47166, _47162))), subset(_47168, _47166), subset(_47164, _47162)], (1176 ^ _17227) ^ [_35872] : [relation(_35872), 1179 ^ _17227 : [(1180 ^ _17227) ^ [_35964] : [_35964 = relation_rng(_35872), 1183 ^ _17227 : [(1191 ^ _17227) ^ [_36146] : [1192 ^ _17227 : [(1193 ^ _17227) ^ [_36190] : [in(ordered_pair(_36190, _36146), _35872)]], -(in(_36146, _35964))], (1184 ^ _17227) ^ [_36051] : [in(_36051, _35964), -(in(ordered_pair(1187 ^ [_35872, _35964, _36051], _36051), _35872))]]], (1197 ^ _17227) ^ [_36246] : [-(_36246 = relation_rng(_35872)), 1201 ^ _17227 : [(1204 ^ _17227) ^ [_36380] : [in(ordered_pair(_36380, 1198 ^ [_35872, _36246]), _35872)], (1202 ^ _17227) ^ [] : [-(in(1198 ^ [_35872, _36246], _36246))]], 1206 ^ _17227 : [(1209 ^ _17227) ^ [] : [in(1198 ^ [_35872, _36246], _36246)], (1207 ^ _17227) ^ [] : [-(in(ordered_pair(1205 ^ [_35872, _36246], 1198 ^ [_35872, _36246]), _35872))]]]]], (302 ^ _17227) ^ [_21536, _21538, _21540, _21542] : [-(unordered_pair(_21542, _21538) = unordered_pair(_21540, _21536)), _21542 = _21540, _21538 = _21536], (2299 ^ _17227) ^ [_52054, _52056] : [subset(_52056, _52054), -(_52054 = set_union2(_52056, set_difference(_52054, _52056)))], (1880 ^ _17227) ^ [_46001, _46003, _46005, _46007] : [in(ordered_pair(_46007, _46005), cartesian_product2(_46003, _46001)), 1883 ^ _17227 : [(1886 ^ _17227) ^ [] : [-(in(_46005, _46001))], (1884 ^ _17227) ^ [] : [-(in(_46007, _46003))]]], (418 ^ _17227) ^ [_23352, _23354] : [-(_23354 = _23352), subset(_23354, _23352), subset(_23352, _23354)], (1908 ^ _17227) ^ [_46377, _46379, _46381] : [relation(_46377), 1911 ^ _17227 : [(1920 ^ _17227) ^ [] : [-(in(_46381, relation_rng(relation_rng_restriction(_46379, _46377)))), in(_46381, _46379), in(_46381, relation_rng(_46377))], (1912 ^ _17227) ^ [] : [in(_46381, relation_rng(relation_rng_restriction(_46379, _46377))), 1915 ^ _17227 : [(1918 ^ _17227) ^ [] : [-(in(_46381, relation_rng(_46377)))], (1916 ^ _17227) ^ [] : [-(in(_46381, _46379))]]]]], (1979 ^ _17227) ^ [_47478] : [-(in(_47478, 1977 ^ [_47478]))], (532 ^ _17227) ^ [_25369] : [relation(_25369), 535 ^ _17227 : [(536 ^ _17227) ^ [_25476, _25478] : [_25476 = relation_image(_25369, _25478), 539 ^ _17227 : [(549 ^ _17227) ^ [_25709] : [-(in(_25709, _25476)), 550 ^ _17227 : [(551 ^ _17227) ^ [_25756] : [in(ordered_pair(_25756, _25709), _25369), in(_25756, _25478)]]], (540 ^ _17227) ^ [_25573] : [in(_25573, _25476), 544 ^ _17227 : [(547 ^ _17227) ^ [] : [-(in(543 ^ [_25369, _25476, _25478, _25573], _25478))], (545 ^ _17227) ^ [] : [-(in(ordered_pair(543 ^ [_25369, _25476, _25478, _25573], _25573), _25369))]]]]], (559 ^ _17227) ^ [_25874, _25876] : [-(_25874 = relation_image(_25369, _25876)), 572 ^ _17227 : [(577 ^ _17227) ^ [] : [in(560 ^ [_25369, _25874, _25876], _25874)], (575 ^ _17227) ^ [] : [-(in(571 ^ [_25369, _25874, _25876], _25876))], (573 ^ _17227) ^ [] : [-(in(ordered_pair(571 ^ [_25369, _25874, _25876], 560 ^ [_25369, _25874, _25876]), _25369))]], 563 ^ _17227 : [(566 ^ _17227) ^ [_26022] : [in(ordered_pair(_26022, 560 ^ [_25369, _25874, _25876]), _25369), in(_26022, _25876)], (564 ^ _17227) ^ [] : [-(in(560 ^ [_25369, _25874, _25876], _25874))]]]]], (1769 ^ _17227) ^ [_44468, _44470] : [subset(_44470, singleton(_44468)), -(_44470 = empty_set), -(_44470 = singleton(_44468))], (1930 ^ _17227) ^ [_46683, _46685] : [relation(_46683), -(subset(relation_rng(relation_rng_restriction(_46685, _46683)), _46685))], (1948 ^ _17227) ^ [_46938, _46940, _46942] : [subset(_46942, _46940), 1951 ^ _17227 : [(1954 ^ _17227) ^ [] : [-(subset(cartesian_product2(_46938, _46942), cartesian_product2(_46938, _46940)))], (1952 ^ _17227) ^ [] : [-(subset(cartesian_product2(_46942, _46938), cartesian_product2(_46940, _46938)))]]], (124 ^ _17227) ^ [_18911, _18913] : [_18913 = _18911, -(set_meet(_18913) = set_meet(_18911))], (1556 ^ _17227) ^ [] : [true___, -(true___)], (130 ^ _17227) ^ [_18996, _18998, _19000, _19002] : [-(relation_rng_restriction(_19002, _18998) = relation_rng_restriction(_19000, _18996)), _19002 = _19000, _18998 = _18996], (182 ^ _17227) ^ [_19762, _19764, _19766, _19768, _19770, _19772] : [-(subset_difference(_19772, _19768, _19764) = subset_difference(_19770, _19766, _19762)), _19772 = _19770, _19768 = _19766, _19764 = _19762], (1697 ^ _17227) ^ [_43478, _43480] : [element(_43478, powerset(powerset(_43480))), -(complements_of_subsets(_43480, complements_of_subsets(_43480, _43478)) = _43478)], (1213 ^ _17227) ^ [_36527, _36529] : [element(_36527, powerset(_36529)), -(subset_complement(_36529, _36527) = set_difference(_36529, _36527))], (2033 ^ _17227) ^ [_48257, _48259, _48261] : [-(subset(_48261, _48257)), subset(_48261, _48259), subset(_48259, _48257)], (2448 ^ _17227) ^ [] : [-(relation_rng(empty_set) = empty_set)], (1823 ^ _17227) ^ [] : [-(relation(1819 ^ []))], (2588 ^ _17227) ^ [_56007, _56009] : [relation(_56007), -(subset(relation_dom_restriction(_56007, _56009), _56007))], (1713 ^ _17227) ^ [_43733, _43735] : [disjoint(singleton(_43735), _43733), in(_43735, _43733)], (1227 ^ _17227) ^ [_36747] : [relation(_36747), 1230 ^ _17227 : [(1231 ^ _17227) ^ [_36835] : [relation(_36835), 1234 ^ _17227 : [(1235 ^ _17227) ^ [] : [_36835 = relation_inverse(_36747), 1238 ^ _17227 : [(1245 ^ _17227) ^ [_37074, _37076] : [in(ordered_pair(_37074, _37076), _36747), -(in(ordered_pair(_37076, _37074), _36835))], (1239 ^ _17227) ^ [_36985, _36987] : [in(ordered_pair(_36987, _36985), _36835), -(in(ordered_pair(_36985, _36987), _36747))]]], (1251 ^ _17227) ^ [] : [-(_36835 = relation_inverse(_36747)), 1256 ^ _17227 : [(1259 ^ _17227) ^ [] : [in(ordered_pair(1253 ^ [_36747, _36835], 1252 ^ [_36747, _36835]), _36747)], (1257 ^ _17227) ^ [] : [-(in(ordered_pair(1252 ^ [_36747, _36835], 1253 ^ [_36747, _36835]), _36835))]], 1260 ^ _17227 : [(1263 ^ _17227) ^ [] : [in(ordered_pair(1252 ^ [_36747, _36835], 1253 ^ [_36747, _36835]), _36835)], (1261 ^ _17227) ^ [] : [-(in(ordered_pair(1253 ^ [_36747, _36835], 1252 ^ [_36747, _36835]), _36747))]]]]]]], (1942 ^ _17227) ^ [_46849, _46851] : [relation(_46849), -(subset(relation_rng(relation_rng_restriction(_46851, _46849)), relation_rng(_46849)))], (1589 ^ _17227) ^ [] : [-(empty(empty_set))], (1486 ^ _17227) ^ [] : [true___, -(true___)], (1492 ^ _17227) ^ [] : [true___, -(true___)], (2045 ^ _17227) ^ [_48408, _48410, _48412] : [relation(_48408), in(ordered_pair(_48412, _48410), _48408), 2052 ^ _17227 : [(2055 ^ _17227) ^ [] : [-(in(_48410, relation_rng(_48408)))], (2053 ^ _17227) ^ [] : [-(in(_48412, relation_dom(_48408)))]]], (1418 ^ _17227) ^ [] : [true___, -(true___)], (1337 ^ _17227) ^ [_38821, _38823] : [element(_38821, powerset(powerset(_38823))), 1340 ^ _17227 : [(1341 ^ _17227) ^ [_38927] : [element(_38927, powerset(powerset(_38823))), 