TSTP Solution File: SEU039+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 : Sun May 5 09:26:48 EDT 2024
% Result : Theorem 43.84s 6.60s
% Output : Refutation 43.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1741
% Syntax : Number of formulae : 5843 ( 123 unt; 0 def)
% Number of atoms : 25722 (2245 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 34329 (14450 ~;17976 |; 163 &)
% (1696 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 1691 (1689 usr;1679 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-3 aty)
% Number of variables : 10851 (10795 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f73643,plain,
$false,
inference(avatar_sat_refutation,[],[f227,f232,f237,f242,f247,f252,f257,f262,f267,f272,f277,f282,f287,f292,f297,f302,f307,f312,f317,f322,f327,f332,f337,f341,f345,f349,f353,f357,f361,f371,f380,f384,f388,f392,f396,f400,f404,f408,f413,f417,f421,f441,f448,f452,f456,f460,f464,f468,f490,f501,f505,f509,f513,f517,f521,f547,f551,f555,f559,f564,f580,f584,f588,f602,f606,f610,f614,f626,f630,f640,f644,f648,f654,f664,f668,f672,f700,f708,f712,f718,f729,f733,f744,f756,f764,f769,f774,f780,f786,f790,f795,f801,f806,f811,f825,f848,f853,f876,f886,f895,f900,f905,f910,f914,f918,f922,f938,f942,f946,f950,f954,f961,f967,f968,f969,f970,f971,f1006,f1051,f1055,f1062,f1066,f1108,f1112,f1129,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1161,f1240,f1244,f1248,f1254,f1276,f1280,f1284,f1288,f1292,f1307,f1339,f1343,f1347,f1382,f1386,f1391,f1395,f1399,f1403,f1407,f1411,f1446,f1510,f1529,f1533,f1537,f1541,f1546,f1581,f1585,f1589,f1593,f1602,f1606,f1610,f1614,f1618,f1682,f1714,f1718,f1722,f1737,f1741,f1770,f1776,f1780,f1784,f1807,f1835,f1839,f1843,f1847,f1851,f1961,f1966,f1985,f1996,f2000,f2005,f2009,f2013,f2085,f2096,f2110,f2120,f2130,f2139,f2143,f2151,f2155,f2159,f2164,f2169,f2215,f2219,f2223,f2233,f2239,f2243,f2252,f2256,f2276,f2296,f2307,f2318,f2346,f2365,f2369,f2373,f2377,f2381,f2385,f2389,f2393,f2397,f2401,f2445,f2449,f2470,f2491,f2512,f2533,f2561,f2565,f2569,f2573,f2577,f2688,f2692,f2696,f2700,f2704,f2708,f2729,f2733,f2737,f2741,f2745,f2885,f2889,f2893,f2897,f2901,f2905,f2909,f2913,f2917,f2921,f2925,f2929,f2933,f2937,f2941,f2945,f2949,f2953,f2957,f2961,f2965,f2969,f2973,f2977,f2981,f2985,f2989,f2993,f2997,f3001,f3223,f3266,f3270,f3274,f3278,f3286,f3290,f3294,f3298,f3302,f3306,f3331,f3388,f3392,f3396,f3400,f3412,f3416,f3420,f3424,f3428,f3432,f3436,f3440,f3444,f3448,f3453,f3457,f3461,f3502,f3536,f3540,f3545,f3549,f3553,f3604,f3608,f3612,f3616,f3620,f3624,f3628,f3669,f3675,f3679,f3683,f3687,f3691,f3695,f3699,f3703,f3857,f3861,f3903,f3907,f3911,f3915,f3919,f3923,f3927,f3931,f3935,f3939,f3948,f3952,f3956,f3960,f3964,f3968,f3972,f3976,f3980,f3984,f3988,f3992,f3996,f4000,f4004,f4008,f4012,f4016,f4020,f4024,f4028,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4128,f4629,f4720,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f4774,f4778,f4782,f4786,f4790,f4839,f4900,f4904,f4938,f4942,f4946,f4950,f4954,f5120,f5124,f5128,f5132,f5236,f5240,f5244,f5248,f5252,f5256,f5260,f5264,f5268,f5272,f5284,f5288,f5292,f5296,f5445,f5657,f5661,f5665,f5669,f5673,f5677,f5681,f5685,f5689,f5693,f5697,f5701,f5705,f5709,f5713,f5717,f5721,f5954,f6238,f6242,f6275,f6279,f6283,f6287,f6291,f6295,f6299,f6303,f6307,f6311,f6335,f6339,f6343,f6347,f6351,f6355,f6359,f6363,f6367,f6371,f6383,f6387,f6391,f6395,f6399,f6403,f6407,f6411,f6415,f7122,f8064,f8068,f8072,f8076,f8080,f8084,f8088,f8351,f8355,f8359,f8363,f8367,f8371,f8375,f8379,f8383,f8387,f8402,f8417,f8432,f8469,f8707,f8991,f8995,f8999,f9003,f9007,f9011,f9015,f9019,f9023,f9027,f9034,f9221,f9225,f9230,f9234,f9238,f9242,f9246,f9250,f9254,f9258,f9262,f9266,f9448,f9492,f9496,f9539,f9582,f9625,f9634,f9677,f9720,f9763,f9806,f9849,f9893,f9936,f9979,f10022,f10082,f10083,f10143,f10228,f10232,f10236,f10240,f10244,f10248,f10254,f10258,f10262,f10266,f10270,f10274,f10278,f10282,f10286,f10290,f10315,f10319,f10323,f10633,f10645,f10649,f10800,f10804,f10808,f10812,f10816,f10820,f10824,f10828,f10832,f10836,f10840,f10844,f10848,f10852,f10857,f10920,f10948,f10978,f10982,f11049,f11053,f11136,f11140,f11144,f11148,f11223,f11227,f11231,f11235,f11239,f11363,f11380,f11384,f11388,f11538,f11542,f11546,f11550,f11554,f11558,f11562,f11566,f11743,f11834,f11953,f11957,f11962,f11966,f11970,f11974,f11978,f11982,f11986,f11990,f11994,f11998,f12002,f12095,f12475,f12513,f12517,f12521,f12779,f12783,f12787,f12791,f12795,f12799,f12803,f12831,f12908,f12912,f12933,f12943,f12947,f12951,f12955,f12959,f12963,f12967,f12971,f12975,f13042,f13046,f13050,f13054,f13058,f13062,f13066,f13070,f13074,f13078,f13082,f13086,f13090,f13094,f13098,f13297,f13329,f13363,f13367,f13371,f13375,f13379,f13383,f13387,f13444,f13636,f13640,f13644,f13648,f13652,f13656,f13660,f13664,f13668,f13672,f13808,f13812,f14165,f14296,f14441,f14586,f14590,f14595,f14599,f14603,f14751,f14762,f14766,f14770,f14774,f14778,f14814,f14818,f14822,f14826,f14830,f14882,f14886,f15035,f15039,f15043,f15047,f15083,f15185,f15189,f15223,f15270,f15302,f15309,f15318,f15322,f15326,f15334,f15342,f15346,f15350,f15351,f15524,f15527,f15534,f15661,f15665,f15670,f15677,f15682,f15757,f15765,f15775,f15779,f15788,f15799,f15837,f15842,f15846,f15850,f15854,f15858,f15862,f15866,f15870,f15883,f15894,f15922,f16092,f16104,f16133,f16139,f16149,f16160,f16225,f16229,f16233,f16237,f16241,f16245,f16253,f16299,f16319,f16323,f16327,f16331,f16335,f16362,f16376,f16380,f16458,f16472,f16485,f16498,f16511,f16515,f16519,f16523,f16527,f16648,f16652,f16656,f16660,f16664,f16668,f16672,f16676,f16680,f16684,f16688,f16692,f16696,f16700,f16704,f16708,f16712,f16716,f16964,f16989,f17002,f17006,f17010,f17014,f17018,f17022,f17026,f17030,f17034,f17038,f17042,f17046,f17050,f17054,f17536,f17542,f17546,f17550,f17554,f17558,f17571,f17602,f17763,f17767,f17771,f17775,f17779,f17784,f17945,f18138,f18142,f18146,f18150,f18464,f18468,f18472,f18476,f18490,f18504,f18518,f18522,f18536,f18550,f18564,f18578,f18592,f18699,f18703,f18707,f18711,f18715,f18719,f18723,f19258,f19410,f19426,f19430,f19434,f19438,f19442,f19446,f19450,f19454,f19458,f19462,f19466,f19470,f19474,f19478,f19482,f19486,f19490,f19494,f19498,f19502,f19506,f19530,f19534,f19538,f19542,f19547,f19646,f19744,f19893,f20198,f20776,f20780,f20784,f20788,f20792,f20796,f20800,f20804,f20808,f20812,f20816,f20820,f20824,f20828,f20832,f20847,f21509,f21513,f21517,f21601,f21761,f21765,f21769,f21773,f21898,f22225,f22328,f22332,f22336,f22340,f22344,f22348,f22352,f22356,f22360,f22364,f22368,f22657,f22760,f22764,f22768,f22772,f22781,f22873,f23043,f23047,f23051,f23055,f23059,f23063,f23171,f23175,f23179,f23348,f23352,f23356,f23360,f23364,f23368,f23396,f23554,f23605,f23609,f23613,f23617,f23621,f23625,f23629,f23633,f23637,f23641,f23645,f23649,f23653,f23657,f23661,f23665,f23669,f23673,f23677,f23681,f23685,f23689,f23693,f23697,f23701,f23705,f23788,f23792,f23796,f23800,f23804,f23808,f23812,f23816,f23820,f23824,f23841,f23845,f23849,f23853,f23857,f23861,f23865,f23869,f23873,f23877,f23895,f23899,f23903,f23907,f23911,f23915,f23919,f23923,f23927,f23931,f24179,f24872,f25922,f25968,f25972,f25976,f25980,f25984,f25988,f26181,f26185,f26189,f26193,f26197,f26201,f26205,f26440,f26936,f26940,f26944,f26948,f26952,f27682,f27686,f27690,f27872,f27876,f27880,f27884,f27888,f27892,f27897,f27901,f27905,f27909,f27913,f27917,f27921,f27925,f27929,f27933,f27937,f27942,f27946,f27950,f28113,f28417,f28698,f28720,f28724,f28728,f28732,f28736,f28740,f28744,f28748,f28753,f28757,f28761,f28765,f28769,f28773,f28777,f28781,f28785,f28789,f28794,f28798,f28802,f28806,f28810,f29172,f29777,f30037,f30041,f30046,f30050,f30054,f30058,f30062,f31367,f31371,f31375,f31379,f31383,f31484,f31541,f31545,f31549,f31553,f31557,f31561,f31565,f31569,f31573,f31577,f31581,f31585,f31589,f31593,f31597,f31601,f31605,f31609,f31614,f31618,f31622,f31626,f31630,f31634,f31638,f31642,f31646,f31650,f31654,f31658,f31662,f31666,f31670,f31674,f31678,f31682,f31686,f31690,f31694,f31698,f31702,f31706,f31710,f31714,f31718,f31722,f31832,f33525,f33661,f33665,f33672,f33676,f33680,f33684,f33688,f33692,f33696,f33700,f33910,f33914,f33918,f33922,f35048,f35052,f35056,f35060,f35065,f35069,f35514,f35518,f35522,f35526,f35531,f35535,f35539,f35689,f35693,f35697,f35863,f35867,f35871,f35875,f35879,f35883,f35887,f35891,f35931,f36430,f37011,f37015,f37019,f37023,f37027,f37031,f37035,f37039,f37043,f37047,f37051,f37055,f37059,f37063,f37067,f37071,f37075,f37145,f38326,f38330,f38334,f38338,f38342,f38346,f38554,f38558,f38562,f38847,f38851,f38855,f38859,f38863,f38867,f39556,f39560,f39564,f39568,f39572,f39576,f39580,f39729,f39733,f39737,f39741,f39745,f39749,f39753,f39757,f39761,f39765,f39914,f39918,f39922,f39926,f39930,f39934,f39938,f39942,f39946,f39950,f40099,f40103,f40107,f40111,f40115,f40119,f40123,f40127,f40131,f40135,f40160,f40164,f40168,f40172,f40176,f40180,f40184,f40188,f40192,f40196,f40204,f40208,f40212,f40216,f40220,f40224,f40228,f40232,f40236,f40240,f40244,f40248,f40252,f40256,f40260,f40264,f40268,f40272,f40276,f40280,f40284,f40288,f40292,f40296,f40300,f40304,f40308,f40312,f40316,f40320,f40324,f40328,f40332,f40336,f40340,f40344,f40348,f40352,f40356,f40360,f40364,f40368,f40372,f40376,f40380,f40384,f40388,f40392,f40616,f41001,f41556,f42446,f45765,f45769,f45924,f45948,f45952,f45956,f45960,f45964,f45968,f45972,f45976,f45980,f45984,f46196,f46200,f46204,f46465,f46616,f46641,f46664,f46668,f46672,f46676,f46680,f46684,f46688,f46692,f46696,f46700,f46704,f46708,f46712,f46716,f46720,f46724,f46728,f46732,f46736,f46740,f46744,f46773,f46777,f46781,f46785,f46887,f46989,f46993,f47065,f47069,f47140,f47144,f47148,f47152,f47156,f47160,f47164,f47168,f47173,f47177,f47181,f47185,f47189,f47193,f47197,f47201,f47205,f47209,f47213,f47218,f47222,f47778,f50647,f50651,f50655,f50659,f50889,f51056,f51060,f51064,f51068,f51072,f51076,f51080,f51184,f51188,f51192,f51196,f51200,f51204,f51208,f51212,f51216,f51220,f51224,f51228,f51232,f51236,f51240,f51244,f51248,f51252,f51256,f51260,f51264,f51268,f51272,f51276,f51280,f51284,