%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU209+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n001.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 12:02:40 EDT 2023

% Result   : Theorem 52.47s 51.00s
% Output   : Proof 52.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU209+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n001.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 13:21:04 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 52.47/51.00  
% 52.47/51.00  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 52.47/51.00  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.47/51.00  %-----------------------------------------------------
% 52.47/51.00  ncf(matrix, plain, [(2843 ^ _61355) ^ [] : [subset(relation_inverse_image(2839 ^ [], 2838 ^ []), relation_dom(2839 ^ []))], (2841 ^ _61355) ^ [] : [-(relation(2839 ^ []))], !, (2486 ^ _17312) ^ [_55121] : [relation(_55121), 2489 ^ _17312 : [(2490 ^ _17312) ^ [_55196] : [relation(_55196), subset(relation_dom(_55121), relation_rng(_55196)), -(relation_rng(relation_composition(_55196, _55121)) = relation_rng(_55121))]]], (1654 ^ _17312) ^ [] : [-(empty(empty_set))], (232 ^ _17312) ^ [_20600, _20602, _20604, _20606] : [-(ordered_pair(_20606, _20602) = ordered_pair(_20604, _20600)), _20606 = _20604, _20602 = _20600], (2194 ^ _17312) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (1545 ^ _17312) ^ [_41889] : [relation(_41889), -(relation(relation_inverse(_41889)))], (2331 ^ _17312) ^ [_52884, _52886, _52888] : [subset(unordered_pair(_52888, _52886), _52884), 2334 ^ _17312 : [(2337 ^ _17312) ^ [] : [-(in(_52886, _52884))], (2335 ^ _17312) ^ [] : [-(in(_52888, _52884))]]], (959 ^ _17312) ^ [_32343, _32345, _32347] : [_32343 = cartesian_product2(_32347, _32345), 962 ^ _17312 : [(975 ^ _17312) ^ [_32638] : [-(in(_32638, _32343)), 976 ^ _17312 : [(977 ^ _17312) ^ [_32696, _32698] : [in(_32698, _32347), in(_32696, _32345), _32638 = ordered_pair(_32698, _32696)]]], (963 ^ _17312) ^ [_32451] : [in(_32451, _32343), 968 ^ _17312 : [(973 ^ _17312) ^ [] : [-(_32451 = ordered_pair(966 ^ [_32343, _32345, _32347, _32451], 967 ^ [_32343, _32345, _32347, _32451]))], (971 ^ _17312) ^ [] : [-(in(967 ^ [_32343, _32345, _32347, _32451], _32345))], (969 ^ _17312) ^ [] : [-(in(966 ^ [_32343, _32345, _32347, _32451], _32347))]]]]], (2587 ^ _17312) ^ [_56477, _56479, _56481] : [in(_56481, _56479), element(_56479, powerset(_56477)), empty(_56477)], (222 ^ _17312) ^ [_20451, _20453, _20455, _20457] : [-(subset_complement(_20457, _20453) = subset_complement(_20455, _20451)), _20457 = _20455, _20453 = _20451], (1603 ^ _17312) ^ [_42657, _42659] : [element(_42657, powerset(powerset(_42659))), -(element(complements_of_subsets(_42659, _42657), powerset(powerset(_42659))))], (2565 ^ _17312) ^ [_56219, _56221, _56223] : [element(_56219, powerset(_56223)), in(_56221, subset_complement(_56223, _56219)), in(_56221, _56219)], (1449 ^ _17312) ^ [_40870, _40872] : [-(proper_subset(_40872, _40870)), subset(_40872, _40870), -(_40872 = _40870)], (1858 ^ _17312) ^ [_45993, _45995, _45997, _45999] : [in(ordered_pair(_45999, _45997), cartesian_product2(_45995, _45993)), 1861 ^ _17312 : [(1864 ^ _17312) ^ [] : [-(in(_45997, _45993))], (1862 ^ _17312) ^ [] : [-(in(_45999, _45995))]]], (2271 ^ _17312) ^ [_51980, _51982, _51984] : [relation(_51980), in(ordered_pair(_51984, _51982), _51980), 2278 ^ _17312 : [(2281 ^ _17312) ^ [] : [-(in(_51982, relation_field(_51980)))], (2279 ^ _17312) ^ [] : [-(in(_51984, relation_field(_51980)))]]], (1866 ^ _17312) ^ [_46108, _46110, _46112, _46114] : [-(in(ordered_pair(_46114, _46112), cartesian_product2(_46110, _46108))), in(_46114, _46110), in(_46112, _46108)], (110 ^ _17312) ^ [_18783, _18785, _18787, _18789] : [-(subset(_18787, _18783)), subset(_18789, _18785), _18789 = _18787, _18785 = _18783], (1905 ^ _17312) ^ [] : [-(relation(1901 ^ []))], (2510 ^ _17312) ^ [_55479, _55481] : [element(_55479, powerset(powerset(_55481))), -(_55479 = empty_set), -(union_of_subsets(_55481, complements_of_subsets(_55481, _55479)) = subset_difference(_55481, cast_to_subset(_55481), meet_of_subsets(_55481, _55479)))], (2456 ^ _17312) ^ [_54659] : [relation(_54659), 2459 ^ _17312 : [(2460 ^ _17312) ^ [_54734] : [relation(_54734), subset(relation_rng(_54659), relation_dom(_54734)), -(relation_dom(relation_composition(_54659, _54734)) = relation_dom(_54659))]]], (742 ^ _17312) ^ [_29061, _29063] : [-(_29061 = singleton(_29063)), 746 ^ _17312 : [(749 ^ _17312) ^ [] : [743 ^ [_29061, _29063] = _29063], (747 ^ _17312) ^ [] : [-(in(743 ^ [_29061, _29063], _29061))]], 750 ^ _17312 : [(753 ^ _17312) ^ [] : [in(743 ^ [_29061, _29063], _29061)], (751 ^ _17312) ^ [] : [-(743 ^ [_29061, _29063] = _29063)]]], (1886 ^ _17312) ^ [] : [-(empty(1884 ^ []))], (2269 ^ _17312) ^ [_51957] : [-(subset(empty_set, _51957))], (86 ^ _17312) ^ [_18469, _18471, _18473, _18475] : [-(in(_18473, _18469)), in(_18475, _18471), _18475 = _18473, _18471 = _18469], (1465 ^ _17312) ^ [] : [true___, -(true___)], (2244 ^ _17312) ^ [_51633, _51635] : [element(_51635, _51633), -(empty(_51633)), -(in(_51635, _51633))], (1579 ^ _17312) ^ [_42306] : [-(relation(identity_relation(_42306)))], (372 ^ _17312) ^ [_22702, _22704] : [relation(_22702), 375 ^ _17312 : [(376 ^ _17312) ^ [] : [_22702 = identity_relation(_22704), 379 ^ _17312 : [(388 ^ _17312) ^ [_22964, _22966] : [-(in(ordered_pair(_22966, _22964), _22702)), in(_22966, _22704), _22966 = _22964], (380 ^ _17312) ^ [_22855, _22857] : [in(ordered_pair(_22857, _22855), _22702), 383 ^ _17312 : [(386 ^ _17312) ^ [] : [-(_22857 = _22855)], (384 ^ _17312) ^ [] : [-(in(_22857, _22704))]]]]], (398 ^ _17312) ^ [] : [-(_22702 = identity_relation(_22704)), 411 ^ _17312 : [(416 ^ _17312) ^ [] : [in(ordered_pair(399 ^ [_22702, _22704], 400 ^ [_22702, _22704]), _22702)], (414 ^ _17312) ^ [] : [-(399 ^ [_22702, _22704] = 400 ^ [_22702, _22704])], (412 ^ _17312) ^ [] : [-(in(399 ^ [_22702, _22704], _22704))]], 403 ^ _17312 : [(406 ^ _17312) ^ [] : [in(399 ^ [_22702, _22704], _22704), 399 ^ [_22702, _22704] = 400 ^ [_22702, _22704]], (404 ^ _17312) ^ [] : [-(in(ordered_pair(399 ^ [_22702, _22704], 400 ^ [_22702, _22704]), _22702))]]]]], (2027 ^ _17312) ^ [_48366, _48368, _48370, _48372] : [-(subset(cartesian_product2(_48372, _48368), cartesian_product2(_48370, _48366))), subset(_48372, _48370), subset(_48368, _48366)], (757 ^ _17312) ^ [_29315] : [_29315 = empty_set, 760 ^ _17312 : [(761 ^ _17312) ^ [_29376] : [in(_29376, _29315)]]], (1503 ^ _17312) ^ [] : [true___, -(true___)], (1018 ^ _17312) ^ [_33394] : [relation(_33394), 1021 ^ _17312 : [(1022 ^ _17312) ^ [_33480] : [relation(_33480), 1025 ^ _17312 : [(1026 ^ _17312) ^ [] : [subset(_33394, _33480), 1029 ^ _17312 : [(1030 ^ _17312) ^ [_33611, _33613] : [in(ordered_pair(_33613, _33611), _33394), -(in(ordered_pair(_33613, _33611), _33480))]]], (1036 ^ _17312) ^ [] : [1039 ^ _17312 : [(1042 ^ _17312) ^ [] : [in(ordered_pair(1037 ^ [_33394, _33480], 1038 ^ [_33394, _33480]), _33480)], (1040 ^ _17312) ^ [] : [-(in(ordered_pair(1037 ^ [_33394, _33480], 1038 ^ [_33394, _33480]), _33394))]], -(subset(_33394, _33480))]]]]], (1796 ^ _17312) ^ [_45143, _45145] : [in(_45145, _45143), -(subset(singleton(_45145), _45143))], (2254 ^ _17312) ^ [_51721, _51723] : [-(_51723 = _51721), 2258 ^ _17312 : [(2261 ^ _17312) ^ [] : [in(2255 ^ [_51721, _51723], _51721)], (2259 ^ _17312) ^ [] : [-(in(2255 ^ [_51721, _51723], _51723))]], 