1344 ^ _17227 : [(1345 ^ _17227) ^ [] : [_38927 = complements_of_subsets(_38823, _38821), 1348 ^ _17227 : [(1349 ^ _17227) ^ [_39078] : [element(_39078, powerset(_38823)), 1352 ^ _17227 : [(1359 ^ _17227) ^ [] : [in(subset_complement(_38823, _39078), _38821), -(in(_39078, _38927))], (1353 ^ _17227) ^ [] : [in(_39078, _38927), -(in(subset_complement(_38823, _39078), _38821))]]]]], (1365 ^ _17227) ^ [] : [-(_38927 = complements_of_subsets(_38823, _38821)), 1367 ^ _17227 : [(1370 ^ _17227) ^ [] : [1371 ^ _17227 : [(1374 ^ _17227) ^ [] : [in(subset_complement(_38823, 1366 ^ [_38821, _38823, _38927]), _38821)], (1372 ^ _17227) ^ [] : [-(in(1366 ^ [_38821, _38823, _38927], _38927))]], 1375 ^ _17227 : [(1378 ^ _17227) ^ [] : [in(1366 ^ [_38821, _38823, _38927], _38927)], (1376 ^ _17227) ^ [] : [-(in(subset_complement(_38823, 1366 ^ [_38821, _38823, _38927]), _38821))]]], (1368 ^ _17227) ^ [] : [-(element(1366 ^ [_38821, _38823, _38927], powerset(_38823)))]]]]]]], (2148 ^ _17227) ^ [_49873] : [relation(_49873), 2151 ^ _17227 : [(2154 ^ _17227) ^ [] : [-(relation_dom(_49873) = relation_rng(relation_inverse(_49873)))], (2152 ^ _17227) ^ [] : [-(relation_rng(_49873) = relation_dom(relation_inverse(_49873)))]]], (1474 ^ _17227) ^ [] : [true___, -(true___)], (34 ^ _17227) ^ [_17680, _17682, _17684, _17686] : [-(proper_subset(_17684, _17680)), proper_subset(_17686, _17682), _17686 = _17684, _17682 = _17680], (2626 ^ _17227) ^ [_56538, _56540] : [in(_56540, _56538), -(subset(_56540, union(_56538)))], (1444 ^ _17227) ^ [] : [true___, -(true___)], (2659 ^ _17227) ^ [_57115, _57117] : [in(_57115, 2645 ^ [_57117]), 2663 ^ _17227 : [(2666 ^ _17227) ^ [_57261] : [subset(_57261, _57115), -(in(_57261, 2662 ^ [_57115, _57117]))], (2664 ^ _17227) ^ [] : [-(in(2662 ^ [_57115, _57117], 2645 ^ [_57117]))]]], (2289 ^ _17227) ^ [_51896] : [relation(_51896), 2292 ^ _17227 : [(2293 ^ _17227) ^ [_51961] : [relation(_51961), -(subset(relation_rng(relation_composition(_51896, _51961)), relation_rng(_51961)))]]], (172 ^ _17227) ^ [_19613, _19615, _19617, _19619] : [-(complements_of_subsets(_19619, _19615) = complements_of_subsets(_19617, _19613)), _19619 = _19617, _19615 = _19613], (1219 ^ _17227) ^ [_36620, _36622] : [-(ordered_pair(_36622, _36620) = unordered_pair(unordered_pair(_36622, _36620), singleton(_36622)))], (1888 ^ _17227) ^ [_46116, _46118, _46120, _46122] : [-(in(ordered_pair(_46122, _46120), cartesian_product2(_46118, _46116))), in(_46122, _46118), in(_46120, _46116)], (428 ^ _17227) ^ [_23483] : [relation(_23483), 431 ^ _17227 : [(432 ^ _17227) ^ [_23583, _23585] : [relation(_23583), 435 ^ _17227 : [(436 ^ _17227) ^ [] : [_23583 = relation_dom_restriction(_23483, _23585), 439 ^ _17227 : [(448 ^ _17227) ^ [_23862, _23864] : [-(in(ordered_pair(_23864, _23862), _23583)), in(_23864, _23585), in(ordered_pair(_23864, _23862), _23483)], (440 ^ _17227) ^ [_23745, _23747] : [in(ordered_pair(_23747, _23745), _23583), 443 ^ _17227 : [(446 ^ _17227) ^ [] : [-(in(ordered_pair(_23747, _23745), _23483))], (444 ^ _17227) ^ [] : [-(in(_23747, _23585))]]]]], (458 ^ _17227) ^ [] : [-(_23583 = relation_dom_restriction(_23483, _23585)), 471 ^ _17227 : [(476 ^ _17227) ^ [] : [in(ordered_pair(459 ^ [_23483, _23583, _23585], 460 ^ [_23483, _23583, _23585]), _23583)], (474 ^ _17227) ^ [] : [-(in(ordered_pair(459 ^ [_23483, _23583, _23585], 460 ^ [_23483, _23583, _23585]), _23483))], (472 ^ _17227) ^ [] : [-(in(459 ^ [_23483, _23583, _23585], _23585))]], 463 ^ _17227 : [(466 ^ _17227) ^ [] : [in(459 ^ [_23483, _23583, _23585], _23585), in(ordered_pair(459 ^ [_23483, _23583, _23585], 460 ^ [_23483, _23583, _23585]), _23483)], (464 ^ _17227) ^ [] : [-(in(ordered_pair(459 ^ [_23483, _23583, _23585], 460 ^ [_23483, _23583, _23585]), _23583))]]]]]]], (1412 ^ _17227) ^ [] : [true___, -(true___)], (2359 ^ _17227) ^ [_52963, _52965] : [element(_52963, powerset(powerset(_52965))), -(_52963 = empty_set), -(union_of_subsets(_52965, complements_of_subsets(_52965, _52963)) = subset_difference(_52965, cast_to_subset(_52965), meet_of_subsets(_52965, _52963)))], (987 ^ _17227) ^ [_32737, _32739] : [subset(_32739, _32737), 990 ^ _17227 : [(991 ^ _17227) ^ [_32800] : [in(_32800, _32739), -(in(_32800, _32737))]]], (1845 ^ _17227) ^ [_45474] : [-(empty(1841 ^ [_45474]))], (1382 ^ _17227) ^ [_39618, _39620] : [proper_subset(_39620, _39618), 1385 ^ _17227 : [(1388 ^ _17227) ^ [] : [_39620 = _39618], (1386 ^ _17227) ^ [] : [-(subset(_39620, _39618))]]], (1613 ^ _17227) ^ [_42433, _42435] : [-(empty(_42435)), empty(set_union2(_42433, _42435))], (959 ^ _17227) ^ [_32249] : [relation(_32249), 962 ^ _17227 : [(963 ^ _17227) ^ [_32335] : [relation(_32335), 966 ^ _17227 : [(967 ^ _17227) ^ [] : [subset(_32249, _32335), 970 ^ _17227 : [(971 ^ _17227) ^ [_32466, _32468] : [in(ordered_pair(_32468, _32466), _32249), -(in(ordered_pair(_32468, _32466), _32335))]]], (977 ^ _17227) ^ [] : [980 ^ _17227 : [(983 ^ _17227) ^ [] : [in(ordered_pair(978 ^ [_32249, _32335], 979 ^ [_32249, _32335]), _32335)], (981 ^ _17227) ^ [] : [-(in(ordered_pair(978 ^ [_32249, _32335], 979 ^ [_32249, _32335]), _32249))]], -(subset(_32249, _32335))]]]]], (410 ^ _17227) ^ [_23253, _23255] : [_23255 = _23253, 413 ^ _17227 : [(416 ^ _17227) ^ [] : [-(subset(_23253, _23255))], (414 ^ _17227) ^ [] : [-(subset(_23255, _23253))]]], (2424 ^ _17227) ^ [_53847] : [relation(_53847), -(in(ordered_pair(2429 ^ [_53847], 2430 ^ [_53847]), _53847)), -(_53847 = empty_set)], (1221 ^ _17227) ^ [_36656] : [relation(_36656), -(relation_field(_36656) = set_union2(relation_dom(_36656), relation_rng(_36656)))], (2063 ^ _17227) ^ [_48666] : [relation(_48666), 2066 ^ _17227 : [(2067 ^ _17227) ^ [_48744] : [relation(_48744), subset(_48666, _48744), 2074 ^ _17227 : [(2077 ^ _17227) ^ [] : [-(subset(relation_rng(_48666), relation_rng(_48744)))], (2075 ^ _17227) ^ [] : [-(subset(relation_dom(_48666), relation_dom(_48744)))]]]]], (2546 ^ _17227) ^ [_55420, _55422] : [in(_55422, _55420), empty(_55420)], (2396 ^ _17227) ^ [_53434] : [-(_53434 = empty_set), 2399 ^ _17227 : [(2400 ^ _17227) ^ [_53517] : [element(_53517, powerset(_53434)), 2403 ^ _17227 : [(2404 ^ _17227) ^ [_53595] : [element(_53595, _53434), -(in(_53595, _53517)), -(in(_53595, subset_complement(_53434, _53517)))]]]]], (2520 ^ _17227) ^ [_55041] : [-(relation_dom(identity_relation(_55041)) = _55041)], (1086 ^ _17227) ^ [_34379] : [-(cast_to_subset(_34379) = _34379)], (2649 ^ _17227) ^ [_56962, _56964, _56966] : [-(in(_56962, 2645 ^ [_56966])), in(_56964, 2645 ^ [_56966]), subset(_56962, _56964)], (344 ^ _17227) ^ [_22222, _22224] : [proper_subset(_22224, _22222), proper_subset(_22222, _22224)], (2118 ^ _17227) ^ [_49441] : [-(subset(empty_set, _49441))], (2319 ^ _17227) ^ [_52371, _52373] : [element(_52371, powerset(powerset(_52373))), -(_52371 = empty_set), complements_of_subsets(_52373, _52371) = empty_set], (1450 ^ _17227) ^ [] : [true___, -(true___)], (202 ^ _17227) ^ [_20068, _20070, _20072, _20074] : [-(meet_of_subsets(_20074, _20070) = meet_of_subsets(_20072, _20068)), _20074 = _20072, _20070 = _20068], (1591 ^ _17227) ^ [_42128, _42130] : [empty(ordered_pair(_42130, _42128))], (1981 ^ _17227) ^ [_47506, _47508, _47510] : [-(in(_47506, 1977 ^ [_47510])), in(_47508, 1977 ^ [_47510]), subset(_47506, _47508)], (1605 ^ _17227) ^ [_42316, _42318] : [-(empty(_42318)), empty(set_union2(_42318, _42316))], (20 ^ _17227) ^ [_17487, _17489, _17491, _17493] : [-(element(_17491, _17487)), element(_17493, _17489), _17493 = _17491, _17489 = _17487], (1532 ^ _17227) ^ [_41374, _41376] : [relation(_41376), -(relation(relation_dom_restriction(_41376, _41374)))], (1793 ^ _17227) ^ [_44789, _44791, _44793, _44795] : [in(ordered_pair(_44795, _44793), cartesian_product2(_44791, _44789)), 1796 ^ _17227 : [(1799 ^ _17227) ^ [] : [-(in(_44793, _44789))], (1797 ^ _17227) ^ [] : [-(in(_44795, _44791))]]], (284 ^ _17227) ^ [_21281, _21283] : [_21283 = _21281, -(union(_21283) = union(_21281))], (667 ^ _17227) ^ [_27681, _27683] : [_27681 = singleton(_27683), 670 ^ _17227 : [(677 ^ _17227) ^ [_27835] : [_27835 = _27683, -(in(_27835, _27681))], (671 ^ _17227) ^ [_27760] : [in(_27760, _27681), -(_27760 = _27683)]]], (1400 ^ _17227) ^ [] : [true___, -(true___)], (1514 ^ _17227) ^ [_41102] : [-(relation(identity_relation(_41102)))], (1424 ^ _17227) ^ [] : [true___, -(true___)], (1538 ^ _17227) ^ [_41453, _41455] : [element(_41453, powerset(powerset(_41455))), -(element(complements_of_subsets(_41455, _41453), powerset(powerset(_41455))))], (356 ^ _17227) ^ [_22371, _22373] : [-(unordered_pair(_22373, _22371) = unordered_pair(_22371, _22373))], (156 ^ _17227) ^ [_19379, _19381] : [_19381 = _19379, -(relation_inverse(_19381) = relation_inverse(_19379))], (2168 ^ _17227) ^ [_50190, _50192] : [subset(singleton(_50192), _50190), -(in(_50192, _50190))], (1611 ^ _17227) ^ [_42407, _42409] : [empty(unordered_pair(_42409, _42407))], (798 ^ _17227) ^ [_29696, _29698] : [empty(_29698), 801 ^ _17227 : [(808 ^ _17227) ^ [] : [empty(_29696), -(element(_29696, _29698))], (802 ^ _17227) ^ [] : [element(_29696, _29698), -(empty(_29696))]]], (2446 ^ _17227) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2514 ^ _17227) ^ [_54958, _54960] : [subset(singleton(_54960), singleton(_54958)), -(_54960 = _54958)], (2638 ^ _17227) ^ [_56710, _56712] : [relation(_56710), -(subset(relation_rng(relation_dom_restriction(_56710, _56712)), relation_rng(_56710)))], (2450 ^ _17227) ^ [_54128, _54130] : [subset(_54130, _54128), proper_subset(_54128, _54130)], (698 ^ _17227) ^ [_28170] : [_28170 = empty_set, 701 ^ _17227 : [(702 ^ _17227) ^ [_28231] : [in(_28231, _28170)]]], (362 ^ _17227) ^ [_22464, _22466] : [relation(_22464), 365 ^ _17227 : [(366 ^ _17227) ^ [] : [_22464 = identity_relation(_22466), 369 ^ _17227 : [(378 ^ _17227) ^ [_22726, _22728] : [-(in(ordered_pair(_22728, _22726), _22464)), in(_22728, _22466), _22728 = _22726], (370 ^ _17227) ^ [_22617, _22619] : [in(ordered_pair(_22619, _22617), _22464), 373 ^ _17227 : [(376 ^ _17227) ^ [] : [-(_22619 = _22617)], (374 ^ _17227) ^ [] : [-(in(_22619, _22466))]]]]], (388 ^ _17227) ^ [] : [-(_22464 = identity_relation(_22466)), 401 ^ _17227 : [(406 ^ _17227) ^ [] : [in(ordered_pair(389 ^ [_22464, _22466], 390 ^ [_22464, _22466]), _22464)], (404 ^ _17227) ^ [] : [-(389 ^ [_22464, _22466] = 390 ^ [_22464, _22466])], (402 ^ _17227) ^ [] : [-(in(389 ^ [_22464, _22466], _22466))]], 393 ^ _17227 : [(396 ^ _17227) ^ [] : [in(389 ^ [_22464, _22466], _22466), 389 ^ [_22464, _22466] = 390 ^ [_22464, _22466]], (394 ^ _17227) ^ [] : [-(in(ordered_pair(389 ^ [_22464, _22466], 390 ^ [_22464, _22466]), _22464))]]]]], (2566 ^ _17227) ^ [_55701, _55703, _55705] : [relation(_55701), 2569 ^ _17227 : [(2578 ^ _17227) ^ [] : [-(in(_55705, relation_dom(relation_dom_restriction(_55701, _55703)))), in(_55705, _55703), in(_55705, relation_dom(_55701))], (2570 ^ _17227) ^ [] : [in(_55705, relation_dom(relation_dom_restriction(_55701, _55703))), 2573 ^ _17227 : [(2576 ^ _17227) ^ [] : [-(in(_55705, relation_dom(_55701)))], (2574 ^ _17227) ^ [] : [-(in(_55705, _55703))]]]]], (857 ^ _17227) ^ [_30558, _30560, _30562] : [_30558 = set_union2(_30562, _30560), 860 ^ _17227 : [(861 ^ _17227) ^ [_30647] : [in(_30647, _30558), -(in(_30647, _30562)), -(in(_30647, _30560))], (871 ^ _17227) ^ [_30737] : [872 ^ _17227 : [(875 ^ _17227) ^ [] : [in(_30737, _30560)], (873 ^ _17227) ^ [] : [in(_30737, _30562)]], -(in(_30737, _30558))]]], (2132 ^ _17227) ^ [_49635, _49637, _49639] : [subset(_49639, _49637), -(subset(set_difference(_49639, _49635), set_difference(_49637, _49635)))], (1707 ^ _17227) ^ [_43646, _43648] : [in(_43648, _43646), -(set_union2(singleton(_43648), _43646) = _43646)], (2644 ^ _17227) ^ [_56799] : [-(union(powerset(_56799)) = _56799)], (930 ^ _17227) ^ [_31731, _31733, _31735] : [-(_31731 = cartesian_product2(_31735, _31733)), 948 ^ _17227 : [(951 ^ _17227) ^ [] : [-(in(947 ^ [_31731, _31733, _31735], _31733))], (953 ^ _17227) ^ [] : [-(931 ^ [_31731, _31733, _31735] = ordered_pair(946 ^ [_31731, _31733, _31735], 947 ^ [_31731, _31733, _31735]))], (955 ^ _17227) ^ [] : [in(931 ^ [_31731, _31733, _31735], _31731)], (949 ^ _17227) ^ [] : [-(in(946 ^ [_31731, _31733, _31735], _31735))]], 934 ^ _17227 : [(937 ^ _17227) ^ [_31901, _31903] : [in(_31903, _31735), in(_31901, _31733), 931 ^ [_31731, _31733, _31735] = ordered_pair(_31903, _31901)], (935 ^ _17227) ^ [] : [-(in(931 ^ [_31731, _31733, _31735], _31731))]]], (814 ^ _17227) ^ [_29918, _29920, _29922] : [_29918 = unordered_pair(_29922, _29920), 817 ^ _17227 : [(818 ^ _17227) ^ [_30007] : [in(_30007, _29918), -(_30007 = _29922), -(_30007 = _29920)], (828 ^ _17227) ^ [_30097] : [829 ^ _17227 : [(832 ^ _17227) ^ [] : [_30097 = _29920], (830 ^ _17227) ^ [] : [_30097 = _29922]], -(in(_30097, _29918))]]], (1872 ^ _17227) ^ [_45878, _45880] : [-(subset(_45880, _45880))], (1743 ^ _17227) ^ [_44116, _44118] : [subset(_44118, _44116), -(set_difference(_44118, _44116) = empty_set)], (2383 ^ _17227) ^ [_53296, _53298] : [-(disjoint(_53298, _53296)), -(in(2386 ^ [_53296, _53298], set_intersection2(_53298, _53296)))], (4 ^ _17227) ^ [_17277, _17279] : [_17279 = _17277, -(_17277 = _17279)], (1850 ^ _17227) ^ [_45533, _45535] : [element(_45533, powerset(powerset(_45535))), -(union_of_subsets(_45535, _45533) = union(_45533))], (86 ^ _17227) ^ [_18384, _18386, _18388, _18390] : [-(are_equipotent(_18388, _18384)), are_equipotent(_18390, _18386), _18390 = _18388, _18386 = _18384], (1685 ^ _17227) ^ [_43304, _43306] : [element(_43304, powerset(_43306)), -(subset_complement(_43306, subset_complement(_43306, _43304)) = _43304)], (2259 ^ _17227) ^ [_51430, _51432] : [element(_51430, powerset(_51432)), 2262 ^ _17227 : [(2263 ^ _17227) ^ [_51508] : [element(_51508, powerset(_51432)), 2266 ^ _17227 : [(2273 ^ _17227) ^ [] : [subset(_51430, subset_complement(_51432, _51508)), -(disjoint(_51430, _51508))], (2267 ^ _17227) ^ [] : [disjoint(_51430, _51508), -(subset(_51430, subset_complement(_51432, _51508)))]]]]], (742 ^ _17227) ^ [_28785] : [relation(_28785), 745 ^ _17227 : [(746 ^ _17227) ^ [_28871] : [relation(_28871), 749 ^ _17227 : [(750 ^ _17227) ^ [] : [_28785 = _28871, 753 ^ _17227 : [(760 ^ _17227) ^ [_29106, _29108] : [in(ordered_pair(_29108, _29106), _28871), -(in(ordered_pair(_29108, _29106), _28785))], (754 ^ _17227) ^ [_29017, _29019] : [in(ordered_pair(_29019, _29017), _28785), -(in(ordered_pair(_29019, _29017), _28871))]]], (766 ^ _17227) ^ [] : [-(_28785 = _28871), 771 ^ _17227 : [(774 ^ _17227) ^ [] : [in(ordered_pair(767 ^ [_28785, _28871], 768 ^ [_28785, _28871]), _28871)], (772 ^ _17227) ^ [] : [-(in(ordered_pair(767 ^ [_28785, _28871], 768 ^ [_28785, _28871]), _28785))]], 775 ^ _17227 : [(778 ^ _17227) ^ [] : [in(ordered_pair(767 ^ [_28785, _28871], 768 ^ [_28785, _28871]), _28785)], (776 ^ _17227) ^ [] : [-(in(ordered_pair(767 ^ [_28785, _28871], 768 ^ [_28785, _28871]), _28871))]]]]]]], (2604 ^ _17227) ^ [_56215, _56217, _56219] : [-(subset(set_union2(_56219, _56215), _56217)), subset(_56219, _56217), subset(_56215, _56217)], (2218 ^ _17227) ^ [_50884] : [-(set_difference(_50884, empty_set) = _50884)], (2524 ^ _17227) ^ [_55094, _55096, _55098, _55100] : [relation(_55094), 2527 ^ _17227 : [(2536 ^ _17227) ^ [] : [-(in(ordered_pair(_55100, _55098), relation_composition(identity_relation(_55096), _55094))), in(_55100, _55096), in(ordered_pair(_55100, _55098), _55094)], (2528 ^ _17227) ^ [] : [in(ordered_pair(_55100, _55098), relation_composition(identity_relation(_55096), _55094)), 2531 ^ _17227 : [(2534 ^ _17227) ^ [] : [-(in(ordered_pair(_55100, _55098), _55094))], (2532 ^ _17227) ^ [] : [-(in(_55100, _55096))]]]]], (162 ^ _17227) ^ [_19464, _19466, _19468, _19470] : [-(union_of_subsets(_19470, _19466) = union_of_subsets(_19468, _19464)), _19470 = _19468, _19466 = _19464], (1498 ^ _17227) ^ [_40878, _40880] : [-(relation(relation_composition(_40880, _40878))), relation(_40880), relation(_40878)], (2043 ^ _17227) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (651 ^ _17227) ^ [_27451, _27453] : [_27453 = empty_set, 654 ^ _17227 : [(661 ^ _17227) ^ [] : [_27451 = empty_set, -(_27451 = set_meet(_27453))], (655 ^ _17227) ^ [] : [_27451 = set_meet(_27453), -(_27451 = empty_set)]]], (1661 ^ _17227) ^ [_42986] : [empty(_42986), 1664 ^ _17227 : [(1667 ^ _17227) ^ [] : [-(relation(relation_rng(_42986)))], (1665 ^ _17227) ^ [] : [-(empty(relation_rng(_42986)))]]], (150 ^ _17227) ^ [_19294, _19296] : [_19296 = _19294, -(relation_field(_19296) = relation_field(_19294))], (2369 ^ _17227) ^ [_53093, _53095] : [-(set_difference(_53095, set_difference(_53095, _53093)) = set_intersection2(_53095, _53093))], (2390 ^ _17227) ^ [_53338, _53340] : [2391 ^ _17227 : [(2392 ^ _17227) ^ [_53380] : [in(_53380, set_intersection2(_53340, _53338))]], disjoint(_53340, _53338)], (2188 ^ _17227) ^ [_50475, _50477, _50479] : [-(subset(unordered_pair(_50479, _50477), _50475)), in(_50479, _50475), in(_50477, _50475)], (581 ^ _17227) ^ [_26288] : [relation(_26288), 584 ^ _17227 : [(585 ^ _17227) ^ [_26364] : [in(_26364, _26288), -(_26364 = ordered_pair(588 ^ [_26288, _26364], 589 ^ [_26288, _26364]))]]], (1508 ^ _17227) ^ [_41007, _41009] : [element(_41007, powerset(powerset(_41009))), -(element(union_of_subsets(_41009, _41007), powerset(_41009)))], (2466 ^ _17227) ^ [_54337] : [relation(_54337), 2471 ^ _17227 : [(2474 ^ _17227) ^ [] : [relation_rng(_54337) = empty_set], (2472 ^ _17227) ^ [] : [relation_dom(_54337) = empty_set]], -(_54337 = empty_set)], (2103 ^ _17227) ^ [_49205, _49207] : [-(_49207 = _49205), 2107 ^ _17227 : [(2110 ^ _17227) ^ [] : [in(2104 ^ [_49205, _49207], _49205)], (2108 ^ _17227) ^ [] : [-(in(2104 ^ [_49205, _49207], _49207))]], 2111 ^ _17227 : [(2114 ^ _17227) ^ [] : [in(2104 ^ [_49205, _49207], _49207)], (2112 ^ _17227) ^ [] : [-(in(2104 ^ [_49205, _49207], _49205))]]], (1565 ^ _17227) ^ [_41777, _41779] : [1572 ^ _17227 : [(1575 ^ _17227) ^ [] : [-(relation(relation_composition(_41777, _41779)))], (1573 ^ _17227) ^ [] : [-(empty(relation_composition(_41777, _41779)))]], empty(_41779), relation(_41777)], (350 ^ _17227) ^ [_22300] : [empty(_22300), -(relation(_22300))], (1653 ^ _17227) ^ [_42883] : [empty(_42883), 1656 ^ _17227 : [(1659 ^ _17227) ^ [] : [-(relation(relation_dom(_42883)))], (1657 ^ _17227) ^ [] : [-(empty(relation_dom(_42883)))]]], (836 ^ _17227) ^ [_30218, _30220, _30222] : [-(_30218 = unordered_pair(_30222, _30220)), 840 ^ _17227 : [(845 ^ _17227) ^ [] : [837 ^ [_30218, _30220, _30222] = _30220], (843 ^ _17227) ^ [] : [837 ^ [_30218, _30220, _30222] = _30222], (841 ^ _17227) ^ [] : [-(in(837 ^ [_30218, _30220, _30222], _30218))]], 846 ^ _17227 : [(847 ^ _17227) ^ [] : [-(837 ^ [_30218, _30220, _30222] = _30222), -(837 ^ [_30218, _30220, _30222] = _30220)], (853 ^ _17227) ^ [] : [in(837 ^ [_30218, _30220, _30222], _30218)]]], (2232 ^ _17227) ^ [_51091, _51093] : [-(disjoint(_51093, _51091)), 2236 ^ _17227 : [(2239 ^ _17227) ^ [] : [-(in(2235 ^ [_51091, _51093], _51091))], (2237 ^ _17227) ^ [] : [-(in(2235 ^ [_51091, _51093], _51093))]]], (2091 ^ _17227) ^ [_49091] : [-(set_intersection2(_49091, empty_set) = empty_set)], (1956 ^ _17227) ^ [_47067, _47069] : [relation(_47067), -(relation_rng(relation_rng_restriction(_47069, _47067)) = set_intersection2(relation_rng(_47067), _47069))], (2226 ^ _17227) ^ [_51002, _51004] : [subset(_51004, _51002), -(element(_51004, powerset(_51002)))], (1456 ^ _17227) ^ [] : [true___, -(true___)], (1991 ^ _17227) ^ [_47659, _47661] : [in(_47659, 1977 ^ [_47661]), -(in(powerset(_47659), 1977 ^ [_47661]))], (2594 ^ _17227) ^ [_56088, _56090] : [empty(_56090), -(_56090 = _56088), empty(_56088)], (2013 ^ _17227) ^ [_47987, _47989] : [-(subset(set_intersection2(_47989, _47987), _47989))], (2257 ^ _17227) ^ [_51396, _51398] : [-(set_difference(set_union2(_51398, _51396), _51396) = set_difference(_51398, _51396))], (997 ^ _17227) ^ [_32879, _32881] : [999 ^ _17227 : [(1002 ^ _17227) ^ [] : [in(998 ^ [_32879, _32881], _32879)], (1000 ^ _17227) ^ [] : [-(in(998 ^ [_32879, _32881], _32881))]], -(subset(_32881, _32879))], (1390 ^ _17227) ^ [_39725, _39727] : [-(proper_subset(_39727, _39725)), subset(_39727, _39725), -(_39727 = _39725)], (480 ^ _17227) ^ [_24432, _24434] : [relation(_24432), 483 ^ _17227 : [(484 ^ _17227) ^ [_24529] : [relation(_24529), 487 ^ _17227 : [(488 ^ _17227) ^ [] : [_24529 = relation_rng_restriction(_24434, _24432), 491 ^ _17227 : [(500 ^ _17227) ^ [_24808, _24810] : [-(in(ordered_pair(_24810, _24808), _24529)), in(_24808, _24434), in(ordered_pair(_24810, _24808), _24432)], (492 ^ _17227) ^ [_24691, _24693] : [in(ordered_pair(_24693, _24691), _24529), 495 ^ _17227 : [(498 ^ _17227) ^ [] : [-(in(ordered_pair(_24693, _24691), _24432))], (496 ^ _17227) ^ [] : [-(in(_24691, _24434))]]]]], (510 ^ _17227) ^ [] : [-(_24529 = relation_rng_restriction(_24434, _24432)), 523 ^ _17227 : [(528 ^ _17227) ^ [] : [in(ordered_pair(511 ^ [_24432, _24434, _24529], 512 ^ [_24432, _24434, _24529]), _24529)], (526 ^ _17227) ^ [] : [-(in(ordered_pair(511 ^ [_24432, _24434, _24529], 512 ^ [_24432, _24434, _24529]), _24432))], (524 ^ _17227) ^ [] : [-(in(512 ^ [_24432, _24434, _24529], _24434))]], 515 ^ _17227 : [(518 ^ _17227) ^ [] : [in(512 ^ [_24432, _24434, _24529], _24434), in(ordered_pair(511 ^ [_24432, _24434, _24529], 512 ^ [_24432, _24434, _24529]), _24432)], (516 ^ _17227) ^ [] : [-(in(ordered_pair(511 ^ [_24432, _24434, _24529], 512 ^ [_24432, _24434, _24529]), _24529))]]]]]]], (711 ^ _17227) ^ [_28308, _28310] : [_28308 = powerset(_28310), 714 ^ _17227 : [(721 ^ _17227) ^ [_28462] : [subset(_28462, _28310), -(in(_28462, _28308))], (715 ^ _17227) ^ [_28387] : [in(_28387, _28308), -(subset(_28387, _28310))]]], (1603 ^ _17227) ^ [_42293] : [empty(singleton(_42293))], (2373 ^ _17227) ^ [_53153, _53155, _53157] : [-(element(_53157, _53153)), in(_53157, _53155), element(_53155, powerset(_53153))], (1623 ^ _17227) ^ [_42544, _42546] : [empty(cartesian_product2(_42546, _42544)), -(empty(_42546)), -(empty(_42544))], (2220 ^ _17227) ^ [_50925, _50927] : [element(_50927, powerset(_50925)), -(subset(_50927, _50925))], (110 ^ _17227) ^ [_18698, _18700, _18702, _18704] : [-(in(_18702, _18698)), in(_18704, _18700), _18704 = _18702, _18700 = _18698], (1544 ^ _17227) ^ [_41552, _41554] : [relation(_41552), -(relation(relation_rng_restriction(_41554, _41552)))], (593 ^ _17227) ^ [_26473] : [595 ^ _17227 : [(598 ^ _17227) ^ [_26586, _26588] : [594 ^ [_26473] = ordered_pair(_26588, _26586)], (596 ^ _17227) ^ [] : [-(in(594 ^ [_26473], _26473))]], -(relation(_26473))], (2560 ^ _17227) ^ [_55616, _55618] : [set_difference(_55618, _55616) = _55618, -(disjoint(_55618, _55616))], (252 ^ _17227) ^ [_20813, _20815, _20817, _20819] : [-(relation_composition(_20819, _20815) = relation_composition(_20817, _20813)), _20819 = _20817, _20815 = _20813], (900 ^ _17227) ^ [_31198, _31200, _31202] : [_31198 = cartesian_product2(_31202, _31200), 903 ^ _17227 : [(916 ^ _17227) ^ [_31493] : [-(in(_31493, _31198)), 917 ^ _17227 : [(918 ^ _17227) ^ [_31551, _31553] : [in(_31553, _31202), in(_31551, _31200), _31493 = ordered_pair(_31553, _31551)]]], (904 ^ _17227) ^ [_31306] : [in(_31306, _31198), 909 ^ _17227 : [(914 ^ _17227) ^ [] : [-(_31306 = ordered_pair(907 ^ [_31198, _31200, _31202, _31306], 908 ^ [_31198, _31200, _31202, _31306]))], (912 ^ _17227) ^ [] : [-(in(908 ^ [_31198, _31200, _31202, _31306], _31200))], (910 ^ _17227) ^ [] : [-(in(907 ^ [_31198, _31200, _31202, _31306], _31202))]]]]], (1593 ^ _17227) ^ [_42155, _42157] : [-(relation(set_union2(_42157, _42155))), relation(_42157), relation(_42155)], (2138 ^ _17227) ^ [_49726, _49728, _49730, _49732] : [ordered_pair(_49732, _49730) = ordered_pair(_49728, _49726), 2141 ^ _17227 : [(2144 ^ _17227) ^ [] : [-(_49730 = _49726)], (2142 ^ _17227) ^ [] : [-(_49732 = _49728)]]], (727 ^ _17227) ^ [_28543, _28545] : [-(_28543 = powerset(_28545)), 731 ^ _17227 : [(734 ^ _17227) ^ [] : [subset(728 ^ [_28543, _28545], _28545)], (732 ^ _17227) ^ [] : [-(in(728 ^ [_28543, _28545], _28543))]], 735 ^ _17227 : [(738 ^ _17227) ^ [] : [in(728 ^ [_28543, _28545], _28543)], (736 ^ _17227) ^ [] : [-(subset(728 ^ [_28543, _28545], _28545))]]], (72 ^ _17227) ^ [_18191, _18193, _18195, _18197] : [-(subset(_18195, _18191)), subset(_18197, _18193), _18197 = _18195, _18193 = _18191], (1691 ^ _17227) ^ [_43397] : [relation(_43397), -(relation_inverse(relation_inverse(_43397)) = _43397)], (1703 ^ _17227) ^ [_43587, _43589] : [proper_subset(_43589, _43589)], (1577 ^ _17227) ^ [_41936, _41938] : [-(relation(set_intersection2(_41938, _41936))), relation(_41938), relation(_41936)], (1997 ^ _17227) ^ [_47756, _47758] : [subset(_47756, 1977 ^ [_47758]), -(are_equipotent(_47756, 1977 ^ [_47758])), -(in(_47756, 1977 ^ [_47758]))], (2200 ^ _17227) ^ [_50665, _50667] : [subset(_50667, singleton(_50665)), -(_50667 = empty_set), -(_50667 = singleton(_50665))], (1843 ^ _17227) ^ [_45447] : [-(element(1841 ^ [_45447], powerset(_45447)))], (1088 ^ _17227) ^ [_34419, _34421] : [_34419 = union(_34421), 1091 ^ _17227 : [(1101 ^ _17227) ^ [_34633] : [-(in(_34633, _34419)), 1102 ^ _17227 : [(1103 ^ _17227) ^ [_34675] : [in(_34633, _34675), in(_34675, _34421)]]], (1092 ^ _17227) ^ [_34509] : [in(_34509, _34419), 1096 ^ _17227 : [(1099 ^ _17227) ^ [] : [-(in(1095 ^ [_34419, _34421, _34509], _34421))], (1097 ^ _17227) ^ [] : [-(in(_34509, 1095 ^ [_34419, _34421, _34509]))]]]]], (2305 ^ _17227) ^ [_52143] : [relation(_52143), 2308 ^ _17227 : [(2309 ^ _17227) ^ [_52218] : [relation(_52218), subset(relation_rng(_52143), relation_dom(_52218)), -(relation_dom(relation_composition(_52143, _52218)) = relation_dom(_52143))]]], (2007 ^ _17227) ^ [_47886, _47888, _47890] : [relation(_47886), -(relation_dom_restriction(relation_rng_restriction(_47890, _47886), _47888) = relation_rng_restriction(_47890, relation_dom_restriction(_47886, _47888)))], (242 ^ _17227) ^ [_20664, _20666, _20668, _20670] : [-(set_intersection2(_20670, _20666) = set_intersection2(_20668, _20664)), _20670 = _20668, _20666 = _20664], (1406 ^ _17227) ^ [] : [true___, -(true___)], (1737 ^ _17227) ^ [_44037, _44039] : [set_difference(_44039, _44037) = empty_set, -(subset(_44039, _44037))], (268 ^ _17227) ^ [_21047, _21049, _21051, _21053] : [-(relation_dom_restriction(_21053, _21049) = relation_dom_restriction(_21051, _21047)), _21053 = _21051, _21049 = _21047], (1759 ^ _17227) ^ [_44351, _44353, _44355] : [subset(_44355, _44353), -(in(_44351, _44355)), -(subset(_44355, set_difference(_44353, singleton(_44351))))], (1587 ^ _17227) ^ [_42074] : [empty(powerset(_42074))], (2057 ^ _17227) ^ [_48579] : [relation(_48579), -(subset(_48579, cartesian_product2(relation_dom(_48579), relation_rng(_48579))))], (2647 ^ _17227) ^ [_56934] : [-(in(_56934, 2645 ^ [_56934]))], (2210 ^ _17227) ^ [_50759, _50761] : [2211 ^ _17227 : [(2214 ^ _17227) ^ [] : [_50761 = singleton(_50759)], (2212 ^ _17227) ^ [] : [_50761 = empty_set]], -(subset(_50761, singleton(_50759)))], (2506 ^ _17227) ^ [_54857] : [-(unordered_pair(_54857, _54857) = singleton(_54857))], (1436 ^ _17227) ^ [_40213] : [-(element(cast_to_subset(_40213), powerset(_40213)))], (2508 ^ _17227) ^ [_54885] : [empty(_54885), -(_54885 = empty_set)], (278 ^ _17227) ^ [_21196, _21198] : [_21198 = _21196, -(relation_rng(_21198) = relation_rng(_21196))], (328 ^ _17227) ^ [_21915, _21917, _21919, _21921] : [-(ordered_pair(_21921, _21917) = ordered_pair(_21919, _21915)), _21921 = _21919, _21917 = _21915], (1862 ^ _17227) ^ [_45723, _45725, _45727] : [-(subset_difference(_45727, _45725, _45723) = set_difference(_45725, _45723)), element(_45725, powerset(_45727)), element(_45723, powerset(_45727))], (1725 ^ _17227) ^ [_43862, _43864] : [subset(singleton(_43864), _43862), -(in(_43864, _43862))], (1462 ^ _17227) ^ [_40476, _40478] : [element(_40476, powerset(_40478)), -(element(subset_complement(_40478, _40476), powerset(_40478)))], (10 ^ _17227) ^ [_17350, _17352, _17354] : [-(_17354 = _17350), _17354 = _17352, _17352 = _17350], (212 ^ _17227) ^ [_20217, _20219, _20221, _20223] : [-(subset_complement(_20223, _20219) = subset_complement(_20221, _20217)), _20223 = _20221, _20219 = _20217], (2 ^ _17227) ^ [_17254] : [-(_17254 = _17254)], (2015 ^ _17227) ^ [_48015, _48017, _48019] : [-(subset(_48019, set_intersection2(_48017, _48015))), subset(_48019, _48017), subset(_48019, _48015)], (704 ^ _17227) ^ [_28252] : [-(in(705 ^ [_28252], _28252)), -(_28252 = empty_set)], (2494 ^ _17227) ^ [_54732, _54734] : [set_difference(_54734, singleton(_54732)) = _54734, in(_54732, _54734)], (338 ^ _17227) ^ [_22144, _22146] : [in(_22146, _22144), in(_22144, _22146)], (232 ^ _17227) ^ [_20515, _20517, _20519, _20521] : [-(set_union2(_20521, _20517) = set_union2(_20519, _20515)), _20521 = _20519, _20517 = _20515], (2120 ^ _17227) ^ [_49464, _49466, _49468] : [relation(_49464), in(ordered_pair(_49468, _49466), _49464), 2127 ^ _17227 : [(2130 ^ _17227) ^ [] : [-(in(_49466, relation_field(_49464)))], (2128 ^ _17227) ^ [] : [-(in(_49468, relation_field(_49464)))]]], (2335 ^ _17227) ^ [_52605] : [relation(_52605), 2338 ^ _17227 : [(2339 ^ _17227) ^ [_52680] : [relation(_52680), subset(relation_dom(_52605), relation_rng(_52680)), -(relation_rng(relation_composition(_52680, _52605)) = relation_rng(_52605))]]], (48 ^ _17227) ^ [_17873, _17875, _17877, _17879] : [-(disjoint(_17877, _17873)), disjoint(_17879, _17875), _17879 = _17877, _17875 = _17873], (1633 ^ _17227) ^ [_42629] : [empty(relation_dom(_42629)), -(empty(_42629)), relation(_42629)], (2371 ^ _17227) ^ [_53127] : [-(set_difference(empty_set, _53127) = empty_set)], (1279 ^ _17227) ^ [_37637] : [relation(_37637), 1282 ^ _17227 : [(1283 ^ _17227) ^ [_37750] : [relation(_37750), 1286 ^ _17227 : [(1287 ^ _17227) ^ [_37855] : [relation(_37855), 1290 ^ _17227 : [(1291 ^ _17227) ^ [] : [_37855 = relation_composition(_37637, _37750), 1294 ^ _17227 : [(1304 ^ _17227) ^ [_38179, _38181] : [-(in(ordered_pair(_38181, _38179), _37855)), 1305 ^ _17227 : [(1306 ^ _17227) ^ [_38234] : [in(ordered_pair(_38181, _38234), _37637), in(ordered_pair(_38234, _38179), _37750)]]], (1295 ^ _17227) ^ [_38025, _38027] : [in(ordered_pair(_38027, _38025), _37855), 1299 ^ _17227 : [(1302 ^ _17227) ^ [] : [-(in(ordered_pair(1298 ^ [_37637, _37750, _37855, _38025, _38027], _38025), _37750))], (1300 ^ _17227) ^ [] : [-(in(ordered_pair(_38027, 1298 ^ [_37637, _37750, _37855, _38025, _38027]), _37637))]]]]], (1314 ^ _17227) ^ [] : [-(_37855 = relation_composition(_37637, _37750)), 1328 ^ _17227 : [(1333 ^ _17227) ^ [] : [in(ordered_pair(1315 ^ [_37637, _37750, _37855], 1316 ^ [_37637, _37750, _37855]), _37855)], (1331 ^ _17227) ^ [] : [-(in(ordered_pair(1327 ^ [_37637, _37750, _37855], 1316 ^ [_37637, _37750, _37855]), _37750))], (1329 ^ _17227) ^ [] : [-(in(ordered_pair(1315 ^ [_37637, _37750, _37855], 1327 ^ [_37637, _37750, _37855]), _37637))]], 1319 ^ _17227 : [(1322 ^ _17227) ^ [_38511] : [in(ordered_pair(1315 ^ [_37637, _37750, _37855], _38511), _37637), in(ordered_pair(_38511, 1316 ^ [_37637, _37750, _37855]), _37750)], (1320 ^ _17227) ^ [] : [-(in(ordered_pair(1315 ^ [_37637, _37750, _37855], 1316 ^ [_37637, _37750, _37855]), _37855))]]]]]]]]], (1516 ^ _17227) ^ [_41126, _41128] : [element(_41126, powerset(powerset(_41128))), -(element(meet_of_subsets(_41128, _41126), powerset(_41128)))], (1840 ^ _17227) ^ [] : [-(relation(1836 ^ []))], (1669 ^ _17227) ^ [_43089, _43091] : [1676 ^ _17227 : [(1679 ^ _17227) ^ [] : [-(relation(relation_composition(_43091, _43089)))], (1677 ^ _17227) ^ [] : [-(empty(relation_composition(_43091, _43089)))]], empty(_43091), relation(_43089)], (879 ^ _17227) ^ [_30858, _30860, _30862] : [-(_30858 = set_union2(_30862, _30860)), 883 ^ _17227 : [(888 ^ _17227) ^ [] : [in(880 ^ [_30858, _30860, _30862], _30860)], (886 ^ _17227) ^ [] : [in(880 ^ [_30858, _30860, _30862], _30862)], (884 ^ _17227) ^ [] : [-(in(880 ^ [_30858, _30860, _30862], _30858))]], 889 ^ _17227 : [(890 ^ _17227) ^ [] : [-(in(880 ^ [_30858, _30860, _30862], _30862)), -(in(880 ^ [_30858, _30860, _30862], _30860))], (896 ^ _17227) ^ [] : [in(880 ^ [_30858, _30860, _30862], _30858)]]], (1787 ^ _17227) ^ [_44687, _44689] : [in(_44689, _44687), -(subset(_44689, union(_44687)))], (1028 ^ _17227) ^ [_33370, _33372, _33374] : [-(_33370 = set_intersection2(_33374, _33372)), 1040 ^ _17227 : [(1045 ^ _17227) ^ [] : [in(1029 ^ [_33370, _33372, _33374], _33370)], (1043 ^ _17227) ^ [] : [-(in(1029 ^ [_33370, _33372, _33374], _33372))], (1041 ^ _17227) ^ [] : [-(in(1029 ^ [_33370, _33372, _33374], _33374))]], 1032 ^ _17227 : [(1035 ^ _17227) ^ [] : [in(1029 ^ [_33370, _33372, _33374], _33374), in(1029 ^ [_33370, _33372, _33374], _33372)], (1033 ^ _17227) ^ [] : [-(in(1029 ^ [_33370, _33372, _33374], _33370))]]], (782 ^ _17227) ^ [_29496, _29498] : [-(empty(_29498)), 785 ^ _17227 : [(792 ^ _17227) ^ [] : [in(_29496, _29498), -(element(_29496, _29498))], (786 ^ _17227) ^ [] : [element(_29496, _29498), -(in(_29496, _29498))]]], (1049 ^ _17227) ^ [_33724] : [relation(_33724), 1052 ^ _17227 : [(1053 ^ _17227) ^ [_33816] : [_33816 = relation_dom(_33724), 1056 ^ _17227 : [(1064 ^ _17227) ^ [_33998] : [1065 ^ _17227 : [(1066 ^ _17227) ^ [_34042] : [in(ordered_pair(_33998, _34042), _33724)]], -(in(_33998, _33816))], (1057 ^ _17227) ^ [_33903] : [in(_33903, _33816), -(in(ordered_pair(_33903, 1060 ^ [_33724, _33816, _33903]), _33724))]]], (1070 ^ _17227) ^ [_34098] : [-(_34098 = relation_dom(_33724)), 1074 ^ _17227 : [(1077 ^ _17227) ^ [_34232] : [in(ordered_pair(1071 ^ [_33724, _34098], _34232), _33724)], (1075 ^ _17227) ^ [] : [-(in(1071 ^ [_33724, _34098], _34098))]], 1079 ^ _17227 : [(1082 ^ _17227) ^ [] : [in(1071 ^ [_33724, _34098], _34098)], (1080 ^ _17227) ^ [] : [-(in(ordered_pair(1071 ^ [_33724, _34098], 1078 ^ [_33724, _34098]), _33724))]]]]], (2614 ^ _17227) ^ [_56354, _56356, _56358] : [singleton(_56358) = unordered_pair(_56356, _56354), -(_56358 = _56356)], (1550 ^ _17227) ^ [] : [true___, -(true___)], (360 ^ _17227) ^ [_22433, _22435] : [-(set_intersection2(_22435, _22433) = set_intersection2(_22433, _22435))], (2672 ^ _17227) ^ [_57356, _57358] : [subset(_57356, 2645 ^ [_57358]), -(are_equipotent(_57356, 2645 ^ [_57358])), -(in(_57356, 2645 ^ [_57358]))], (1801 ^ _17227) ^ [_44904, _44906, _44908, _44910] : [-(in(ordered_pair(_44910, _44908), cartesian_product2(_44906, _44904))), in(_44910, _44906), in(_44908, _44904)], (1838 ^ _17227) ^ [] : [empty(1836 ^ [])], (322 ^ _17227) ^ [_21834, _21836] : [_21836 = _21834, -(relation_dom(_21836) = relation_dom(_21834))], (2456 ^ _17227) ^ [_54204, _54206, _54208] : [-(disjoint(_54208, _54204)), subset(_54208, _54206), disjoint(_54206, _54204)], (1522 ^ _17227) ^ [_41221, _41223, _41225] : [-(element(subset_difference(_41225, _41223, _41221), powerset(_41225))), element(_41223, powerset(_41225)), element(_41221, powerset(_41225))], (1006 ^ _17227) ^ [_33039, _33041, _33043] : [_33039 = set_intersection2(_33043, _33041), 1009 ^ _17227 : [(1018 ^ _17227) ^ [_33231] : [-(in(_33231, _33039)), in(_33231, _33043), in(_33231, _33041)], (1010 ^ _17227) ^ [_33128] : [in(_33128, _33039), 1013 ^ _17227 : [(1016 ^ _17227) ^ [] : [-(in(_33128, _33041))], (1014 ^ _17227) ^ [] : [-(in(_33128, _33043))]]]]], (1719 ^ _17227) ^ [_43809, _43811] : [-(in(_43811, _43809)), -(disjoint(singleton(_43811), _43809))], (2554 ^ _17227) ^ [_55537, _55539] : [disjoint(_55539, _55537), -(set_difference(_55539, _55537) = _55539)], (2251 ^ _17227) ^ [_51321] : [subset(_51321, empty_set), -(_51321 = empty_set)], (2156 ^ _17227) ^ [_50011, _50013] : [set_difference(_50013, _50011) = empty_set, -(subset(_50013, _50011))], (100 ^ _17227) ^ [_18577, _18579] : [-(relation(_18577)), _18579 = _18577, relation(_18579)], (2180 ^ _17227) ^ [_50368, _50370, _50372] : [subset(unordered_pair(_50372, _50370), _50368), 2183 ^ _17227 : [(2186 ^ _17227) ^ [] : [-(in(_50370, _50368))], (2184 ^ _17227) ^ [] : [-(in(_50372, _50368))]]], (1480 ^ _17227) ^ [_40685] : [relation(_40685), -(relation(relation_inverse(_40685)))], (1111 ^ _17227) ^ [_34785, _34787] : [-(_34785 = union(_34787)), 1124 ^ _17227 : [(1129 ^ _17227) ^ [] : [in(1112 ^ [_34785, _34787], _34785)], (1127 ^ _17227) ^ [] : [-(in(1123 ^ [_34785, _34787], _34787))], (1125 ^ _17227) ^ [] : [-(in(1112 ^ [_34785, _34787], 1123 ^ [_34785, _34787]))]], 1115 ^ _17227 : [(1118 ^ _17227) ^ [_34918] : [in(1112 ^ [_34785, _34787], _34918), in(_34918, _34787)], (1116 ^ _17227) ^ [] : [-(in(1112 ^ [_34785, _34787], _34785))]]], (1821 ^ _17227) ^ [] : [-(empty(1819 ^ []))], (2620 ^ _17227) ^ [_56443, _56445] : [relation(_56443), -(relation_dom(relation_dom_restriction(_56443, _56445)) = set_intersection2(relation_dom(_56443), _56445))], (2329 ^ _17227) ^ [_52518, _52520] : [in(_52520, _52518), -(set_union2(singleton(_52520), _52518) = _52518)], (602 ^ _17227) ^ [_26658, _26660] : [-(_26660 = empty_set), 605 ^ _17227 : [(606 ^ _17227) ^ [] : [_26658 = set_meet(_26660), 609 ^ _17227 : [(610 ^ _17227) ^ [_26805] : [in(_26805, _26658), 613 ^ _17227 : [(614 ^ _17227) ^ [_26870] : [in(_26870, _26660), -(in(_26805, _26870))]]], (620 ^ _17227) ^ [_26951] : [622 ^ _17227 : [(625 ^ _17227) ^ [] : [in(_26951, 621 ^ [_26658, _26660, _26951])], (623 ^ _17227) ^ [] : [-(in(621 ^ [_26658, _26660, _26951], _26660))]], -(in(_26951, _26658))]]], (629 ^ _17227) ^ [] : [-(_26658 = set_meet(_26660)), 633 ^ _17227 : [(639 ^ _17227) ^ [] : [in(630 ^ [_26658, _26660], 635 ^ [_26658, _26660])], (637 ^ _17227) ^ [] : [-(in(635 ^ [_26658, _26660], _26660))], (634 ^ _17227) ^ [] : [-(in(630 ^ [_26658, _26660], _26658))]], 640 ^ _17227 : [(641 ^ _17227) ^ [_27295] : [in(_27295, _26660), -(in(630 ^ [_26658, _26660], _27295))], (647 ^ _17227) ^ [] : [in(630 ^ [_26658, _26660], _26658)]]]]], (262 ^ _17227) ^ [_20962, _20964] : [_20964 = _20962, -(identity_relation(_20964) = identity_relation(_20962))], (1811 ^ _17227) ^ [_45055, _45057] : [1813 ^ _17227 : [(1816 ^ _17227) ^ [] : [in(1812 ^ [_45055, _45057], _45055)], (1814 ^ _17227) ^ [] : [-(in(1812 ^ [_45055, _45057], _45057))]], -(element(_45057, powerset(_45055)))], (1155 ^ _17227) ^ [_35506, _35508, _35510] : [-(_35506 = set_difference(_35510, _35508)), 1167 ^ _17227 : [(1172 ^ _17227) ^ [] : [in(1156 ^ [_35506, _35508, _35510], _35506)], (1170 ^ _17227) ^ [] : [in(1156 ^ [_35506, _35508, _35510], _35508)], (1168 ^ _17227) ^ [] : [-(in(1156 ^ [_35506, _35508, _35510], _35510))]], 1159 ^ _17227 : [(1162 ^ _17227) ^ [] : [in(1156 ^ [_35506, _35508, _35510], _35510), -(in(1156 ^ [_35506, _35508, _35510], _35508))], (1160 ^ _17227) ^ [] : [-(in(1156 ^ [_35506, _35508, _35510], _35506))]]], (1621 ^ _17227) ^ [] : [-(relation(empty_set))], (1273 ^ _17227) ^ [_37552, _37554] : [set_intersection2(_37554, _37552) = empty_set, -(disjoint(_37554, _37552))], (2436 ^ _17227) ^ [_53961, _53963, _53965] : [in(_53965, _53963), element(_53963, powerset(_53961)), empty(_53961)], (2162 ^ _17227) ^ [_50090, _50092] : [subset(_50092, _50090), -(set_difference(_50092, _50090) = empty_set)], (1681 ^ _17227) ^ [_43248, _43250] : [-(set_union2(_43250, _43250) = _43250)], (2085 ^ _17227) ^ [_49008, _49010] : [subset(_49010, _49008), -(set_intersection2(_49010, _49008) = _49010)], (1898 ^ _17227) ^ [_46267, _46269, _46271, _46273] : [unordered_pair(_46273, _46271) = unordered_pair(_46269, _46267), -(_46273 = _46269), -(_46273 = _46267)], (296 ^ _17227) ^ [_21451, _21453] : [_21453 = _21451, -(singleton(_21453) = singleton(_21451))], (2027 ^ _17227) ^ [_48180, _48182] : [in(_48182, _48180), -(element(_48182, _48180))], (222 ^ _17227) ^ [_20366, _20368, _20370, _20372] : [-(set_difference(_20372, _20368) = set_difference(_20370, _20366)), _20372 = _20370, _20368 = _20366], (2025 ^ _17227) ^ [_48154] : [-(set_union2(_48154, empty_set) = _48154)], (2241 ^ _17227) ^ [_51174, _51176] : [disjoint(_51176, _51174), 2242 ^ _17227 : [(2243 ^ _17227) ^ [_51214] : [in(_51214, _51176), in(_51214, _51174)]]], (2478 ^ _17227) ^ [_54506] : [relation(_54506), 2481 ^ _17227 : [(2488 ^ _17227) ^ [] : [relation_rng(_54506) = empty_set, -(relation_dom(_54506) = empty_set)], (2482 ^ _17227) ^ [] : [relation_dom(_54506) = empty_set, -(relation_rng(_54506) = empty_set)]]], (1856 ^ _17227) ^ [_45628, _45630] : [element(_45628, powerset(powerset(_45630))), -(meet_of_subsets(_45630, _45628) = set_meet(_45628))], (290 ^ _17227) ^ [_21366, _21368] : [_21368 = _21366, -(powerset(_21368) = powerset(_21366))]], input).