f51288,f51292,f51296,f51300,f51304,f51308,f51312,f51316,f51320,f51324,f51328,f51332,f51336,f51340,f51344,f51348,f51352,f51356,f51360,f51364,f51368,f51372,f51376,f51380,f51384,f51388,f51392,f51396,f51400,f51404,f51408,f51412,f51416,f51420,f51424,f51428,f51432,f51436,f51440,f51444,f51448,f51452,f51456,f51460,f51464,f51468,f51472,f51476,f51480,f51484,f51488,f51492,f51496,f51500,f57079,f57114,f57118,f57122,f57126,f57130,f57134,f57138,f57149,f57153,f57182,f57211,f57240,f57400,f57979,f57983,f58035,f58039,f58043,f58047,f58051,f58055,f58059,f58063,f58067,f58071,f58075,f58079,f58083,f58087,f58091,f58095,f58099,f58103,f58107,f58111,f58193,f58197,f58201,f58205,f58209,f58213,f58217,f58221,f58225,f58229,f58233,f58237,f58241,f58245,f58249,f58253,f58257,f58261,f58265,f58269,f58273,f58277,f58281,f60887,f62057,f62061,f62065,f62069,f62330,f62342,f62346,f62817,f62821,f62825,f62829,f62833,f62837,f62841,f62845,f62849,f62853,f63319,f63323,f63327,f63331,f63335,f63339,f63343,f63347,f63351,f63355,f63359,f63363,f63367,f63371,f63375,f63379,f63383,f63387,f63391,f63395,f63399,f63403,f63407,f63411,f63415,f63419,f63423,f63427,f63431,f63435,f63439,f63443,f64338,f65962,f66011,f66015,f66019,f66023,f66079,f66083,f66087,f66091,f66095,f66099,f66103,f66107,f66111,f66115,f66119,f66123,f66127,f66131,f66135,f66139,f66143,f66147,f66151,f66155,f66159,f66163,f66536,f66540,f66544,f66548,f66552,f66556,f66560,f66564,f66568,f66572,f66945,f66949,f66953,f66957,f66961,f66965,f66969,f66973,f66977,f66981,f67354,f67434,f67514,f67518,f67522,f67526,f67530,f67534,f67538,f67542,f67546,f67550,f67554,f67558,f67562,f67566,f67570,f67574,f67578,f67582,f67586,f67590,f67594,f67598,f67602,f67606,f67610,f67614,f67618,f67622,f67636,f67640,f67644,f67648,f67652,f67656,f67660,f67664,f67668,f67672,f67676,f67680,f67684,f67688,f67692,f67696,f67700,f67704,f67708,f67712,f67716,f67720,f67724,f67728,f67732,f67736,f71666,f71972,f73642]) ).
fof(f73642,plain,
( ~ spl22_2
| ~ spl22_1
| ~ spl22_240
| spl22_1678 ),
inference(avatar_split_clause,[],[f73098,f71969,f2694,f224,f229]) ).
fof(f229,plain,
( spl22_2
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_2])]) ).
fof(f224,plain,
( spl22_1
<=> relation(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1])]) ).
fof(f2694,plain,
( spl22_240
<=> ! [X0,X1] :
( ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_240])]) ).
fof(f71969,plain,
( spl22_1678
<=> sP1(relation_dom_restriction(sK5,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1678])]) ).
fof(f73098,plain,
( ~ relation(sK5)
| ~ function(sK5)
| ~ spl22_240
| spl22_1678 ),
inference(resolution,[],[f71971,f2695]) ).
fof(f2695,plain,
( ! [X0,X1] :
( sP1(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_240 ),
inference(avatar_component_clause,[],[f2694]) ).
fof(f71971,plain,
( ~ sP1(relation_dom_restriction(sK5,sK3))
| spl22_1678 ),
inference(avatar_component_clause,[],[f71969]) ).
fof(f71972,plain,
( ~ spl22_1678
| spl22_5
| ~ spl22_47
| ~ spl22_699 ),
inference(avatar_split_clause,[],[f15371,f15300,f462,f244,f71969]) ).
fof(f244,plain,
( spl22_5
<=> in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_5])]) ).
fof(f462,plain,
( spl22_47
<=> ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_47])]) ).
fof(f15300,plain,
( spl22_699
<=> ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_699])]) ).
fof(f15371,plain,
( in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
| ~ sP1(relation_dom_restriction(sK5,sK3))
| ~ spl22_47
| ~ spl22_699 ),
inference(resolution,[],[f15301,f463]) ).
fof(f463,plain,
( ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_47 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f15301,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),X0)
| in(apply(sK5,sK4),X0) )
| ~ spl22_699 ),
inference(avatar_component_clause,[],[f15300]) ).
fof(f71666,plain,
( spl22_1677
| ~ spl22_241
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4440,f4126,f2698,f71664]) ).
fof(f71664,plain,
( spl22_1677
<=> ! [X0,X1] :
( ~ empty(set_intersection2(relation_dom(sK5),X0))
| sP0(relation_dom_restriction(sK5,X0),X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1677])]) ).
fof(f2698,plain,
( spl22_241
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_241])]) ).
fof(f4126,plain,
( spl22_371
<=> ! [X0] : set_intersection2(relation_dom(sK5),X0) = relation_dom(relation_dom_restriction(sK5,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_371])]) ).
fof(f4440,plain,
( ! [X0,X1] :
( ~ empty(set_intersection2(relation_dom(sK5),X0))
| sP0(relation_dom_restriction(sK5,X0),X1)
| ~ empty(X1) )
| ~ spl22_241
| ~ spl22_371 ),
inference(superposition,[],[f2699,f4127]) ).
fof(f4127,plain,
( ! [X0] : set_intersection2(relation_dom(sK5),X0) = relation_dom(relation_dom_restriction(sK5,X0))
| ~ spl22_371 ),
inference(avatar_component_clause,[],[f4126]) ).
fof(f2699,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_241 ),
inference(avatar_component_clause,[],[f2698]) ).
fof(f67736,plain,
( spl22_1676
| ~ spl22_115
| ~ spl22_523 ),
inference(avatar_split_clause,[],[f10016,f9977,f959,f67734]) ).
fof(f67734,plain,
( spl22_1676
<=> ! [X0,X1] :
( apply(sK15,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK15,X0),sK13(X0,X1,sK15))
| sP2(X0,X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1676])]) ).
fof(f959,plain,
( spl22_115
<=> ! [X1] : ~ in(X1,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_115])]) ).
fof(f9977,plain,
( spl22_523
<=> ! [X2,X0,X1] :
( apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X0),sK13(X0,X1,X2))
| in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_523])]) ).
fof(f10016,plain,
( ! [X0,X1] :
( apply(sK15,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK15,X0),sK13(X0,X1,sK15))
| sP2(X0,X1,sK15) )
| ~ spl22_115
| ~ spl22_523 ),
inference(resolution,[],[f9978,f960]) ).
fof(f960,plain,
( ! [X1] : ~ in(X1,sK15)
| ~ spl22_115 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f9978,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X0),sK13(X0,X1,X2))
| sP2(X0,X1,X2) )
| ~ spl22_523 ),
inference(avatar_component_clause,[],[f9977]) ).
fof(f67732,plain,
( spl22_1675
| ~ spl22_115
| ~ spl22_522 ),
inference(avatar_split_clause,[],[f9973,f9934,f959,f67730]) ).
fof(f67730,plain,
( spl22_1675
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK20,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK20,X0),sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1675])]) ).
fof(f9934,plain,
( spl22_522
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2)
| apply(sK20,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK20,X0),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_522])]) ).
fof(f9973,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK20,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK20,X0),sK13(X0,X1,sK15)) )
| ~ spl22_115
| ~ spl22_522 ),
inference(resolution,[],[f9935,f960]) ).
fof(f9935,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(sK20,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK20,X0),sK13(X0,X1,X2)) )
| ~ spl22_522 ),
inference(avatar_component_clause,[],[f9934]) ).
fof(f67728,plain,
( spl22_1674
| ~ spl22_115
| ~ spl22_521 ),
inference(avatar_split_clause,[],[f9930,f9891,f959,f67726]) ).
fof(f67726,plain,
( spl22_1674
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK19,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK19,X0),sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1674])]) ).
fof(f9891,plain,
( spl22_521
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2)
| apply(sK19,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK19,X0),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_521])]) ).
fof(f9930,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK19,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK19,X0),sK13(X0,X1,sK15)) )
| ~ spl22_115
| ~ spl22_521 ),
inference(resolution,[],[f9892,f960]) ).
fof(f9892,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(sK19,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK19,X0),sK13(X0,X1,X2)) )
| ~ spl22_521 ),
inference(avatar_component_clause,[],[f9891]) ).
fof(f67724,plain,
( spl22_1673
| ~ spl22_115
| ~ spl22_520 ),
inference(avatar_split_clause,[],[f9887,f9847,f959,f67722]) ).
fof(f67722,plain,
( spl22_1673
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X0),sK13(sK15,X1,X0)) = apply(sK15,sK13(sK15,X1,X0))
| sP2(sK15,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1673])]) ).
fof(f9847,plain,
( spl22_520
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_520])]) ).
fof(f9887,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X0),sK13(sK15,X1,X0)) = apply(sK15,sK13(sK15,X1,X0))
| sP2(sK15,X1,X0) )
| ~ spl22_115
| ~ spl22_520 ),
inference(resolution,[],[f9848,f960]) ).
fof(f9848,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| sP2(X0,X1,X2) )
| ~ spl22_520 ),
inference(avatar_component_clause,[],[f9847]) ).
fof(f67720,plain,
( spl22_1672
| ~ spl22_53
| ~ spl22_1590 ),
inference(avatar_split_clause,[],[f67120,f66121,f511,f67718]) ).
fof(f67718,plain,
( spl22_1672
<=> ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK20)))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1672])]) ).
fof(f511,plain,
( spl22_53
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_53])]) ).
fof(f66121,plain,
( spl22_1590
<=> ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK20),X0))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1590])]) ).
fof(f67120,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK20)))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) )
| ~ spl22_53
| ~ spl22_1590 ),
inference(superposition,[],[f66122,f512]) ).
fof(f512,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
| ~ spl22_53 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f66122,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK20),X0))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) )
| ~ spl22_1590 ),
inference(avatar_component_clause,[],[f66121]) ).