2262 ^ _17312 : [(2265 ^ _17312) ^ [] : [in(2255 ^ [_51721, _51723], _51723)], (2263 ^ _17312) ^ [] : [-(in(2255 ^ [_51721, _51723], _51721))]]], (1527 ^ _17312) ^ [_41680, _41682] : [element(_41680, powerset(_41682)), -(element(subset_complement(_41682, _41680), powerset(_41682)))], (62 ^ _17312) ^ [_18151, _18153] : [-(empty(_18151)), _18153 = _18151, empty(_18153)], (2062 ^ _17312) ^ [_48960, _48962] : [subset(_48960, 2042 ^ [_48962]), -(are_equipotent(_48960, 2042 ^ [_48962])), -(in(_48960, 2042 ^ [_48962]))], (2798 ^ _17312) ^ [_59450] : [-(in(_59450, 2796 ^ [_59450]))], (2166 ^ _17312) ^ [_50531, _50533, _50535] : [-(subset(_50535, set_intersection2(_50533, _50531))), subset(_50535, _50533), subset(_50535, _50531)], (1147 ^ _17312) ^ [_35564, _35566] : [_35564 = union(_35566), 1150 ^ _17312 : [(1160 ^ _17312) ^ [_35778] : [-(in(_35778, _35564)), 1161 ^ _17312 : [(1162 ^ _17312) ^ [_35820] : [in(_35778, _35820), in(_35820, _35566)]]], (1151 ^ _17312) ^ [_35654] : [in(_35654, _35564), 1155 ^ _17312 : [(1158 ^ _17312) ^ [] : [-(in(1154 ^ [_35564, _35566, _35654], _35566))], (1156 ^ _17312) ^ [] : [-(in(_35654, 1154 ^ [_35564, _35566, _35654]))]]]]], (786 ^ _17312) ^ [_29688, _29690] : [-(_29688 = powerset(_29690)), 790 ^ _17312 : [(793 ^ _17312) ^ [] : [subset(787 ^ [_29688, _29690], _29690)], (791 ^ _17312) ^ [] : [-(in(787 ^ [_29688, _29690], _29688))]], 794 ^ _17312 : [(797 ^ _17312) ^ [] : [in(787 ^ [_29688, _29690], _29688)], (795 ^ _17312) ^ [] : [-(subset(787 ^ [_29688, _29690], _29690))]]], (661 ^ _17312) ^ [_27803, _27805] : [-(_27805 = empty_set), 664 ^ _17312 : [(665 ^ _17312) ^ [] : [_27803 = set_meet(_27805), 668 ^ _17312 : [(669 ^ _17312) ^ [_27950] : [in(_27950, _27803), 672 ^ _17312 : [(673 ^ _17312) ^ [_28015] : [in(_28015, _27805), -(in(_27950, _28015))]]], (679 ^ _17312) ^ [_28096] : [681 ^ _17312 : [(684 ^ _17312) ^ [] : [in(_28096, 680 ^ [_27803, _27805, _28096])], (682 ^ _17312) ^ [] : [-(in(680 ^ [_27803, _27805, _28096], _27805))]], -(in(_28096, _27803))]]], (688 ^ _17312) ^ [] : [-(_27803 = set_meet(_27805)), 692 ^ _17312 : [(698 ^ _17312) ^ [] : [in(689 ^ [_27803, _27805], 694 ^ [_27803, _27805])], (696 ^ _17312) ^ [] : [-(in(694 ^ [_27803, _27805], _27805))], (693 ^ _17312) ^ [] : [-(in(689 ^ [_27803, _27805], _27803))]], 699 ^ _17312 : [(700 ^ _17312) ^ [_28440] : [in(_28440, _27805), -(in(689 ^ [_27803, _27805], _28440))], (706 ^ _17312) ^ [] : [in(689 ^ [_27803, _27805], _27803)]]]]], (2823 ^ _17312) ^ [_59872, _59874] : [subset(_59872, 2796 ^ [_59874]), -(are_equipotent(_59872, 2796 ^ [_59874])), -(in(_59872, 2796 ^ [_59874]))], (841 ^ _17312) ^ [_30641, _30643] : [-(empty(_30643)), 844 ^ _17312 : [(851 ^ _17312) ^ [] : [in(_30641, _30643), -(element(_30641, _30643))], (845 ^ _17312) ^ [] : [element(_30641, _30643), -(in(_30641, _30643))]]], (710 ^ _17312) ^ [_28596, _28598] : [_28598 = empty_set, 713 ^ _17312 : [(720 ^ _17312) ^ [] : [_28596 = empty_set, -(_28596 = set_meet(_28598))], (714 ^ _17312) ^ [] : [_28596 = set_meet(_28598), -(_28596 = empty_set)]]], (1824 ^ _17312) ^ [_45555, _45557, _45559] : [subset(_45559, _45557), -(in(_45555, _45559)), -(subset(_45559, set_difference(_45557, singleton(_45555))))], (2575 ^ _17312) ^ [_56363] : [relation(_56363), -(in(ordered_pair(2580 ^ [_56363], 2581 ^ [_56363]), _56363)), -(_56363 = empty_set)], (1192 ^ _17312) ^ [_36307, _36309, _36311] : [_36307 = set_difference(_36311, _36309), 1195 ^ _17312 : [(1204 ^ _17312) ^ [_36509] : [-(in(_36509, _36307)), in(_36509, _36311), -(in(_36509, _36309))], (1196 ^ _17312) ^ [_36398] : [in(_36398, _36307), 1199 ^ _17312 : [(1202 ^ _17312) ^ [] : [in(_36398, _36309)], (1200 ^ _17312) ^ [] : [-(in(_36398, _36311))]]]]], (368 ^ _17312) ^ [_22640, _22642] : [-(set_union2(_22642, _22640) = set_union2(_22640, _22642))], (1688 ^ _17312) ^ [_43748, _43750] : [empty(cartesian_product2(_43750, _43748)), -(empty(_43750)), -(empty(_43748))], (2651 ^ _17312) ^ [_57330, _57332] : [-(in(_57330, _57332)), -(set_difference(_57332, singleton(_57330)) = _57332)], (2164 ^ _17312) ^ [_50503, _50505] : [-(subset(set_intersection2(_50505, _50503), _50505))], (1770 ^ _17312) ^ [_44825] : [singleton(_44825) = empty_set], (1652 ^ _17312) ^ [_43278] : [empty(powerset(_43278))], (2783 ^ _17312) ^ [_59135, _59137] : [relation(_59135), -(relation_dom_restriction(_59135, _59137) = relation_composition(identity_relation(_59137), _59135))], (2176 ^ _17312) ^ [_50670] : [-(set_union2(_50670, empty_set) = _50670)], (1658 ^ _17312) ^ [_43359, _43361] : [-(relation(set_union2(_43361, _43359))), relation(_43361), relation(_43359)], (2307 ^ _17312) ^ [_52527, _52529] : [set_difference(_52529, _52527) = empty_set, -(subset(_52529, _52527))], (1973 ^ _17312) ^ [_47581, _47583, _47585] : [relation(_47581), 1976 ^ _17312 : [(1985 ^ _17312) ^ [] : [-(in(_47585, relation_rng(relation_rng_restriction(_47583, _47581)))), in(_47585, _47583), in(_47585, relation_rng(_47581))], (1977 ^ _17312) ^ [] : [in(_47585, relation_rng(relation_rng_restriction(_47583, _47581))), 1980 ^ _17312 : [(1983 ^ _17312) ^ [] : [-(in(_47585, relation_rng(_47581)))], (1981 ^ _17312) ^ [] : [-(in(_47585, _47583))]]]]], (1790 ^ _17312) ^ [_45066, _45068] : [subset(singleton(_45068), _45066), -(in(_45068, _45066))], (1065 ^ _17312) ^ [_34184, _34186, _34188] : [_34184 = set_intersection2(_34188, _34186), 1068 ^ _17312 : [(1077 ^ _17312) ^ [_34376] : [-(in(_34376, _34184)), in(_34376, _34188), in(_34376, _34186)], (1069 ^ _17312) ^ [_34273] : [in(_34273, _34184), 1072 ^ _17312 : [(1075 ^ _17312) ^ [] : [-(in(_34273, _34186))], (1073 ^ _17312) ^ [] : [-(in(_34273, _34188))]]]]], (1668 ^ _17312) ^ [_43497] : [empty(singleton(_43497))], (1937 ^ _17312) ^ [_47082, _47084] : [-(subset(_47084, _47084))], (2524 ^ _17312) ^ [_55669, _55671, _55673] : [-(element(_55673, _55669)), in(_55673, _55671), element(_55671, powerset(_55669))], (1533 ^ _17312) ^ [] : [true___, -(true___)], (1573 ^ _17312) ^ [_42211, _42213] : [element(_42211, powerset(powerset(_42213))), -(element(union_of_subsets(_42213, _42211), powerset(_42213)))], (1772 ^ _17312) ^ [_44850, _44852] : [in(_44852, _44850), -(set_union2(singleton(_44852), _44850) = _44850)], (2675 ^ _17312) ^ [_57610, _57612, _57614, _57616] : [relation(_57610), 2678 ^ _17312 : [(2687 ^ _17312) ^ [] : [-(in(ordered_pair(_57616, _57614), relation_composition(identity_relation(_57612), _57610))), in(_57616, _57612), in(ordered_pair(_57616, _57614), _57610)], (2679 ^ _17312) ^ [] : [in(ordered_pair(_57616, _57614), relation_composition(identity_relation(_57612), _57610)), 2682 ^ _17312 : [(2685 ^ _17312) ^ [] : [-(in(ordered_pair(_57616, _57614), _57610))], (2683 ^ _17312) ^ [] : [-(in(_57616, _57612))]]]]], (20 ^ _17312) ^ [_17572, _17574, _17576, _17578] : [-(element(_17576, _17572)), element(_17578, _17574), _17578 = _17576, _17574 = _17572], (2297 ^ _17312) ^ [_52361, _52363] : [-(subset(set_difference(_52363, _52361), _52363))], (1903 ^ _17312) ^ [] : [empty(1901 ^ [])], (212 ^ _17312) ^ [_20302, _20304, _20306, _20308] : [-(meet_of_subsets(_20308, _20304) = meet_of_subsets(_20306, _20302)), _20308 = _20306, _20304 = _20302], (1808 ^ _17312) ^ [_45320, _45322] : [subset(_45322, _45320), -(set_difference(_45322, _45320) = empty_set)], (1459 ^ _17312) ^ [] : [true___, -(true___)], (916 ^ _17312) ^ [_31703, _31705, _31707] : [_31703 = set_union2(_31707, _31705), 919 ^ _17312 : [(920 ^ _17312) ^ [_31792] : [in(_31792, _31703), -(in(_31792, _31707)), -(in(_31792, _31705))], (930 ^ _17312) ^ [_31882] : [931 ^ _17312 : [(934 ^ _17312) ^ [] : [in(_31882, _31705)], (932 ^ _17312) ^ [] : [in(_31882, _31707)]], -(in(_31882, _31703))]]], (288 ^ _17312) ^ [_21430, _21432, _21434, _21436] : [-(relation_dom_restriction(_21436, _21432) = relation_dom_restriction(_21434, _21430)), _21436 = _21434, _21432 = _21430], (2119 ^ _17312) ^ [_49811] : [relation(_49811), -(relation_image(_49811, relation_dom(_49811)) = relation_rng(_49811))], (172 ^ _17312) ^ [_19698, _19700, _19702, _19704] : [-(union_of_subsets(_19704, _19700) = union_of_subsets(_19702, _19698)), _19704 = _19702, _19700 = _19698], (1963 ^ _17312) ^ [_47471, _47473, _47475, _47477] : [unordered_pair(_47477, _47475) = unordered_pair(_47473, _47471), -(_47477 = _47473), -(_47477 = _47471)], (1108 ^ _17312) ^ [_34869] : [relation(_34869), 1111 ^ _17312 : [(1112 ^ _17312) ^ [_34961] : [_34961 = relation_dom(_34869), 1115 ^ _17312 : [(1123 ^ _17312) ^ [_35143] : [1124 ^ _17312 : [(1125 ^ _17312) ^ [_35187] : [in(ordered_pair(_35143, _35187), _34869)]], -(in(_35143, _34961))], (1116 ^ _17312) ^ [_35048] : [in(_35048, _34961), -(in(ordered_pair(_35048, 1119 ^ [_34869, _34961, _35048]), _34869))]]], (1129 ^ _17312) ^ [_35243] : [-(_35243 = relation_dom(_34869)), 1133 ^ _17312 : [(1136 ^ _17312) ^ [_35377] : [in(ordered_pair(1130 ^ [_34869, _35243], _35377), _34869)], (1134 ^ _17312) ^ [] : [-(in(1130 ^ [_34869, _35243], _35243))]], 1138 ^ _17312 : [(1141 ^ _17312) ^ [] : [in(1130 ^ [_34869, _35243], _35243)], (1139 ^ _17312) ^ [] : [-(in(ordered_pair(1130 ^ [_34869, _35243], 1137 ^ [_34869, _35243]), _34869))]]]]], (989 ^ _17312) ^ [_32876, _32878, _32880] : [-(_32876 = cartesian_product2(_32880, _32878)), 1007 ^ _17312 : [(1010 ^ _17312) ^ [] : [-(in(1006 ^ [_32876, _32878, _32880], _32878))], (1012 ^ _17312) ^ [] : [-(990 ^ [_32876, _32878, _32880] = ordered_pair(1005 ^ [_32876, _32878, _32880], 1006 ^ [_32876, _32878, _32880]))], (1014 ^ _17312) ^ [] : [in(990 ^ [_32876, _32878, _32880], _32876)], (1008 ^ _17312) ^ [] : [-(in(1005 ^ [_32876, _32878, _32880], _32880))]], 993 ^ _17312 : [(996 ^ _17312) ^ [_33046, _33048] : [in(_33048, _32880), in(_33046, _32878), 990 ^ [_32876, _32878, _32880] = ordered_pair(_33048, _33046)], (994 ^ _17312) ^ [] : [-(in(990 ^ [_32876, _32878, _32880], _32876))]]], (2196 ^ _17312) ^ [_50924, _50926, _50928] : [relation(_50924), in(ordered_pair(_50928, _50926), _50924), 2203 ^ _17312 : [(2206 ^ _17312) ^ [] : [-(in(_50926, relation_rng(_50924)))], (2204 ^ _17312) ^ [] : [-(in(_50928, relation_dom(_50924)))]]], (1910 ^ _17312) ^ [_46678] : [-(empty(1906 ^ [_46678]))], (1145 ^ _17312) ^ [_35524] : [-(cast_to_subset(_35524) = _35524)], (726 ^ _17312) ^ [_28826, _28828] : [_28826 = singleton(_28828), 729 ^ _17312 : [(736 ^ _17312) ^ [_28980] : [_28980 = _28828, -(in(_28980, _28826))], (730 ^ _17312) ^ [_28905] : [in(_28905, _28826), -(_28905 = _28828)]]], (1656 ^ _17312) ^ [_43332, _43334] : [empty(ordered_pair(_43334, _43332))], (1927 ^ _17312) ^ [_46927, _46929, _46931] : [-(subset_difference(_46931, _46929, _46927) = set_difference(_46929, _46927)), element(_46929, powerset(_46931)), element(_46927, powerset(_46931))], (1332 ^ _17312) ^ [_38697, _38699] : [set_intersection2(_38699, _38697) = empty_set, -(disjoint(_38699, _38697))], (130 ^ _17312) ^ [_19081, _19083, _19085, _19087] : [-(relation_rng_restriction(_19087, _19083) = relation_rng_restriction(_19085, _19081)), _19087 = _19085, _19083 = _19081], (2777 ^ _17312) ^ [_59054, _59056] : [in(_59056, _59054), -(subset(_59056, union(_59054)))], (1615 ^ _17312) ^ [] : [true___, -(true___)], (1170 ^ _17312) ^ [_35930, _35932] : [-(_35930 = union(_35932)), 1183 ^ _17312 : [(1188 ^ _17312) ^ [] : [in(1171 ^ [_35930, _35932], _35930)], (1186 ^ _17312) ^ [] : [-(in(1182 ^ [_35930, _35932], _35932))], (1184 ^ _17312) ^ [] : [-(in(1171 ^ [_35930, _35932], 1182 ^ [_35930, _35932]))]], 1174 ^ _17312 : [(1177 ^ _17312) ^ [_36063] : [in(1171 ^ [_35930, _35932], _36063), in(_36063, _35932)], (1175 ^ _17312) ^ [] : [-(in(1171 ^ [_35930, _35932], _35930))]]], (2135 ^ _17312) ^ [_50065, _50067, _50069] : [relation(_50065), 2138 ^ _17312 : [(2150 ^ _17312) ^ [] : [-(in(_50069, relation_inverse_image(_50065, _50067))), 2151 ^ _17312 : [(2152 ^ _17312) ^ [_50320] : [in(_50320, relation_rng(_50065)), in(ordered_pair(_50069, _50320), _50065), in(_50320, _50067)]]], (2139 ^ _17312) ^ [] : [in(_50069, relation_inverse_image(_50065, _50067)), 2143 ^ _17312 : [(2148 ^ _17312) ^ [] : [-(in(2142 ^ [_50065, _50067, _50069], _50067))], (2146 ^ _17312) ^ [] : [-(in(ordered_pair(_50069, 2142 ^ [_50065, _50067, _50069]), _50065))], (2144 ^ _17312) ^ [] : [-(in(2142 ^ [_50065, _50067, _50069], relation_rng(_50065)))]]]]], (48 ^ _17312) ^ [_17958, _17960, _17962, _17964] : [-(disjoint(_17962, _17958)), disjoint(_17964, _17960), _17964 = _17962, _17960 = _17958], (1509 ^ _17312) ^ [] : [true___, -(true___)], (1670 ^ _17312) ^ [_43520, _43522] : [-(empty(_43522)), empty(set_union2(_43522, _43520))], (1915 ^ _17312) ^ [_46737, _46739] : [element(_46737, powerset(powerset(_46739))), -(union_of_subsets(_46739, _46737) = union(_46737))], (2369 ^ _17312) ^ [_53400] : [-(set_difference(_53400, empty_set) = _53400)], (1876 ^ _17312) ^ [_46259, _46261] : [1878 ^ _17312 : [(1881 ^ _17312) ^ [] : [in(1877 ^ [_46259, _46261], _46259)], (1879 ^ _17312) ^ [] : [-(in(1877 ^ [_46259, _46261], _46261))]], -(element(_46261, powerset(_46259)))], (1278 ^ _17312) ^ [_37765, _37767] : [-(ordered_pair(_37767, _37765) = unordered_pair(unordered_pair(_37767, _37765), singleton(_37767)))], (1495 ^ _17312) ^ [] : [true___, -(true___)], (100 ^ _17312) ^ [_18662, _18664] : [-(relation(_18662)), _18664 = _18662, relation(_18664)], (1802 ^ _17312) ^ [_45241, _45243] : [set_difference(_45243, _45241) = empty_set, -(subset(_45243, _45241))], (801 ^ _17312) ^ [_29930] : [relation(_29930), 804 ^ _17312 : [(805 ^ _17312) ^ [_30016] : [relation(_30016), 808 ^ _17312 : [(809 ^ _17312) ^ [] : [_29930 = _30016, 812 ^ _17312 : [(819 ^ _17312) ^ [_30251, _30253] : [in(ordered_pair(_30253, _30251), _30016), -(in(ordered_pair(_30253, _30251), _29930))], (813 ^ _17312) ^ [_30162, _30164] : [in(ordered_pair(_30164, _30162), _29930), -(in(ordered_pair(_30164, _30162), _30016))]]], (825 ^ _17312) ^ [] : [-(_29930 = _30016), 830 ^ _17312 : [(833 ^ _17312) ^ [] : [in(ordered_pair(826 ^ [_29930, _30016], 827 ^ [_29930, _30016]), _30016)], (831 ^ _17312) ^ [] : [-(in(ordered_pair(826 ^ [_29930, _30016], 827 ^ [_29930, _30016]), _29930))]], 834 ^ _17312 : [(837 ^ _17312) ^ [] : [in(ordered_pair(826 ^ [_29930, _30016], 827 ^ [_29930, _30016]), _29930)], (835 ^ _17312) ^ [] : [-(in(ordered_pair(826 ^ [_29930, _30016], 827 ^ [_29930, _30016]), _30016))]]]]]]], (2703 ^ _17312) ^ [_58010, _58012] : [-(subset(_58012, set_union2(_58012, _58010)))], (2339 ^ _17312) ^ [_52991, _52993, _52995] : [-(subset(unordered_pair(_52995, _52993), _52991)), in(_52995, _52991), in(_52993, _52991)], (2745 ^ _17312) ^ [_58604, _58606] : [empty(_58606), -(_58606 = _58604), empty(_58604)], (342 ^ _17312) ^ [_22213, _22215] : [_22215 = _22213, -(relation_dom(_22215) = relation_dom(_22213))], (166 ^ _17312) ^ [_19613, _19615] : [_19615 = _19613, -(relation_inverse(_19615) = relation_inverse(_19613))], (2541 ^ _17312) ^ [_55854, _55856] : [2542 ^ _17312 : [(2543 ^ _17312) ^ [_55896] : [in(_55896, set_intersection2(_55856, _55854))]], disjoint(_55856, _55854)], (2313 ^ _17312) ^ [_52606, _52608] : [subset(_52608, _52606), -(set_difference(_52608, _52606) = empty_set)], (2800 ^ _17312) ^ [_59478, _59480, _59482] : [-(in(_59478, 2796 ^ [_59482])), in(_59480, 2796 ^ [_59482]), subset(_59478, _59480)], (2021 ^ _17312) ^ [_48271, _48273] : [relation(_48271), -(relation_rng(relation_rng_restriction(_48273, _48271)) = set_intersection2(relation_rng(_48271), _48273))], (895 ^ _17312) ^ [_31363, _31365, _31367] : [-(_31363 = unordered_pair(_31367, _31365)), 899 ^ _17312 : [(904 ^ _17312) ^ [] : [896 ^ [_31363, _31365, _31367] = _31365], (902 ^ _17312) ^ [] : [896 ^ [_31363, _31365, _31367] = _31367], (900 ^ _17312) ^ [] : [-(in(896 ^ [_31363, _31365, _31367], _31363))]], 905 ^ _17312 : [(906 ^ _17312) ^ [] : [-(896 ^ [_31363, _31365, _31367] = _31367), -(896 ^ [_31363, _31365, _31367] = _31365)], (912 ^ _17312) ^ [] : [in(896 ^ [_31363, _31365, _31367], _31363)]]], (1708 ^ _17312) ^ [_43960] : [empty(relation_rng(_43960)), -(empty(_43960)), relation(_43960)], (1521 ^ _17312) ^ [] : [true___, -(true___)], (2534 ^ _17312) ^ [_55812, _55814] : [-(disjoint(_55814, _55812)), -(in(2537 ^ [_55812, _55814], set_intersection2(_55814, _55812)))], (1214 ^ _17312) ^ [_36651, _36653, _36655] : [-(_36651 = set_difference(_36655, _36653)), 1226 ^ _17312 : [(1231 ^ _17312) ^ [] : [in(1215 ^ [_36651, _36653, _36655], _36651)], (1229 ^ _17312) ^ [] : [in(1215 ^ [_36651, _36653, _36655], _36653)], (1227 ^ _17312) ^ [] : [-(in(1215 ^ [_36651, _36653, _36655], _36655))]], 1218 ^ _17312 : [(1221 ^ _17312) ^ [] : [in(1215 ^ [_36651, _36653, _36655], _36655), -(in(1215 ^ [_36651, _36653, _36655], _36653))], (1219 ^ _17312) ^ [] : [-(in(1215 ^ [_36651, _36653, _36655], _36651))]]], (2125 ^ _17312) ^ [_49898] : [relation(_49898), 2128 ^ _17312 : [(2129 ^ _17312) ^ [_49966] : [relation(_49966), -(relation_rng(relation_composition(_49898, _49966)) = relation_image(_49966, relation_rng(_49898)))]]], (2402 ^ _17312) ^ [_53837] : [subset(_53837, empty_set), -(_53837 = empty_set)], (1587 ^ _17312) ^ [_42425, _42427, _42429] : [-(element(subset_difference(_42429, _42427, _42425), powerset(_42429))), element(_42427, powerset(_42429)), element(_42425, powerset(_42429))], (2645 ^ _17312) ^ [_57248, _57250] : [set_difference(_57250, singleton(_57248)) = _57250, in(_57248, _57250)], (1913 ^ _17312) ^ [] : [empty(1911 ^ [])], (2410 ^ _17312) ^ [_53946, _53948] : [element(_53946, powerset(_53948)), 2413 ^ _17312 : [(2414 ^ _17312) ^ [_54024] : [element(_54024, powerset(_53948)), 2417 ^ _17312 : [(2424 ^ _17312) ^ [] : [subset(_53946, subset_complement(_53948, _54024)), -(disjoint(_53946, _54024))], (2418 ^ _17312) ^ [] : [disjoint(_53946, _54024), -(subset(_53946, subset_complement(_53948, _54024)))]]]]], (2046 ^ _17312) ^ [_48710, _48712, _48714] : [-(in(_48710, 2042 ^ [_48714])), in(_48712, 2042 ^ [_48714]), subset(_48710, _48712)], (242 ^ _17312) ^ [_20749, _20751, _20753, _20755] : [-(set_difference(_20755, _20751) = set_difference(_20753, _20749)), _20755 = _20753, _20751 = _20749], (2629 ^ _17312) ^ [_57022] : [relation(_57022), 2632 ^ _17312 : [(2639 ^ _17312) ^ [] : [relation_rng(_57022) = empty_set, -(relation_dom(_57022) = empty_set)], (2633 ^ _17312) ^ [] : [relation_dom(_57022) = empty_set, -(relation_rng(_57022) = empty_set)]]], (2500 ^ _17312) ^ [_55349, _55351] : [element(_55349, powerset(powerset(_55351))), -(_55349 = empty_set), -(subset_difference(_55351, cast_to_subset(_55351), union_of_subsets(_55351, _55349)) = meet_of_subsets(_55351, complements_of_subsets(_55351, _55349)))], (2113 ^ _17312) ^ [_49714, _49716] : [relation(_49714), -(relation_image(_49714, _49716) = relation_image(_49714, set_intersection2(relation_dom(_49714), _49716)))], (1235 ^ _17312) ^ [_37017] : [relation(_37017), 1238 ^ _17312 : [(1239 ^ _17312) ^ [_37109] : [_37109 = relation_rng(_37017), 1242 ^ _17312 : [(1250 ^ _17312) ^ [_37291] : [1251 ^ _17312 : [(1252 ^ _17312) ^ [_37335] : [in(ordered_pair(_37335, _37291), _37017)]], -(in(_37291, _37109))], (1243 ^ _17312) ^ [_37196] : [in(_37196, _37109), -(in(ordered_pair(1246 ^ [_37017, _37109, _37196], _37196), _37017))]]], (1256 ^ _17312) ^ [_37391] : [-(_37391 = relation_rng(_37017)), 1260 ^ _17312 : [(1263 ^ _17312) ^ [_37525] : [in(ordered_pair(_37525, 1257 ^ [_37017, _37391]), _37017)], (1261 ^ _17312) ^ [] : [-(in(1257 ^ [_37017, _37391], _37391))]], 1265 ^ _17312 : [(1268 ^ _17312) ^ [] : [in(1257 ^ [_37017, _37391], _37391)], (1266 ^ _17312) ^ [] : [-(in(ordered_pair(1264 ^ [_37017, _37391], 1257 ^ [_37017, _37391]), _37017))]]]]], (2450 ^ _17312) ^ [_54570, _54572] : [subset(_54572, _54570), -(_54570 = set_union2(_54572, set_difference(_54570, _54572)))], (2659 ^ _17312) ^ [_57401] : [empty(_57401), -(_57401 = empty_set)], (1888 ^ _17312) ^ [] : [-(relation(1884 ^ []))], (873 ^ _17312) ^ [_31063, _31065, _31067] : [_31063 = unordered_pair(_31067, _31065), 876 ^ _17312 : [(877 ^ _17312) ^ [_31152] : [in(_31152, _31063), -(_31152 = _31067), -(_31152 = _31065)], (887 ^ _17312) ^ [_31242] : [888 ^ _17312 : [(891 ^ _17312) ^ [] : [_31242 = _31065], (889 ^ _17312) ^ [] : [_31242 = _31067]], -(in(_31242, _31063))]]], (1684 ^ _17312) ^ [] : [-(empty(empty_set))], (1686 ^ _17312) ^ [] : [-(relation(empty_set))], (140 ^ _17312) ^ [_19230, _19232, _19234, _19236] : [-(relation_image(_19236, _19232) = relation_image(_19234, _19230)), _19236 = _19234, _19232 = _19230], (1501 ^ _17312) ^ [_41417] : [-(element(cast_to_subset(_41417), powerset(_41417)))], (1539 ^ _17312) ^ [] : [true___, -(true___)], (1945 ^ _17312) ^ [_47205, _47207, _47209, _47211] : [in(ordered_pair(_47211, _47209), cartesian_product2(_47207, _47205)), 1948 ^ _17312 : [(1951 ^ _17312) ^ [] : [-(in(_47209, _47205))], (1949 ^ _17312) ^ [] : [-(in(_47211, _47207))]]], (1676 ^ _17312) ^ [_43611, _43613] : [empty(unordered_pair(_43613, _43611))], (2377 ^ _17312) ^ [_53518, _53520] : [subset(_53520, _53518), -(element(_53520, powerset(_53518)))], (1477 ^ _17312) ^ [] : [true___, -(true___)], (304 ^ _17312) ^ [_21664, _21666] : [_21666 = _21664, -(union(_21666) = union(_21664))], (366 ^ _17312) ^ [_22609, _22611] : [-(unordered_pair(_22611, _22609) = unordered_pair(_22609, _22611))], (72 ^ _17312) ^ [_18276, _18278, _18280, _18282] : [-(are_equipotent(_18280, _18276)), are_equipotent(_18282, _18278), _18282 = _18280, _18278 = _18276], (4 ^ _17312) ^ [_17362, _17364] : [_17364 = _17362, -(_17362 = _17364)], (2795 ^ _17312) ^ [_59315] : [-(union(powerset(_59315)) = _59315)], (310 ^ _17312) ^ [_21749, _21751] : [_21751 = _21749, -(powerset(_21751) = powerset(_21749))], (490 ^ _17312) ^ [_24670, _24672] : [relation(_24670), 493 ^ _17312 : [(494 ^ _17312) ^ [_24767] : [relation(_24767), 497 ^ _17312 : [(498 ^ _17312) ^ [] : [_24767 = relation_rng_restriction(_24672, _24670), 501 ^ _17312 : [(510 ^ _17312) ^ [_25046, _25048] : [-(in(ordered_pair(_25048, _25046), _24767)), in(_25046, _24672), in(ordered_pair(_25048, _25046), _24670)], (502 ^ _17312) ^ [_24929, _24931] : [in(ordered_pair(_24931, _24929), _24767), 505 ^ _17312 : [(508 ^ _17312) ^ [] : [-(in(ordered_pair(_24931, _24929), _24670))], (506 ^ _17312) ^ [] : [-(in(_24929, _24672))]]]]], (520 ^ _17312) ^ [] : [-(_24767 = relation_rng_restriction(_24672, _24670)), 533 ^ _17312 : [(538 ^ _17312) ^ [] : [in(ordered_pair(521 ^ [_24670, _24672, _24767], 522 ^ [_24670, _24672, _24767]), _24767)], (536 ^ _17312) ^ [] : [-(in(ordered_pair(521 ^ [_24670, _24672, _24767], 522 ^ [_24670, _24672, _24767]), _24670))], (534 ^ _17312) ^ [] : [-(in(522 ^ [_24670, _24672, _24767], _24672))]], 525 ^ _17312 : [(528 ^ _17312) ^ [] : [in(522 ^ [_24670, _24672, _24767], _24672), in(ordered_pair(521 ^ [_24670, _24672, _24767], 522 ^ [_24670, _24672, _24767]), _24670)], (526 ^ _17312) ^ [] : [-(in(ordered_pair(521 ^ [_24670, _24672, _24767], 522 ^ [_24670, _24672, _24767]), _24767))]]]]]]], (1900 ^ _17312) ^ [] : [-(empty(1898 ^ []))], (1678 ^ _17312) ^ [_43637, _43639] : [-(empty(_43639)), empty(set_union2(_43637, _43639))], (1953 ^ _17312) ^ [_47320, _47322, _47324, _47326] : [-(in(ordered_pair(_47326, _47324), cartesian_product2(_47322, _47320))), in(_47326, _47322), in(_47324, _47320)], (1471 ^ _17312) ^ [] : [true___, -(true___)], (1890 ^ _17312) ^ [_46443] : [-(empty(_46443)), 1894 ^ _17312 : [(1897 ^ _17312) ^ [] : [empty(1893 ^ [_46443])], (1895 ^ _17312) ^ [] : [-(element(1893 ^ [_46443], powerset(_46443)))]]], (1834 ^ _17312) ^ [_45672, _45674] : [subset(_45674, singleton(_45672)), -(_45674 = empty_set), -(_45674 = singleton(_45672))], (2214 ^ _17312) ^ [_51182] : [relation(_51182), 2217 ^ _17312 : [(2218 ^ _17312) ^ [_51260] : [relation(_51260), subset(_51182, _51260), 2225 ^ _17312 : [(2228 ^ _17312) ^ [] : [-(subset(relation_rng(_51182), relation_rng(_51260)))], (2226 ^ _17312) ^ [] : [-(subset(relation_dom(_51182), relation_dom(_51260)))]]]]], (124 ^ _17312) ^ [_18996, _18998] : [_18998 = _18996, -(set_meet(_18998) = set_meet(_18996))], (2184 ^ _17312) ^ [_50773, _50775, _50777] : [-(subset(_50777, _50773)), subset(_50777, _50775), subset(_50775, _50773)], (1734 ^ _17312) ^ [_44293, _44295] : [1741 ^ _17312 : [(1744 ^ _17312) ^ [] : [-(relation(relation_composition(_44295, _44293)))], (1742 ^ _17312) ^ [] : [-(empty(relation_composition(_44295, _44293)))]], empty(_44295), relation(_44293)], (1326 ^ _17312) ^ [_38618, _38620] : [disjoint(_38620, _38618), -(set_intersection2(_38620, _38618) = empty_set)], (857 ^ _17312) ^ [_30841, _30843] : [empty(_30843), 860 ^ _17312 : [(867 ^ _17312) ^ [] : [empty(_30841), -(element(_30841, _30843))], (861 ^ _17312) ^ [] : [element(_30841, _30843), -(empty(_30841))]]], (1597 ^ _17312) ^ [_42578, _42580] : [relation(_42580), -(relation(relation_dom_restriction(_42580, _42578)))], (1563 ^ _17312) ^ [_42082, _42084] : [-(relation(relation_composition(_42084, _42082))), relation(_42084), relation(_42082)], (2705 ^ _17312) ^ [_58053, _58055] : [disjoint(_58055, _58053), -(set_difference(_58055, _58053) = _58055)], (770 ^ _17312) ^ [_29453, _29455] : [_29453 = powerset(_29455), 773 ^ _17312 : [(780 ^ _17312) ^ [_29607] : [subset(_29607, _29455), -(in(_29607, _29453))], (774 ^ _17312) ^ [_29532] : [in(_29532, _29453), -(subset(_29532, _29455))]]], (1756 ^ _17312) ^ [_44601] : [relation(_44601), -(relation_inverse(relation_inverse(_44601)) = _44601)], (1286 ^ _17312) ^ [_37892] : [relation(_37892), 1289 ^ _17312 : [(1290 ^ _17312) ^ [_37980] : [relation(_37980), 1293 ^ _17312 : [(1294 ^ _17312) ^ [] : [_37980 = relation_inverse(_37892), 1297 ^ _17312 : [(1304 ^ _17312) ^ [_38219, _38221] : [in(ordered_pair(_38219, _38221), _37892), -(in(ordered_pair(_38221, _38219), _37980))], (1298 ^ _17312) ^ [_38130, _38132] : [in(ordered_pair(_38132, _38130), _37980), -(in(ordered_pair(_38130, _38132), _37892))]]], (1310 ^ _17312) ^ [] : [-(_37980 = relation_inverse(_37892)), 1315 ^ _17312 : [(1318 ^ _17312) ^ [] : [in(ordered_pair(1312 ^ [_37892, _37980], 1311 ^ [_37892, _37980]), _37892)], (1316 ^ _17312) ^ [] : [-(in(ordered_pair(1311 ^ [_37892, _37980], 1312 ^ [_37892, _37980]), _37980))]], 1319 ^ _17312 : [(1322 ^ _17312) ^ [] : [in(ordered_pair(1311 ^ [_37892, _37980], 1312 ^ [_37892, _37980]), _37980)], (1320 ^ _17312) ^ [] : [-(in(ordered_pair(1312 ^ [_37892, _37980], 1311 ^ [_37892, _37980]), _37892))]]]]]]], (2078 ^ _17312) ^ [_49191, _49193, _49195] : [relation(_49191), 2081 ^ _17312 : [(2093 ^ _17312) ^ [] : [-(in(_49195, relation_image(_49191, _49193))), 2094 ^ _17312 : [(2095 ^ _17312) ^ [_49446] : [in(_49446, relation_dom(_49191)), in(ordered_pair(_49446, _49195), _49191), in(_49446, _49193)]]], (2082 ^ _17312) ^ [] : [in(_49195, relation_image(_49191, _49193)), 2086 ^ _17312 : [(2091 ^ _17312) ^ [] : [-(in(2085 ^ [_49191, _49193, _49195], _49193))], (2089 ^ _17312) ^ [] : [-(in(ordered_pair(2085 ^ [_49191, _49193, _49195], _49195), _49191))], (2087 ^ _17312) ^ [] : [-(in(2085 ^ [_49191, _49193, _49195], relation_dom(_49191)))]]]]], (2044 ^ _17312) ^ [_48682] : [-(in(_48682, 2042 ^ [_48682]))], (2107 ^ _17312) ^ [_49629, _49631] : [relation(_49629), -(subset(relation_image(_49629, _49631), relation_rng(_49629)))], (2178 ^ _17312) ^ [_50696, _50698] : [in(_50698, _50696), -(element(_50698, _50696))], (354 ^ _17312) ^ [_22460, _22462] : [proper_subset(_22462, _22460), proper_subset(_22460, _22462)], (1272 ^ _17312) ^ [_37672, _37674] : [element(_37672, powerset(_37674)), -(subset_complement(_37674, _37672) = set_difference(_37674, _37672))], (2671 ^ _17312) ^ [_57557] : [-(relation_dom(identity_relation(_57557)) = _57557)], (1746 ^ _17312) ^ [_44452, _44454] : [-(set_union2(_44454, _44454) = _44454)], (2755 ^ _17312) ^ [_58731, _58733, _58735] : [-(subset(set_union2(_58735, _58731), _58733)), subset(_58735, _58733), subset(_58731, _58733)], (2440 ^ _17312) ^ [_54412] : [relation(_54412), 2443 ^ _17312 : [(2444 ^ _17312) ^ [_54477] : [relation(_54477), -(subset(relation_rng(relation_composition(_54412, _54477)), relation_rng(_54477)))]]], (2289 ^ _17312) ^ [_52242, _52244, _52246, _52248] : [ordered_pair(_52248, _52246) = ordered_pair(_52244, _52242), 2292 ^ _17312 : [(2295 ^ _17312) ^ [] : [-(_52246 = _52242)], (2293 ^ _17312) ^ [] : [-(_52248 = _52244)]]], (2520 ^ _17312) ^ [_55609, _55611] : [-(set_difference(_55611, set_difference(_55611, _55609)) = set_intersection2(_55611, _55609))], (2765 ^ _17312) ^ [_58870, _58872, _58874] : [singleton(_58874) = unordered_pair(_58872, _58870), -(_58874 = _58872)], (2037 ^ _17312) ^ [_48515, _48517] : [subset(_48517, _48515), -(set_union2(_48517, _48515) = _48515)], (1630 ^ _17312) ^ [_42981, _42983] : [1637 ^ _17312 : [(1640 ^ _17312) ^ [] : [-(relation(relation_composition(_42981, _42983)))], (1638 ^ _17312) ^ [] : [-(empty(relation_composition(_42981, _42983)))]], empty(_42983), relation(_42981)], (1056 ^ _17312) ^ [_34024, _34026] : [1058 ^ _17312 : [(1061 ^ _17312) ^ [] : [in(1057 ^ [_34024, _34026], _34024)], (1059 ^ _17312) ^ [] : [-(in(1057 ^ [_34024, _34026], _34026))]], -(subset(_34026, _34024))], (2319 ^ _17312) ^ [_52706, _52708] : [subset(singleton(_52708), _52706), -(in(_52708, _52706))], (2522 ^ _17312) ^ [_55643] : [-(set_difference(empty_set, _55643) = empty_set)], (1642 ^ _17312) ^ [_43140, _43142] : [-(relation(set_intersection2(_43142, _43140))), relation(_43142), relation(_43140)], (2547 ^ _17312) ^ [_55950] : [-(_55950 = empty_set), 2550 ^ _17312 : [(2551 ^ _17312) ^ [_56033] : [element(_56033, powerset(_55950)), 2554 ^ _17312 : [(2555 ^ _17312) ^ [_56111] : [element(_56111, _55950), -(in(_56111, _56033)), -(in(_56111, subset_complement(_55950, _56033)))]]]]], (160 ^ _17312) ^ [_19528, _19530] : [_19530 = _19528, -(relation_field(_19530) = relation_field(_19528))], (2597 ^ _17312) ^ [] : [-(relation_dom(empty_set) = empty_set)], (150 ^ _17312) ^ [_19379, _19381, _19383, _19385] : [-(cartesian_product2(_19385, _19381) = cartesian_product2(_19383, _19379)), _19385 = _19383, _19381 = _19379], (1921 ^ _17312) ^ [_46832, _46834] : [element(_46832, powerset(powerset(_46834))), -(meet_of_subsets(_46834, _46832) = set_meet(_46832))], (34 ^ _17312) ^ [_17765, _17767, _17769, _17771] : [-(proper_subset(_17769, _17765)), proper_subset(_17771, _17767), _17771 = _17769, _17767 = _17765], (1762 ^ _17312) ^ [_44682, _44684] : [element(_44682, powerset(powerset(_44684))), -(complements_of_subsets(_44684, complements_of_subsets(_44684, _44682)) = _44682)], (262 ^ _17312) ^ [_21047, _21049, _21051, _21053] : [-(set_intersection2(_21053, _21049) = set_intersection2(_21051, _21047)), _21053 = _21051, _21049 = _21047], (2673 ^ _17312) ^ [_57581] : [-(relation_rng(identity_relation(_57581)) = _57581)], (370 ^ _17312) ^ [_22671, _22673] : [-(set_intersection2(_22673, _22671) = set_intersection2(_22671, _22673))], (1338 ^ _17312) ^ [_38782] : [relation(_38782), 1341 ^ _17312 : [(1342 ^ _17312) ^ [_38895] : [relation(_38895), 1345 ^ _17312 : [(1346 ^ _17312) ^ [_39000] : [relation(_39000), 1349 ^ _17312 : [(1350 ^ _17312) ^ [] : [_39000 = relation_composition(_38782, _38895), 1353 ^ _17312 : [(1363 ^ _17312) ^ [_39324, _39326] : [-(in(ordered_pair(_39326, _39324), _39000)), 1364 ^ _17312 : [(1365 ^ _17312) ^ [_39379] : [in(ordered_pair(_39326, _39379), _38782), in(ordered_pair(_39379, _39324), _38895)]]], (1354 ^ _17312) ^ [_39170, _39172] : [in(ordered_pair(_39172, _39170), _39000), 1358 ^ _17312 : [(1361 ^ _17312) ^ [] : [-(in(ordered_pair(1357 ^ [_38782, _38895, _39000, _39170, _39172], _39170), _38895))], (1359 ^ _17312) ^ [] : [-(in(ordered_pair(_39172, 1357 ^ [_38782, _38895, _39000, _39170, _39172]), _38782))]]]]], (1373 ^ _17312) ^ [] : [-(_39000 = relation_composition(_38782, _38895)), 1387 ^ _17312 : [(1392 ^ _17312) ^ [] : [in(ordered_pair(1374 ^ [_38782, _38895, _39000], 1375 ^ [_38782, _38895, _39000]), _39000)], (1390 ^ _17312) ^ [] : [-(in(ordered_pair(1386 ^ [_38782, _38895, _39000], 1375 ^ [_38782, _38895, _39000]), _38895))], (1388 ^ _17312) ^ [] : [-(in(ordered_pair(1374 ^ [_38782, _38895, _39000], 1386 ^ [_38782, _38895, _39000]), _38782))]], 1378 ^ _17312 : [(1381 ^ _17312) ^ [_39656] : [in(ordered_pair(1374 ^ [_38782, _38895, _39000], _39656), _38782), in(ordered_pair(_39656, 1375 ^ [_38782, _38895, _39000]), _38895)], (1379 ^ _17312) ^ [] : [-(in(ordered_pair(1374 ^ [_38782, _38895, _39000], 1375 ^ [_38782, _38895, _39000]), _39000))]]]]]]]]], (2283 ^ _17312) ^ [_52151, _52153, _52155] : [subset(_52155, _52153), -(subset(set_difference(_52155, _52151), set_difference(_52153, _52151)))], (1087 ^ _17312) ^ [_34515, _34517, _34519] : [-(_34515 = set_intersection2(_34519, _34517)), 1099 ^ _17312 : [(1104 ^ _17312) ^ [] : [in(1088 ^ [_34515, _34517, _34519], _34515)], (1102 ^ _17312) ^ [] : [-(in(1088 ^ [_34515, _34517, _34519], _34517))], (1100 ^ _17312) ^ [] : [-(in(1088 ^ [_34515, _34517, _34519], _34519))]], 1091 ^ _17312 : [(1094 ^ _17312) ^ [] : [in(1088 ^ [_34515, _34517, _34519], _34519), in(1088 ^ [_34515, _34517, _34519], _34517)], (1092 ^ _17312) ^ [] : [-(in(1088 ^ [_34515, _34517, _34519], _34515))]]], (2599 ^ _17312) ^ [] : [-(relation_rng(empty_set) = empty_set)], (1280 ^ _17312) ^ [_37801] : [relation(_37801), -(relation_field(_37801) = set_union2(relation_dom(_37801), relation_rng(_37801)))], (2665 ^ _17312) ^ [_57474, _57476] : [subset(singleton(_57476), singleton(_57474)), -(_57476 = _57474)], (282 ^ _17312) ^ [_21345, _21347] : [_21347 = _21345, -(identity_relation(_21347) = identity_relation(_21345))], (542 ^ _17312) ^ [_25607] : [relation(_25607), 545 ^ _17312 : [(546 ^ _17312) ^ [_25714, _25716] : [_25714 = relation_image(_25607, _25716), 549 ^ _17312 : [(559 ^ _17312) ^ [_25947] : [-(in(_25947, _25714)), 560 ^ _17312 : [(561 ^ _17312) ^ [_25994] : [in(ordered_pair(_25994, _25947), _25607), in(_25994, _25716)]]], (550 ^ _17312) ^ [_25811] : [in(_25811, _25714), 554 ^ _17312 : [(557 ^ _17312) ^ [] : [-(in(553 ^ [_25607, _25714, _25716, _25811], _25716))], (555 ^ _17312) ^ [] : [-(in(ordered_pair(553 ^ [_25607, _25714, _25716, _25811], _25811), _25607))]]]]], (569 ^ _17312) ^ [_26112, _26114] : [-(_26112 = relation_image(_25607, _26114)), 582 ^ _17312 : [(587 ^ _17312) ^ [] : [in(570 ^ [_25607, _26112, _26114], _26112)], (585 ^ _17312) ^ [] : [-(in(581 ^ [_25607, _26112, _26114], _26114))], (583 ^ _17312) ^ [] : [-(in(ordered_pair(581 ^ [_25607, _26112, _26114], 570 ^ [_25607, _26112, _26114]), _25607))]], 573 ^ _17312 : [(576 ^ _17312) ^ [_26260] : [in(ordered_pair(_26260, 570 ^ [_25607, _26112, _26114]), _25607), in(_26260, _26114)], (574 ^ _17312) ^ [] : [-(in(570 ^ [_25607, _26112, _26114], _26112))]]]]], (2717 ^ _17312) ^ [_58217, _58219, _58221] : [relation(_58217), 2720 ^ _17312 : [(2729 ^ _17312) ^ [] : [-(in(_58221, relation_dom(relation_dom_restriction(_58217, _58219)))), in(_58221, _58219), in(_58221, relation_dom(_58217))], (2721 ^ _17312) ^ [] : [in(_58221, relation_dom(relation_dom_restriction(_58217, _58219))), 2724 ^ _17312 : [(2727 ^ _17312) ^ [] : [-(in(_58221, relation_dom(_58217)))], (2725 ^ _17312) ^ [] : [-(in(_58221, _58219))]]]]], (2697 ^ _17312) ^ [_57936, _57938] : [in(_57938, _57936), empty(_57936)], (1778 ^ _17312) ^ [_44937, _44939] : [disjoint(singleton(_44939), _44937), in(_44939, _44937)], (2013 ^ _17312) ^ [_48142, _48144, _48146] : [subset(_48146, _48144), 2016 ^ _17312 : [(2019 ^ _17312) ^ [] : [-(subset(cartesian_product2(_48142, _48146), cartesian_product2(_48142, _48144)))], (2017 ^ _17312) ^ [] : [-(subset(cartesian_product2(_48146, _48142), cartesian_product2(_48144, _48142)))]]], (182 ^ _17312) ^ [_19847, _19849, _19851, _19853] : [-(complements_of_subsets(_19853, _19849) = complements_of_subsets(_19851, _19847)), _19853 = _19851, _19849 = _19847], (1784 ^ _17312) ^ [_45013, _45015] : [-(in(_45015, _45013)), -(disjoint(singleton(_45015), _45013))], (348 ^ _17312) ^ [_22382, _22384] : [in(_22384, _22382), in(_22382, _22384)], (1852 ^ _17312) ^ [_45891, _45893] : [in(_45893, _45891), -(subset(_45893, union(_45891)))], (2601 ^ _17312) ^ [_56644, _56646] : [subset(_56646, _56644), proper_subset(_56644, _56646)], (2208 ^ _17312) ^ [_51095] : [relation(_51095), -(subset(_51095, cartesian_product2(relation_dom(_51095), relation_rng(_51095))))], (1515 ^ _17312) ^ [] : [true___, -(true___)], (1908 ^ _17312) ^ [_46651] : [-(element(1906 ^ [_46651], powerset(_46651)))], (2430 ^ _17312) ^ [_54254] : [relation(_54254), 2433 ^ _17312 : [(2434 ^ _17312) ^ [_54319] : [relation(_54319), -(subset(relation_dom(relation_composition(_54254, _54319)), relation_dom(_54254)))]]], (1768 ^ _17312) ^ [_44791, _44793] : [proper_subset(_44793, _44793)], (2072 ^ _17312) ^ [_49090, _49092, _49094] : [relation(_49090), -(relation_dom_restriction(relation_rng_restriction(_49094, _49090), _49092) = relation_rng_restriction(_49094, relation_dom_restriction(_49090, _49092)))], (2299 ^ _17312) ^ [_52389] : [relation(_52389), 2302 ^ _17312 : [(2305 ^ _17312) ^ [] : [-(relation_dom(_52389) = relation_rng(relation_inverse(_52389)))], (2303 ^ _17312) ^ [] : [-(relation_rng(_52389) = relation_dom(relation_inverse(_52389)))]]], (1939 ^ _17312) ^ [_47107, _47109] : [disjoint(_47109, _47107), -(disjoint(_47107, _47109))], (1441 ^ _17312) ^ [_40763, _40765] : [proper_subset(_40765, _40763), 1444 ^ _17312 : [(1447 ^ _17312) ^ [] : [_40765 = _40763], (1445 ^ _17312) ^ [] : [-(subset(_40765, _40763))]]], (2833 ^ _17312) ^ [_59998, _60000, _60002] : [singleton(_60002) = unordered_pair(_60000, _59998), -(_60000 = _59998)], (1557 ^ _17312) ^ [] : [true___, -(true___)], (2351 ^ _17312) ^ [_53181, _53183] : [subset(_53183, singleton(_53181)), -(_53183 = empty_set), -(_53183 = singleton(_53181))], (591 ^ _17312) ^ [_26514] : [relation(_26514), 594 ^ _17312 : [(595 ^ _17312) ^ [_26621, _26623] : [_26621 = relation_inverse_image(_26514, _26623), 598 ^ _17312 : [(608 ^ _17312) ^ [_26854] : [-(in(_26854, _26621)), 609 ^ _17312 : [(610 ^ _17312) ^ [_26901] : [in(ordered_pair(_26854, _26901), _26514), in(_26901, _26623)]]], (599 ^ _17312) ^ [_26718] : [in(_26718, _26621), 603 ^ _17312 : [(606 ^ _17312) ^ [] : [-(in(602 ^ [_26514, _26621, _26623, _26718], _26623))], (604 ^ _17312) ^ [] : [-(in(ordered_pair(_26718, 602 ^ [_26514, _26621, _26623, _26718]), _26514))]]]]], (618 ^ _17312) ^ [_27019, _27021] : [-(_27019 = relation_inverse_image(_26514, _27021)), 631 ^ _17312 : [(636 ^ _17312) ^ [] : [in(619 ^ [_26514, _27019, _27021], _27019)], (634 ^ _17312) ^ [] : [-(in(630 ^ [_26514, _27019, _27021], _27021))], (632 ^ _17312) ^ [] : [-(in(ordered_pair(619 ^ [_26514, _27019, _27021], 630 ^ [_26514, _27019, _27021]), _26514))]], 622 ^ _17312 : [(625 ^ _17312) ^ [_27167] : [in(ordered_pair(619 ^ [_26514, _27019, _27021], _27167), _26514), in(_27167, _27021)], (623 ^ _17312) ^ [] : [-(in(619 ^ [_26514, _27019, _27021], _27019))]]]]], (1581 ^ _17312) ^ [_42330, _42332] : [element(_42330, powerset(powerset(_42332))), -(element(meet_of_subsets(_42332, _42330), powerset(_42332)))], (1698 ^ _17312) ^ [_43833] : [empty(relation_dom(_43833)), -(empty(_43833)), relation(_43833)], (1718 ^ _17312) ^ [_44087] : [empty(_44087), 1721 ^ _17312 : [(1724 ^ _17312) ^ [] : [-(relation(relation_dom(_44087)))], (1722 ^ _17312) ^ [] : [-(empty(relation_dom(_44087)))]]], (2480 ^ _17312) ^ [_55034, _55036] : [in(_55036, _55034), -(set_union2(singleton(_55036), _55034) = _55034)], (2711 ^ _17312) ^ [_58132, _58134] : [set_difference(_58134, _58132) = _58134, -(disjoint(_58134, _58132))], (2392 ^ _17312) ^ [_53690, _53692] : [disjoint(_53692, _53690), 2393 ^ _17312 : [(2394 ^ _17312) ^ [_53730] : [in(_53730, _53692), in(_53730, _53690)]]], (192 ^ _17312) ^ [_19996, _19998, _20000, _20002, _20004, _20006] : [-(subset_difference(_20006, _20002, _19998) = subset_difference(_20004, _20000, _19996)), _20006 = _20004, _20002 = _20000, _19998 = _19996], (763 ^ _17312) ^ [_29397] : [-(in(764 ^ [_29397], _29397)), -(_29397 = empty_set)], (2383 ^ _17312) ^ [_53607, _53609] : [-(disjoint(_53609, _53607)), 2387 ^ _17312 : [(2390 ^ _17312) ^ [] : [-(in(2386 ^ [_53607, _53609], _53607))], (2388 ^ _17312) ^ [] : [-(in(2386 ^ [_53607, _53609], _53609))]]], (206 ^ _17312) ^ [_20217, _20219] : [_20219 = _20217, -(cast_to_subset(_20219) = cast_to_subset(_20217))], (1628 ^ _17312) ^ [_42953] : [-(element(1626 ^ [_42953], _42953))], (332 ^ _17312) ^ [_22068, _22070, _22072, _22074] : [-(relation_inverse_image(_22074, _22070) = relation_inverse_image(_22072, _22068)), _22074 = _22072, _22070 = _22068], (2001 ^ _17312) ^ [_47972, _47974] : [relation(_47972), -(subset(relation_rng_restriction(_47974, _47972), _47972))], (438 ^ _17312) ^ [_23721] : [relation(_23721), 441 ^ _17312 : [(442 ^ _17312) ^ [_23821, _23823] : [relation(_23821), 445 ^ _17312 : [(446 ^ _17312) ^ [] : [_23821 = relation_dom_restriction(_23721, _23823), 449 ^ _17312 : [(458 ^ _17312) ^ [_24100, _24102] : [-(in(ordered_pair(_24102, _24100), _23821)), in(_24102, _23823), in(ordered_pair(_24102, _24100), _23721)], (450 ^ _17312) ^ [_23983, _23985] : [in(ordered_pair(_23985, _23983), _23821), 453 ^ _17312 : [(456 ^ _17312) ^ [] : [-(in(ordered_pair(_23985, _23983), _23721))], (454 ^ _17312) ^ [] : [-(in(_23985, _23823))]]]]], (468 ^ _17312) ^ [] : [-(_23821 = relation_dom_restriction(_23721, _23823)), 481 ^ _17312 : [(486 ^ _17312) ^ [] : [in(ordered_pair(469 ^ [_23721, _23821, _23823], 470 ^ [_23721, _23821, _23823]), _23821)], (484 ^ _17312) ^ [] : [-(in(ordered_pair(469 ^ [_23721, _23821, _23823], 470 ^ [_23721, _23821, _23823]), _23721))], (482 ^ _17312) ^ [] : [-(in(469 ^ [_23721, _23821, _23823], _23823))]], 473 ^ _17312 : [(476 ^ _17312) ^ [] : [in(469 ^ [_23721, _23821, _23823], _23823), in(ordered_pair(469 ^ [_23721, _23821, _23823], 470 ^ [_23721, _23821, _23823]), _23721)], (474 ^ _17312) ^ [] : [-(in(ordered_pair(469 ^ [_23721, _23821, _23823], 470 ^ [_23721, _23821, _23823]), _23821))]]]]]]], (1750 ^ _17312) ^ [_44508, _44510] : [element(_44508, powerset(_44510)), -(subset_complement(_44510, subset_complement(_44510, _44508)) = _44508)], (428 ^ _17312) ^ [_23590, _23592] : [-(_23592 = _23590), subset(_23592, _23590), subset(_23590, _23592)], (2810 ^ _17312) ^ [_59631, _59633] : [in(_59631, 2796 ^ [_59633]), 2814 ^ _17312 : [(2817 ^ _17312) ^ [_59777] : [subset(_59777, _59631), -(in(_59777, 2813 ^ [_59631, _59633]))], (2815 ^ _17312) ^ [] : [-(in(2813 ^ [_59631, _59633], 2796 ^ [_59633]))]]], (316 ^ _17312) ^ [_21834, _21836] : [_21836 = _21834, -(singleton(_21836) = singleton(_21834))], (1609 ^ _17312) ^ [_42756, _42758] : [relation(_42756), -(relation(relation_rng_restriction(_42758, _42756)))], (2236 ^ _17312) ^ [_51524, _51526] : [subset(_51526, _51524), -(set_intersection2(_51526, _51524) = _51526)], (2789 ^ _17312) ^ [_59226, _59228] : [relation(_59226), -(subset(relation_rng(relation_dom_restriction(_59226, _59228)), relation_rng(_59226)))], (1621 ^ _17312) ^ [] : [true___, -(true___)], (2242 ^ _17312) ^ [_51607] : [-(set_intersection2(_51607, empty_set) = empty_set)], (2230 ^ _17312) ^ [_51433, _51435, _51437] : [subset(_51437, _51435), -(subset(set_intersection2(_51437, _51433), set_intersection2(_51435, _51433)))], (2325 ^ _17312) ^ [_52783, _52785] : [in(_52785, _52783), -(subset(singleton(_52785), _52783))], (322 ^ _17312) ^ [_21919, _21921, _21923, _21925] : [-(unordered_pair(_21925, _21921) = unordered_pair(_21923, _21919)), _21925 = _21923, _21921 = _21919], (1551 ^ _17312) ^ [] : [true___, -(true___)], (652 ^ _17312) ^ [_27618] : [654 ^ _17312 : [(657 ^ _17312) ^ [_27731, _27733] : [653 ^ [_27618] = ordered_pair(_27733, _27731)], (655 ^ _17312) ^ [] : [-(in(653 ^ [_27618], _27618))]], -(relation(_27618))], (1814 ^ _17312) ^ [_45405, _45407] : [element(_45405, powerset(_45407)), 1817 ^ _17312 : [(1818 ^ _17312) ^ [_45472] : [in(_45472, _45405), -(in(_45472, _45407))]]], (2056 ^ _17312) ^ [_48863, _48865] : [in(_48863, 2042 ^ [_48865]), -(in(powerset(_48863), 2042 ^ [_48865]))], (420 ^ _17312) ^ [_23491, _23493] : [_23493 = _23491, 423 ^ _17312 : [(426 ^ _17312) ^ [] : [-(subset(_23491, _23493))], (424 ^ _17312) ^ [] : [-(subset(_23493, _23491))]]], (2408 ^ _17312) ^ [_53912, _53914] : [-(set_difference(set_union2(_53914, _53912), _53912) = set_difference(_53914, _53912))], (1844 ^ _17312) ^ [_45766, _45768] : [1845 ^ _17312 : [(1848 ^ _17312) ^ [] : [_45768 = singleton(_45766)], (1846 ^ _17312) ^ [] : [_45768 = empty_set]], -(subset(_45768, singleton(_45766)))], (2470 ^ _17312) ^ [_54887, _54889] : [element(_54887, powerset(powerset(_54889))), -(_54887 = empty_set), complements_of_subsets(_54889, _54887) = empty_set], (1046 ^ _17312) ^ [_33882, _33884] : [subset(_33884, _33882), 1049 ^ _17312 : [(1050 ^ _17312) ^ [_33945] : [in(_33945, _33884), -(in(_33945, _33882))]]], (2657 ^ _17312) ^ [_57373] : [-(unordered_pair(_57373, _57373) = singleton(_57373))], (1489 ^ _17312) ^ [] : [true___, -(true___)], (2617 ^ _17312) ^ [_56853] : [relation(_56853), 2622 ^ _17312 : [(2625 ^ _17312) ^ [] : [relation_rng(_56853) = empty_set], (2623 ^ _17312) ^ [] : [relation_dom(_56853) = empty_set]], -(_56853 = empty_set)], (1483 ^ _17312) ^ [] : [true___, -(true___)], (2739 ^ _17312) ^ [_58523, _58525] : [relation(_58523), -(subset(relation_dom_restriction(_58523, _58525), _58523))], (640 ^ _17312) ^ [_27433] : [relation(_27433), 643 ^ _17312 : [(644 ^ _17312) ^ [_27509] : [in(_27509, _27433), -(_27509 = ordered_pair(647 ^ [_27433, _27509], 648 ^ [_27433, _27509]))]]], (10 ^ _17312) ^ [_17435, _17437, _17439] : [-(_17439 = _17435), _17439 = _17437, _17437 = _17435], (1726 ^ _17312) ^ [_44190] : [empty(_44190), 1729 ^ _17312 : [(1732 ^ _17312) ^ [] : [-(relation(relation_rng(_44190)))], (1730 ^ _17312) ^ [] : [-(empty(relation_rng(_44190)))]]], (2361 ^ _17312) ^ [_53275, _53277] : [2362 ^ _17312 : [(2365 ^ _17312) ^ [] : [_53277 = singleton(_53275)], (2363 ^ _17312) ^ [] : [_53277 = empty_set]], -(subset(_53277, singleton(_53275)))], (2007 ^ _17312) ^ [_48053, _48055] : [relation(_48053), -(subset(relation_rng(relation_rng_restriction(_48055, _48053)), relation_rng(_48053)))], (1748 ^ _17312) ^ [_44480, _44482] : [-(set_intersection2(_44482, _44482) = _44482)], (272 ^ _17312) ^ [_21196, _21198, _21200, _21202] : [-(relation_composition(_21202, _21198) = relation_composition(_21200, _21196)), _21202 = _21200, _21198 = _21196], (1995 ^ _17312) ^ [_47887, _47889] : [relation(_47887), -(subset(relation_rng(relation_rng_restriction(_47889, _47887)), _47889))], (2771 ^ _17312) ^ [_58959, _58961] : [relation(_58959), -(relation_dom(relation_dom_restriction(_58959, _58961)) = set_intersection2(relation_dom(_58959), _58961))], (2371 ^ _17312) ^ [_53441, _53443] : [element(_53443, powerset(_53441)), -(subset(_53443, _53441))], (360 ^ _17312) ^ [_22538] : [empty(_22538), -(relation(_22538))], (2349 ^ _17312) ^ [_53132, _53134] : [-(set_union2(_53134, set_difference(_53132, _53134)) = set_union2(_53134, _53132))], (298 ^ _17312) ^ [_21579, _21581] : [_21581 = _21579, -(relation_rng(_21581) = relation_rng(_21579))], (2 ^ _17312) ^ [_17339] : [-(_17339 = _17339)], (252 ^ _17312) ^ [_20898, _20900, _20902, _20904] : [-(set_union2(_20904, _20900) = set_union2(_20902, _20898)), _20904 = _20902, _20900 = _20898], (1396 ^ _17312) ^ [_39966, _39968] : [element(_39966, powerset(powerset(_39968))), 1399 ^ _17312 : [(1400 ^ _17312) ^ [_40072] : [element(_40072, powerset(powerset(_39968))), 1403 ^ _17312 : [(1404 ^ _17312) ^ [] : [_40072 = complements_of_subsets(_39968, _39966), 1407 ^ _17312 : [(1408 ^ _17312) ^ [_40223] : [element(_40223, powerset(_39968)), 1411 ^ _17312 : [(1418 ^ _17312) ^ [] : [in(subset_complement(_39968, _40223), _39966), -(in(_40223, _40072))], (1412 ^ _17312) ^ [] : [in(_40223, _40072), -(in(subset_complement(_39968, _40223), _39966))]]]]], (1424 ^ _17312) ^ [] : [-(_40072 = complements_of_subsets(_39968, _39966)), 1426 ^ _17312 : [(1429 ^ _17312) ^ [] : [1430 ^ _17312 : [(1433 ^ _17312) ^ [] : [in(subset_complement(_39968, 1425 ^ [_39966, _39968, _40072]), _39966)], (1431 ^ _17312) ^ [] : [-(in(1425 ^ [_39966, _39968, _40072], _40072))]], 1434 ^ _17312 : [(1437 ^ _17312) ^ [] : [in(1425 ^ [_39966, _39968, _40072], _40072)], (1435 ^ _17312) ^ [] : [-(in(subset_complement(_39968, 1425 ^ [_39966, _39968, _40072]), _39966))]]], (1427 ^ _17312) ^ [] : [-(element(1425 ^ [_39966, _39968, _40072], powerset(_39968)))]]]]]]], (938 ^ _17312) ^ [_32003, _32005, _32007] : [-(_32003 = set_union2(_32007, _32005)), 942 ^ _17312 : [(947 ^ _17312) ^ [] : [in(939 ^ [_32003, _32005, _32007], _32005)], (945 ^ _17312) ^ [] : [in(939 ^ [_32003, _32005, _32007], _32007)], (943 ^ _17312) ^ [] : [-(in(939 ^ [_32003, _32005, _32007], _32003))]], 948 ^ _17312 : [(949 ^ _17312) ^ [] : [-(in(939 ^ [_32003, _32005, _32007], _32007)), -(in(939 ^ [_32003, _32005, _32007], _32005))], (955 ^ _17312) ^ [] : [in(939 ^ [_32003, _32005, _32007], _32003)]]], (2607 ^ _17312) ^ [_56720, _56722, _56724] : [-(disjoint(_56724, _56720)), subset(_56724, _56722), disjoint(_56722, _56720)]], input).
% 52.47/51.00  ncf('1',plain,[-(relation(2839 ^ []))],start(2841 ^ 0)).
% 52.47/51.00  ncf('1.1',plain,[relation(2839 ^ []), 1022 : relation(2839 ^ []), 1026 : subset(2839 ^ [], 2839 ^ []), 1030 : in(ordered_pair(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], 2142 ^ [2839 ^ [], 2838 ^ [], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]), 2839 ^ []), 1030 : -(in(ordered_pair(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], 2142 ^ [2839 ^ [], 2838 ^ [], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]), 2839 ^ []))],extension(1018 ^ 1,bind([[_33394, _33480, _33611, _33613], [2839 ^ [], 2839 ^ [], 2142 ^ [2839 ^ [], 2838 ^ [], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]]))).
% 52.47/51.00  ncf('1.1.1',plain,[-(relation(2839 ^ []))],reduction('1')).
% 52.47/51.00  ncf('1.1.2',plain,[-(subset(2839 ^ [], 2839 ^ [])), 1042 : in(ordered_pair(1037 ^ [2839 ^ [], 2839 ^ []], 1038 ^ [2839 ^ [], 2839 ^ []]), 2839 ^ [])],extension(1036 ^ 6)).
% 52.47/51.00  ncf('1.1.2.1',plain,[-(in(ordered_pair(1037 ^ [2839 ^ [], 2839 ^ []], 1038 ^ [2839 ^ [], 2839 ^ []]), 2839 ^ []))],extension(1040 ^ 9)).
% 52.47/51.00  ncf('1.1.3',plain,[-(in(ordered_pair(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], 2142 ^ [2839 ^ [], 2838 ^ [], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]), 2839 ^ [])), 2139 : in(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], relation_inverse_image(2839 ^ [], 2838 ^ [])), 2139 : relation(2839 ^ [])],extension(2135 ^ 8,bind([[_50065, _50067, _50069], [2839 ^ [], 2838 ^ [], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]]))).
% 52.50/51.00  ncf('1.1.3.1',plain,[-(in(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], relation_inverse_image(2839 ^ [], 2838 ^ []))), -(subset(relation_inverse_image(2839 ^ [], 2838 ^ []), relation_dom(2839 ^ [])))],extension(1056 ^ 11,bind([[_34024, _34026], [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]))).
% 52.50/51.00  ncf('1.1.3.1.1',plain,[subset(relation_inverse_image(2839 ^ [], 2838 ^ []), relation_dom(2839 ^ []))],extension(2843 ^ 12)).
% 52.50/51.00  ncf('1.1.3.2',plain,[-(relation(2839 ^ []))],lemmata('[1].x')).
% 52.50/51.00  ncf('1.1.4',plain,[in(ordered_pair(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], 2142 ^ [2839 ^ [], 2838 ^ [], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]), 2839 ^ []), relation(2839 ^ []), 2204 : -(in(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], relation_dom(2839 ^ [])))],extension(2196 ^ 8,bind([[_50924, _50926, _50928], [2839 ^ [], 2142 ^ [2839 ^ [], 2838 ^ [], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]], 1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]]))).
% 52.50/51.00  ncf('1.1.4.1',plain,[-(relation(2839 ^ []))],lemmata('[1].x')).
% 52.50/51.00  ncf('1.1.4.2',plain,[in(1057 ^ [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])], relation_dom(2839 ^ [])), -(subset(relation_inverse_image(2839 ^ [], 2838 ^ []), relation_dom(2839 ^ [])))],extension(1056 ^ 11,bind([[_34024, _34026], [relation_dom(2839 ^ []), relation_inverse_image(2839 ^ [], 2838 ^ [])]]))).
% 52.50/51.00  ncf('1.1.4.2.1',plain,[subset(relation_inverse_image(2839 ^ [], 2838 ^ []), relation_dom(2839 ^ []))],extension(2843 ^ 12)).
% 52.50/51.00  %-----------------------------------------------------
% 52.50/51.00  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------