% 63.32/61.45  ncf('1',plain,[2710 : -(in(ordered_pair(2706 ^ [], 2687 ^ []), 2689 ^ [])), 2697 : in(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], relation_dom(2689 ^ [])), 2697 : in(ordered_pair(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], 2687 ^ []), 2689 ^ []), 2697 : in(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], 2688 ^ [])],start(2693 ^ 0,bind([[_58876], [543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []]]]))).
% 63.32/61.45  ncf('1.1',plain,[in(ordered_pair(2706 ^ [], 2687 ^ []), 2689 ^ []), 1145 : -(in(ordered_pair(2706 ^ [], 2687 ^ []), relation_image(2689 ^ [], 2688 ^ []))), 1145 : -(in(ordered_pair(2706 ^ [], 2687 ^ []), relation_image(2689 ^ [], 2688 ^ []))), 1145 : relation_image(2689 ^ [], 2688 ^ []) = set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ []))],extension(1133 ^ 3,bind([[_35162, _35164, _35166, _35364], [relation_image(2689 ^ [], 2688 ^ []), relation_image(2689 ^ [], 2688 ^ []), 2689 ^ [], ordered_pair(2706 ^ [], 2687 ^ [])]]))).
% 63.32/61.45  ncf('1.1.1',plain,[in(ordered_pair(2706 ^ [], 2687 ^ []), relation_image(2689 ^ [], 2688 ^ [])), 1143 : in(ordered_pair(2706 ^ [], 2687 ^ []), relation_image(2689 ^ [], 2688 ^ []))],extension(1137 ^ 6,bind([[_35253], [ordered_pair(2706 ^ [], 2687 ^ [])]]))).
% 63.32/61.45  ncf('1.1.1.1',plain,[-(in(ordered_pair(2706 ^ [], 2687 ^ []), relation_image(2689 ^ [], 2688 ^ [])))],reduction('1.1')).
% 63.32/61.45  ncf('1.1.2',plain,[in(ordered_pair(2706 ^ [], 2687 ^ []), relation_image(2689 ^ [], 2688 ^ []))],lemmata('[1].x')).
% 63.32/61.45  ncf('1.1.3',plain,[-(relation_image(2689 ^ [], 2688 ^ []) = set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ []))), unordered_pair(relation_image(2689 ^ [], 2688 ^ []), set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ []))) = unordered_pair(set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ [])), relation_image(2689 ^ [], 2688 ^ [])), -(relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ []))],extension(1898 ^ 4,bind([[_46267, _46269, _46271, _46273], [relation_image(2689 ^ [], 2688 ^ []), set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ [])), set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ [])), relation_image(2689 ^ [], 2688 ^ [])]]))).
% 63.32/61.45  ncf('1.1.3.1',plain,[-(unordered_pair(relation_image(2689 ^ [], 2688 ^ []), set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ []))) = unordered_pair(set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ [])), relation_image(2689 ^ [], 2688 ^ [])))],extension(356 ^ 5,bind([[_22371, _22373], [set_difference(2689 ^ [], relation_image(2689 ^ [], 2688 ^ [])), relation_image(2689 ^ [], 2688 ^ [])]]))).
% 63.32/61.45  ncf('1.1.3.2',plain,[relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ []), 549 : -(in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ []))), 551 : in(ordered_pair(2706 ^ [], 2687 ^ []), 2689 ^ []), 551 : in(2706 ^ [], 2688 ^ []), 536 : relation(2689 ^ [])],extension(532 ^ 5,bind([[_25369, _25476, _25478, _25709, _25756], [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ [], 2706 ^ []]]))).
% 63.32/61.45  ncf('1.1.3.2.1',plain,[in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ []))],extension(2714 ^ 10)).
% 63.32/61.45  ncf('1.1.3.2.2',plain,[-(in(ordered_pair(2706 ^ [], 2687 ^ []), 2689 ^ []))],reduction('1')).
% 63.32/61.45  ncf('1.1.3.2.3',plain,[-(in(2706 ^ [], 2688 ^ []))],extension(2712 ^ 12)).
% 63.32/61.45  ncf('1.1.3.2.4',plain,[-(relation(2689 ^ []))],extension(2691 ^ 6)).
% 63.32/61.45  ncf('1.2',plain,[-(in(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], relation_dom(2689 ^ []))), relation(2689 ^ []), in(ordered_pair(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], 2687 ^ []), 2689 ^ [])],extension(2045 ^ 3,bind([[_48408, _48410, _48412], [2689 ^ [], 2687 ^ [], 543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []]]]))).
% 63.32/61.45  ncf('1.2.1',plain,[-(relation(2689 ^ []))],extension(2691 ^ 4)).
% 63.32/61.45  ncf('1.2.2',plain,[-(in(ordered_pair(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], 2687 ^ []), 2689 ^ [])), 540 : in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ [])), 540 : relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ []), 536 : relation(2689 ^ [])],extension(532 ^ 4,bind([[_25369, _25476, _25478, _25573], [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []]]))).
% 63.32/61.45  ncf('1.2.2.1',plain,[-(in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ [])))],extension(2695 ^ 9)).
% 63.32/61.45  ncf('1.2.2.2',plain,[-(relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ []))],extension(2 ^ 7,bind([[_17254], [relation_image(2689 ^ [], 2688 ^ [])]]))).
% 63.32/61.45  ncf('1.2.2.3',plain,[-(relation(2689 ^ []))],lemmata('[1].x')).
% 63.32/61.45  ncf('1.3',plain,[-(in(ordered_pair(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], 2687 ^ []), 2689 ^ [])), 540 : in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ [])), 540 : relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ []), 536 : relation(2689 ^ [])],extension(532 ^ 3,bind([[_25369, _25476, _25478, _25573], [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []]]))).
% 63.32/61.45  ncf('1.3.1',plain,[-(in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ [])))],extension(2695 ^ 8)).
% 63.32/61.45  ncf('1.3.2',plain,[-(relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ [])), 2689 ^ [] = 2689 ^ [], 2688 ^ [] = 2688 ^ []],extension(312 ^ 6,bind([[_21685, _21687, _21689, _21691], [2688 ^ [], 2688 ^ [], 2689 ^ [], 2689 ^ []]]))).
% 63.32/61.45  ncf('1.3.2.1',plain,[-(2689 ^ [] = 2689 ^ [])],extension(2 ^ 7,bind([[_17254], [2689 ^ []]]))).
% 63.32/61.45  ncf('1.3.2.2',plain,[-(2688 ^ [] = 2688 ^ [])],extension(2 ^ 7,bind([[_17254], [2688 ^ []]]))).
% 63.32/61.45  ncf('1.3.3',plain,[-(relation(2689 ^ []))],extension(2691 ^ 4)).
% 63.32/61.45  ncf('1.4',plain,[-(in(543 ^ [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []], 2688 ^ [])), 540 : in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ [])), 540 : relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ []), 536 : relation(2689 ^ [])],extension(532 ^ 3,bind([[_25369, _25476, _25478, _25573], [2689 ^ [], relation_image(2689 ^ [], 2688 ^ []), 2688 ^ [], 2687 ^ []]]))).
% 63.32/61.45  ncf('1.4.1',plain,[-(in(2687 ^ [], relation_image(2689 ^ [], 2688 ^ [])))],extension(2695 ^ 8)).
% 63.32/61.45  ncf('1.4.2',plain,[-(relation_image(2689 ^ [], 2688 ^ []) = relation_image(2689 ^ [], 2688 ^ [])), 2689 ^ [] = 2689 ^ [], 2688 ^ [] = 2688 ^ []],extension(312 ^ 6,bind([[_21685, _21687, _21689, _21691], [2688 ^ [], 2688 ^ [], 2689 ^ [], 2689 ^ []]]))).
% 63.32/61.45  ncf('1.4.2.1',plain,[-(2689 ^ [] = 2689 ^ [])],extension(2 ^ 7,bind([[_17254], [2689 ^ []]]))).
% 63.32/61.45  ncf('1.4.2.2',plain,[-(2688 ^ [] = 2688 ^ [])],extension(2 ^ 7,bind([[_17254], [2688 ^ []]]))).
% 63.32/61.45  ncf('1.4.3',plain,[-(relation(2689 ^ []))],extension(2691 ^ 4)).
% 63.32/61.45  %-----------------------------------------------------
% 63.32/61.45  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------