fof(f67716,plain,
( spl22_1671
| ~ spl22_115
| ~ spl22_519 ),
inference(avatar_split_clause,[],[f9843,f9804,f959,f67714]) ).
fof(f67714,plain,
( spl22_1671
<=> ! [X0,X1] :
( sP2(sK15,X0,X1)
| apply(relation_dom_restriction(sK20,X1),sK13(sK15,X0,X1)) = apply(sK20,sK13(sK15,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1671])]) ).
fof(f9804,plain,
( spl22_519
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| apply(relation_dom_restriction(sK20,X2),sK13(X0,X1,X2)) = apply(sK20,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_519])]) ).
fof(f9843,plain,
( ! [X0,X1] :
( sP2(sK15,X0,X1)
| apply(relation_dom_restriction(sK20,X1),sK13(sK15,X0,X1)) = apply(sK20,sK13(sK15,X0,X1)) )
| ~ spl22_115
| ~ spl22_519 ),
inference(resolution,[],[f9805,f960]) ).
fof(f9805,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK20,X2),sK13(X0,X1,X2)) = apply(sK20,sK13(X0,X1,X2)) )
| ~ spl22_519 ),
inference(avatar_component_clause,[],[f9804]) ).
fof(f67712,plain,
( spl22_1670
| ~ spl22_115
| ~ spl22_518 ),
inference(avatar_split_clause,[],[f9800,f9761,f959,f67710]) ).
fof(f67710,plain,
( spl22_1670
<=> ! [X0,X1] :
( sP2(sK15,X0,X1)
| apply(relation_dom_restriction(sK19,X1),sK13(sK15,X0,X1)) = apply(sK19,sK13(sK15,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1670])]) ).
fof(f9761,plain,
( spl22_518
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| apply(relation_dom_restriction(sK19,X2),sK13(X0,X1,X2)) = apply(sK19,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_518])]) ).
fof(f9800,plain,
( ! [X0,X1] :
( sP2(sK15,X0,X1)
| apply(relation_dom_restriction(sK19,X1),sK13(sK15,X0,X1)) = apply(sK19,sK13(sK15,X0,X1)) )
| ~ spl22_115
| ~ spl22_518 ),
inference(resolution,[],[f9762,f960]) ).
fof(f9762,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK19,X2),sK13(X0,X1,X2)) = apply(sK19,sK13(X0,X1,X2)) )
| ~ spl22_518 ),
inference(avatar_component_clause,[],[f9761]) ).
fof(f67708,plain,
( spl22_1669
| ~ spl22_115
| ~ spl22_517 ),
inference(avatar_split_clause,[],[f9757,f9718,f959,f67706]) ).
fof(f67706,plain,
( spl22_1669
<=> ! [X0,X1] :
( apply(sK15,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK15,X1),sK13(X0,X1,sK15))
| sP2(X0,X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1669])]) ).
fof(f9718,plain,
( spl22_517
<=> ! [X2,X0,X1] :
( apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X1),sK13(X0,X1,X2))
| in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_517])]) ).
fof(f9757,plain,
( ! [X0,X1] :
( apply(sK15,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK15,X1),sK13(X0,X1,sK15))
| sP2(X0,X1,sK15) )
| ~ spl22_115
| ~ spl22_517 ),
inference(resolution,[],[f9719,f960]) ).
fof(f9719,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X1),sK13(X0,X1,X2))
| sP2(X0,X1,X2) )
| ~ spl22_517 ),
inference(avatar_component_clause,[],[f9718]) ).
fof(f67704,plain,
( spl22_1668
| ~ spl22_115
| ~ spl22_516 ),
inference(avatar_split_clause,[],[f9714,f9675,f959,f67702]) ).
fof(f67702,plain,
( spl22_1668
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK20,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK20,X1),sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1668])]) ).
fof(f9675,plain,
( spl22_516
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2)
| apply(sK20,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK20,X1),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_516])]) ).
fof(f9714,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK20,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK20,X1),sK13(X0,X1,sK15)) )
| ~ spl22_115
| ~ spl22_516 ),
inference(resolution,[],[f9676,f960]) ).
fof(f9676,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(sK20,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK20,X1),sK13(X0,X1,X2)) )
| ~ spl22_516 ),
inference(avatar_component_clause,[],[f9675]) ).
fof(f67700,plain,
( spl22_1667
| ~ spl22_115
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f9671,f9623,f959,f67698]) ).
fof(f67698,plain,
( spl22_1667
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK19,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK19,X1),sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1667])]) ).
fof(f9623,plain,
( spl22_513
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2)
| apply(sK19,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK19,X1),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_513])]) ).
fof(f9671,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK19,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK19,X1),sK13(X0,X1,sK15)) )
| ~ spl22_115
| ~ spl22_513 ),
inference(resolution,[],[f9624,f960]) ).
fof(f9624,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(sK19,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK19,X1),sK13(X0,X1,X2)) )
| ~ spl22_513 ),
inference(avatar_component_clause,[],[f9623]) ).
fof(f67696,plain,
( spl22_1666
| ~ spl22_115
| ~ spl22_512 ),
inference(avatar_split_clause,[],[f9619,f9580,f959,f67694]) ).
fof(f67694,plain,
( spl22_1666
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X0),sK13(X1,sK15,X0)) = apply(sK15,sK13(X1,sK15,X0))
| sP2(X1,sK15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1666])]) ).
fof(f9580,plain,
( spl22_512
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_512])]) ).
fof(f9619,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X0),sK13(X1,sK15,X0)) = apply(sK15,sK13(X1,sK15,X0))
| sP2(X1,sK15,X0) )
| ~ spl22_115
| ~ spl22_512 ),
inference(resolution,[],[f9581,f960]) ).
fof(f9581,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| sP2(X0,X1,X2) )
| ~ spl22_512 ),
inference(avatar_component_clause,[],[f9580]) ).
fof(f67692,plain,
( spl22_1665
| ~ spl22_115
| ~ spl22_511 ),
inference(avatar_split_clause,[],[f9576,f9537,f959,f67690]) ).
fof(f67690,plain,
( spl22_1665
<=> ! [X0,X1] :
( sP2(X0,sK15,X1)
| apply(relation_dom_restriction(sK20,X1),sK13(X0,sK15,X1)) = apply(sK20,sK13(X0,sK15,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1665])]) ).
fof(f9537,plain,
( spl22_511
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| apply(relation_dom_restriction(sK20,X2),sK13(X0,X1,X2)) = apply(sK20,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_511])]) ).
fof(f9576,plain,
( ! [X0,X1] :
( sP2(X0,sK15,X1)
| apply(relation_dom_restriction(sK20,X1),sK13(X0,sK15,X1)) = apply(sK20,sK13(X0,sK15,X1)) )
| ~ spl22_115
| ~ spl22_511 ),
inference(resolution,[],[f9538,f960]) ).
fof(f9538,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK20,X2),sK13(X0,X1,X2)) = apply(sK20,sK13(X0,X1,X2)) )
| ~ spl22_511 ),
inference(avatar_component_clause,[],[f9537]) ).
fof(f67688,plain,
( spl22_1664
| ~ spl22_115
| ~ spl22_510 ),
inference(avatar_split_clause,[],[f9533,f9494,f959,f67686]) ).
fof(f67686,plain,
( spl22_1664
<=> ! [X0,X1] :
( sP2(X0,sK15,X1)
| apply(relation_dom_restriction(sK19,X1),sK13(X0,sK15,X1)) = apply(sK19,sK13(X0,sK15,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1664])]) ).
fof(f9494,plain,
( spl22_510
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| apply(relation_dom_restriction(sK19,X2),sK13(X0,X1,X2)) = apply(sK19,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_510])]) ).
fof(f9533,plain,
( ! [X0,X1] :
( sP2(X0,sK15,X1)
| apply(relation_dom_restriction(sK19,X1),sK13(X0,sK15,X1)) = apply(sK19,sK13(X0,sK15,X1)) )
| ~ spl22_115
| ~ spl22_510 ),
inference(resolution,[],[f9495,f960]) ).
fof(f9495,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK19,X2),sK13(X0,X1,X2)) = apply(sK19,sK13(X0,X1,X2)) )
| ~ spl22_510 ),
inference(avatar_component_clause,[],[f9494]) ).
fof(f67684,plain,
( spl22_1663
| ~ spl22_41
| ~ spl22_484 ),
inference(avatar_split_clause,[],[f8709,f8705,f419,f67682]) ).
fof(f67682,plain,
( spl22_1663
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,X1)) = apply(sK15,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1663])]) ).
fof(f419,plain,
( spl22_41
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_41])]) ).
fof(f8705,plain,
( spl22_484
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,X1)) = apply(sK15,sK8(X0,X1))
| sP0(X0,X1)
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_484])]) ).
fof(f8709,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,X1)) = apply(sK15,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_484 ),
inference(resolution,[],[f8706,f420]) ).
fof(f420,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl22_41 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f8706,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,X1)) = apply(sK15,sK8(X0,X1)) )
| ~ spl22_484 ),
inference(avatar_component_clause,[],[f8705]) ).
fof(f67680,plain,
( spl22_1662
| ~ spl22_41
| ~ spl22_483 ),
inference(avatar_split_clause,[],[f8471,f8467,f419,f67678]) ).
fof(f67678,plain,
( spl22_1662
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,X1)) = apply(sK20,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1662])]) ).
fof(f8467,plain,
( spl22_483
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,X1)) = apply(sK20,sK8(X0,X1))
| sP0(X0,X1)
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_483])]) ).
fof(f8471,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,X1)) = apply(sK20,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_483 ),
inference(resolution,[],[f8468,f420]) ).
fof(f8468,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,X1)) = apply(sK20,sK8(X0,X1)) )
| ~ spl22_483 ),
inference(avatar_component_clause,[],[f8467]) ).
fof(f67676,plain,
( spl22_1661
| ~ spl22_53
| ~ spl22_1579 ),
inference(avatar_split_clause,[],[f66711,f66077,f511,f67674]) ).
fof(f67674,plain,
( spl22_1661
<=> ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK19)))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1661])]) ).
fof(f66077,plain,
( spl22_1579
<=> ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK19),X0))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1579])]) ).
fof(f66711,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK19)))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) )
| ~ spl22_53
| ~ spl22_1579 ),
inference(superposition,[],[f66078,f512]) ).
fof(f66078,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK19),X0))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) )
| ~ spl22_1579 ),
inference(avatar_component_clause,[],[f66077]) ).
fof(f67672,plain,
( spl22_1660
| ~ spl22_41
| ~ spl22_482 ),
inference(avatar_split_clause,[],[f8434,f8430,f419,f67670]) ).
fof(f67670,plain,
( spl22_1660
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,X1)) = apply(sK19,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1660])]) ).
fof(f8430,plain,
( spl22_482
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,X1)) = apply(sK19,sK8(X0,X1))
| sP0(X0,X1)
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_482])]) ).
fof(f8434,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,X1)) = apply(sK19,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_482 ),
inference(resolution,[],[f8431,f420]) ).
fof(f8431,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,X1)) = apply(sK19,sK8(X0,X1)) )
| ~ spl22_482 ),
inference(avatar_component_clause,[],[f8430]) ).
fof(f67668,plain,
( spl22_1659
| ~ spl22_41
| ~ spl22_481 ),
inference(avatar_split_clause,[],[f8423,f8415,f419,f67666]) ).
fof(f67666,plain,
( spl22_1659
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1))
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1659])]) ).
fof(f8415,plain,
( spl22_481
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X0),sK7(X1,X0)) = apply(sK15,sK7(X1,X0))
| sP0(X1,X0)
| in(sK8(X1,X0),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_481])]) ).
fof(f8423,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1))
| ~ empty(relation_dom(X0)) )
| ~ spl22_41
| ~ spl22_481 ),
inference(resolution,[],[f8416,f420]) ).
fof(f8416,plain,
( ! [X0,X1] :
( in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0)
| apply(relation_dom_restriction(sK15,X0),sK7(X1,X0)) = apply(sK15,sK7(X1,X0)) )
| ~ spl22_481 ),
inference(avatar_component_clause,[],[f8415]) ).
