%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU239+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n003.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 12:02:50 EDT 2023

% Result   : Theorem 46.84s 46.02s
% Output   : Proof 46.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU239+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 12:58:30 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 46.84/46.02  
% 46.84/46.02  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 46.84/46.02  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.84/46.02  %-----------------------------------------------------
% 46.84/46.02  ncf(matrix, plain, [(4361 ^ _247496) ^ [] : [4362 ^ _247496 : [(4368 ^ _247496) ^ [] : [in(ordered_pair(4364 ^ [], 4364 ^ []), 4357 ^ [])], (4366 ^ _247496) ^ [] : [-(in(4364 ^ [], relation_field(4357 ^ [])))], (4363 ^ _247496) ^ [] : [-(reflexive(4357 ^ []))]], 4369 ^ _247496 : [(4370 ^ _247496) ^ [_247855] : [in(_247855, relation_field(4357 ^ [])), -(in(ordered_pair(_247855, _247855), 4357 ^ []))], (4376 ^ _247496) ^ [] : [reflexive(4357 ^ [])]]], (4359 ^ _247496) ^ [] : [-(relation(4357 ^ []))], !, (298 ^ _96150) ^ [_105844, _105846] : [_105846 = _105844, -(succ(_105846) = succ(_105844))], (2570 ^ _96150) ^ [_184888] : [relation(_184888), -(relation_inverse(relation_inverse(_184888)) = _184888)], (2338 ^ _96150) ^ [] : [-(relation(empty_set))], (2759 ^ _96150) ^ [] : [-(function(2753 ^ []))], (542 ^ _96150) ^ [_114521] : [-(ordinal(_114521)), epsilon_transitive(_114521), epsilon_connected(_114521)], (1217 ^ _96150) ^ [_139301] : [1219 ^ _96150 : [(1222 ^ _96150) ^ [] : [subset(1218 ^ [_139301], _139301)], (1220 ^ _96150) ^ [] : [-(in(1218 ^ [_139301], _139301))]], -(epsilon_transitive(_139301))], (2604 ^ _96150) ^ [_186179, _186181] : [subset(singleton(_186181), _186179), -(in(_186181, _186179))], (2374 ^ _96150) ^ [_178624] : [empty(succ(_178624))], (2225 ^ _96150) ^ [] : [true___, -(true___)], (3162 ^ _96150) ^ [_204942, _204944] : [-(subset(set_intersection2(_204944, _204942), _204944))], (2576 ^ _96150) ^ [_185098, _185100] : [element(_185098, powerset(powerset(_185100))), -(complements_of_subsets(_185100, complements_of_subsets(_185100, _185098)) = _185098)], (4317 ^ _96150) ^ [_243343] : [-(in(_243343, 4315 ^ [_243343]))], (2400 ^ _96150) ^ [] : [-(function(empty_set))], (4204 ^ _96150) ^ [_239503, _239505] : [set_difference(_239505, _239503) = _239505, -(disjoint(_239505, _239503))], (3206 ^ _96150) ^ [_206462, _206464] : [relation(_206462), function(_206462), 3213 ^ _96150 : [(3214 ^ _96150) ^ [_206712] : [relation(_206712), function(_206712), 3221 ^ _96150 : [(3230 ^ _96150) ^ [] : [-(in(_206464, relation_dom(relation_composition(_206712, _206462)))), in(_206464, relation_dom(_206712)), in(apply(_206712, _206464), relation_dom(_206462))], (3222 ^ _96150) ^ [] : [in(_206464, relation_dom(relation_composition(_206712, _206462))), 3225 ^ _96150 : [(3228 ^ _96150) ^ [] : [-(in(apply(_206712, _206464), relation_dom(_206462)))], (3226 ^ _96150) ^ [] : [-(in(_206464, relation_dom(_206712)))]]]]]]], (2390 ^ _96150) ^ [_179146, _179148] : [empty(ordered_pair(_179148, _179146))], (410 ^ _96150) ^ [_109886, _109888] : [_109888 = _109886, -(relation_dom(_109888) = relation_dom(_109886))], (2680 ^ _96150) ^ [_188795, _188797, _188799, _188801] : [-(in(ordered_pair(_188801, _188799), cartesian_product2(_188797, _188795))), in(_188801, _188797), in(_188799, _188795)], (638 ^ _96150) ^ [_117736, _117738] : [-(_117738 = _117736), subset(_117738, _117736), subset(_117736, _117738)], (10 ^ _96150) ^ [_96585, _96587, _96589] : [-(_96589 = _96585), _96589 = _96587, _96587 = _96585], (3588 ^ _96150) ^ [_219051, _219053, _219055] : [in(_219055, _219053), in(_219053, _219051), in(_219051, _219055)], (98 ^ _96150) ^ [_99289, _99291, _99293, _99295] : [-(element(_99293, _99289)), element(_99295, _99291), _99295 = _99293, _99291 = _99289], (3354 ^ _96150) ^ [_211104, _211106] : [subset(_211106, _211104), -(set_intersection2(_211106, _211104) = _211106)], (582 ^ _96150) ^ [_115818, _115820] : [relation(_115818), 585 ^ _96150 : [(586 ^ _96150) ^ [] : [_115818 = identity_relation(_115820), 589 ^ _96150 : [(598 ^ _96150) ^ [_116391, _116393] : [-(in(ordered_pair(_116393, _116391), _115818)), in(_116393, _115820), _116393 = _116391], (590 ^ _96150) ^ [_116128, _116130] : [in(ordered_pair(_116130, _116128), _115818), 593 ^ _96150 : [(596 ^ _96150) ^ [] : [-(_116130 = _116128)], (594 ^ _96150) ^ [] : [-(in(_116130, _115820))]]]]], (608 ^ _96150) ^ [] : [-(_115818 = identity_relation(_115820)), 621 ^ _96150 : [(626 ^ _96150) ^ [] : [in(ordered_pair(609 ^ [_115818, _115820], 610 ^ [_115818, _115820]), _115818)], (624 ^ _96150) ^ [] : [-(609 ^ [_115818, _115820] = 610 ^ [_115818, _115820])], (622 ^ _96150) ^ [] : [-(in(609 ^ [_115818, _115820], _115820))]], 613 ^ _96150 : [(616 ^ _96150) ^ [] : [in(609 ^ [_115818, _115820], _115820), 609 ^ [_115818, _115820] = 610 ^ [_115818, _115820]], (614 ^ _96150) ^ [] : [-(in(ordered_pair(609 ^ [_115818, _115820], 610 ^ [_115818, _115820]), _115818))]]]]], (3749 ^ _96150) ^ [_224391, _224393] : [element(_224391, powerset(powerset(_224393))), -(_224391 = empty_set), complements_of_subsets(_224393, _224391) = empty_set], (2402 ^ _96150) ^ [] : [-(one_to_one(empty_set))], (1964 ^ _96150) ^ [_166295] : [relation(_166295), 1967 ^ _96150 : [(1968 ^ _96150) ^ [_166480] : [relation(_166480), 1971 ^ _96150 : [(1972 ^ _96150) ^ [_166661] : [relation(_166661), 1975 ^ _96150 : [(1976 ^ _96150) ^ [] : [_166661 = relation_composition(_166295, _166480), 1979 ^ _96150 : [(1989 ^ _96150) ^ [_167381, _167383] : [-(in(ordered_pair(_167383, _167381), _166661)), 1990 ^ _96150 : [(1991 ^ _96150) ^ [_167494] : [in(ordered_pair(_167383, _167494), _166295), in(ordered_pair(_167494, _167381), _166480)]]], (1980 ^ _96150) ^ [_166996, _166998] : [in(ordered_pair(_166998, _166996), _166661), 1984 ^ _96150 : [(1987 ^ _96150) ^ [] : [-(in(ordered_pair(1983 ^ [_166295, _166480, _166661, _166996, _166998], _166996), _166480))], (1985 ^ _96150) ^ [] : [-(in(ordered_pair(_166998, 1983 ^ [_166295, _166480, _166661, _166996, _166998]), _166295))]]]]], (1999 ^ _96150) ^ [] : [-(_166661 = relation_composition(_166295, _166480)), 2013 ^ _96150 : [(2018 ^ _96150) ^ [] : [in(ordered_pair(2000 ^ [_166295, _166480, _166661], 2001 ^ [_166295, _166480, _166661]), _166661)], (2016 ^ _96150) ^ [] : [-(in(ordered_pair(2012 ^ [_166295, _166480, _166661], 2001 ^ [_166295, _166480, _166661]), _166480))], (2014 ^ _96150) ^ [] : [-(in(ordered_pair(2000 ^ [_166295, _166480, _166661], 2012 ^ [_166295, _166480, _166661]), _166295))]], 2004 ^ _96150 : [(2007 ^ _96150) ^ [_168125] : [in(ordered_pair(2000 ^ [_166295, _166480, _166661], _168125), _166295), in(ordered_pair(_168125, 2001 ^ [_166295, _166480, _166661]), _166480)], (2005 ^ _96150) ^ [] : [-(in(ordered_pair(2000 ^ [_166295, _166480, _166661], 2001 ^ [_166295, _166480, _166661]), _166661))]]]]]]]]], (2189 ^ _96150) ^ [] : [true___, -(true___)], (4109 ^ _96150) ^ [_236206] : [-(unordered_pair(_236206, _236206) = singleton(_236206))], (4028 ^ _96150) ^ [_233612] : [relation(_233612), 4033 ^ _96150 : [(4036 ^ _96150) ^ [] : [relation_rng(_233612) = empty_set], (4034 ^ _96150) ^ [] : [relation_dom(_233612) = empty_set]], -(_233612 = empty_set)], (3260 ^ _96150) ^ [_208118, _208120] : [relation(_208118), function(_208118), 3267 ^ _96150 : [(3268 ^ _96150) ^ [_208367] : [relation(_208367), function(_208367), in(_208120, relation_dom(relation_composition(_208367, _208118))), -(apply(relation_composition(_208367, _208118), _208120) = apply(_208118, apply(_208367, _208120)))]]], (3542 ^ _96150) ^ [_217443, _217445] : [in(_217445, _217443), -(subset(singleton(_217445), _217443))], (3079 ^ _96150) ^ [_202231, _202233] : [relation(_202231), function(_202231), subset(_202233, relation_rng(_202231)), -(relation_image(_202231, relation_inverse_image(_202231, _202233)) = _202233)], (3414 ^ _96150) ^ [_213135, _213137] : [ordinal(_213135), subset(_213137, _213135), -(_213137 = empty_set), 3426 ^ _96150 : [(3431 ^ _96150) ^ [_213687] : [ordinal(_213687), in(_213687, _213137), -(ordinal_subset(3425 ^ [_213135, _213137], _213687))], (3429 ^ _96150) ^ [] : [-(in(3425 ^ [_213135, _213137], _213137))], (3427 ^ _96150) ^ [] : [-(ordinal(3425 ^ [_213135, _213137]))]]], (2295 ^ _96150) ^ [_176346, _176348] : [relation(_176346), -(relation(relation_rng_restriction(_176348, _176346)))], (3629 ^ _96150) ^ [_220453] : [subset(_220453, empty_set), -(_220453 = empty_set)], (252 ^ _96150) ^ [_104218, _104220, _104222, _104224] : [-(relation_rng_restriction(_104224, _104220) = relation_rng_restriction(_104222, _104218)), _104224 = _104222, _104220 = _104218], (2187 ^ _96150) ^ [_173248] : [-(element(cast_to_subset(_173248), powerset(_173248)))], (232 ^ _96150) ^ [_103512, _103514, _103516, _103518, _103520, _103522] : [-(unordered_triple(_103522, _103518, _103514) = unordered_triple(_103520, _103516, _103512)), _103522 = _103520, _103518 = _103516, _103514 = _103512], (2787 ^ _96150) ^ [] : [empty(2785 ^ [])], (4290 ^ _96150) ^ [_242243, _242245] : [relation(_242243), -(relation_dom(relation_dom_restriction(_242243, _242245)) = set_intersection2(relation_dom(_242243), _242245))], (2201 ^ _96150) ^ [] : [true___, -(true___)], (2839 ^ _96150) ^ [_193918, _193920] : [ordinal(_193920), ordinal(_193918), 2846 ^ _96150 : [(2853 ^ _96150) ^ [] : [subset(_193920, _193918), -(ordinal_subset(_193920, _193918))], (2847 ^ _96150) ^ [] : [ordinal_subset(_193920, _193918), -(subset(_193920, _193918))]]], (3475 ^ _96150) ^ [_215207, _215209] : [relation(_215207), function(_215207), 3482 ^ _96150 : [(3495 ^ _96150) ^ [] : [-(_215207 = identity_relation(_215209)), relation_dom(_215207) = _215209, 3501 ^ _96150 : [(3504 ^ _96150) ^ [] : [apply(_215207, 3500 ^ [_215207, _215209]) = 3500 ^ [_215207, _215209]], (3502 ^ _96150) ^ [] : [-(in(3500 ^ [_215207, _215209], _215209))]]], (3483 ^ _96150) ^ [] : [_215207 = identity_relation(_215209), 3486 ^ _96150 : [(3489 ^ _96150) ^ [_215626] : [in(_215626, _215209), -(apply(_215207, _215626) = _215626)], (3487 ^ _96150) ^ [] : [-(relation_dom(_215207) = _215209)]]]]], (126 ^ _96150) ^ [_100149, _100151] : [-(one_to_one(_100149)), _100151 = _100149, one_to_one(_100151)], (3516 ^ _96150) ^ [_216534] : [relation(_216534), 3519 ^ _96150 : [(3522 ^ _96150) ^ [] : [-(relation_dom(_216534) = relation_rng(relation_inverse(_216534)))], (3520 ^ _96150) ^ [] : [-(relation_rng(_216534) = relation_dom(relation_inverse(_216534)))]]], (198 ^ _96150) ^ [_102366, _102368] : [-(relation(_102366)), _102368 = _102366, relation(_102368)], (1169 ^ _96150) ^ [_137638] : [-(in(1170 ^ [_137638], _137638)), -(_137638 = empty_set)], (3952 ^ _96150) ^ [_231302] : [relation(_231302), -(in(ordered_pair(3957 ^ [_231302], 3958 ^ [_231302]), _231302)), -(_231302 = empty_set)], (2610 ^ _96150) ^ [_186345, _186347] : [in(_186347, _186345), -(subset(singleton(_186347), _186345))], (4342 ^ _96150) ^ [_244289, _244291] : [subset(_244289, 4315 ^ [_244291]), -(are_equipotent(_244289, 4315 ^ [_244291])), -(in(_244289, 4315 ^ [_244291]))], (4302 ^ _96150) ^ [_242685, _242687] : [relation(_242685), -(relation_dom_restriction(_242685, _242687) = relation_composition(identity_relation(_242687), _242685))], (2169 ^ _96150) ^ [_172796] : [2176 ^ _96150 : [(2179 ^ _96150) ^ [] : [-(function(function_inverse(_172796)))], (2177 ^ _96150) ^ [] : [-(relation(function_inverse(_172796)))]], relation(_172796), function(_172796)], (552 ^ _96150) ^ [_114790] : [empty(_114790), 555 ^ _96150 : [(560 ^ _96150) ^ [] : [-(ordinal(_114790))], (558 ^ _96150) ^ [] : [-(epsilon_connected(_114790))], (556 ^ _96150) ^ [] : [-(epsilon_transitive(_114790))]]], (2648 ^ _96150) ^ [_187705, _187707] : [subset(_187707, singleton(_187705)), -(_187707 = empty_set), -(_187707 = singleton(_187705))], (3152 ^ _96150) ^ [_204638, _204640, _204642] : [relation(_204638), subset(_204642, _204640), -(subset(relation_inverse_image(_204638, _204642), relation_inverse_image(_204638, _204640)))], (1691 ^ _96150) ^ [_156357, _156359] : [-(_156357 = union(_156359)), 1704 ^ _96150 : [(1709 ^ _96150) ^ [] : [in(1692 ^ [_156357, _156359], _156357)], (1707 ^ _96150) ^ [] : [-(in(1703 ^ [_156357, _156359], _156359))], (1705 ^ _96150) ^ [] : [-(in(1692 ^ [_156357, _156359], 1703 ^ [_156357, _156359]))]], 1695 ^ _96150 : [(1698 ^ _96150) ^ [_156640] : [in(1692 ^ [_156357, _156359], _156640), in(_156640, _156359)], (1696 ^ _96150) ^ [] : [-(in(1692 ^ [_156357, _156359], _156357))]]], (562 ^ _96150) ^ [_115116, _115118] : [-(unordered_pair(_115118, _115116) = unordered_pair(_115116, _115118))], (2249 ^ _96150) ^ [_174725, _174727] : [-(relation(relation_composition(_174727, _174725))), relation(_174727), relation(_174725)], (2784 ^ _96150) ^ [_192077] : [-(empty(2780 ^ [_192077]))], (3138 ^ _96150) ^ [_204224, _204226] : [relation(_204224), -(_204226 = empty_set), subset(_204226, relation_rng(_204224)), relation_inverse_image(_204224, _204226) = empty_set], (1298 ^ _96150) ^ [_142029, _142031, _142033] : [_142029 = unordered_pair(_142033, _142031), 1301 ^ _96150 : [(1302 ^ _96150) ^ [_142211] : [in(_142211, _142029), -(_142211 = _142033), -(_142211 = _142031)], (1312 ^ _96150) ^ [_142489] : [1313 ^ _96150 : [(1316 ^ _96150) ^ [] : [_142489 = _142031], (1314 ^ _96150) ^ [] : [_142489 = _142033]], -(in(_142489, _142029))]]], (2085 ^ _96150) ^ [_170930] : [relation(_170930), function(_170930), one_to_one(_170930), -(function_inverse(_170930) = relation_inverse(_170930))], (3063 ^ _96150) ^ [_201716, _201718] : [relation(_201716), subset(_201718, relation_dom(_201716)), -(subset(_201718, relation_inverse_image(_201716, relation_image(_201716, _201718))))], (2067 ^ _96150) ^ [_170402, _170404] : [proper_subset(_170404, _170402), 2070 ^ _96150 : [(2073 ^ _96150) ^ [] : [_170404 = _170402], (2071 ^ _96150) ^ [] : [-(subset(_170404, _170402))]]], (4352 ^ _96150) ^ [_244623, _244625, _244627] : [singleton(_244627) = unordered_pair(_244625, _244623), -(_244625 = _244623)], (2929 ^ _96150) ^ [_196836, _196838] : [relation(_196836), -(subset(relation_rng(relation_rng_restriction(_196838, _196836)), _196838))], (917 ^ _96150) ^ [_128273] : [relation(_128273), 920 ^ _96150 : [(921 ^ _96150) ^ [_128480, _128482] : [_128480 = relation_inverse_image(_128273, _128482), 924 ^ _96150 : [(934 ^ _96150) ^ [_129026] : [-(in(_129026, _128480)), 935 ^ _96150 : [(936 ^ _96150) ^ [_129131] : [in(ordered_pair(_129026, _129131), _128273), in(_129131, _128482)]]], (925 ^ _96150) ^ [_128672] : [in(_128672, _128480), 929 ^ _96150 : [(932 ^ _96150) ^ [] : [-(in(928 ^ [_128273, _128480, _128482, _128672], _128482))], (930 ^ _96150) ^ [] : [-(in(ordered_pair(_128672, 928 ^ [_128273, _128480, _128482, _128672]), _128273))]]]]], (944 ^ _96150) ^ [_129386, _129388] : [-(_129386 = relation_inverse_image(_128273, _129388)), 957 ^ _96150 : [(962 ^ _96150) ^ [] : [in(945 ^ [_128273, _129386, _129388], _129386)], (960 ^ _96150) ^ [] : [-(in(956 ^ [_128273, _129386, _129388], _129388))], (958 ^ _96150) ^ [] : [-(in(ordered_pair(945 ^ [_128273, _129386, _129388], 956 ^ [_128273, _129386, _129388]), _128273))]], 948 ^ _96150 : [(951 ^ _96150) ^ [_129690] : [in(ordered_pair(945 ^ [_128273, _129386, _129388], _129690), _128273), in(_129690, _129388)], (949 ^ _96150) ^ [] : [-(in(945 ^ [_128273, _129386, _129388], _129386))]]]]], (3461 ^ _96150) ^ [_214638, _214640, _214642] : [subset(_214642, _214640), -(subset(set_difference(_214642, _214638), set_difference(_214640, _214638)))], (1846 ^ _96150) ^ [_162202, _162204] : [element(_162202, powerset(_162204)), -(subset_complement(_162204, _162202) = set_difference(_162204, _162202))], (2410 ^ _96150) ^ [] : [-(ordinal(empty_set))], (2289 ^ _96150) ^ [_176114, _176116] : [element(_176114, powerset(powerset(_176116))), -(element(complements_of_subsets(_176116, _176114), powerset(powerset(_176116))))], (3729 ^ _96150) ^ [_223710, _223712] : [subset(_223712, _223710), -(_223710 = set_union2(_223712, set_difference(_223710, _223712)))], (2430 ^ _96150) ^ [_180420] : [2441 ^ _96150 : [(2444 ^ _96150) ^ [] : [-(function(relation_inverse(_180420)))], (2442 ^ _96150) ^ [] : [-(relation(relation_inverse(_180420)))]], relation(_180420), function(_180420), one_to_one(_180420)], (432 ^ _96150) ^ [_110709, _110711, _110713, _110715] : [-(relation_dom_restriction(_110715, _110711) = relation_dom_restriction(_110713, _110709)), _110715 = _110713, _110711 = _110709], (3765 ^ _96150) ^ [_224914] : [relation(_224914), 3768 ^ _96150 : [(3769 ^ _96150) ^ [_225061] : [relation(_225061), subset(relation_dom(_224914), relation_rng(_225061)), -(relation_rng(relation_composition(_225061, _224914)) = relation_rng(_224914))]]], (3194 ^ _96150) ^ [_206064, _206066, _206068] : [relation(_206064), in(ordered_pair(_206068, _206066), _206064), 3201 ^ _96150 : [(3204 ^ _96150) ^ [] : [-(in(_206066, relation_rng(_206064)))], (3202 ^ _96150) ^ [] : [-(in(_206068, relation_dom(_206064)))]]], (2885 ^ _96150) ^ [_195386, _195388, _195390, _195392] : [-(in(ordered_pair(_195392, _195390), cartesian_product2(_195388, _195386))), in(_195392, _195388), in(_195390, _195386)], (218 ^ _96150) ^ [_102964, _102966, _102968, _102970] : [-(in(_102968, _102964)), in(_102970, _102966), _102970 = _102968, _102966 = _102964], (518 ^ _96150) ^ [_113842] : [empty(_113842), -(relation(_113842))], (4329 ^ _96150) ^ [_243770, _243772] : [in(_243770, 4315 ^ [_243772]), 4333 ^ _96150 : [(4336 ^ _96150) ^ [_244082] : [subset(_244082, _243770), -(in(_244082, 4332 ^ [_243770, _243772]))], (4334 ^ _96150) ^ [] : [-(in(4332 ^ [_243770, _243772], 4315 ^ [_243772]))]]], (2772 ^ _96150) ^ [] : [-(epsilon_connected(2760 ^ []))], (2394 ^ _96150) ^ [_179293] : [-(function(identity_relation(_179293)))], (4248 ^ _96150) ^ [_240919, _240921, _240923] : [relation(_240919), function(_240919), 4255 ^ _96150 : [(4264 ^ _96150) ^ [] : [-(in(ordered_pair(_240923, _240921), _240919)), in(_240923, relation_dom(_240919)), _240921 = apply(_240919, _240923)], (4256 ^ _96150) ^ [] : [in(ordered_pair(_240923, _240921), _240919), 4259 ^ _96150 : [(4262 ^ _96150) ^ [] : [-(_240921 = apply(_240919, _240923))], (4260 ^ _96150) ^ [] : [-(in(_240923, relation_dom(_240919)))]]]]], (1854 ^ _96150) ^ [_162548] : [being_limit_ordinal(_162548), -(_162548 = union(_162548))], (2733 ^ _96150) ^ [] : [-(epsilon_connected(2729 ^ []))], (2897 ^ _96150) ^ [_195827, _195829, _195831, _195833] : [unordered_pair(_195833, _195831) = unordered_pair(_195829, _195827), -(_195833 = _195829), -(_195833 = _195827)], (3182 ^ _96150) ^ [_205688, _205690, _205692] : [-(subset(_205692, _205688)), subset(_205692, _205690), subset(_205690, _205688)], (3598 ^ _96150) ^ [_219388, _219390] : [element(_219390, powerset(_219388)), -(subset(_219390, _219388))], (2388 ^ _96150) ^ [] : [-(empty(empty_set))], (2752 ^ _96150) ^ [] : [-(empty(2750 ^ []))], (2404 ^ _96150) ^ [] : [-(empty(empty_set))], (150 ^ _96150) ^ [_100888, _100890] : [-(empty(_100888)), _100890 = _100888, empty(_100890)], (2231 ^ _96150) ^ [_174283] : [relation(_174283), -(relation(relation_inverse(_174283)))], (1384 ^ _96150) ^ [_145067, _145069, _145071] : [_145067 = cartesian_product2(_145071, _145069), 1387 ^ _96150 : [(1400 ^ _96150) ^ [_145828] : [-(in(_145828, _145067)), 1401 ^ _96150 : [(1402 ^ _96150) ^ [_145958, _145960] : [in(_145960, _145071), in(_145958, _145069), _145828 = ordered_pair(_145960, _145958)]]], (1388 ^ _96150) ^ [_145268] : [in(_145268, _145067), 1393 ^ _96150 : [(1398 ^ _96150) ^ [] : [-(_145268 = ordered_pair(1391 ^ [_145067, _145069, _145071, _145268], 1392 ^ [_145067, _145069, _145071, _145268]))], (1396 ^ _96150) ^ [] : [-(in(1392 ^ [_145067, _145069, _145071, _145268], _145069))], (1394 ^ _96150) ^ [] : [-(in(1391 ^ [_145067, _145069, _145071, _145268], _145071))]]]]], (2666 ^ _96150) ^ [_188259, _188261] : [in(_188261, _188259), -(subset(_188261, union(_188259)))], (2797 ^ _96150) ^ [] : [empty(2795 ^ [])], (2690 ^ _96150) ^ [_189128, _189130] : [2692 ^ _96150 : [(2695 ^ _96150) ^ [] : [in(2691 ^ [_189128, _189130], _189128)], (2693 ^ _96150) ^ [] : [-(in(2691 ^ [_189128, _189130], _189130))]], -(element(_189130, powerset(_189128)))], (2794 ^ _96150) ^ [] : [-(one_to_one(2788 ^ []))], (112 ^ _96150) ^ [_99733, _99735, _99737, _99739] : [-(proper_subset(_99737, _99733)), proper_subset(_99739, _99735), _99739 = _99737, _99735 = _99733], (4137 ^ _96150) ^ [_237157] : [-(relation_dom(identity_relation(_237157)) = _237157)], (442 ^ _96150) ^ [_111040, _111042] : [_111042 = _111040, -(relation_rng(_111042) = relation_rng(_111040))], (2446 ^ _96150) ^ [_180851] : [ordinal(_180851), 2449 ^ _96150 : [(2452 ^ _96150) ^ [] : [-(epsilon_transitive(succ(_180851)))], (2454 ^ _96150) ^ [] : [-(epsilon_connected(succ(_180851)))], (2456 ^ _96150) ^ [] : [-(ordinal(succ(_180851)))], (2450 ^ _96150) ^ [] : [empty(succ(_180851))]]], (3789 ^ _96150) ^ [_225727, _225729] : [element(_225727, powerset(powerset(_225729))), -(_225727 = empty_set), -(union_of_subsets(_225729, complements_of_subsets(_225729, _225727)) = subset_difference(_225729, cast_to_subset(_225729), meet_of_subsets(_225729, _225727)))], (3387 ^ _96150) ^ [_212200] : [-(subset(empty_set, _212200))], (2498 ^ _96150) ^ [] : [-(empty(empty_set))], (2871 ^ _96150) ^ [_194854, _194856] : [disjoint(_194856, _194854), -(disjoint(_194854, _194856))], (3779 ^ _96150) ^ [_225387, _225389] : [element(_225387, powerset(powerset(_225389))), -(_225387 = empty_set), -(subset_difference(_225389, cast_to_subset(_225389), union_of_subsets(_225389, _225387)) = meet_of_subsets(_225389, complements_of_subsets(_225389, _225387)))], (2941 ^ _96150) ^ [_197268, _197270] : [relation(_197268), -(subset(relation_rng(relation_rng_restriction(_197270, _197268)), relation_rng(_197268)))], (1519 ^ _96150) ^ [_150328, _150330] : [1521 ^ _96150 : [(1524 ^ _96150) ^ [] : [in(1520 ^ [_150328, _150330], _150328)], (1522 ^ _96150) ^ [] : [-(in(1520 ^ [_150328, _150330], _150330))]], -(subset(_150330, _150328))], (2502 ^ _96150) ^ [_182714, _182716] : [empty(cartesian_product2(_182716, _182714)), -(empty(_182716)), -(empty(_182714))], (2586 ^ _96150) ^ [_185500, _185502] : [in(_185502, _185500), -(set_union2(singleton(_185502), _185500) = _185500)], (2728 ^ _96150) ^ [] : [-(function(2724 ^ []))], (4284 ^ _96150) ^ [_242017, _242019, _242021] : [singleton(_242021) = unordered_pair(_242019, _242017), -(_242021 = _242019)], (3666 ^ _96150) ^ [_221618] : [ordinal(_221618), 3669 ^ _96150 : [(3679 ^ _96150) ^ [] : [being_limit_ordinal(_221618), 3680 ^ _96150 : [(3681 ^ _96150) ^ [_222089] : [ordinal(_222089), _221618 = succ(_222089)]]], (3670 ^ _96150) ^ [] : [-(being_limit_ordinal(_221618)), 3674 ^ _96150 : [(3677 ^ _96150) ^ [] : [-(_221618 = succ(3673 ^ [_221618]))], (3675 ^ _96150) ^ [] : [-(ordinal(3673 ^ [_221618]))]]]]], (1809 ^ _96150) ^ [_160747] : [relation(_160747), 1812 ^ _96150 : [(1813 ^ _96150) ^ [_160928] : [_160928 = relation_rng(_160747), 1816 ^ _96150 : [(1824 ^ _96150) ^ [_161352] : [1825 ^ _96150 : [(1826 ^ _96150) ^ [_161431] : [in(ordered_pair(_161431, _161352), _160747)]], -(in(_161352, _160928))], (1817 ^ _96150) ^ [_161108] : [in(_161108, _160928), -(in(ordered_pair(1820 ^ [_160747, _160928, _161108], _161108), _160747))]]], (1830 ^ _96150) ^ [_161559] : [-(_161559 = relation_rng(_160747)), 1834 ^ _96150 : [(1837 ^ _96150) ^ [_161822] : [in(ordered_pair(_161822, 1831 ^ [_160747, _161559]), _160747)], (1835 ^ _96150) ^ [] : [-(in(1831 ^ [_160747, _161559], _161559))]], 1839 ^ _96150 : [(1842 ^ _96150) ^ [] : [in(1831 ^ [_160747, _161559], _161559)], (1840 ^ _96150) ^ [] : [-(in(ordered_pair(1838 ^ [_160747, _161559], 1831 ^ [_160747, _161559]), _160747))]]]]], (3801 ^ _96150) ^ [_226141] : [-(set_difference(empty_set, _226141) = empty_set)], (2947 ^ _96150) ^ [_197504, _197506, _197508] : [subset(_197508, _197506), 2950 ^ _96150 : [(2953 ^ _96150) ^ [] : [-(subset(cartesian_product2(_197504, _197508), cartesian_product2(_197504, _197506)))], (2951 ^ _96150) ^ [] : [-(subset(cartesian_product2(_197508, _197504), cartesian_product2(_197506, _197504)))]]], (2764 ^ _96150) ^ [] : [-(function(2760 ^ []))], (2139 ^ _96150) ^ [] : [true___, -(true___)], (3813 ^ _96150) ^ [_226598, _226600] : [-(disjoint(_226600, _226598)), -(in(3816 ^ [_226598, _226600], set_intersection2(_226600, _226598)))], (1629 ^ _96150) ^ [_153948] : [relation(_153948), 1632 ^ _96150 : [(1633 ^ _96150) ^ [_154129] : [_154129 = relation_dom(_153948), 1636 ^ _96150 : [(1644 ^ _96150) ^ [_154553] : [1645 ^ _96150 : [(1646 ^ _96150) ^ [_154632] : [in(ordered_pair(_154553, _154632), _153948)]], -(in(_154553, _154129))], (1637 ^ _96150) ^ [_154309] : [in(_154309, _154129), -(in(ordered_pair(_154309, 1640 ^ [_153948, _154129, _154309]), _153948))]]], (1650 ^ _96150) ^ [_154760] : [-(_154760 = relation_dom(_153948)), 1654 ^ _96150 : [(1657 ^ _96150) ^ [_155023] : [in(ordered_pair(1651 ^ [_153948, _154760], _155023), _153948)], (1655 ^ _96150) ^ [] : [-(in(1651 ^ [_153948, _154760], _154760))]], 1659 ^ _96150 : [(1662 ^ _96150) ^ [] : [in(1651 ^ [_153948, _154760], _154760)], (1660 ^ _96150) ^ [] : [-(in(ordered_pair(1651 ^ [_153948, _154760], 1658 ^ [_153948, _154760]), _153948))]]]]], (2731 ^ _96150) ^ [] : [-(epsilon_transitive(2729 ^ []))], (2726 ^ _96150) ^ [] : [-(relation(2724 ^ []))], (2265 ^ _96150) ^ [_175223] : [-(relation(identity_relation(_175223)))], (4177 ^ _96150) ^ [_238471, _238473] : [in(_238473, _238471), empty(_238471)], (2584 ^ _96150) ^ [_185391] : [singleton(_185391) = empty_set], (2961 ^ _96150) ^ [_198077, _198079, _198081, _198083] : [-(subset(cartesian_product2(_198083, _198079), cartesian_product2(_198081, _198077))), subset(_198083, _198081), subset(_198079, _198077)], (160 ^ _96150) ^ [_101183, _101185] : [-(function(_101183)), _101185 = _101183, function(_101185)], (2376 ^ _96150) ^ [_178732, _178734] : [-(relation(set_intersection2(_178734, _178732))), relation(_178734), relation(_178732)], (3057 ^ _96150) ^ [_201486, _201488] : [relation(_201486), -(relation_image(_201486, _201488) = relation_image(_201486, set_intersection2(relation_dom(_201486), _201488)))], (2792 ^ _96150) ^ [] : [-(function(2788 ^ []))], (2512 ^ _96150) ^ [_183006] : [empty(relation_dom(_183006)), -(empty(_183006)), relation(_183006)], (700 ^ _96150) ^ [_119968] : [relation(_119968), function(_119968), 707 ^ _96150 : [(708 ^ _96150) ^ [_120266, _120268] : [_120266 = relation_image(_119968, _120268), 711 ^ _96150 : [(723 ^ _96150) ^ [_120921] : [-(in(_120921, _120266)), 724 ^ _96150 : [(725 ^ _96150) ^ [_121034] : [in(_121034, relation_dom(_119968)), in(_121034, _120268), _120921 = apply(_119968, _121034)]]], (712 ^ _96150) ^ [_120466] : [in(_120466, _120266), 716 ^ _96150 : [(721 ^ _96150) ^ [] : [-(_120466 = apply(_119968, 715 ^ [_119968, _120266, _120268, _120466]))], (719 ^ _96150) ^ [] : [-(in(715 ^ [_119968, _120266, _120268, _120466], _120268))], (717 ^ _96150) ^ [] : [-(in(715 ^ [_119968, _120266, _120268, _120466], relation_dom(_119968)))]]]]], (737 ^ _96150) ^ [_121394, _121396] : [-(_121394 = relation_image(_119968, _121396)), 754 ^ _96150 : [(757 ^ _96150) ^ [] : [-(in(753 ^ [_119968, _121394, _121396], _121396))], (759 ^ _96150) ^ [] : [-(738 ^ [_119968, _121394, _121396] = apply(_119968, 753 ^ [_119968, _121394, _121396]))], (761 ^ _96150) ^ [] : [in(738 ^ [_119968, _121394, _121396], _121394)], (755 ^ _96150) ^ [] : [-(in(753 ^ [_119968, _121394, _121396], relation_dom(_119968)))]], 741 ^ _96150 : [(744 ^ _96150) ^ [_121714] : [in(_121714, relation_dom(_119968)), in(_121714, _121396), 738 ^ [_119968, _121394, _121396] = apply(_119968, _121714)], (742 ^ _96150) ^ [] : [-(in(738 ^ [_119968, _121394, _121396], _121394))]]]]], (44 ^ _96150) ^ [_97637, _97639] : [-(relation_empty_yielding(_97637)), _97639 = _97637, relation_empty_yielding(_97639)], (2219 ^ _96150) ^ [] : [true___, -(true___)], (3012 ^ _96150) ^ [_199963, _199965, _199967] : [relation(_199963), 3015 ^ _96150 : [(3027 ^ _96150) ^ [] : [-(in(_199967, relation_image(_199963, _199965))), 3028 ^ _96150 : [(3029 ^ _96150) ^ [_200564] : [in(_200564, relation_dom(_199963)), in(ordered_pair(_200564, _199967), _199963), in(_200564, _199965)]]], (3016 ^ _96150) ^ [] : [in(_199967, relation_image(_199963, _199965)), 3020 ^ _96150 : [(3025 ^ _96150) ^ [] : [-(in(3019 ^ [_199963, _199965, _199967], _199965))], (3023 ^ _96150) ^ [] : [-(in(ordered_pair(3019 ^ [_199963, _199965, _199967], _199967), _199963))], (3021 ^ _96150) ^ [] : [-(in(3019 ^ [_199963, _199965, _199967], relation_dom(_199963)))]]]]], (4238 ^ _96150) ^ [_240608, _240610] : [empty(_240610), -(_240610 = _240608), empty(_240608)], (364 ^ _96150) ^ [_108232, _108234] : [_108234 = _108232, -(function_inverse(_108234) = function_inverse(_108232))], (2540 ^ _96150) ^ [_183825] : [empty(_183825), 2543 ^ _96150 : [(2546 ^ _96150) ^ [] : [-(relation(relation_rng(_183825)))], (2544 ^ _96150) ^ [] : [-(empty(relation_rng(_183825)))]]], (4111 ^ _96150) ^ [_236304] : [empty(_236304), -(_236304 = empty_set)], (4062 ^ _96150) ^ [_234621, _234623] : [-(in(_234621, _234623)), -(set_difference(_234623, singleton(_234621)) = _234623)], (1872 ^ _96150) ^ [_163106] : [relation(_163106), 1875 ^ _96150 : [(1876 ^ _96150) ^ [_163266] : [relation(_163266), 1879 ^ _96150 : [(1880 ^ _96150) ^ [] : [_163266 = relation_inverse(_163106), 1883 ^ _96150 : [(1890 ^ _96150) ^ [_163765, _163767] : [in(ordered_pair(_163765, _163767), _163106), -(in(ordered_pair(_163767, _163765), _163266))], (1884 ^ _96150) ^ [_163575, _163577] : [in(ordered_pair(_163577, _163575), _163266), -(in(ordered_pair(_163575, _163577), _163106))]]], (1896 ^ _96150) ^ [] : [-(_163266 = relation_inverse(_163106)), 1901 ^ _96150 : [(1904 ^ _96150) ^ [] : [in(ordered_pair(1898 ^ [_163106, _163266], 1897 ^ [_163106, _163266]), _163106)], (1902 ^ _96150) ^ [] : [-(in(ordered_pair(1897 ^ [_163106, _163266], 1898 ^ [_163106, _163266]), _163266))]], 1905 ^ _96150 : [(1908 ^ _96150) ^ [] : [in(ordered_pair(1897 ^ [_163106, _163266], 1898 ^ [_163106, _163266]), _163266)], (1906 ^ _96150) ^ [] : [-(in(ordered_pair(1898 ^ [_163106, _163266], 1897 ^ [_163106, _163266]), _163106))]]]]]]], (3548 ^ _96150) ^ [_217702, _217704, _217706] : [subset(unordered_pair(_217706, _217704), _217702), 3551 ^ _96150 : [(3554 ^ _96150) ^ [] : [-(in(_217704, _217702))], (3552 ^ _96150) ^ [] : [-(in(_217706, _217702))]]], (4068 ^ _96150) ^ [_234846, _234848] : [relation(_234846), function(_234846), 4075 ^ _96150 : [(4076 ^ _96150) ^ [_235113] : [relation(_235113), function(_235113), 4083 ^ _96150 : [(4096 ^ _96150) ^ [] : [-(_234846 = relation_dom_restriction(_235113, _234848)), relation_dom(_234846) = set_intersection2(relation_dom(_235113), _234848), 4102 ^ _96150 : [(4105 ^ _96150) ^ [] : [apply(_234846, 4101 ^ [_234846, _234848, _235113]) = apply(_235113, 4101 ^ [_234846, _234848, _235113])], (4103 ^ _96150) ^ [] : [-(in(4101 ^ [_234846, _234848, _235113], relation_dom(_234846)))]]], (4084 ^ _96150) ^ [] : [_234846 = relation_dom_restriction(_235113, _234848), 4087 ^ _96150 : [(4090 ^ _96150) ^ [_235567] : [in(_235567, relation_dom(_234846)), -(apply(_234846, _235567) = apply(_235113, _235567))], (4088 ^ _96150) ^ [] : [-(relation_dom(_234846) = set_intersection2(relation_dom(_235113), _234848))]]]]]]], (4004 ^ _96150) ^ [_232931] : [relation(_232931), function(_232931), one_to_one(_232931), -(one_to_one(function_inverse(_232931)))], (2548 ^ _96150) ^ [_184104, _184106] : [2555 ^ _96150 : [(2558 ^ _96150) ^ [] : [-(relation(relation_composition(_184106, _184104)))], (2556 ^ _96150) ^ [] : [-(empty(relation_composition(_184106, _184104)))]], empty(_184106), relation(_184104)], (2829 ^ _96150) ^ [_193587, _193589, _193591] : [-(subset_difference(_193591, _193589, _193587) = set_difference(_193589, _193587)), element(_193589, powerset(_193591)), element(_193587, powerset(_193591))], (2181 ^ _96150) ^ [] : [true___, -(true___)], (2398 ^ _96150) ^ [] : [-(relation_empty_yielding(empty_set))], (20 ^ _96150) ^ [_96926, _96928, _96930, _96932] : [-(is_reflexive_in(_96930, _96926)), is_reflexive_in(_96932, _96928), _96932 = _96930, _96928 = _96926], (3332 ^ _96150) ^ [_210317] : [relation(_210317), 3335 ^ _96150 : [(3336 ^ _96150) ^ [_210467] : [relation(_210467), subset(_210317, _210467), 3343 ^ _96150 : [(3346 ^ _96150) ^ [] : [-(subset(relation_rng(_210317), relation_rng(_210467)))], (3344 ^ _96150) ^ [] : [-(subset(relation_dom(_210317), relation_dom(_210467)))]]]]], (314 ^ _96150) ^ [_106449, _106451, _106453, _106455] : [-(complements_of_subsets(_106455, _106451) = complements_of_subsets(_106453, _106449)), _106455 = _106453, _106451 = _106449], (2768 ^ _96150) ^ [] : [-(empty(2760 ^ []))], (817 ^ _96150) ^ [_124447] : [relation(_124447), function(_124447), 824 ^ _96150 : [(825 ^ _96150) ^ [_124734, _124736] : [_124734 = relation_inverse_image(_124447, _124736), 828 ^ _96150 : [(837 ^ _96150) ^ [_125192] : [-(in(_125192, _124734)), in(_125192, relation_dom(_124447)), in(apply(_124447, _125192), _124736)], (829 ^ _96150) ^ [_124923] : [in(_124923, _124734), 832 ^ _96150 : [(835 ^ _96150) ^ [] : [-(in(apply(_124447, _124923), _124736))], (833 ^ _96150) ^ [] : [-(in(_124923, relation_dom(_124447)))]]]]], (847 ^ _96150) ^ [_125486, _125488] : [-(_125486 = relation_inverse_image(_124447, _125488)), 859 ^ _96150 : [(864 ^ _96150) ^ [] : [in(848 ^ [_124447, _125486, _125488], _125486)], (862 ^ _96150) ^ [] : [-(in(apply(_124447, 848 ^ [_124447, _125486, _125488]), _125488))], (860 ^ _96150) ^ [] : [-(in(848 ^ [_124447, _125486, _125488], relation_dom(_124447)))]], 851 ^ _96150 : [(854 ^ _96150) ^ [] : [in(848 ^ [_124447, _125486, _125488], relation_dom(_124447)), in(apply(_124447, 848 ^ [_124447, _125486, _125488]), _125488)], (852 ^ _96150) ^ [] : [-(in(848 ^ [_124447, _125486, _125488], _125486))]]]]], (2806 ^ _96150) ^ [] : [-(relation(2804 ^ []))], (4198 ^ _96150) ^ [_239335, _239337] : [disjoint(_239337, _239335), -(set_difference(_239337, _239335) = _239337)], (2422 ^ _96150) ^ [_180110] : [empty(singleton(_180110))], (1619 ^ _96150) ^ [_153677] : [-(ordinal(_153677)), epsilon_transitive(_153677), epsilon_connected(_153677)], (3719 ^ _96150) ^ [_223344] : [relation(_223344), 3722 ^ _96150 : [(3723 ^ _96150) ^ [_223481] : [relation(_223481), -(subset(relation_rng(relation_composition(_223344, _223481)), relation_rng(_223481)))]]], (3637 ^ _96150) ^ [_220746] : [ordinal(_220746), 3640 ^ _96150 : [(3641 ^ _96150) ^ [] : [being_limit_ordinal(_220746), 3644 ^ _96150 : [(3645 ^ _96150) ^ [_220992] : [ordinal(_220992), in(_220992, _220746), -(in(succ(_220992), _220746))]]], (3655 ^ _96150) ^ [] : [3657 ^ _96150 : [(3662 ^ _96150) ^ [] : [in(succ(3656 ^ [_220746]), _220746)], (3660 ^ _96150) ^ [] : [-(in(3656 ^ [_220746], _220746))], (3658 ^ _96150) ^ [] : [-(ordinal(3656 ^ [_220746]))]], -(being_limit_ordinal(_220746))]]], (1924 ^ _96150) ^ [_164985] : [relation(_164985), function(_164985), 1931 ^ _96150 : [(1932 ^ _96150) ^ [] : [one_to_one(_164985), 1935 ^ _96150 : [(1936 ^ _96150) ^ [_165348, _165350] : [-(_165350 = _165348), in(_165350, relation_dom(_164985)), in(_165348, relation_dom(_164985)), apply(_164985, _165350) = apply(_164985, _165348)]]], (1950 ^ _96150) ^ [] : [1953 ^ _96150 : [(1956 ^ _96150) ^ [] : [-(in(1952 ^ [_164985], relation_dom(_164985)))], (1958 ^ _96150) ^ [] : [-(apply(_164985, 1951 ^ [_164985]) = apply(_164985, 1952 ^ [_164985]))], (1960 ^ _96150) ^ [] : [1951 ^ [_164985] = 1952 ^ [_164985]], (1954 ^ _96150) ^ [] : [-(in(1951 ^ [_164985], relation_dom(_164985)))]], -(one_to_one(_164985))]]], (2738 ^ _96150) ^ [] : [-(empty(2736 ^ []))], (4139 ^ _96150) ^ [_237205] : [-(relation_rng(identity_relation(_237205)) = _237205)], (2823 ^ _96150) ^ [_193345, _193347] : [element(_193345, powerset(powerset(_193347))), -(meet_of_subsets(_193347, _193345) = set_meet(_193345))], (3164 ^ _96150) ^ [_205068, _205070, _205072] : [-(subset(_205072, set_intersection2(_205070, _205068))), subset(_205072, _205070), subset(_205072, _205068)], (1021 ^ _96150) ^ [_132300] : [-(succ(_132300) = set_union2(_132300, singleton(_132300)))], (3047 ^ _96150) ^ [_201179, _201181] : [-(subset(relation_image(_201179, relation_inverse_image(_201179, _201181)), _201181)), relation(_201179), function(_201179)], (3362 ^ _96150) ^ [_211401, _211403] : [element(_211403, _211401), -(empty(_211401)), -(in(_211403, _211401))], (510 ^ _96150) ^ [_113585] : [ordinal(_113585), 513 ^ _96150 : [(516 ^ _96150) ^ [] : [-(epsilon_connected(_113585))], (514 ^ _96150) ^ [] : [-(epsilon_transitive(_113585))]]], (3578 ^ _96150) ^ [_218662, _218664] : [3579 ^ _96150 : [(3582 ^ _96150) ^ [] : [_218664 = singleton(_218662)], (3580 ^ _96150) ^ [] : [_218664 = empty_set]], -(subset(_218664, singleton(_218662)))], (630 ^ _96150) ^ [_117499, _117501] : [_117501 = _117499, 633 ^ _96150 : [(636 ^ _96150) ^ [] : [-(subset(_117499, _117501))], (634 ^ _96150) ^ [] : [-(subset(_117501, _117499))]]], (2801 ^ _96150) ^ [] : [-(epsilon_connected(2795 ^ []))], (2386 ^ _96150) ^ [_179001] : [empty(powerset(_179001))], (1866 ^ _96150) ^ [_162900] : [relation(_162900), -(relation_field(_162900) = set_union2(relation_dom(_162900), relation_rng(_162900)))], (3103 ^ _96150) ^ [_203008, _203010, _203012] : [relation(_203008), 3106 ^ _96150 : [(3118 ^ _96150) ^ [] : [-(in(_203012, relation_inverse_image(_203008, _203010))), 3119 ^ _96150 : [(3120 ^ _96150) ^ [_203609] : [in(_203609, relation_rng(_203008)), in(ordered_pair(_203012, _203609), _203008), in(_203609, _203010)]]], (3107 ^ _96150) ^ [] : [in(_203012, relation_inverse_image(_203008, _203010)), 3111 ^ _96150 : [(3116 ^ _96150) ^ [] : [-(in(3110 ^ [_203008, _203010, _203012], _203010))], (3114 ^ _96150) ^ [] : [-(in(ordered_pair(_203012, 3110 ^ [_203008, _203010, _203012]), _203008))], (3112 ^ _96150) ^ [] : [-(in(3110 ^ [_203008, _203010, _203012], relation_rng(_203008)))]]]]], (3936 ^ _96150) ^ [_230849] : [relation(_230849), function(_230849), one_to_one(_230849), 3947 ^ _96150 : [(3950 ^ _96150) ^ [] : [-(relation_dom(_230849) = relation_rng(function_inverse(_230849)))], (3948 ^ _96150) ^ [] : [-(relation_rng(_230849) = relation_dom(function_inverse(_230849)))]]], (2133 ^ _96150) ^ [] : [true___, -(true___)], (2616 ^ _96150) ^ [_186590, _186592] : [set_difference(_186592, _186590) = empty_set, -(subset(_186592, _186590))], (2237 ^ _96150) ^ [] : [true___, -(true___)], (184 ^ _96150) ^ [_101950, _101952, _101954, _101956] : [-(are_equipotent(_101954, _101950)), are_equipotent(_101956, _101952), _101956 = _101954, _101952 = _101950], (3389 ^ _96150) ^ [_212321, _212323, _212325] : [relation(_212321), in(ordered_pair(_212325, _212323), _212321), 3396 ^ _96150 : [(3399 ^ _96150) ^ [] : [-(in(_212323, relation_field(_212321)))], (3397 ^ _96150) ^ [] : [-(in(_212325, relation_field(_212321)))]]], (2790 ^ _96150) ^ [] : [-(relation(2788 ^ []))], (3610 ^ _96150) ^ [_219790, _219792] : [-(disjoint(_219792, _219790)), 3614 ^ _96150 : [(3617 ^ _96150) ^ [] : [-(in(3613 ^ [_219790, _219792], _219790))], (3615 ^ _96150) ^ [] : [-(in(3613 ^ [_219790, _219792], _219792))]]], (3282 ^ _96150) ^ [_208812, _208814] : [relation(_208812), function(_208812), 3289 ^ _96150 : [(3290 ^ _96150) ^ [_209058] : [relation(_209058), function(_209058), in(_208814, relation_dom(_208812)), -(apply(relation_composition(_208812, _209058), _208814) = apply(_209058, apply(_208812, _208814)))]]], (3314 ^ _96150) ^ [_209778] : [ordinal(_209778), 3317 ^ _96150 : [(3318 ^ _96150) ^ [_209928] : [ordinal(_209928), -(in(_209778, _209928)), -(_209778 = _209928), -(in(_209928, _209778))]]], (3803 ^ _96150) ^ [_226265, _226267, _226269] : [-(element(_226269, _226265)), in(_226269, _226267), element(_226267, powerset(_226265))], (1611 ^ _96150) ^ [_153454] : [ordinal(_153454), 1614 ^ _96150 : [(1617 ^ _96150) ^ [] : [-(epsilon_connected(_153454))], (1615 ^ _96150) ^ [] : [-(epsilon_transitive(_153454))]]], (2476 ^ _96150) ^ [_181889, _181891] : [2483 ^ _96150 : [(2486 ^ _96150) ^ [] : [-(function(relation_dom_restriction(_181891, _181889)))], (2484 ^ _96150) ^ [] : [-(relation(relation_dom_restriction(_181891, _181889)))]], relation(_181891), function(_181891)], (4 ^ _96150) ^ [_96381, _96383] : [_96383 = _96381, -(_96381 = _96383)], (3254 ^ _96150) ^ [_207902] : [relation(_207902), -(subset(_207902, cartesian_product2(relation_dom(_207902), relation_rng(_207902))))], (3240 ^ _96150) ^ [_207476] : [epsilon_transitive(_207476), 3243 ^ _96150 : [(3244 ^ _96150) ^ [_207612] : [ordinal(_207612), proper_subset(_207476, _207612), -(in(_207476, _207612))]]], (338 ^ _96150) ^ [_107296, _107298] : [_107298 = _107296, -(cast_to_subset(_107298) = cast_to_subset(_107296))], (2740 ^ _96150) ^ [] : [-(relation(2736 ^ []))], (2458 ^ _96150) ^ [_181279, _181281] : [-(relation(set_difference(_181281, _181279))), relation(_181281), relation(_181279)], (1148 ^ _96150) ^ [_136908, _136910] : [-(_136908 = singleton(_136910)), 1152 ^ _96150 : [(1155 ^ _96150) ^ [] : [1149 ^ [_136908, _136910] = _136910], (1153 ^ _96150) ^ [] : [-(in(1149 ^ [_136908, _136910], _136908))]], 1156 ^ _96150 : [(1159 ^ _96150) ^ [] : [in(1149 ^ [_136908, _136910], _136908)], (1157 ^ _96150) ^ [] : [-(1149 ^ [_136908, _136910] = _136910)]]], (1320 ^ _96150) ^ [_142754, _142756, _142758] : [-(_142754 = unordered_pair(_142758, _142756)), 1324 ^ _96150 : [(1329 ^ _96150) ^ [] : [1321 ^ [_142754, _142756, _142758] = _142756], (1327 ^ _96150) ^ [] : [1321 ^ [_142754, _142756, _142758] = _142758], (1325 ^ _96150) ^ [] : [-(in(1321 ^ [_142754, _142756, _142758], _142754))]], 1330 ^ _96150 : [(1331 ^ _96150) ^ [] : [-(1321 ^ [_142754, _142756, _142758] = _142758), -(1321 ^ [_142754, _142756, _142758] = _142756)], (1337 ^ _96150) ^ [] : [in(1321 ^ [_142754, _142756, _142758], _142754)]]], (2672 ^ _96150) ^ [_188530, _188532, _188534, _188536] : [in(ordered_pair(_188536, _188534), cartesian_product2(_188532, _188530)), 2675 ^ _96150 : [(2678 ^ _96150) ^ [] : [-(in(_188534, _188530))], (2676 ^ _96150) ^ [] : [-(in(_188536, _188532))]]], (136 ^ _96150) ^ [_100472, _100474, _100476, _100478] : [-(disjoint(_100476, _100472)), disjoint(_100478, _100474), _100478 = _100476, _100474 = _100472], (2803 ^ _96150) ^ [] : [-(ordinal(2795 ^ []))], (2145 ^ _96150) ^ [] : [true___, -(true___)], (2598 ^ _96150) ^ [_185933, _185935] : [-(in(_185935, _185933)), -(disjoint(singleton(_185935), _185933))], (2978 ^ _96150) ^ [_198730] : [-(in(_198730, 2976 ^ [_198730]))], (1713 ^ _96150) ^ [_157247, _157249, _157251] : [_157247 = set_difference(_157251, _157249), 1716 ^ _96150 : [(1725 ^ _96150) ^ [_157691] : [-(in(_157691, _157247)), in(_157691, _157251), -(in(_157691, _157249))], (1717 ^ _96150) ^ [_157431] : [in(_157431, _157247), 1720 ^ _96150 : [(1723 ^ _96150) ^ [] : [in(_157431, _157249)], (1721 ^ _96150) ^ [] : [-(in(_157431, _157251))]]]]], (208 ^ _96150) ^ [_102661, _102663] : [-(reflexive(_102661)), _102663 = _102661, reflexive(_102663)], (2500 ^ _96150) ^ [] : [-(relation(empty_set))], (54 ^ _96150) ^ [_97932, _97934] : [-(epsilon_transitive(_97932)), _97934 = _97932, epsilon_transitive(_97934)], (1918 ^ _96150) ^ [_164781, _164783] : [set_intersection2(_164783, _164781) = empty_set, -(disjoint(_164783, _164781))], (416 ^ _96150) ^ [_110132, _110134, _110136, _110138] : [-(relation_composition(_110138, _110134) = relation_composition(_110136, _110132)), _110138 = _110136, _110134 = _110132], (1550 ^ _96150) ^ [_151453, _151455, _151457] : [-(_151453 = set_intersection2(_151457, _151455)), 1562 ^ _96150 : [(1567 ^ _96150) ^ [] : [in(1551 ^ [_151453, _151455, _151457], _151453)], (1565 ^ _96150) ^ [] : [-(in(1551 ^ [_151453, _151455, _151457], _151455))], (1563 ^ _96150) ^ [] : [-(in(1551 ^ [_151453, _151455, _151457], _151457))]], 1554 ^ _96150 : [(1557 ^ _96150) ^ [] : [in(1551 ^ [_151453, _151455, _151457], _151457), in(1551 ^ [_151453, _151455, _151457], _151455)], (1555 ^ _96150) ^ [] : [-(in(1551 ^ [_151453, _151455, _151457], _151453))]]], (3926 ^ _96150) ^ [_230543, _230545, _230547] : [element(_230543, powerset(_230547)), in(_230545, subset_complement(_230547, _230543)), in(_230545, _230543)], (1509 ^ _96150) ^ [_150014, _150016] : [subset(_150016, _150014), 1512 ^ _96150 : [(1513 ^ _96150) ^ [_150151] : [in(_150151, _150016), -(in(_150151, _150014))]]], (1912 ^ _96150) ^ [_164613, _164615] : [disjoint(_164615, _164613), -(set_intersection2(_164615, _164613) = empty_set)], (966 ^ _96150) ^ [_130363, _130365, _130367, _130369] : [_130363 = unordered_triple(_130369, _130367, _130365), 969 ^ _96150 : [(970 ^ _96150) ^ [_130565] : [in(_130565, _130363), -(_130565 = _130369), -(_130565 = _130367), -(_130565 = _130365)], (984 ^ _96150) ^ [_130965] : [985 ^ _96150 : [(990 ^ _96150) ^ [] : [_130965 = _130365], (988 ^ _96150) ^ [] : [_130965 = _130367], (986 ^ _96150) ^ [] : [_130965 = _130369]], -(in(_130965, _130363))]]], (2766 ^ _96150) ^ [] : [-(one_to_one(2760 ^ []))], (1443 ^ _96150) ^ [_147587] : [epsilon_connected(_147587), 1446 ^ _96150 : [(1447 ^ _96150) ^ [_147763, _147765] : [in(_147765, _147587), in(_147763, _147587), -(in(_147765, _147763)), -(_147765 = _147763), -(in(_147763, _147765))]]], (2735 ^ _96150) ^ [] : [-(ordinal(2729 ^ []))], (324 ^ _96150) ^ [_106836, _106838, _106840, _106842, _106844, _106846] : [-(subset_difference(_106846, _106842, _106838) = subset_difference(_106844, _106840, _106836)), _106846 = _106844, _106842 = _106840, _106838 = _106836], (2470 ^ _96150) ^ [_181673, _181675] : [-(empty(_181675)), empty(set_union2(_181673, _181675))], (1132 ^ _96150) ^ [_136387, _136389] : [_136387 = singleton(_136389), 1135 ^ _96150 : [(1142 ^ _96150) ^ [_136729] : [_136729 = _136389, -(in(_136729, _136387))], (1136 ^ _96150) ^ [_136557] : [in(_136557, _136387), -(_136557 = _136389)]]], (400 ^ _96150) ^ [_109555, _109557, _109559, _109561] : [-(set_intersection2(_109561, _109557) = set_intersection2(_109559, _109555)), _109561 = _109559, _109557 = _109555], (2777 ^ _96150) ^ [] : [empty(2775 ^ [])], (454 ^ _96150) ^ [_111476, _111478] : [_111478 = _111476, -(powerset(_111478) = powerset(_111476))], (2259 ^ _96150) ^ [_175024, _175026] : [element(_175024, powerset(powerset(_175026))), -(element(union_of_subsets(_175026, _175024), powerset(_175026)))], (1207 ^ _96150) ^ [_139001] : [epsilon_transitive(_139001), 1210 ^ _96150 : [(1211 ^ _96150) ^ [_139132] : [in(_139132, _139001), -(subset(_139132, _139001))]]], (3536 ^ _96150) ^ [_217277, _217279] : [subset(singleton(_217279), _217277), -(in(_217279, _217277))], (2157 ^ _96150) ^ [] : [true___, -(true___)], (1571 ^ _96150) ^ [_152192] : [relation(_152192), function(_152192), 1578 ^ _96150 : [(1595 ^ _96150) ^ [_152936, _152938] : [-(in(_152938, relation_dom(_152192))), 1598 ^ _96150 : [(1605 ^ _96150) ^ [] : [_152936 = empty_set, -(_152936 = apply(_152192, _152938))], (1599 ^ _96150) ^ [] : [_152936 = apply(_152192, _152938), -(_152936 = empty_set)]]], (1579 ^ _96150) ^ [_152484, _152486] : [in(_152486, relation_dom(_152192)), 1582 ^ _96150 : [(1589 ^ _96150) ^ [] : [in(ordered_pair(_152486, _152484), _152192), -(_152484 = apply(_152192, _152486))], (1583 ^ _96150) ^ [] : [_152484 = apply(_152192, _152486), -(in(ordered_pair(_152486, _152484), _152192))]]]]], (765 ^ _96150) ^ [_122524, _122526] : [relation(_122524), 768 ^ _96150 : [(769 ^ _96150) ^ [_122695] : [relation(_122695), 772 ^ _96150 : [(773 ^ _96150) ^ [] : [_122695 = relation_rng_restriction(_122526, _122524), 776 ^ _96150 : [(785 ^ _96150) ^ [_123301, _123303] : [-(in(ordered_pair(_123303, _123301), _122695)), in(_123301, _122526), in(ordered_pair(_123303, _123301), _122524)], (777 ^ _96150) ^ [_123022, _123024] : [in(ordered_pair(_123024, _123022), _122695), 780 ^ _96150 : [(783 ^ _96150) ^ [] : [-(in(ordered_pair(_123024, _123022), _122524))], (781 ^ _96150) ^ [] : [-(in(_123022, _122526))]]]]], (795 ^ _96150) ^ [] : [-(_122695 = relation_rng_restriction(_122526, _122524)), 808 ^ _96150 : [(813 ^ _96150) ^ [] : [in(ordered_pair(796 ^ [_122524, _122526, _122695], 797 ^ [_122524, _122526, _122695]), _122695)], (811 ^ _96150) ^ [] : [-(in(ordered_pair(796 ^ [_122524, _122526, _122695], 797 ^ [_122524, _122526, _122695]), _122524))], (809 ^ _96150) ^ [] : [-(in(797 ^ [_122524, _122526, _122695], _122526))]], 800 ^ _96150 : [(803 ^ _96150) ^ [] : [in(797 ^ [_122524, _122526, _122695], _122526), in(ordered_pair(796 ^ [_122524, _122526, _122695], 797 ^ [_122524, _122526, _122695]), _122524)], (801 ^ _96150) ^ [] : [-(in(ordered_pair(796 ^ [_122524, _122526, _122695], 797 ^ [_122524, _122526, _122695]), _122695))]]]]]]], (3304 ^ _96150) ^ [_209497, _209499] : [ordinal(_209497), in(_209499, _209497), -(ordinal(_209499))], (3556 ^ _96150) ^ [_217953, _217955, _217957] : [-(subset(unordered_pair(_217957, _217955), _217953)), in(_217957, _217953), in(_217955, _217953)], (3348 ^ _96150) ^ [_210876, _210878, _210880] : [subset(_210880, _210878), -(subset(set_intersection2(_210880, _210876), set_intersection2(_210878, _210876)))], (2955 ^ _96150) ^ [_197821, _197823] : [relation(_197821), -(relation_rng(relation_rng_restriction(_197823, _197821)) = set_intersection2(relation_rng(_197821), _197823))], (4141 ^ _96150) ^ [_237332, _237334, _237336] : [relation(_237332), function(_237332), in(_237334, _237336), -(apply(relation_dom_restriction(_237332, _237336), _237334) = apply(_237332, _237334))], (292 ^ _96150) ^ [_105626, _105628] : [_105628 = _105626, -(relation_inverse(_105628) = relation_inverse(_105626))], (3514 ^ _96150) ^ [_216436, _216438] : [-(subset(set_difference(_216438, _216436), _216438))], (3709 ^ _96150) ^ [_222992] : [relation(_222992), 3712 ^ _96150 : [(3713 ^ _96150) ^ [_223129] : [relation(_223129), -(subset(relation_dom(relation_composition(_222992, _223129)), relation_dom(_222992)))]]], (1852 ^ _96150) ^ [_162413, _162415] : [-(ordered_pair(_162415, _162413) = unordered_pair(unordered_pair(_162415, _162413), singleton(_162415)))], (1067 ^ _96150) ^ [_134183, _134185] : [-(_134185 = empty_set), 1070 ^ _96150 : [(1071 ^ _96150) ^ [] : [_134183 = set_meet(_134185), 1074 ^ _96150 : [(1075 ^ _96150) ^ [_134481] : [in(_134481, _134183), 1078 ^ _96150 : [(1079 ^ _96150) ^ [_134626] : [in(_134626, _134185), -(in(_134481, _134626))]]], (1085 ^ _96150) ^ [_134811] : [1087 ^ _96150 : [(1090 ^ _96150) ^ [] : [in(_134811, 1086 ^ [_134183, _134185, _134811])], (1088 ^ _96150) ^ [] : [-(in(1086 ^ [_134183, _134185, _134811], _134185))]], -(in(_134811, _134183))]]], (1094 ^ _96150) ^ [] : [-(_134183 = set_meet(_134185)), 1098 ^ _96150 : [(1104 ^ _96150) ^ [] : [in(1095 ^ [_134183, _134185], 1100 ^ [_134183, _134185])], (1102 ^ _96150) ^ [] : [-(in(1100 ^ [_134183, _134185], _134185))], (1099 ^ _96150) ^ [] : [-(in(1095 ^ [_134183, _134185], _134183))]], 1105 ^ _96150 : [(1106 ^ _96150) ^ [_135585] : [in(_135585, _134185), -(in(1095 ^ [_134183, _134185], _135585))], (1112 ^ _96150) ^ [] : [in(1095 ^ [_134183, _134185], _134183)]]]]], (4319 ^ _96150) ^ [_243455, _243457, _243459] : [-(in(_243455, 4315 ^ [_243459])), in(_243457, 4315 ^ [_243459]), subset(_243455, _243457)], (3568 ^ _96150) ^ [_218402, _218404] : [subset(_218404, singleton(_218402)), -(_218404 = empty_set), -(_218404 = singleton(_218402))], (2779 ^ _96150) ^ [] : [-(relation(2775 ^ []))], (2755 ^ _96150) ^ [] : [-(relation(2753 ^ []))], (2342 ^ _96150) ^ [_177724, _177726] : [2349 ^ _96150 : [(2352 ^ _96150) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_177726, _177724)))], (2350 ^ _96150) ^ [] : [-(relation(relation_dom_restriction(_177726, _177724)))]], relation(_177726), relation_empty_yielding(_177726)], (3176 ^ _96150) ^ [_205464, _205466] : [in(_205466, _205464), -(element(_205466, _205464))], (994 ^ _96150) ^ [_131327, _131329, _131331, _131333] : [-(_131327 = unordered_triple(_131333, _131331, _131329)), 998 ^ _96150 : [(1001 ^ _96150) ^ [] : [995 ^ [_131327, _131329, _131331, _131333] = _131333], (1003 ^ _96150) ^ [] : [995 ^ [_131327, _131329, _131331, _131333] = _131331], (1005 ^ _96150) ^ [] : [995 ^ [_131327, _131329, _131331, _131333] = _131329], (999 ^ _96150) ^ [] : [-(in(995 ^ [_131327, _131329, _131331, _131333], _131327))]], 1006 ^ _96150 : [(1007 ^ _96150) ^ [] : [-(995 ^ [_131327, _131329, _131331, _131333] = _131333), -(995 ^ [_131327, _131329, _131331, _131333] = _131331), -(995 ^ [_131327, _131329, _131331, _131333] = _131329)], (1017 ^ _96150) ^ [] : [in(995 ^ [_131327, _131329, _131331, _131333], _131327)]]], (1176 ^ _96150) ^ [_137929, _137931] : [_137929 = powerset(_137931), 1179 ^ _96150 : [(1186 ^ _96150) ^ [_138271] : [subset(_138271, _137931), -(in(_138271, _137929))], (1180 ^ _96150) ^ [_138099] : [in(_138099, _137929), -(subset(_138099, _137931))]]], (2622 ^ _96150) ^ [_186758, _186760] : [subset(_186760, _186758), -(set_difference(_186760, _186758) = empty_set)], (4210 ^ _96150) ^ [_239735, _239737, _239739] : [relation(_239735), 4213 ^ _96150 : [(4222 ^ _96150) ^ [] : [-(in(_239739, relation_dom(relation_dom_restriction(_239735, _239737)))), in(_239739, _239737), in(_239739, relation_dom(_239735))], (4214 ^ _96150) ^ [] : [in(_239739, relation_dom(relation_dom_restriction(_239735, _239737))), 4217 ^ _96150 : [(4220 ^ _96150) ^ [] : [-(in(_239739, relation_dom(_239735)))], (4218 ^ _96150) ^ [] : [-(in(_239739, _239737))]]]]], (3530 ^ _96150) ^ [_217030, _217032] : [subset(_217032, _217030), -(set_difference(_217032, _217030) = empty_set)], (246 ^ _96150) ^ [_103972, _103974] : [_103974 = _103972, -(set_meet(_103974) = set_meet(_103972))], (3073 ^ _96150) ^ [_202015] : [relation(_202015), -(relation_image(_202015, relation_dom(_202015)) = relation_rng(_202015))], (354 ^ _96150) ^ [_107901, _107903, _107905, _107907] : [-(subset_complement(_107907, _107903) = subset_complement(_107905, _107901)), _107907 = _107905, _107903 = _107901], (3844 ^ _96150) ^ [_227690] : [relation(_227690), function(_227690), one_to_one(_227690), 3855 ^ _96150 : [(3856 ^ _96150) ^ [_228077] : [relation(_228077), function(_228077), 3863 ^ _96150 : [(3864 ^ _96150) ^ [] : [_228077 = function_inverse(_227690), 3867 ^ _96150 : [(3882 ^ _96150) ^ [_228968, _228970] : [3889 ^ _96150 : [(3892 ^ _96150) ^ [] : [-(_228968 = apply(_228077, _228970))], (3890 ^ _96150) ^ [] : [-(in(_228970, relation_rng(_227690)))]], in(_228968, relation_dom(_227690)), _228970 = apply(_227690, _228968)], (3870 ^ _96150) ^ [_228594, _228596] : [3877 ^ _96150 : [(3880 ^ _96150) ^ [] : [-(_228596 = apply(_227690, _228594))], (3878 ^ _96150) ^ [] : [-(in(_228594, relation_dom(_227690)))]], in(_228596, relation_rng(_227690)), _228594 = apply(_228077, _228596)], (3868 ^ _96150) ^ [] : [-(relation_dom(_228077) = relation_rng(_227690))]]], (3894 ^ _96150) ^ [] : [-(_228077 = function_inverse(_227690)), relation_dom(_228077) = relation_rng(_227690), 3903 ^ _96150 : [(3908 ^ _96150) ^ [] : [in(3900 ^ [_227690, _228077], relation_dom(_227690)), 3899 ^ [_227690, _228077] = apply(_227690, 3900 ^ [_227690, _228077])], (3906 ^ _96150) ^ [] : [-(3900 ^ [_227690, _228077] = apply(_228077, 3899 ^ [_227690, _228077]))], (3904 ^ _96150) ^ [] : [-(in(3899 ^ [_227690, _228077], relation_rng(_227690)))]], 3913 ^ _96150 : [(3918 ^ _96150) ^ [] : [in(3899 ^ [_227690, _228077], relation_rng(_227690)), 3900 ^ [_227690, _228077] = apply(_228077, 3899 ^ [_227690, _228077])], (3916 ^ _96150) ^ [] : [-(3899 ^ [_227690, _228077] = apply(_227690, 3900 ^ [_227690, _228077]))], (3914 ^ _96150) ^ [] : [-(in(3900 ^ [_227690, _228077], relation_dom(_227690)))]]]]]]], (2099 ^ _96150) ^ [_171294] : [relation(_171294), 2102 ^ _96150 : [(2109 ^ _96150) ^ [] : [is_reflexive_in(_171294, relation_field(_171294)), -(reflexive(_171294))], (2103 ^ _96150) ^ [] : [reflexive(_171294), -(is_reflexive_in(_171294, relation_field(_171294)))]]], (2895 ^ _96150) ^ [_195690] : [-(in(_195690, succ(_195690)))], (3998 ^ _96150) ^ [_232736, _232738] : [subset(_232738, _232736), proper_subset(_232736, _232738)], (1860 ^ _96150) ^ [_162706] : [_162706 = union(_162706), -(being_limit_ordinal(_162706))], (2127 ^ _96150) ^ [] : [true___, -(true___)], (2 ^ _96150) ^ [_96274] : [-(_96274 = _96274)], (448 ^ _96150) ^ [_111258, _111260] : [_111260 = _111258, -(union(_111260) = union(_111258))], (1226 ^ _96150) ^ [_139626] : [relation(_139626), 1229 ^ _96150 : [(1230 ^ _96150) ^ [_139784] : [relation(_139784), 1233 ^ _96150 : [(1234 ^ _96150) ^ [] : [_139626 = _139784, 1237 ^ _96150 : [(1244 ^ _96150) ^ [_140279, _140281] : [in(ordered_pair(_140281, _140279), _139784), -(in(ordered_pair(_140281, _140279), _139626))], (1238 ^ _96150) ^ [_140089, _140091] : [in(ordered_pair(_140091, _140089), _139626), -(in(ordered_pair(_140091, _140089), _139784))]]], (1250 ^ _96150) ^ [] : [-(_139626 = _139784), 1255 ^ _96150 : [(1258 ^ _96150) ^ [] : [in(ordered_pair(1251 ^ [_139626, _139784], 1252 ^ [_139626, _139784]), _139784)], (1256 ^ _96150) ^ [] : [-(in(ordered_pair(1251 ^ [_139626, _139784], 1252 ^ [_139626, _139784]), _139626))]], 1259 ^ _96150 : [(1262 ^ _96150) ^ [] : [in(ordered_pair(1251 ^ [_139626, _139784], 1252 ^ [_139626, _139784]), _139626)], (1260 ^ _96150) ^ [] : [-(in(ordered_pair(1251 ^ [_139626, _139784], 1252 ^ [_139626, _139784]), _139784))]]]]]]], (2782 ^ _96150) ^ [_192026] : [-(element(2780 ^ [_192026], powerset(_192026)))], (524 ^ _96150) ^ [_114028] : [535 ^ _96150 : [(540 ^ _96150) ^ [] : [-(one_to_one(_114028))], (538 ^ _96150) ^ [] : [-(function(_114028))], (536 ^ _96150) ^ [] : [-(relation(_114028))]], relation(_114028), empty(_114028), function(_114028)], (2195 ^ _96150) ^ [] : [true___, -(true___)], (2468 ^ _96150) ^ [_181562, _181564] : [empty(unordered_pair(_181564, _181562))], (1266 ^ _96150) ^ [_141116, _141118] : [-(empty(_141118)), 1269 ^ _96150 : [(1276 ^ _96150) ^ [] : [in(_141116, _141118), -(element(_141116, _141118))], (1270 ^ _96150) ^ [] : [element(_141116, _141118), -(in(_141116, _141118))]]], (2980 ^ _96150) ^ [_198842, _198844, _198846] : [-(in(_198842, 2976 ^ [_198846])), in(_198844, 2976 ^ [_198846]), subset(_198842, _198844)], (4117 ^ _96150) ^ [_236506, _236508] : [subset(singleton(_236508), singleton(_236506)), -(_236508 = _236506)], (4274 ^ _96150) ^ [_241688, _241690, _241692] : [-(subset(set_union2(_241692, _241688), _241690)), subset(_241692, _241690), subset(_241688, _241690)], (1528 ^ _96150) ^ [_150728, _150730, _150732] : [_150728 = set_intersection2(_150732, _150730), 1531 ^ _96150 : [(1540 ^ _96150) ^ [_151169] : [-(in(_151169, _150728)), in(_151169, _150732), in(_151169, _150730)], (1532 ^ _96150) ^ [_150910] : [in(_150910, _150728), 1535 ^ _96150 : [(1538 ^ _96150) ^ [] : [-(in(_150910, _150730))], (1536 ^ _96150) ^ [] : [-(in(_150910, _150732))]]]]], (566 ^ _96150) ^ [_115316, _115318] : [-(set_intersection2(_115318, _115316) = set_intersection2(_115316, _115318))], (2307 ^ _96150) ^ [] : [true___, -(true___)], (2564 ^ _96150) ^ [_184676, _184678] : [element(_184676, powerset(_184678)), -(subset_complement(_184678, subset_complement(_184678, _184676)) = _184676)], (2488 ^ _96150) ^ [_182253] : [ordinal(_182253), 2491 ^ _96150 : [(2496 ^ _96150) ^ [] : [-(ordinal(union(_182253)))], (2494 ^ _96150) ^ [] : [-(epsilon_connected(union(_182253)))], (2492 ^ _96150) ^ [] : [-(epsilon_transitive(union(_182253)))]]], (2340 ^ _96150) ^ [] : [-(relation_empty_yielding(empty_set))], (3996 ^ _96150) ^ [] : [-(relation_rng(empty_set) = empty_set)], (282 ^ _96150) ^ [_105295, _105297, _105299, _105301] : [-(cartesian_product2(_105301, _105297) = cartesian_product2(_105299, _105295)), _105301 = _105299, _105297 = _105295], (3994 ^ _96150) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2392 ^ _96150) ^ [_179248] : [-(relation(identity_relation(_179248)))], (2406 ^ _96150) ^ [] : [-(epsilon_transitive(empty_set))], (2582 ^ _96150) ^ [_185312, _185314] : [proper_subset(_185314, _185314)], (2799 ^ _96150) ^ [] : [-(epsilon_transitive(2795 ^ []))], (1044 ^ _96150) ^ [_133284] : [relation(_133284), 1047 ^ _96150 : [(1048 ^ _96150) ^ [_133458] : [is_reflexive_in(_133284, _133458), 1051 ^ _96150 : [(1052 ^ _96150) ^ [_133600] : [in(_133600, _133458), -(in(ordered_pair(_133600, _133600), _133284))]]], (1058 ^ _96150) ^ [_133783] : [1060 ^ _96150 : [(1063 ^ _96150) ^ [] : [in(ordered_pair(1059 ^ [_133284, _133783], 1059 ^ [_133284, _133783]), _133284)], (1061 ^ _96150) ^ [] : [-(in(1059 ^ [_133284, _133783], _133783))]], -(is_reflexive_in(_133284, _133783))]]], (2301 ^ _96150) ^ [] : [true___, -(true___)], (2815 ^ _96150) ^ [] : [-(function(2809 ^ []))], (2638 ^ _96150) ^ [_187356, _187358, _187360] : [subset(_187360, _187358), -(in(_187356, _187360)), -(subset(_187360, set_difference(_187358, singleton(_187356))))], (2314 ^ _96150) ^ [_176806] : [-(element(2312 ^ [_176806], _176806))], (2808 ^ _96150) ^ [] : [-(relation_empty_yielding(2804 ^ []))], (1116 ^ _96150) ^ [_135890, _135892] : [_135892 = empty_set, 1119 ^ _96150 : [(1126 ^ _96150) ^ [] : [_135890 = empty_set, -(_135890 = set_meet(_135892))], (1120 ^ _96150) ^ [] : [_135890 = set_meet(_135892), -(_135890 = empty_set)]]], (1735 ^ _96150) ^ [_157978, _157980, _157982] : [-(_157978 = set_difference(_157982, _157980)), 1747 ^ _96150 : [(1752 ^ _96150) ^ [] : [in(1736 ^ [_157978, _157980, _157982], _157978)], (1750 ^ _96150) ^ [] : [in(1736 ^ [_157978, _157980, _157982], _157980)], (1748 ^ _96150) ^ [] : [-(in(1736 ^ [_157978, _157980, _157982], _157982))]], 1739 ^ _96150 : [(1742 ^ _96150) ^ [] : [in(1736 ^ [_157978, _157980, _157982], _157982), -(in(1736 ^ [_157978, _157980, _157982], _157980))], (1740 ^ _96150) ^ [] : [-(in(1736 ^ [_157978, _157980, _157982], _157978))]]], (3759 ^ _96150) ^ [_224708, _224710] : [in(_224710, _224708), -(set_union2(singleton(_224710), _224708) = _224708)], (3174 ^ _96150) ^ [_205354] : [-(set_union2(_205354, empty_set) = _205354)], (3689 ^ _96150) ^ [_222356, _222358] : [element(_222356, powerset(_222358)), 3692 ^ _96150 : [(3693 ^ _96150) ^ [_222508] : [element(_222508, powerset(_222358)), 3696 ^ _96150 : [(3703 ^ _96150) ^ [] : [subset(_222356, subset_complement(_222358, _222508)), -(disjoint(_222356, _222508))], (3697 ^ _96150) ^ [] : [disjoint(_222356, _222508), -(subset(_222356, subset_complement(_222358, _222508)))]]]]], (3401 ^ _96150) ^ [_212705] : [-(ordinal(_212705)), 3403 ^ _96150 : [(3406 ^ _96150) ^ [] : [ordinal(3402 ^ [_212705]), subset(3402 ^ [_212705], _212705)], (3404 ^ _96150) ^ [] : [-(in(3402 ^ [_212705], _212705))]]], (2757 ^ _96150) ^ [] : [-(empty(2753 ^ []))], (564 ^ _96150) ^ [_115216, _115218] : [-(set_union2(_115218, _115216) = set_union2(_115216, _115218))], (4296 ^ _96150) ^ [_242471, _242473] : [in(_242473, _242471), -(subset(_242473, union(_242471)))], (3360 ^ _96150) ^ [_211291] : [-(set_intersection2(_211291, empty_set) = empty_set)], (4123 ^ _96150) ^ [_236738, _236740, _236742] : [relation(_236738), function(_236738), in(_236740, relation_dom(relation_dom_restriction(_236738, _236742))), -(apply(relation_dom_restriction(_236738, _236742), _236740) = apply(_236738, _236740))], (3826 ^ _96150) ^ [_227058] : [-(_227058 = empty_set), 3829 ^ _96150 : [(3830 ^ _96150) ^ [_227218] : [element(_227218, powerset(_227058)), 3833 ^ _96150 : [(3834 ^ _96150) ^ [_227372] : [element(_227372, _227058), -(in(_227372, _227218)), -(in(_227372, subset_complement(_227058, _227218)))]]]]], (4183 ^ _96150) ^ [_238678, _238680] : [in(_238680, _238678), 4187 ^ _96150 : [(4190 ^ _96150) ^ [_238969] : [in(_238969, _238678), in(_238969, 4186 ^ [_238678, _238680])], (4188 ^ _96150) ^ [] : [-(in(4186 ^ [_238678, _238680], _238678))]]], (2813 ^ _96150) ^ [] : [-(relation_empty_yielding(2809 ^ []))], (2907 ^ _96150) ^ [_196177, _196179, _196181] : [relation(_196177), 2910 ^ _96150 : [(2919 ^ _96150) ^ [] : [-(in(_196181, relation_rng(relation_rng_restriction(_196179, _196177)))), in(_196181, _196179), in(_196181, relation_rng(_196177))], (2911 ^ _96150) ^ [] : [in(_196181, relation_rng(relation_rng_restriction(_196179, _196177))), 2914 ^ _96150 : [(2917 ^ _96150) ^ [] : [-(in(_196181, relation_rng(_196177)))], (2915 ^ _96150) ^ [] : [-(in(_196181, _196179))]]]]], (2022 ^ _96150) ^ [_168811, _168813] : [element(_168811, powerset(powerset(_168813))), 2025 ^ _96150 : [(2026 ^ _96150) ^ [_168991] : [element(_168991, powerset(powerset(_168813))), 2029 ^ _96150 : [(2030 ^ _96150) ^ [] : [_168991 = complements_of_subsets(_168813, _168811), 2033 ^ _96150 : [(2034 ^ _96150) ^ [_169279] : [element(_169279, powerset(_168813)), 2037 ^ _96150 : [(2044 ^ _96150) ^ [] : [in(subset_complement(_168813, _169279), _168811), -(in(_169279, _168991))], (2038 ^ _96150) ^ [] : [in(_169279, _168991), -(in(subset_complement(_168813, _169279), _168811))]]]]], (2050 ^ _96150) ^ [] : [-(_168991 = complements_of_subsets(_168813, _168811)), 2052 ^ _96150 : [(2055 ^ _96150) ^ [] : [2056 ^ _96150 : [(2059 ^ _96150) ^ [] : [in(subset_complement(_168813, 2051 ^ [_168811, _168813, _168991]), _168811)], (2057 ^ _96150) ^ [] : [-(in(2051 ^ [_168811, _168813, _168991], _168991))]], 2060 ^ _96150 : [(2063 ^ _96150) ^ [] : [in(2051 ^ [_168811, _168813, _168991], _168991)], (2061 ^ _96150) ^ [] : [-(in(subset_complement(_168813, 2051 ^ [_168811, _168813, _168991]), _168811))]]], (2053 ^ _96150) ^ [] : [-(element(2051 ^ [_168811, _168813, _168991], powerset(_168813)))]]]]]]], (2770 ^ _96150) ^ [] : [-(epsilon_transitive(2760 ^ []))], (2213 ^ _96150) ^ [_173835, _173837] : [element(_173835, powerset(_173837)), -(element(subset_complement(_173837, _173835), powerset(_173837)))], (344 ^ _96150) ^ [_107542, _107544, _107546, _107548] : [-(meet_of_subsets(_107548, _107544) = meet_of_subsets(_107546, _107542)), _107548 = _107546, _107544 = _107542], (3093 ^ _96150) ^ [_202619] : [relation(_202619), 3096 ^ _96150 : [(3097 ^ _96150) ^ [_202759] : [relation(_202759), -(relation_rng(relation_composition(_202619, _202759)) = relation_image(_202759, relation_rng(_202619)))]]], (1282 ^ _96150) ^ [_141529, _141531] : [empty(_141531), 1285 ^ _96150 : [(1292 ^ _96150) ^ [] : [empty(_141529), -(element(_141529, _141531))], (1286 ^ _96150) ^ [] : [element(_141529, _141531), -(empty(_141529))]]], (2996 ^ _96150) ^ [_199357, _199359] : [subset(_199357, 2976 ^ [_199359]), -(are_equipotent(_199357, 2976 ^ [_199359])), -(in(_199357, 2976 ^ [_199359]))], (1666 ^ _96150) ^ [_155374] : [-(cast_to_subset(_155374) = _155374)], (390 ^ _96150) ^ [_109196, _109198, _109200, _109202] : [-(set_union2(_109202, _109198) = set_union2(_109200, _109196)), _109202 = _109200, _109198 = _109196], (3566 ^ _96150) ^ [_218255, _218257] : [-(set_union2(_218257, set_difference(_218255, _218257)) = set_union2(_218257, _218255))], (2328 ^ _96150) ^ [_177282] : [empty(_177282), 2331 ^ _96150 : [(2334 ^ _96150) ^ [] : [-(relation(relation_inverse(_177282)))], (2332 ^ _96150) ^ [] : [-(empty(relation_inverse(_177282)))]]], (2971 ^ _96150) ^ [_198408, _198410] : [subset(_198410, _198408), -(set_union2(_198410, _198408) = _198408)], (370 ^ _96150) ^ [_108478, _108480, _108482, _108484] : [-(set_difference(_108484, _108480) = set_difference(_108482, _108478)), _108484 = _108482, _108480 = _108478], (380 ^ _96150) ^ [_108837, _108839, _108841, _108843] : [-(apply(_108843, _108839) = apply(_108841, _108837)), _108843 = _108841, _108839 = _108837], (460 ^ _96150) ^ [_111694, _111696] : [_111696 = _111694, -(singleton(_111696) = singleton(_111694))], (4018 ^ _96150) ^ [_233317, _233319, _233321] : [-(disjoint(_233321, _233317)), subset(_233321, _233319), disjoint(_233319, _233317)], (2163 ^ _96150) ^ [] : [true___, -(true___)], (1341 ^ _96150) ^ [_143548, _143550, _143552] : [_143548 = set_union2(_143552, _143550), 1344 ^ _96150 : [(1345 ^ _96150) ^ [_143730] : [in(_143730, _143548), -(in(_143730, _143552)), -(in(_143730, _143550))], (1355 ^ _96150) ^ [_144008] : [1356 ^ _96150 : [(1359 ^ _96150) ^ [] : [in(_144008, _143550)], (1357 ^ _96150) ^ [] : [in(_144008, _143552)]], -(in(_144008, _143548))]]], (498 ^ _96150) ^ [_113202, _113204] : [proper_subset(_113204, _113202), proper_subset(_113202, _113204)], (4314 ^ _96150) ^ [_243102] : [-(union(powerset(_243102)) = _243102)], (3799 ^ _96150) ^ [_226052, _226054] : [-(set_difference(_226054, set_difference(_226054, _226052)) = set_intersection2(_226054, _226052))], (2408 ^ _96150) ^ [] : [-(epsilon_connected(empty_set))], (2774 ^ _96150) ^ [] : [-(ordinal(2760 ^ []))], (3604 ^ _96150) ^ [_219554, _219556] : [subset(_219556, _219554), -(element(_219556, powerset(_219554)))], (4155 ^ _96150) ^ [_237778, _237780, _237782, _237784] : [relation(_237778), 4158 ^ _96150 : [(4167 ^ _96150) ^ [] : [-(in(ordered_pair(_237784, _237782), relation_composition(identity_relation(_237780), _237778))), in(_237784, _237780), in(ordered_pair(_237784, _237782), _237778)], (4159 ^ _96150) ^ [] : [in(ordered_pair(_237784, _237782), relation_composition(identity_relation(_237780), _237778)), 4162 ^ _96150 : [(4165 ^ _96150) ^ [] : [-(in(ordered_pair(_237784, _237782), _237778))], (4163 ^ _96150) ^ [] : [-(in(_237784, _237780))]]]]], (2762 ^ _96150) ^ [] : [-(relation(2760 ^ []))], (426 ^ _96150) ^ [_110463, _110465] : [_110465 = _110463, -(identity_relation(_110465) = identity_relation(_110463))], (170 ^ _96150) ^ [_101506, _101508, _101510, _101512] : [-(subset(_101510, _101506)), subset(_101512, _101508), _101512 = _101510, _101508 = _101506], (3524 ^ _96150) ^ [_216862, _216864] : [set_difference(_216864, _216862) = empty_set, -(subset(_216864, _216862))], (1363 ^ _96150) ^ [_144273, _144275, _144277] : [-(_144273 = set_union2(_144277, _144275)), 1367 ^ _96150 : [(1372 ^ _96150) ^ [] : [in(1364 ^ [_144273, _144275, _144277], _144275)], (1370 ^ _96150) ^ [] : [in(1364 ^ [_144273, _144275, _144277], _144277)], (1368 ^ _96150) ^ [] : [-(in(1364 ^ [_144273, _144275, _144277], _144273))]], 1373 ^ _96150 : [(1374 ^ _96150) ^ [] : [-(in(1364 ^ [_144273, _144275, _144277], _144277)), -(in(1364 ^ [_144273, _144275, _144277], _144275))], (1380 ^ _96150) ^ [] : [in(1364 ^ [_144273, _144275, _144277], _144273)]]], (2532 ^ _96150) ^ [_183560] : [empty(_183560), 2535 ^ _96150 : [(2538 ^ _96150) ^ [] : [-(relation(relation_dom(_183560)))], (2536 ^ _96150) ^ [] : [-(empty(relation_dom(_183560)))]]], (34 ^ _96150) ^ [_97342, _97344] : [-(epsilon_connected(_97342)), _97344 = _97342, epsilon_connected(_97344)], (3984 ^ _96150) ^ [_232318, _232320, _232322] : [in(_232322, _232320), element(_232320, powerset(_232318)), empty(_232318)], (3508 ^ _96150) ^ [_216231, _216233] : [in(_216231, _216233), -(apply(identity_relation(_216233), _216231) = _216231)], (262 ^ _96150) ^ [_104577, _104579, _104581, _104583] : [-(relation_image(_104583, _104579) = relation_image(_104581, _104577)), _104583 = _104581, _104579 = _104577], (1192 ^ _96150) ^ [_138450, _138452] : [-(_138450 = powerset(_138452)), 1196 ^ _96150 : [(1199 ^ _96150) ^ [] : [subset(1193 ^ [_138450, _138452], _138452)], (1197 ^ _96150) ^ [] : [-(in(1193 ^ [_138450, _138452], _138450))]], 1200 ^ _96150 : [(1203 ^ _96150) ^ [] : [in(1193 ^ [_138450, _138452], _138450)], (1201 ^ _96150) ^ [] : [-(subset(1193 ^ [_138450, _138452], _138452))]]], (2354 ^ _96150) ^ [_178102, _178104] : [2369 ^ _96150 : [(2372 ^ _96150) ^ [] : [-(function(relation_composition(_178104, _178102)))], (2370 ^ _96150) ^ [] : [-(relation(relation_composition(_178104, _178102)))]], relation(_178104), function(_178104), relation(_178102), function(_178102)], (3820 ^ _96150) ^ [_226833, _226835] : [3821 ^ _96150 : [(3822 ^ _96150) ^ [_226906] : [in(_226906, set_intersection2(_226835, _226833))]], disjoint(_226835, _226833)], (4232 ^ _96150) ^ [_240394, _240396] : [relation(_240394), -(subset(relation_dom_restriction(_240394, _240396), _240394))], (3372 ^ _96150) ^ [_211699, _211701] : [-(_211701 = _211699), 3376 ^ _96150 : [(3379 ^ _96150) ^ [] : [in(3373 ^ [_211699, _211701], _211699)], (3377 ^ _96150) ^ [] : [-(in(3373 ^ [_211699, _211701], _211701))]], 3380 ^ _96150 : [(3383 ^ _96150) ^ [] : [in(3373 ^ [_211699, _211701], _211701)], (3381 ^ _96150) ^ [] : [-(in(3373 ^ [_211699, _211701], _211699))]]], (2859 ^ _96150) ^ [_194465, _194467] : [-(ordinal_subset(_194467, _194467)), ordinal(_194467), ordinal(_194465)], (3635 ^ _96150) ^ [_220642, _220644] : [-(set_difference(set_union2(_220644, _220642), _220642) = set_difference(_220644, _220642))], (4196 ^ _96150) ^ [_239194, _239196] : [-(subset(_239196, set_union2(_239196, _239194)))], (1756 ^ _96150) ^ [_158721] : [relation(_158721), function(_158721), 1763 ^ _96150 : [(1764 ^ _96150) ^ [_158993] : [_158993 = relation_rng(_158721), 1767 ^ _96150 : [(1777 ^ _96150) ^ [_159523] : [-(in(_159523, _158993)), 1778 ^ _96150 : [(1779 ^ _96150) ^ [_159626] : [in(_159626, relation_dom(_158721)), _159523 = apply(_158721, _159626)]]], (1768 ^ _96150) ^ [_159181] : [in(_159181, _158993), 1772 ^ _96150 : [(1775 ^ _96150) ^ [] : [-(_159181 = apply(_158721, 1771 ^ [_158721, _158993, _159181]))], (1773 ^ _96150) ^ [] : [-(in(1771 ^ [_158721, _158993, _159181], relation_dom(_158721)))]]]]], (1787 ^ _96150) ^ [_159875] : [-(_159875 = relation_rng(_158721)), 1800 ^ _96150 : [(1805 ^ _96150) ^ [] : [in(1788 ^ [_158721, _159875], _159875)], (1803 ^ _96150) ^ [] : [-(1788 ^ [_158721, _159875] = apply(_158721, 1799 ^ [_158721, _159875]))], (1801 ^ _96150) ^ [] : [-(in(1799 ^ [_158721, _159875], relation_dom(_158721)))]], 1791 ^ _96150 : [(1794 ^ _96150) ^ [_160170] : [in(_160170, relation_dom(_158721)), 1788 ^ [_158721, _159875] = apply(_158721, _160170)], (1792 ^ _96150) ^ [] : [-(in(1788 ^ [_158721, _159875], _159875))]]]]], (1668 ^ _96150) ^ [_155512, _155514] : [_155512 = union(_155514), 1671 ^ _96150 : [(1681 ^ _96150) ^ [_156020] : [-(in(_156020, _155512)), 1682 ^ _96150 : [(1683 ^ _96150) ^ [_156118] : [in(_156020, _156118), in(_156118, _155514)]]], (1672 ^ _96150) ^ [_155693] : [in(_155693, _155512), 1676 ^ _96150 : [(1679 ^ _96150) ^ [] : [-(in(1675 ^ [_155512, _155514, _155693], _155514))], (1677 ^ _96150) ^ [] : [-(in(_155693, 1675 ^ [_155512, _155514, _155693]))]]]]], (2207 ^ _96150) ^ [] : [true___, -(true___)], (3132 ^ _96150) ^ [_204006, _204008] : [relation(_204006), -(subset(relation_inverse_image(_204006, _204008), relation_dom(_204006)))], (304 ^ _96150) ^ [_106090, _106092, _106094, _106096] : [-(union_of_subsets(_106096, _106092) = union_of_subsets(_106094, _106090)), _106096 = _106094, _106092 = _106090], (2115 ^ _96150) ^ [] : [true___, -(true___)], (2592 ^ _96150) ^ [_185720, _185722] : [disjoint(singleton(_185722), _185720), in(_185722, _185720)], (2283 ^ _96150) ^ [_175902, _175904] : [relation(_175904), -(relation(relation_dom_restriction(_175904, _175902)))], (492 ^ _96150) ^ [_112991, _112993] : [in(_112993, _112991), in(_112991, _112993)], (3619 ^ _96150) ^ [_220104, _220106] : [disjoint(_220106, _220104), 3620 ^ _96150 : [(3621 ^ _96150) ^ [_220196] : [in(_220196, _220106), in(_220196, _220104)]]], (504 ^ _96150) ^ [_113399] : [empty(_113399), -(function(_113399))], (272 ^ _96150) ^ [_104936, _104938, _104940, _104942] : [-(relation_inverse_image(_104942, _104938) = relation_inverse_image(_104940, _104936)), _104942 = _104940, _104938 = _104936], (2811 ^ _96150) ^ [] : [-(relation(2809 ^ []))], (466 ^ _96150) ^ [_111940, _111942, _111944, _111946] : [-(unordered_pair(_111946, _111942) = unordered_pair(_111944, _111940)), _111946 = _111944, _111942 = _111940], (2316 ^ _96150) ^ [_176918, _176920] : [2323 ^ _96150 : [(2326 ^ _96150) ^ [] : [-(relation(relation_composition(_176918, _176920)))], (2324 ^ _96150) ^ [] : [-(empty(relation_composition(_176918, _176920)))]], empty(_176920), relation(_176918)], (2742 ^ _96150) ^ [_190746] : [-(empty(_190746)), 2746 ^ _96150 : [(2749 ^ _96150) ^ [] : [empty(2745 ^ [_190746])], (2747 ^ _96150) ^ [] : [-(element(2745 ^ [_190746], powerset(_190746)))]]], (2562 ^ _96150) ^ [_184564, _184566] : [-(set_intersection2(_184566, _184566) = _184566)], (2522 ^ _96150) ^ [_183283] : [empty(relation_rng(_183283)), -(empty(_183283)), relation(_183283)], (2560 ^ _96150) ^ [_184467, _184469] : [-(set_union2(_184469, _184469) = _184469)], (2121 ^ _96150) ^ [] : [true___, -(true___)], (3735 ^ _96150) ^ [_223918] : [relation(_223918), 3738 ^ _96150 : [(3739 ^ _96150) ^ [_224065] : [relation(_224065), subset(relation_rng(_223918), relation_dom(_224065)), -(relation_dom(relation_composition(_223918, _224065)) = relation_dom(_223918))]]], (4308 ^ _96150) ^ [_242909, _242911] : [relation(_242909), -(subset(relation_rng(relation_dom_restriction(_242909, _242911)), relation_rng(_242909)))], (2151 ^ _96150) ^ [] : [true___, -(true___)], (4040 ^ _96150) ^ [_233965] : [relation(_233965), 4043 ^ _96150 : [(4050 ^ _96150) ^ [] : [relation_rng(_233965) = empty_set, -(relation_dom(_233965) = empty_set)], (4044 ^ _96150) ^ [] : [relation_dom(_233965) = empty_set, -(relation_rng(_233965) = empty_set)]]], (1414 ^ _96150) ^ [_146324, _146326, _146328] : [-(_146324 = cartesian_product2(_146328, _146326)), 1432 ^ _96150 : [(1435 ^ _96150) ^ [] : [-(in(1431 ^ [_146324, _146326, _146328], _146326))], (1437 ^ _96150) ^ [] : [-(1415 ^ [_146324, _146326, _146328] = ordered_pair(1430 ^ [_146324, _146326, _146328], 1431 ^ [_146324, _146326, _146328]))], (1439 ^ _96150) ^ [] : [in(1415 ^ [_146324, _146326, _146328], _146324)], (1433 ^ _96150) ^ [] : [-(in(1430 ^ [_146324, _146326, _146328], _146328))]], 1418 ^ _96150 : [(1421 ^ _96150) ^ [_146662, _146664] : [in(_146664, _146328), in(_146662, _146326), 1415 ^ [_146324, _146326, _146328] = ordered_pair(_146664, _146662)], (1419 ^ _96150) ^ [] : [-(in(1415 ^ [_146324, _146326, _146328], _146324))]]], (476 ^ _96150) ^ [_112271, _112273] : [_112273 = _112271, -(relation_field(_112273) = relation_field(_112271))], (568 ^ _96150) ^ [_115431, _115433] : [ordinal(_115433), ordinal(_115431), -(ordinal_subset(_115433, _115431)), -(ordinal_subset(_115431, _115433))], (2935 ^ _96150) ^ [_197054, _197056] : [relation(_197054), -(subset(relation_rng_restriction(_197056, _197054), _197054))], (2273 ^ _96150) ^ [_175573, _175575, _175577] : [-(element(subset_difference(_175577, _175575, _175573), powerset(_175577))), element(_175575, powerset(_175577)), element(_175573, powerset(_175577))], (2396 ^ _96150) ^ [] : [-(relation(empty_set))], (1481 ^ _96150) ^ [_148931] : [relation(_148931), 1484 ^ _96150 : [(1485 ^ _96150) ^ [_149089] : [relation(_149089), 1488 ^ _96150 : [(1489 ^ _96150) ^ [] : [subset(_148931, _149089), 1492 ^ _96150 : [(1493 ^ _96150) ^ [_149365, _149367] : [in(ordered_pair(_149367, _149365), _148931), -(in(ordered_pair(_149367, _149365), _149089))]]], (1499 ^ _96150) ^ [] : [1502 ^ _96150 : [(1505 ^ _96150) ^ [] : [in(ordered_pair(1500 ^ [_148931, _149089], 1501 ^ [_148931, _149089]), _149089)], (1503 ^ _96150) ^ [] : [-(in(ordered_pair(1500 ^ [_148931, _149089], 1501 ^ [_148931, _149089]), _148931))]], -(subset(_148931, _149089))]]]]], (1035 ^ _96150) ^ [_132890] : [1037 ^ _96150 : [(1040 ^ _96150) ^ [_133127, _133129] : [1036 ^ [_132890] = ordered_pair(_133129, _133127)], (1038 ^ _96150) ^ [] : [-(in(1036 ^ [_132890], _132890))]], -(relation(_132890))], (78 ^ _96150) ^ [_98671, _98673] : [-(ordinal(_98671)), _98673 = _98671, ordinal(_98673)], (3006 ^ _96150) ^ [_199711, _199713, _199715] : [relation(_199711), -(relation_dom_restriction(relation_rng_restriction(_199715, _199711), _199713) = relation_rng_restriction(_199715, relation_dom_restriction(_199711, _199713)))], (2267 ^ _96150) ^ [_175331, _175333] : [element(_175331, powerset(powerset(_175333))), -(element(meet_of_subsets(_175333, _175331), powerset(_175333)))], (2628 ^ _96150) ^ [_186976, _186978] : [element(_186976, powerset(_186978)), 2631 ^ _96150 : [(2632 ^ _96150) ^ [_187117] : [in(_187117, _186976), -(in(_187117, _186978))]]], (482 ^ _96150) ^ [_112497, _112499, _112501, _112503] : [-(ordered_pair(_112503, _112499) = ordered_pair(_112501, _112497)), _112503 = _112501, _112499 = _112497], (3586 ^ _96150) ^ [_218927] : [-(set_difference(_218927, empty_set) = _218927)], (3467 ^ _96150) ^ [_214894, _214896, _214898, _214900] : [ordered_pair(_214900, _214898) = ordered_pair(_214896, _214894), 3470 ^ _96150 : [(3473 ^ _96150) ^ [] : [-(_214898 = _214894)], (3471 ^ _96150) ^ [] : [-(_214900 = _214896)]]], (3041 ^ _96150) ^ [_200961, _200963] : [relation(_200961), -(subset(relation_image(_200961, _200963), relation_rng(_200961)))], (1023 ^ _96150) ^ [_132429] : [relation(_132429), 1026 ^ _96150 : [(1027 ^ _96150) ^ [_132577] : [in(_132577, _132429), -(_132577 = ordered_pair(1030 ^ [_132429, _132577], 1031 ^ [_132429, _132577]))]]], (2412 ^ _96150) ^ [_179841, _179843] : [-(relation(set_union2(_179843, _179841))), relation(_179843), relation(_179841)], (2424 ^ _96150) ^ [_180218, _180220] : [-(empty(_180220)), empty(set_union2(_180220, _180218))], (64 ^ _96150) ^ [_98255, _98257, _98259, _98261] : [-(ordinal_subset(_98259, _98255)), ordinal_subset(_98261, _98257), _98261 = _98259, _98257 = _98255], (1163 ^ _96150) ^ [_137459] : [_137459 = empty_set, 1166 ^ _96150 : [(1167 ^ _96150) ^ [_137572] : [in(_137572, _137459)]]], (2658 ^ _96150) ^ [_187965, _187967] : [2659 ^ _96150 : [(2662 ^ _96150) ^ [] : [_187967 = singleton(_187965)], (2660 ^ _96150) ^ [] : [_187967 = empty_set]], -(subset(_187967, singleton(_187965)))], (648 ^ _96150) ^ [_118023] : [relation(_118023), 651 ^ _96150 : [(652 ^ _96150) ^ [_118209, _118211] : [relation(_118209), 655 ^ _96150 : [(656 ^ _96150) ^ [] : [_118209 = relation_dom_restriction(_118023, _118211), 659 ^ _96150 : [(668 ^ _96150) ^ [_118813, _118815] : [-(in(ordered_pair(_118815, _118813), _118209)), in(_118815, _118211), in(ordered_pair(_118815, _118813), _118023)], (660 ^ _96150) ^ [_118534, _118536] : [in(ordered_pair(_118536, _118534), _118209), 663 ^ _96150 : [(666 ^ _96150) ^ [] : [-(in(ordered_pair(_118536, _118534), _118023))], (664 ^ _96150) ^ [] : [-(in(_118536, _118211))]]]]], (678 ^ _96150) ^ [] : [-(_118209 = relation_dom_restriction(_118023, _118211)), 691 ^ _96150 : [(696 ^ _96150) ^ [] : [in(ordered_pair(679 ^ [_118023, _118209, _118211], 680 ^ [_118023, _118209, _118211]), _118209)], (694 ^ _96150) ^ [] : [-(in(ordered_pair(679 ^ [_118023, _118209, _118211], 680 ^ [_118023, _118209, _118211]), _118023))], (692 ^ _96150) ^ [] : [-(in(679 ^ [_118023, _118209, _118211], _118211))]], 683 ^ _96150 : [(686 ^ _96150) ^ [] : [in(679 ^ [_118023, _118209, _118211], _118211), in(ordered_pair(679 ^ [_118023, _118209, _118211], 680 ^ [_118023, _118209, _118211]), _118023)], (684 ^ _96150) ^ [] : [-(in(ordered_pair(679 ^ [_118023, _118209, _118211], 680 ^ [_118023, _118209, _118211]), _118209))]]]]]]], (2990 ^ _96150) ^ [_199157, _199159] : [in(_199157, 2976 ^ [_199159]), -(in(powerset(_199157), 2976 ^ [_199159]))], (88 ^ _96150) ^ [_98966, _98968] : [-(being_limit_ordinal(_98966)), _98968 = _98966, being_limit_ordinal(_98968)], (4056 ^ _96150) ^ [_234448, _234450] : [set_difference(_234450, singleton(_234448)) = _234450, in(_234448, _234450)], (3192 ^ _96150) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2336 ^ _96150) ^ [] : [-(empty(empty_set))], (1465 ^ _96150) ^ [_148225] : [1468 ^ _96150 : [(1469 ^ _96150) ^ [] : [-(in(1466 ^ [_148225], _148225))], (1473 ^ _96150) ^ [] : [in(1466 ^ [_148225], 1467 ^ [_148225])], (1477 ^ _96150) ^ [] : [in(1467 ^ [_148225], 1466 ^ [_148225])], (1475 ^ _96150) ^ [] : [1466 ^ [_148225] = 1467 ^ [_148225]], (1471 ^ _96150) ^ [] : [-(in(1467 ^ [_148225], _148225))]], -(epsilon_connected(_148225))], (3964 ^ _96150) ^ [_231720, _231722] : [relation(_231720), function(_231720), 3979 ^ _96150 : [(3982 ^ _96150) ^ [] : [-(_231722 = apply(relation_composition(function_inverse(_231720), _231720), _231722))], (3980 ^ _96150) ^ [] : [-(_231722 = apply(_231720, apply(function_inverse(_231720), _231722)))]], one_to_one(_231720), in(_231722, relation_rng(_231720))], (2877 ^ _96150) ^ [_195121, _195123, _195125, _195127] : [in(ordered_pair(_195127, _195125), cartesian_product2(_195123, _195121)), 2880 ^ _96150 : [(2883 ^ _96150) ^ [] : [-(in(_195125, _195121))], (2881 ^ _96150) ^ [] : [-(in(_195127, _195123))]]], (868 ^ _96150) ^ [_126254] : [relation(_126254), 871 ^ _96150 : [(872 ^ _96150) ^ [_126461, _126463] : [_126461 = relation_image(_126254, _126463), 875 ^ _96150 : [(885 ^ _96150) ^ [_127007] : [-(in(_127007, _126461)), 886 ^ _96150 : [(887 ^ _96150) ^ [_127112] : [in(ordered_pair(_127112, _127007), _126254), in(_127112, _126463)]]], (876 ^ _96150) ^ [_126653] : [in(_126653, _126461), 880 ^ _96150 : [(883 ^ _96150) ^ [] : [-(in(879 ^ [_126254, _126461, _126463, _126653], _126463))], (881 ^ _96150) ^ [] : [-(in(ordered_pair(879 ^ [_126254, _126461, _126463, _126653], _126653), _126254))]]]]], (895 ^ _96150) ^ [_127367, _127369] : [-(_127367 = relation_image(_126254, _127369)), 908 ^ _96150 : [(913 ^ _96150) ^ [] : [in(896 ^ [_126254, _127367, _127369], _127367)], (911 ^ _96150) ^ [] : [-(in(907 ^ [_126254, _127367, _127369], _127369))], (909 ^ _96150) ^ [] : [-(in(ordered_pair(907 ^ [_126254, _127367, _127369], 896 ^ [_126254, _127367, _127369]), _126254))]], 899 ^ _96150 : [(902 ^ _96150) ^ [_127671] : [in(ordered_pair(_127671, 896 ^ [_126254, _127367, _127369]), _126254), in(_127671, _127369)], (900 ^ _96150) ^ [] : [-(in(896 ^ [_126254, _127367, _127369], _127367))]]]]], (2075 ^ _96150) ^ [_170640, _170642] : [-(proper_subset(_170642, _170640)), subset(_170642, _170640), -(_170642 = _170640)], (3441 ^ _96150) ^ [_214015] : [ordinal(_214015), 3444 ^ _96150 : [(3445 ^ _96150) ^ [_214153] : [ordinal(_214153), 3448 ^ _96150 : [(3455 ^ _96150) ^ [] : [ordinal_subset(succ(_214015), _214153), -(in(_214015, _214153))], (3449 ^ _96150) ^ [] : [in(_214015, _214153), -(ordinal_subset(succ(_214015), _214153))]]]]], (2243 ^ _96150) ^ [] : [true___, -(true___)], (2699 ^ _96150) ^ [_189501, _189503, _189505] : [relation(_189501), function(_189501), 2706 ^ _96150 : [(2715 ^ _96150) ^ [] : [-(in(_189503, relation_dom(relation_dom_restriction(_189501, _189505)))), in(_189503, relation_dom(_189501)), in(_189503, _189505)], (2707 ^ _96150) ^ [] : [in(_189503, relation_dom(relation_dom_restriction(_189501, _189505))), 2710 ^ _96150 : [(2713 ^ _96150) ^ [] : [-(in(_189503, _189505))], (2711 ^ _96150) ^ [] : [-(in(_189503, relation_dom(_189501)))]]]]], (2817 ^ _96150) ^ [_193117, _193119] : [element(_193117, powerset(powerset(_193119))), -(union_of_subsets(_193119, _193117) = union(_193117))], (2869 ^ _96150) ^ [_194745, _194747] : [-(subset(_194747, _194747))]], input).
% 46.84/46.02  ncf('1',plain,[4368 : in(ordered_pair(4364 ^ [], 4364 ^ []), 4357 ^ []), 4370 : in(1059 ^ [4357 ^ [], relation_field(4357 ^ [])], relation_field(4357 ^ [])), 4370 : -(in(ordered_pair(1059 ^ [4357 ^ [], relation_field(4357 ^ [])], 1059 ^ [4357 ^ [], relation_field(4357 ^ [])]), 4357 ^ []))],start(4361 ^ 0,bind([[_247855], [1059 ^ [4357 ^ [], relation_field(4357 ^ [])]]]))).
% 46.84/46.02  ncf('1.1',plain,[-(in(ordered_pair(4364 ^ [], 4364 ^ []), 4357 ^ [])), 1052 : in(4364 ^ [], relation_field(4357 ^ [])), 1052 : is_reflexive_in(4357 ^ [], relation_field(4357 ^ [])), 1048 : relation(4357 ^ [])],extension(1044 ^ 3,bind([[_133284, _133458, _133600], [4357 ^ [], relation_field(4357 ^ []), 4364 ^ []]]))).
% 46.84/46.02  ncf('1.1.1',plain,[-(in(4364 ^ [], relation_field(4357 ^ [])))],extension(4366 ^ 8)).
% 46.84/46.02  ncf('1.1.2',plain,[-(is_reflexive_in(4357 ^ [], relation_field(4357 ^ []))), 2103 : reflexive(4357 ^ []), 2103 : relation(4357 ^ [])],extension(2099 ^ 6,bind([[_171294], [4357 ^ []]]))).
% 46.84/46.02  ncf('1.1.2.1',plain,[-(reflexive(4357 ^ []))],extension(4363 ^ 9)).
% 46.84/46.02  ncf('1.1.2.2',plain,[-(relation(4357 ^ []))],extension(4359 ^ 7)).
% 46.84/46.02  ncf('1.1.3',plain,[-(relation(4357 ^ []))],extension(4359 ^ 4)).
% 46.84/46.02  ncf('1.2',plain,[-(in(1059 ^ [4357 ^ [], relation_field(4357 ^ [])], relation_field(4357 ^ []))), 1058 : -(is_reflexive_in(4357 ^ [], relation_field(4357 ^ []))), 1058 : relation(4357 ^ [])],extension(1044 ^ 3,bind([[_133284, _133783], [4357 ^ [], relation_field(4357 ^ [])]]))).
% 46.84/46.02  ncf('1.2.1',plain,[is_reflexive_in(4357 ^ [], relation_field(4357 ^ [])), 2109 : -(reflexive(4357 ^ [])), 2109 : relation(4357 ^ [])],extension(2099 ^ 6,bind([[_171294], [4357 ^ []]]))).
% 46.84/46.02  ncf('1.2.1.1',plain,[reflexive(4357 ^ [])],extension(4376 ^ 9)).
% 46.84/46.02  ncf('1.2.1.2',plain,[-(relation(4357 ^ []))],extension(4359 ^ 7)).
% 46.84/46.02  ncf('1.2.2',plain,[-(relation(4357 ^ []))],extension(4359 ^ 4)).
% 46.84/46.02  ncf('1.3',plain,[in(ordered_pair(1059 ^ [4357 ^ [], relation_field(4357 ^ [])], 1059 ^ [4357 ^ [], relation_field(4357 ^ [])]), 4357 ^ []), 1058 : -(is_reflexive_in(4357 ^ [], relation_field(4357 ^ []))), 1058 : relation(4357 ^ [])],extension(1044 ^ 3,bind([[_133284, _133783], [4357 ^ [], relation_field(4357 ^ [])]]))).
% 46.84/46.02  ncf('1.3.1',plain,[is_reflexive_in(4357 ^ [], relation_field(4357 ^ [])), 2109 : -(reflexive(4357 ^ [])), 2109 : relation(4357 ^ [])],extension(2099 ^ 6,bind([[_171294], [4357 ^ []]]))).
% 46.84/46.02  ncf('1.3.1.1',plain,[reflexive(4357 ^ [])],extension(4376 ^ 9)).
% 46.84/46.02  ncf('1.3.1.2',plain,[-(relation(4357 ^ []))],extension(4359 ^ 7)).
% 46.84/46.02  ncf('1.3.2',plain,[-(relation(4357 ^ []))],extension(4359 ^ 4)).
% 46.84/46.02  %-----------------------------------------------------
% 46.84/46.02  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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