fof(f67664,plain,
( spl22_1658
| ~ spl22_233
| ~ spl22_481 ),
inference(avatar_split_clause,[],[f8419,f8415,f2559,f67662]) ).
fof(f67662,plain,
( spl22_1658
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1658])]) ).
fof(f2559,plain,
( spl22_233
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_233])]) ).
fof(f8419,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_481 ),
inference(resolution,[],[f8416,f2560]) ).
fof(f2560,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,sK15) )
| ~ spl22_233 ),
inference(avatar_component_clause,[],[f2559]) ).
fof(f67660,plain,
( spl22_1657
| ~ spl22_41
| ~ spl22_480 ),
inference(avatar_split_clause,[],[f8408,f8400,f419,f67658]) ).
fof(f67658,plain,
( spl22_1657
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,X1),sK7(X0,X1)) = apply(sK20,sK7(X0,X1))
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1657])]) ).
fof(f8400,plain,
( spl22_480
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK20,X0),sK7(X1,X0)) = apply(sK20,sK7(X1,X0))
| sP0(X1,X0)
| in(sK8(X1,X0),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_480])]) ).
fof(f8408,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,X1),sK7(X0,X1)) = apply(sK20,sK7(X0,X1))
| ~ empty(relation_dom(X0)) )
| ~ spl22_41
| ~ spl22_480 ),
inference(resolution,[],[f8401,f420]) ).
fof(f8401,plain,
( ! [X0,X1] :
( in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0)
| apply(relation_dom_restriction(sK20,X0),sK7(X1,X0)) = apply(sK20,sK7(X1,X0)) )
| ~ spl22_480 ),
inference(avatar_component_clause,[],[f8400]) ).
fof(f67656,plain,
( spl22_1656
| ~ spl22_233
| ~ spl22_480 ),
inference(avatar_split_clause,[],[f8404,f8400,f2559,f67654]) ).
fof(f67654,plain,
( spl22_1656
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,X1),sK7(X0,X1)) = apply(sK20,sK7(X0,X1))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1656])]) ).
fof(f8404,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,X1),sK7(X0,X1)) = apply(sK20,sK7(X0,X1))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_480 ),
inference(resolution,[],[f8401,f2560]) ).
fof(f67652,plain,
( spl22_1655
| ~ spl22_41
| ~ spl22_479 ),
inference(avatar_split_clause,[],[f8393,f8385,f419,f67650]) ).
fof(f67650,plain,
( spl22_1655
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,X1),sK7(X0,X1)) = apply(sK19,sK7(X0,X1))
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1655])]) ).
fof(f8385,plain,
( spl22_479
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK19,X0),sK7(X1,X0)) = apply(sK19,sK7(X1,X0))
| sP0(X1,X0)
| in(sK8(X1,X0),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_479])]) ).
fof(f8393,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,X1),sK7(X0,X1)) = apply(sK19,sK7(X0,X1))
| ~ empty(relation_dom(X0)) )
| ~ spl22_41
| ~ spl22_479 ),
inference(resolution,[],[f8386,f420]) ).
fof(f8386,plain,
( ! [X0,X1] :
( in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0)
| apply(relation_dom_restriction(sK19,X0),sK7(X1,X0)) = apply(sK19,sK7(X1,X0)) )
| ~ spl22_479 ),
inference(avatar_component_clause,[],[f8385]) ).
fof(f67648,plain,
( spl22_1654
| ~ spl22_233
| ~ spl22_479 ),
inference(avatar_split_clause,[],[f8389,f8385,f2559,f67646]) ).
fof(f67646,plain,
( spl22_1654
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,X1),sK7(X0,X1)) = apply(sK19,sK7(X0,X1))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1654])]) ).
fof(f8389,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,X1),sK7(X0,X1)) = apply(sK19,sK7(X0,X1))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_479 ),
inference(resolution,[],[f8386,f2560]) ).
fof(f67644,plain,
( spl22_1653
| ~ spl22_233
| ~ spl22_460 ),
inference(avatar_split_clause,[],[f8012,f6409,f2559,f67642]) ).
fof(f67642,plain,
( spl22_1653
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1653])]) ).
fof(f6409,plain,
( spl22_460
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_460])]) ).
fof(f8012,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_460 ),
inference(resolution,[],[f6410,f2560]) ).
fof(f6410,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_460 ),
inference(avatar_component_clause,[],[f6409]) ).
fof(f67640,plain,
( spl22_1652
| ~ spl22_233
| ~ spl22_459 ),
inference(avatar_split_clause,[],[f7962,f6405,f2559,f67638]) ).
fof(f67638,plain,
( spl22_1652
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1652])]) ).
fof(f6405,plain,
( spl22_459
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_459])]) ).
fof(f7962,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_459 ),
inference(resolution,[],[f6406,f2560]) ).
fof(f6406,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_459 ),
inference(avatar_component_clause,[],[f6405]) ).
fof(f67636,plain,
( spl22_1651
| ~ spl22_233
| ~ spl22_456 ),
inference(avatar_split_clause,[],[f7811,f6393,f2559,f67634]) ).
fof(f67634,plain,
( spl22_1651
<=> ! [X0,X3,X2,X1] :
( element(sK13(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| sP2(set_intersection2(relation_dom(X0),X1),X2,X3)
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1651])]) ).
fof(f6393,plain,
( spl22_456
<=> ! [X0,X3,X2,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_456])]) ).
fof(f7811,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| sP2(set_intersection2(relation_dom(X0),X1),X2,X3)
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_456 ),
inference(resolution,[],[f6394,f2560]) ).
fof(f6394,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X0)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_456 ),
inference(avatar_component_clause,[],[f6393]) ).
fof(f67622,plain,
( spl22_1650
| ~ spl22_233
| ~ spl22_455 ),
inference(avatar_split_clause,[],[f7760,f6389,f2559,f67620]) ).
fof(f67620,plain,
( spl22_1650
<=> ! [X0,X3,X2,X1] :
( element(sK13(set_intersection2(X0,relation_dom(X1)),X2,X3),X3)
| sP2(set_intersection2(X0,relation_dom(X1)),X2,X3)
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1650])]) ).
fof(f6389,plain,
( spl22_455
<=> ! [X0,X3,X2,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_455])]) ).
fof(f7760,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(X0,relation_dom(X1)),X2,X3),X3)
| sP2(set_intersection2(X0,relation_dom(X1)),X2,X3)
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_455 ),
inference(resolution,[],[f6390,f2560]) ).
fof(f6390,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X1)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_455 ),
inference(avatar_component_clause,[],[f6389]) ).
fof(f67618,plain,
( spl22_1649
| ~ spl22_233
| ~ spl22_452 ),
inference(avatar_split_clause,[],[f7611,f6369,f2559,f67616]) ).
fof(f67616,plain,
( spl22_1649
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1649])]) ).
fof(f6369,plain,
( spl22_452
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_452])]) ).
fof(f7611,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_452 ),
inference(resolution,[],[f6370,f2560]) ).
fof(f6370,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_452 ),
inference(avatar_component_clause,[],[f6369]) ).
fof(f67614,plain,
( spl22_1648
| ~ spl22_233
| ~ spl22_451 ),
inference(avatar_split_clause,[],[f7553,f6365,f2559,f67612]) ).
fof(f67612,plain,
( spl22_1648
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1648])]) ).
fof(f6365,plain,
( spl22_451
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_451])]) ).
fof(f7553,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_451 ),
inference(resolution,[],[f6366,f2560]) ).
fof(f6366,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_451 ),
inference(avatar_component_clause,[],[f6365]) ).
fof(f67610,plain,
( spl22_1647
| ~ spl22_233
| ~ spl22_448 ),
inference(avatar_split_clause,[],[f7408,f6353,f2559,f67608]) ).
fof(f67608,plain,
( spl22_1647
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| sP2(X0,set_intersection2(relation_dom(X1),X2),X3)
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1647])]) ).
fof(f6353,plain,
( spl22_448
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_448])]) ).
fof(f7408,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| sP2(X0,set_intersection2(relation_dom(X1),X2),X3)
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_448 ),
inference(resolution,[],[f6354,f2560]) ).
fof(f6354,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X1)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_448 ),
inference(avatar_component_clause,[],[f6353]) ).
fof(f67606,plain,
( spl22_1646
| ~ spl22_233
| ~ spl22_447 ),
inference(avatar_split_clause,[],[f7360,f6349,f2559,f67604]) ).
fof(f67604,plain,
( spl22_1646
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| sP2(X0,set_intersection2(X1,relation_dom(X2)),X3)
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1646])]) ).
fof(f6349,plain,
( spl22_447
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_447])]) ).
fof(f7360,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| sP2(X0,set_intersection2(X1,relation_dom(X2)),X3)
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_447 ),
inference(resolution,[],[f6350,f2560]) ).
fof(f6350,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X2)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_447 ),
inference(avatar_component_clause,[],[f6349]) ).
fof(f67602,plain,
( spl22_1645
| ~ spl22_233
| ~ spl22_442 ),
inference(avatar_split_clause,[],[f7166,f6309,f2559,f67600]) ).
fof(f67600,plain,
( spl22_1645
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(X0,relation_dom(X1)),X2,X3),X3)
| sP2(set_intersection2(X0,relation_dom(X1)),X2,X3)
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1645])]) ).
fof(f6309,plain,
( spl22_442
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X1)
| in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_442])]) ).
fof(f7166,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,relation_dom(X1)),X2,X3),X3)
| sP2(set_intersection2(X0,relation_dom(X1)),X2,X3)
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_442 ),
inference(resolution,[],[f6310,f2560]) ).
fof(f6310,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X1)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_442 ),
inference(avatar_component_clause,[],[f6309]) ).
fof(f67598,plain,
( spl22_1644
| ~ spl22_233
| ~ spl22_442 ),
inference(avatar_split_clause,[],[f7136,f6309,f2559,f67596]) ).
fof(f67596,plain,
( spl22_1644
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(X0,X1),X2,relation_dom(X3)),X1)
| sP2(set_intersection2(X0,X1),X2,relation_dom(X3))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1644])]) ).
fof(f7136,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,relation_dom(X3)),X1)
| sP2(set_intersection2(X0,X1),X2,relation_dom(X3))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_442 ),
inference(resolution,[],[f6310,f2560]) ).
fof(f67594,plain,
( spl22_1643
| ~ spl22_233
| ~ spl22_441 ),
inference(avatar_split_clause,[],[f7085,f6305,f2559,f67592]) ).
fof(f67592,plain,
( spl22_1643
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| sP2(X0,set_intersection2(X1,relation_dom(X2)),X3)
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1643])]) ).
fof(f6305,plain,
( spl22_441
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X2)
| in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_441])]) ).
fof(f7085,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| sP2(X0,set_intersection2(X1,relation_dom(X2)),X3)
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_441 ),
inference(resolution,[],[f6306,f2560]) ).
fof(f6306,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X2)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_441 ),
inference(avatar_component_clause,[],[f6305]) ).
fof(f67590,plain,
( spl22_1642
| ~ spl22_233
| ~ spl22_441 ),
inference(avatar_split_clause,[],[f7056,f6305,f2559,f67588]) ).
fof(f67588,plain,
( spl22_1642
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(X1,X2),relation_dom(X3)),X2)
| sP2(X0,set_intersection2(X1,X2),relation_dom(X3))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1642])]) ).
fof(f7056,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),relation_dom(X3)),X2)
| sP2(X0,set_intersection2(X1,X2),relation_dom(X3))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_441 ),
inference(resolution,[],[f6306,f2560]) ).
fof(f67586,plain,
( spl22_1641
| ~ spl22_233
| ~ spl22_440 ),
inference(avatar_split_clause,[],[f7009,f6301,f2559,f67584]) ).
fof(f67584,plain,
( spl22_1641
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| sP2(X0,relation_dom(X1),set_intersection2(X2,X3))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1641])]) ).
fof(f6301,plain,
( spl22_440
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_440])]) ).
fof(f7009,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| sP2(X0,relation_dom(X1),set_intersection2(X2,X3))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_440 ),
inference(resolution,[],[f6302,f2560]) ).
fof(f6302,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_440 ),
inference(avatar_component_clause,[],[f6301]) ).
fof(f67582,plain,
( ~ spl22_105
| spl22_1640
| ~ spl22_61
| ~ spl22_202
| ~ spl22_876 ),
inference(avatar_split_clause,[],[f21967,f19891,f2161,f578,f67580,f907]) ).
fof(f907,plain,
( spl22_105
<=> sP1(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_105])]) ).
fof(f67580,plain,
( spl22_1640
<=> ! [X0] :
( relation_dom(X0) = sK15
| ~ sP1(X0)
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1640])]) ).
fof(f578,plain,
( spl22_61
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_61])]) ).
fof(f2161,plain,
( spl22_202
<=> sK15 = relation_rng(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_202])]) ).
fof(f19891,plain,
( spl22_876
<=> ! [X0] :
( sP0(sK15,relation_dom(X0))
| ~ empty(relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_876])]) ).
fof(f21967,plain,
( ! [X0] :
( relation_dom(X0) = sK15
| ~ empty(relation_rng(X0))
| ~ sP1(X0)
| ~ sP1(sK15) )
| ~ spl22_61
| ~ spl22_202
| ~ spl22_876 ),
inference(forward_demodulation,[],[f21902,f2163]) ).
fof(f2163,plain,
( sK15 = relation_rng(sK15)
| ~ spl22_202 ),
inference(avatar_component_clause,[],[f2161]) ).
fof(f21902,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| ~ sP1(X0)
| relation_dom(X0) = relation_rng(sK15)
| ~ sP1(sK15) )
| ~ spl22_61
| ~ spl22_876 ),
inference(resolution,[],[f19892,f579]) ).
fof(f579,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| relation_rng(X0) = X1
| ~ sP1(X0) )
| ~ spl22_61 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f19892,plain,
( ! [X0] :
( sP0(sK15,relation_dom(X0))
| ~ empty(relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_876 ),
inference(avatar_component_clause,[],[f19891]) ).
fof(f67578,plain,
( spl22_1639
| ~ spl22_233
| ~ spl22_440 ),
inference(avatar_split_clause,[],[f6979,f6301,f2559,f67576]) ).
fof(f67576,plain,
( spl22_1639
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1639])]) ).
fof(f6979,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_440 ),
inference(resolution,[],[f6302,f2560]) ).
fof(f67574,plain,
( spl22_1638
| ~ spl22_233
| ~ spl22_439 ),
inference(avatar_split_clause,[],[f6933,f6297,f2559,f67572]) ).
fof(f67572,plain,
( spl22_1638
<=> ! [X0,X3,X2,X1] :
( in(sK13(relation_dom(X0),X1,set_intersection2(X2,X3)),X3)
| sP2(relation_dom(X0),X1,set_intersection2(X2,X3))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1638])]) ).
fof(f6297,plain,
( spl22_439
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_439])]) ).
fof(f6933,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(relation_dom(X0),X1,set_intersection2(X2,X3)),X3)
| sP2(relation_dom(X0),X1,set_intersection2(X2,X3))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_439 ),
inference(resolution,[],[f6298,f2560]) ).
fof(f6298,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_439 ),
inference(avatar_component_clause,[],[f6297]) ).
fof(f67570,plain,
( spl22_1637
| ~ spl22_233
| ~ spl22_439 ),
inference(avatar_split_clause,[],[f6903,f6297,f2559,f67568]) ).
fof(f67568,plain,
( spl22_1637
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1637])]) ).
fof(f6903,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,relation_dom(X3))),X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_439 ),
inference(resolution,[],[f6298,f2560]) ).
fof(f67566,plain,
( spl22_1636
| ~ spl22_233
| ~ spl22_438 ),
inference(avatar_split_clause,[],[f6851,f6293,f2559,f67564]) ).
fof(f67564,plain,
( spl22_1636
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| sP2(set_intersection2(relation_dom(X0),X1),X2,X3)
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1636])]) ).
fof(f6293,plain,
( spl22_438
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X0)
| in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_438])]) ).
fof(f6851,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| sP2(set_intersection2(relation_dom(X0),X1),X2,X3)
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_438 ),
inference(resolution,[],[f6294,f2560]) ).
fof(f6294,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X0)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_438 ),
inference(avatar_component_clause,[],[f6293]) ).
fof(f67562,plain,
( spl22_1635
| ~ spl22_233
| ~ spl22_438 ),
inference(avatar_split_clause,[],[f6821,f6293,f2559,f67560]) ).
fof(f67560,plain,
( spl22_1635
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(X0,X1),X2,relation_dom(X3)),X0)
| sP2(set_intersection2(X0,X1),X2,relation_dom(X3))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1635])]) ).
fof(f6821,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,relation_dom(X3)),X0)
| sP2(set_intersection2(X0,X1),X2,relation_dom(X3))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_438 ),
inference(resolution,[],[f6294,f2560]) ).
fof(f67558,plain,
( spl22_1634
| ~ spl22_233
| ~ spl22_437 ),
inference(avatar_split_clause,[],[f6768,f6289,f2559,f67556]) ).
fof(f67556,plain,
( spl22_1634
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| sP2(X0,set_intersection2(relation_dom(X1),X2),X3)
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1634])]) ).
fof(f6289,plain,
( spl22_437
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X1)
| in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_437])]) ).
fof(f6768,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| sP2(X0,set_intersection2(relation_dom(X1),X2),X3)
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_437 ),
inference(resolution,[],[f6290,f2560]) ).
fof(f6290,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X1)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_437 ),
inference(avatar_component_clause,[],[f6289]) ).
fof(f67554,plain,
( spl22_1633
| ~ spl22_233
| ~ spl22_437 ),
inference(avatar_split_clause,[],[f6739,f6289,f2559,f67552]) ).
fof(f67552,plain,
( spl22_1633
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(X1,X2),relation_dom(X3)),X1)
| sP2(X0,set_intersection2(X1,X2),relation_dom(X3))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1633])]) ).
fof(f6739,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),relation_dom(X3)),X1)
| sP2(X0,set_intersection2(X1,X2),relation_dom(X3))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_437 ),
inference(resolution,[],[f6290,f2560]) ).
fof(f67550,plain,
( spl22_1632
| ~ spl22_233
| ~ spl22_436 ),
inference(avatar_split_clause,[],[f6686,f6285,f2559,f67548]) ).
fof(f67548,plain,
( spl22_1632
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| sP2(X0,relation_dom(X1),set_intersection2(X2,X3))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1632])]) ).
fof(f6285,plain,
( spl22_436
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_436])]) ).
fof(f6686,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| sP2(X0,relation_dom(X1),set_intersection2(X2,X3))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_436 ),
inference(resolution,[],[f6286,f2560]) ).
fof(f6286,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_436 ),
inference(avatar_component_clause,[],[f6285]) ).
fof(f67546,plain,
( spl22_1631
| ~ spl22_233
| ~ spl22_436 ),
inference(avatar_split_clause,[],[f6656,f6285,f2559,f67544]) ).
fof(f67544,plain,
( spl22_1631
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1631])]) ).
fof(f6656,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_436 ),
inference(resolution,[],[f6286,f2560]) ).
fof(f67542,plain,
( spl22_1630
| ~ spl22_233
| ~ spl22_435 ),
inference(avatar_split_clause,[],[f6604,f6281,f2559,f67540]) ).
fof(f67540,plain,
( spl22_1630
<=> ! [X0,X3,X2,X1] :
( in(sK13(relation_dom(X0),X1,set_intersection2(X2,X3)),X2)
| sP2(relation_dom(X0),X1,set_intersection2(X2,X3))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1630])]) ).
fof(f6281,plain,
( spl22_435
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_435])]) ).
fof(f6604,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(relation_dom(X0),X1,set_intersection2(X2,X3)),X2)
| sP2(relation_dom(X0),X1,set_intersection2(X2,X3))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_435 ),
inference(resolution,[],[f6282,f2560]) ).
fof(f6282,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_435 ),
inference(avatar_component_clause,[],[f6281]) ).
fof(f67538,plain,
( spl22_1629
| ~ spl22_68
| ~ spl22_203
| ~ spl22_809 ),
inference(avatar_split_clause,[],[f17667,f17544,f2166,f624,f67536]) ).
fof(f67536,plain,
( spl22_1629
<=> ! [X0,X1] :
( in(sK9(sK15,X1),sK15)
| ~ empty(X0)
| ~ in(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1629])]) ).
fof(f624,plain,
( spl22_68
<=> ! [X5,X0,X1] :
( in(sK9(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_68])]) ).
fof(f2166,plain,
( spl22_203
<=> sK15 = relation_dom(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_203])]) ).
fof(f17544,plain,
( spl22_809
<=> ! [X0] :
( ~ empty(X0)
| sP0(sK15,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_809])]) ).
fof(f17667,plain,
( ! [X0,X1] :
( in(sK9(sK15,X1),sK15)
| ~ empty(X0)
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_68
| ~ spl22_203
| ~ spl22_809 ),
inference(forward_demodulation,[],[f17607,f2168]) ).
fof(f2168,plain,
( sK15 = relation_dom(sK15)
| ~ spl22_203 ),
inference(avatar_component_clause,[],[f2166]) ).
fof(f17607,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X0))
| in(sK9(sK15,X1),relation_dom(sK15)) )
| ~ spl22_68
| ~ spl22_809 ),
inference(resolution,[],[f17545,f625]) ).
fof(f625,plain,
( ! [X0,X1,X5] :
( ~ sP0(X0,X1)
| ~ in(X5,X1)
| in(sK9(X0,X5),relation_dom(X0)) )
| ~ spl22_68 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f17545,plain,
( ! [X0] :
( sP0(sK15,relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_809 ),
inference(avatar_component_clause,[],[f17544]) ).
fof(f67534,plain,
( spl22_1628
| ~ spl22_233
| ~ spl22_435 ),
inference(avatar_split_clause,[],[f6574,f6281,f2559,f67532]) ).
fof(f67532,plain,
( spl22_1628
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1628])]) ).
fof(f6574,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(relation_dom(X2),X3)),X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_435 ),
inference(resolution,[],[f6282,f2560]) ).
fof(f67530,plain,
( spl22_1627
| ~ spl22_233
| ~ spl22_434 ),
inference(avatar_split_clause,[],[f6543,f6277,f2559,f67528]) ).
fof(f67528,plain,
( spl22_1627
<=> ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,relation_dom(X2)),X0)
| sP2(sK10(powerset(X0)),X1,relation_dom(X2))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1627])]) ).
fof(f6277,plain,
( spl22_434
<=> ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X0)
| in(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_434])]) ).
fof(f6543,plain,
( ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,relation_dom(X2)),X0)
| sP2(sK10(powerset(X0)),X1,relation_dom(X2))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_434 ),
inference(resolution,[],[f6278,f2560]) ).
fof(f6278,plain,
( ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X0)
| in(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2) )
| ~ spl22_434 ),
inference(avatar_component_clause,[],[f6277]) ).
fof(f67526,plain,
( spl22_1626
| ~ spl22_233
| ~ spl22_433 ),
inference(avatar_split_clause,[],[f6508,f6273,f2559,f67524]) ).
fof(f67524,plain,
( spl22_1626
<=> ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),relation_dom(X2)),X1)
| sP2(X0,sK10(powerset(X1)),relation_dom(X2))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1626])]) ).
fof(f6273,plain,
( spl22_433
<=> ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X1)
| in(sK13(X0,sK10(powerset(X1)),X2),X2)
| sP2(X0,sK10(powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_433])]) ).
fof(f6508,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),relation_dom(X2)),X1)
| sP2(X0,sK10(powerset(X1)),relation_dom(X2))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_433 ),
inference(resolution,[],[f6274,f2560]) ).
fof(f6274,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X1)
| in(sK13(X0,sK10(powerset(X1)),X2),X2)
| sP2(X0,sK10(powerset(X1)),X2) )
| ~ spl22_433 ),
inference(avatar_component_clause,[],[f6273]) ).
fof(f67522,plain,
( spl22_1625
| ~ spl22_233
| ~ spl22_432 ),
inference(avatar_split_clause,[],[f6473,f6240,f2559,f67520]) ).
fof(f67520,plain,
( spl22_1625
<=> ! [X2,X0,X1] :
( element(sK13(X0,relation_dom(X1),sK10(powerset(X2))),X2)
| sP2(X0,relation_dom(X1),sK10(powerset(X2)))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1625])]) ).
fof(f6240,plain,
( spl22_432
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_432])]) ).
fof(f6473,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,relation_dom(X1),sK10(powerset(X2))),X2)
| sP2(X0,relation_dom(X1),sK10(powerset(X2)))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_432 ),
inference(resolution,[],[f6241,f2560]) ).
fof(f6241,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_432 ),
inference(avatar_component_clause,[],[f6240]) ).
fof(f67518,plain,
( spl22_1624
| ~ spl22_233
| ~ spl22_431 ),
inference(avatar_split_clause,[],[f6432,f6236,f2559,f67516]) ).
fof(f67516,plain,
( spl22_1624
<=> ! [X2,X0,X1] :
( element(sK13(relation_dom(X0),X1,sK10(powerset(X2))),X2)
| sP2(relation_dom(X0),X1,sK10(powerset(X2)))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1624])]) ).
fof(f6236,plain,
( spl22_431
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_431])]) ).
fof(f6432,plain,
( ! [X2,X0,X1] :
( element(sK13(relation_dom(X0),X1,sK10(powerset(X2))),X2)
| sP2(relation_dom(X0),X1,sK10(powerset(X2)))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_431 ),
inference(resolution,[],[f6237,f2560]) ).
fof(f6237,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_431 ),
inference(avatar_component_clause,[],[f6236]) ).
fof(f67514,plain,
( spl22_1623
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5861,f5675,f798,f254,f410,f67512]) ).
fof(f67512,plain,
( spl22_1623
<=> ! [X0] :
( apply(relation_dom_restriction(sK15,powerset(X0)),sK6(X0)) = apply(sK15,sK6(X0))
| empty(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1623])]) ).
fof(f410,plain,
( spl22_39
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_39])]) ).
fof(f254,plain,
( spl22_7
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_7])]) ).
fof(f798,plain,
( spl22_92
<=> empty_set = sK15 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_92])]) ).
fof(f5675,plain,
( spl22_418
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(X0)
| apply(relation_dom_restriction(X1,powerset(X0)),sK6(X0)) = apply(X1,sK6(X0))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_418])]) ).
fof(f5861,plain,
( ! [X0] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,powerset(X0)),sK6(X0)) = apply(sK15,sK6(X0))
| empty(X0)
| empty(powerset(X0)) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_418 ),
inference(forward_demodulation,[],[f5860,f800]) ).
fof(f800,plain,
( empty_set = sK15
| ~ spl22_92 ),
inference(avatar_component_clause,[],[f798]) ).
fof(f5860,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK15,powerset(X0)),sK6(X0)) = apply(sK15,sK6(X0))
| empty(X0)
| ~ function(empty_set)
| empty(powerset(X0)) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_418 ),
inference(forward_demodulation,[],[f5851,f800]) ).
fof(f5851,plain,
( ! [X0] :
( empty(X0)
| apply(relation_dom_restriction(empty_set,powerset(X0)),sK6(X0)) = apply(empty_set,sK6(X0))
| ~ function(empty_set)
| empty(powerset(X0)) )
| ~ spl22_7
| ~ spl22_418 ),
inference(resolution,[],[f5676,f256]) ).
fof(f256,plain,
( relation(empty_set)
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f5676,plain,
( ! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| apply(relation_dom_restriction(X1,powerset(X0)),sK6(X0)) = apply(X1,sK6(X0))
| ~ function(X1)
| empty(powerset(X0)) )
| ~ spl22_418 ),
inference(avatar_component_clause,[],[f5675]) ).
fof(f67434,plain,
( ~ spl22_20
| spl22_1622
| ~ spl22_19
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5858,f5675,f314,f67432,f319]) ).
fof(f319,plain,
( spl22_20
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_20])]) ).
fof(f67432,plain,
( spl22_1622
<=> ! [X0] :
( empty(X0)
| empty(powerset(X0))
| apply(relation_dom_restriction(sK20,powerset(X0)),sK6(X0)) = apply(sK20,sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1622])]) ).
fof(f314,plain,
( spl22_19
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_19])]) ).
fof(f5858,plain,
( ! [X0] :
( empty(X0)
| apply(relation_dom_restriction(sK20,powerset(X0)),sK6(X0)) = apply(sK20,sK6(X0))
| ~ function(sK20)
| empty(powerset(X0)) )
| ~ spl22_19
| ~ spl22_418 ),
inference(resolution,[],[f5676,f316]) ).
fof(f316,plain,
( relation(sK20)
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f67354,plain,
( ~ spl22_18
| spl22_1621
| ~ spl22_17
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5857,f5675,f304,f67352,f309]) ).
fof(f309,plain,
( spl22_18
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_18])]) ).
fof(f67352,plain,
( spl22_1621
<=> ! [X0] :
( empty(X0)
| empty(powerset(X0))
| apply(relation_dom_restriction(sK19,powerset(X0)),sK6(X0)) = apply(sK19,sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1621])]) ).
fof(f304,plain,
( spl22_17
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_17])]) ).
fof(f5857,plain,
( ! [X0] :
( empty(X0)
| apply(relation_dom_restriction(sK19,powerset(X0)),sK6(X0)) = apply(sK19,sK6(X0))
| ~ function(sK19)
| empty(powerset(X0)) )
| ~ spl22_17
| ~ spl22_418 ),
inference(resolution,[],[f5676,f306]) ).
fof(f306,plain,
( relation(sK19)
| ~ spl22_17 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f66981,plain,
( spl22_1620
| ~ spl22_233
| ~ spl22_417 ),
inference(avatar_split_clause,[],[f5830,f5671,f2559,f66979]) ).
fof(f66979,plain,
( spl22_1620
<=> ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,relation_dom(X2)),X0)
| empty(X0)
| sP2(sK6(X0),X1,relation_dom(X2))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1620])]) ).
fof(f5671,plain,
( spl22_417
<=> ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,X2),X0)
| empty(X0)
| in(sK13(sK6(X0),X1,X2),X2)
| sP2(sK6(X0),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_417])]) ).
fof(f5830,plain,
( ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,relation_dom(X2)),X0)
| empty(X0)
| sP2(sK6(X0),X1,relation_dom(X2))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_417 ),
inference(resolution,[],[f5672,f2560]) ).
fof(f5672,plain,
( ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,X2),X0)
| in(sK13(sK6(X0),X1,X2),X2)
| empty(X0)
| sP2(sK6(X0),X1,X2) )
| ~ spl22_417 ),
inference(avatar_component_clause,[],[f5671]) ).
fof(f66977,plain,
( spl22_1619
| ~ spl22_233
| ~ spl22_416 ),
inference(avatar_split_clause,[],[f5799,f5667,f2559,f66975]) ).
fof(f66975,plain,
( spl22_1619
<=> ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),relation_dom(X2)),X1)
| empty(X1)
| sP2(X0,sK6(X1),relation_dom(X2))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1619])]) ).
fof(f5667,plain,
( spl22_416
<=> ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),X2),X1)
| empty(X1)
| in(sK13(X0,sK6(X1),X2),X2)
| sP2(X0,sK6(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_416])]) ).
fof(f5799,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),relation_dom(X2)),X1)
| empty(X1)
| sP2(X0,sK6(X1),relation_dom(X2))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_416 ),
inference(resolution,[],[f5668,f2560]) ).
fof(f5668,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),X2),X1)
| in(sK13(X0,sK6(X1),X2),X2)
| empty(X1)
| sP2(X0,sK6(X1),X2) )
| ~ spl22_416 ),
inference(avatar_component_clause,[],[f5667]) ).
fof(f66973,plain,
( spl22_1618
| ~ spl22_233
| ~ spl22_414 ),
inference(avatar_split_clause,[],[f5768,f5659,f2559,f66971]) ).
fof(f66971,plain,
( spl22_1618
<=> ! [X2,X0,X1] :
( element(sK13(X0,relation_dom(X1),sK6(X2)),X2)
| empty(X2)
| sP2(X0,relation_dom(X1),sK6(X2))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1618])]) ).
fof(f5659,plain,
( spl22_414
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2)
| in(sK13(X0,X1,sK6(X2)),X1)
| sP2(X0,X1,sK6(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_414])]) ).
fof(f5768,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,relation_dom(X1),sK6(X2)),X2)
| empty(X2)
| sP2(X0,relation_dom(X1),sK6(X2))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_414 ),
inference(resolution,[],[f5660,f2560]) ).
fof(f5660,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| in(sK13(X0,X1,sK6(X2)),X1)
| empty(X2)
| sP2(X0,X1,sK6(X2)) )
| ~ spl22_414 ),
inference(avatar_component_clause,[],[f5659]) ).
fof(f66969,plain,
( spl22_1617
| ~ spl22_233
| ~ spl22_413 ),
inference(avatar_split_clause,[],[f5737,f5655,f2559,f66967]) ).
fof(f66967,plain,
( spl22_1617
<=> ! [X2,X0,X1] :
( element(sK13(relation_dom(X0),X1,sK6(X2)),X2)
| empty(X2)
| sP2(relation_dom(X0),X1,sK6(X2))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1617])]) ).
fof(f5655,plain,
( spl22_413
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2)
| in(sK13(X0,X1,sK6(X2)),X0)
| sP2(X0,X1,sK6(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_413])]) ).
fof(f5737,plain,
( ! [X2,X0,X1] :
( element(sK13(relation_dom(X0),X1,sK6(X2)),X2)
| empty(X2)
| sP2(relation_dom(X0),X1,sK6(X2))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_413 ),
inference(resolution,[],[f5656,f2560]) ).
fof(f5656,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| in(sK13(X0,X1,sK6(X2)),X0)
| empty(X2)
| sP2(X0,X1,sK6(X2)) )
| ~ spl22_413 ),
inference(avatar_component_clause,[],[f5655]) ).
fof(f66965,plain,
( spl22_1616
| ~ spl22_121
| ~ spl22_409 ),
inference(avatar_split_clause,[],[f5568,f5286,f1110,f66963]) ).
fof(f66963,plain,
( spl22_1616
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(sK10(powerset(X1)),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1616])]) ).
fof(f1110,plain,
( spl22_121
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_121])]) ).
fof(f5286,plain,
( spl22_409
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| in(sK7(X0,set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_409])]) ).
fof(f5568,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(sK10(powerset(X1)),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_409 ),
inference(resolution,[],[f5287,f1111]) ).
fof(f1111,plain,
( ! [X0,X1] :
( ~ in(X1,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_121 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f5287,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X1)
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_409 ),
inference(avatar_component_clause,[],[f5286]) ).
fof(f66961,plain,
( spl22_1615
| ~ spl22_121
| ~ spl22_408 ),
inference(avatar_split_clause,[],[f5531,f5282,f1110,f66959]) ).
fof(f66959,plain,
( spl22_1615
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,sK10(powerset(X2)))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1615])]) ).
fof(f5282,plain,
( spl22_408
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| in(sK7(X0,set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_408])]) ).
fof(f5531,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,sK10(powerset(X2)))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_408 ),
inference(resolution,[],[f5283,f1111]) ).
fof(f5283,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X2)
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_408 ),
inference(avatar_component_clause,[],[f5282]) ).
fof(f66957,plain,
( spl22_1614
| ~ spl22_121
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5417,f5246,f1110,f66955]) ).
fof(f66955,plain,
( spl22_1614
<=> ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,sK10(powerset(X2)))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1614])]) ).
fof(f5246,plain,
( spl22_401
<=> ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_401])]) ).
fof(f5417,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,sK10(powerset(X2)))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_401 ),
inference(resolution,[],[f5247,f1111]) ).
fof(f5247,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X2)
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_401 ),
inference(avatar_component_clause,[],[f5246]) ).
fof(f66953,plain,
( spl22_1613
| ~ spl22_121
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5367,f5242,f1110,f66951]) ).
fof(f66951,plain,
( spl22_1613
<=> ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(sK10(powerset(X1)),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1613])]) ).
fof(f5242,plain,
( spl22_400
<=> ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_400])]) ).
fof(f5367,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(sK10(powerset(X1)),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_400 ),
inference(resolution,[],[f5243,f1111]) ).
fof(f5243,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X1)
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_400 ),
inference(avatar_component_clause,[],[f5242]) ).
fof(f66949,plain,
( spl22_1612
| ~ spl22_281
| ~ spl22_398 ),
inference(avatar_split_clause,[],[f5325,f5234,f3264,f66947]) ).
fof(f66947,plain,
( spl22_1612
<=> ! [X2,X0,X1] :
( sK7(X0,sK10(powerset(X1))) = apply(X0,sK8(X0,sK10(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1612])]) ).
fof(f3264,plain,
( spl22_281
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_281])]) ).
fof(f5234,plain,
( spl22_398
<=> ! [X0,X1] :
( ~ empty(X0)
| sK7(X1,sK10(powerset(X0))) = apply(X1,sK8(X1,sK10(powerset(X0))))
| sP0(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_398])]) ).
fof(f5325,plain,
( ! [X2,X0,X1] :
( sK7(X0,sK10(powerset(X1))) = apply(X0,sK8(X0,sK10(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,relation_dom(X0)) )
| ~ spl22_281
| ~ spl22_398 ),
inference(duplicate_literal_removal,[],[f5298]) ).
fof(f5298,plain,
( ! [X2,X0,X1] :
( sK7(X0,sK10(powerset(X1))) = apply(X0,sK8(X0,sK10(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,relation_dom(X0))
| ~ empty(X1) )
| ~ spl22_281
| ~ spl22_398 ),
inference(resolution,[],[f5235,f3265]) ).
fof(f3265,plain,
( ! [X2,X0,X1] :
( ~ sP0(X2,sK10(powerset(X0)))
| ~ in(X1,relation_dom(X2))
| ~ empty(X0) )
| ~ spl22_281 ),
inference(avatar_component_clause,[],[f3264]) ).
fof(f5235,plain,
( ! [X0,X1] :
( sP0(X1,sK10(powerset(X0)))
| sK7(X1,sK10(powerset(X0))) = apply(X1,sK8(X1,sK10(powerset(X0))))
| ~ empty(X0) )
| ~ spl22_398 ),
inference(avatar_component_clause,[],[f5234]) ).
fof(f66945,plain,
( spl22_1611
| ~ spl22_56
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5169,f5126,f545,f66943]) ).
fof(f66943,plain,
( spl22_1611
<=> ! [X0,X1] :
( element(sK8(X0,sK6(X1)),relation_dom(X0))
| sP0(X0,sK6(X1))
| empty(X1)
| in(sK7(X0,sK6(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1611])]) ).
fof(f545,plain,
( spl22_56
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_56])]) ).
fof(f5126,plain,
( spl22_396
<=> ! [X0,X1] :
( element(sK8(X0,sK6(X1)),relation_dom(X0))
| sP0(X0,sK6(X1))
| element(sK7(X0,sK6(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_396])]) ).
fof(f5169,plain,
( ! [X0,X1] :
( element(sK8(X0,sK6(X1)),relation_dom(X0))
| sP0(X0,sK6(X1))
| empty(X1)
| in(sK7(X0,sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_396 ),
inference(duplicate_literal_removal,[],[f5164]) ).
fof(f5164,plain,
( ! [X0,X1] :
( element(sK8(X0,sK6(X1)),relation_dom(X0))
| sP0(X0,sK6(X1))
| empty(X1)
| empty(X1)
| in(sK7(X0,sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_396 ),
inference(resolution,[],[f5127,f546]) ).
fof(f546,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl22_56 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f5127,plain,
( ! [X0,X1] :
( element(sK8(X0,sK6(X1)),relation_dom(X0))
| element(sK7(X0,sK6(X1)),X1)
| sP0(X0,sK6(X1))
| empty(X1) )
| ~ spl22_396 ),
inference(avatar_component_clause,[],[f5126]) ).
fof(f66572,plain,
( spl22_1610
| ~ spl22_56
| ~ spl22_394 ),
inference(avatar_split_clause,[],[f5146,f5118,f545,f66570]) ).
fof(f66570,plain,
( spl22_1610
<=> ! [X0,X1] :
( in(sK8(X0,sK6(X1)),relation_dom(X0))
| empty(X1)
| sP0(X0,sK6(X1))
| in(sK7(X0,sK6(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1610])]) ).
fof(f5118,plain,
( spl22_394
<=> ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| in(sK8(X0,sK6(X1)),relation_dom(X0))
| sP0(X0,sK6(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_394])]) ).
fof(f5146,plain,
( ! [X0,X1] :
( in(sK8(X0,sK6(X1)),relation_dom(X0))
| empty(X1)
| sP0(X0,sK6(X1))
| in(sK7(X0,sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_394 ),
inference(duplicate_literal_removal,[],[f5141]) ).
fof(f5141,plain,
( ! [X0,X1] :
( in(sK8(X0,sK6(X1)),relation_dom(X0))
| empty(X1)
| sP0(X0,sK6(X1))
| empty(X1)
| in(sK7(X0,sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_394 ),
inference(resolution,[],[f5119,f546]) ).
fof(f5119,plain,
( ! [X0,X1] :
( in(sK8(X0,sK6(X1)),relation_dom(X0))
| element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) )
| ~ spl22_394 ),
inference(avatar_component_clause,[],[f5118]) ).
fof(f66568,plain,
( spl22_1609
| ~ spl22_45
| ~ spl22_394 ),
inference(avatar_split_clause,[],[f5140,f5118,f454,f66566]) ).
fof(f66566,plain,
( spl22_1609
<=> ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1))
| ~ in(relation_dom(X0),sK8(X0,sK6(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1609])]) ).
fof(f454,plain,
( spl22_45
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_45])]) ).
fof(f5140,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1))
| ~ in(relation_dom(X0),sK8(X0,sK6(X1))) )
| ~ spl22_45
| ~ spl22_394 ),
inference(resolution,[],[f5119,f455]) ).
fof(f455,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl22_45 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f66564,plain,
( spl22_1608
| ~ spl22_237
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4687,f4006,f2575,f66562]) ).
fof(f66562,plain,
( spl22_1608
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_dom(relation_dom(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1608])]) ).
fof(f2575,plain,
( spl22_237
<=> ! [X0] :
( sK15 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_237])]) ).
fof(f4006,plain,
( spl22_358
<=> ! [X0] :
( sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| ~ sP1(X0)
| empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_358])]) ).
fof(f4687,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_dom(relation_dom(relation_rng(X0))) )
| ~ spl22_237
| ~ spl22_358 ),
inference(resolution,[],[f4007,f2576]) ).
fof(f2576,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_dom(relation_dom(X0)) )
| ~ spl22_237 ),
inference(avatar_component_clause,[],[f2575]) ).
fof(f4007,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0)))) )
| ~ spl22_358 ),
inference(avatar_component_clause,[],[f4006]) ).
fof(f66560,plain,
( spl22_1607
| ~ spl22_236
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4686,f4006,f2571,f66558]) ).
fof(f66558,plain,
( spl22_1607
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_dom(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1607])]) ).
fof(f2571,plain,
( spl22_236
<=> ! [X0] :
( sK15 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_236])]) ).
fof(f4686,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_dom(relation_rng(relation_rng(X0))) )
| ~ spl22_236
| ~ spl22_358 ),
inference(resolution,[],[f4007,f2572]) ).
fof(f2572,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_dom(relation_rng(X0)) )
| ~ spl22_236 ),
inference(avatar_component_clause,[],[f2571]) ).
fof(f66556,plain,
( spl22_1606
| ~ spl22_235
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4685,f4006,f2567,f66554]) ).
fof(f66554,plain,
( spl22_1606
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_rng(relation_dom(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1606])]) ).
fof(f2567,plain,
( spl22_235
<=> ! [X0] :
( sK15 = relation_rng(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_235])]) ).
fof(f4685,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_rng(relation_dom(relation_rng(X0))) )
| ~ spl22_235
| ~ spl22_358 ),
inference(resolution,[],[f4007,f2568]) ).
fof(f2568,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_rng(relation_dom(X0)) )
| ~ spl22_235 ),
inference(avatar_component_clause,[],[f2567]) ).
fof(f66552,plain,
( spl22_1605
| ~ spl22_234
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4684,f4006,f2563,f66550]) ).
fof(f66550,plain,
( spl22_1605
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_rng(relation_rng(relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1605])]) ).
fof(f2563,plain,
( spl22_234
<=> ! [X0] :
( sK15 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_234])]) ).
fof(f4684,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_rng(relation_rng(relation_rng(X0))) )
| ~ spl22_234
| ~ spl22_358 ),
inference(resolution,[],[f4007,f2564]) ).
fof(f2564,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_rng(relation_rng(X0)) )
| ~ spl22_234 ),
inference(avatar_component_clause,[],[f2563]) ).
fof(f66548,plain,
( spl22_1604
| ~ spl22_55
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4673,f4006,f519,f66546]) ).
fof(f66546,plain,
( spl22_1604
<=> ! [X0,X1] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| relation_rng(X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1604])]) ).
fof(f519,plain,
( spl22_55
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_55])]) ).
fof(f4673,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| relation_rng(X0) = X1
| ~ empty(X1) )
| ~ spl22_55
| ~ spl22_358 ),
inference(resolution,[],[f4007,f520]) ).
fof(f520,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl22_55 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f66544,plain,
( spl22_1603
| ~ spl22_69
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3803,f3697,f628,f66542]) ).
fof(f66542,plain,
( spl22_1603
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1603])]) ).
fof(f628,plain,
( spl22_69
<=> ! [X6,X0,X1] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_69])]) ).
fof(f3697,plain,
( spl22_328
<=> ! [X2,X0,X1,X3] :
( ~ sP0(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_328])]) ).
fof(f3803,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,apply(X1,X0)) )
| ~ spl22_69
| ~ spl22_328 ),
inference(resolution,[],[f3698,f629]) ).
fof(f629,plain,
( ! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) )
| ~ spl22_69 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f3698,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,apply(X0,X2))
| ~ in(X2,relation_dom(X0))
| ~ empty(X1)
| ~ sP0(X0,powerset(X1)) )
| ~ spl22_328 ),
inference(avatar_component_clause,[],[f3697]) ).
fof(f66540,plain,
( spl22_1602
| ~ spl22_63
| ~ spl22_327 ),
inference(avatar_split_clause,[],[f3801,f3693,f586,f66538]) ).
fof(f66538,plain,
( spl22_1602
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1602])]) ).
fof(f586,plain,
( spl22_63
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_63])]) ).
fof(f3693,plain,
( spl22_327
<=> ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| ~ empty(relation_dom(X0))
| element(sK7(X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_327])]) ).
fof(f3801,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl22_63
| ~ spl22_327 ),
inference(resolution,[],[f3694,f587]) ).
fof(f587,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl22_63 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f3694,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| ~ empty(relation_dom(X0))
| sP0(X0,sK10(powerset(X1))) )
| ~ spl22_327 ),
inference(avatar_component_clause,[],[f3693]) ).
fof(f66536,plain,
( spl22_1601
| ~ spl22_128
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3784,f3685,f1151,f66534]) ).
fof(f66534,plain,
( spl22_1601
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| element(sK7(X0,set_intersection2(sK10(powerset(X1)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1601])]) ).
fof(f1151,plain,
( spl22_128
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_128])]) ).
fof(f3685,plain,
( spl22_325
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| ~ empty(relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_325])]) ).
fof(f3784,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| element(sK7(X0,set_intersection2(sK10(powerset(X1)),X2)),X1) )
| ~ spl22_128
| ~ spl22_325 ),
inference(resolution,[],[f3686,f1152]) ).
fof(f1152,plain,
( ! [X0,X1] :
( ~ in(X0,sK10(powerset(X1)))
| element(X0,X1) )
| ~ spl22_128 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f3686,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_325 ),
inference(avatar_component_clause,[],[f3685]) ).
fof(f66163,plain,
( spl22_1600
| ~ spl22_132
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3783,f3685,f1242,f66161]) ).
fof(f66161,plain,
( spl22_1600
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(sK6(X1),X2))
| element(sK7(X0,set_intersection2(sK6(X1),X2)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1600])]) ).
fof(f1242,plain,
( spl22_132
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_132])]) ).
fof(f3783,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(sK6(X1),X2))
| element(sK7(X0,set_intersection2(sK6(X1),X2)),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_325 ),
inference(resolution,[],[f3686,f1243]) ).
fof(f1243,plain,
( ! [X0,X1] :
( ~ in(X0,sK6(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl22_132 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f66159,plain,
( spl22_1599
| ~ spl22_129
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3774,f3685,f1155,f66157]) ).
fof(f66157,plain,
( spl22_1599
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(set_intersection2(X1,X2),X3))
| in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1599])]) ).
fof(f1155,plain,
( spl22_129
<=> ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_129])]) ).
fof(f3774,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(set_intersection2(X1,X2),X3))
| in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3)),X1) )
| ~ spl22_129
| ~ spl22_325 ),
inference(resolution,[],[f3686,f1156]) ).
fof(f1156,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) )
| ~ spl22_129 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f66155,plain,
( spl22_1598
| ~ spl22_130
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3773,f3685,f1159,f66153]) ).
fof(f66153,plain,
( spl22_1598
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(set_intersection2(X1,X2),X3))
| in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1598])]) ).
fof(f1159,plain,
( spl22_130
<=> ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_130])]) ).
fof(f3773,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(set_intersection2(X1,X2),X3))
| in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3)),X2) )
| ~ spl22_130
| ~ spl22_325 ),
inference(resolution,[],[f3686,f1160]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) )
| ~ spl22_130 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f66151,plain,
( spl22_1597
| ~ spl22_128
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3759,f3681,f1151,f66149]) ).
fof(f66149,plain,
( spl22_1597
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| element(sK7(X0,set_intersection2(X1,sK10(powerset(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1597])]) ).
fof(f3681,plain,
( spl22_324
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| ~ empty(relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_324])]) ).
fof(f3759,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| element(sK7(X0,set_intersection2(X1,sK10(powerset(X2)))),X2) )
| ~ spl22_128
| ~ spl22_324 ),
inference(resolution,[],[f3682,f1152]) ).
fof(f3682,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_324 ),
inference(avatar_component_clause,[],[f3681]) ).
fof(f66147,plain,
( spl22_1596
| ~ spl22_132
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3758,f3681,f1242,f66145]) ).
fof(f66145,plain,
( spl22_1596
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK6(X2)))
| element(sK7(X0,set_intersection2(X1,sK6(X2))),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1596])]) ).
fof(f3758,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK6(X2)))
| element(sK7(X0,set_intersection2(X1,sK6(X2))),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_324 ),
inference(resolution,[],[f3682,f1243]) ).
fof(f66143,plain,
( spl22_1595
| ~ spl22_129
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3749,f3681,f1155,f66141]) ).
fof(f66141,plain,
( spl22_1595
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,set_intersection2(X2,X3)))
| in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1595])]) ).
fof(f3749,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,set_intersection2(X2,X3)))
| in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X3))),X2) )
| ~ spl22_129
| ~ spl22_324 ),
inference(resolution,[],[f3682,f1156]) ).
fof(f66139,plain,
( spl22_1594
| ~ spl22_130
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3748,f3681,f1159,f66137]) ).
fof(f66137,plain,
( spl22_1594
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,set_intersection2(X2,X3)))
| in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1594])]) ).
fof(f3748,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,set_intersection2(X2,X3)))
| in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X3))),X3) )
| ~ spl22_130
| ~ spl22_324 ),
inference(resolution,[],[f3682,f1160]) ).
fof(f66135,plain,
( spl22_1593
| ~ spl22_63
| ~ spl22_323 ),
inference(avatar_split_clause,[],[f3730,f3677,f586,f66133]) ).
fof(f66133,plain,
( spl22_1593
<=> ! [X2,X0,X1,X3] :
( empty(powerset(X0))
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X3,apply(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1593])]) ).
fof(f3677,plain,
( spl22_323
<=> ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| empty(X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK6(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_323])]) ).
fof(f3730,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(X0))
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X3,apply(X2,X1)) )
| ~ spl22_63
| ~ spl22_323 ),
inference(resolution,[],[f3678,f587]) ).
fof(f3678,plain,
( ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| empty(X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK6(X2)) )
| ~ spl22_323 ),
inference(avatar_component_clause,[],[f3677]) ).
fof(f66131,plain,
( spl22_1592
| ~ spl22_63
| ~ spl22_318 ),
inference(avatar_split_clause,[],[f3662,f3618,f586,f66129]) ).
fof(f66129,plain,
( spl22_1592
<=> ! [X2,X0,X1] :
( element(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1592])]) ).
fof(f3618,plain,
( spl22_318
<=> ! [X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_318])]) ).
fof(f3662,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_63
| ~ spl22_318 ),
inference(resolution,[],[f3619,f587]) ).
fof(f3619,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| element(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_318 ),
inference(avatar_component_clause,[],[f3618]) ).
fof(f66127,plain,
( spl22_1591
| ~ spl22_44
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3577,f3551,f450,f66125]) ).
fof(f66125,plain,
( spl22_1591
<=> ! [X2,X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| set_intersection2(relation_dom(relation_dom_restriction(X0,X1)),X2) = relation_dom(relation_dom_restriction(relation_dom_restriction(X0,X1),X2))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1591])]) ).
fof(f450,plain,
( spl22_44
<=> ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_44])]) ).
fof(f3551,plain,
( spl22_313
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_313])]) ).
fof(f3577,plain,
( ! [X2,X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| set_intersection2(relation_dom(relation_dom_restriction(X0,X1)),X2) = relation_dom(relation_dom_restriction(relation_dom_restriction(X0,X1),X2))
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_313 ),
inference(resolution,[],[f3552,f451]) ).
fof(f451,plain,
( ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) )
| ~ spl22_44 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f3552,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ spl22_313 ),
inference(avatar_component_clause,[],[f3551]) ).
fof(f66123,plain,
( spl22_1590
| ~ spl22_646
| ~ spl22_1041 ),
inference(avatar_split_clause,[],[f28237,f28111,f13295,f66121]) ).
fof(f13295,plain,
( spl22_646
<=> ! [X0] :
( sP0(sK15,relation_dom(X0))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_646])]) ).
fof(f28111,plain,
( spl22_1041
<=> ! [X0] : set_intersection2(relation_dom(sK20),X0) = relation_dom(relation_dom_restriction(sK20,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1041])]) ).
fof(f28237,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK20),X0))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) )
| ~ spl22_646
| ~ spl22_1041 ),
inference(superposition,[],[f13296,f28112]) ).
fof(f28112,plain,
( ! [X0] : set_intersection2(relation_dom(sK20),X0) = relation_dom(relation_dom_restriction(sK20,X0))
| ~ spl22_1041 ),
inference(avatar_component_clause,[],[f28111]) ).
fof(f13296,plain,
( ! [X0] :
( sP0(sK15,relation_dom(X0))
| ~ sP0(X0,sK15) )
| ~ spl22_646 ),
inference(avatar_component_clause,[],[f13295]) ).
fof(f66119,plain,
( spl22_1589
| ~ spl22_158
| ~ spl22_311 ),
inference(avatar_split_clause,[],[f3571,f3543,f1544,f66117]) ).
fof(f66117,plain,
( spl22_1589
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| element(sK7(X0,X1),X1)
| ~ empty(X2)
| sK7(X0,X2) = apply(X0,sK8(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1589])]) ).
fof(f1544,plain,
( spl22_158
<=> ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_158])]) ).
fof(f3543,plain,
( spl22_311
<=> ! [X2,X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_311])]) ).
fof(f3571,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| element(sK7(X0,X1),X1)
| ~ empty(X2)
| sK7(X0,X2) = apply(X0,sK8(X0,X2)) )
| ~ spl22_158
| ~ spl22_311 ),
inference(duplicate_literal_removal,[],[f3566]) ).
fof(f3566,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| element(sK7(X0,X1),X1)
| ~ empty(X2)
| sK7(X0,X2) = apply(X0,sK8(X0,X2))
| ~ empty(X2) )
| ~ spl22_158
| ~ spl22_311 ),
inference(resolution,[],[f3544,f1545]) ).
fof(f1545,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_158 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f3544,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X2)
| sP0(X0,X1)
| element(sK7(X0,X1),X1)
| ~ empty(X2) )
| ~ spl22_311 ),
inference(avatar_component_clause,[],[f3543]) ).
fof(f66115,plain,
( spl22_1588
| ~ spl22_158
| ~ spl22_310 ),
inference(avatar_split_clause,[],[f3564,f3538,f1544,f66113]) ).
fof(f66113,plain,
( spl22_1588
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK7(X1,X2),X2)
| sP0(X1,X2)
| sK7(X1,X0) = apply(X1,sK8(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1588])]) ).
fof(f3538,plain,
( spl22_310
<=> ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK7(X0,X2),X2)
| sP0(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_310])]) ).
fof(f3564,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK7(X1,X2),X2)
| sP0(X1,X2)
| sK7(X1,X0) = apply(X1,sK8(X1,X0)) )
| ~ spl22_158
| ~ spl22_310 ),
inference(duplicate_literal_removal,[],[f3559]) ).
fof(f3559,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK7(X1,X2),X2)
| sP0(X1,X2)
| sK7(X1,X0) = apply(X1,sK8(X1,X0))
| ~ empty(X0) )
| ~ spl22_158
| ~ spl22_310 ),
inference(resolution,[],[f3539,f1545]) ).
fof(f3539,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK7(X0,X2),X2)
| sP0(X0,X2) )
| ~ spl22_310 ),
inference(avatar_component_clause,[],[f3538]) ).
fof(f66111,plain,
( spl22_1587
| ~ spl22_76
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3375,f3304,f670,f66109]) ).
fof(f66109,plain,
( spl22_1587
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(relation_rng(X0),X2,X3),X3)
| sP2(relation_rng(X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1587])]) ).
fof(f670,plain,
( spl22_76
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_76])]) ).
fof(f3304,plain,
( spl22_290
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_290])]) ).
fof(f3375,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(relation_rng(X0),X2,X3),X3)
| sP2(relation_rng(X0),X2,X3) )
| ~ spl22_76
| ~ spl22_290 ),
inference(resolution,[],[f3305,f671]) ).
fof(f671,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2) )
| ~ spl22_76 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f3305,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_290 ),
inference(avatar_component_clause,[],[f3304]) ).
fof(f66107,plain,
( spl22_1586
| ~ spl22_163
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3373,f3304,f1600,f66105]) ).
fof(f66105,plain,
( spl22_1586
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(relation_rng(X0),X2,X3),X3)
| sP2(relation_rng(X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1586])]) ).
fof(f1600,plain,
( spl22_163
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_163])]) ).
fof(f3373,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(relation_rng(X0),X2,X3),X3)
| sP2(relation_rng(X0),X2,X3) )
| ~ spl22_163
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1601]) ).
fof(f1601,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2) )
| ~ spl22_163 ),
inference(avatar_component_clause,[],[f1600]) ).
fof(f66103,plain,
( spl22_1585
| ~ spl22_75
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3371,f3304,f666,f66101]) ).
fof(f66101,plain,
( spl22_1585
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,relation_rng(X0),X3),X3)
| sP2(X2,relation_rng(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1585])]) ).
fof(f666,plain,
( spl22_75
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_75])]) ).
fof(f3371,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,relation_rng(X0),X3),X3)
| sP2(X2,relation_rng(X0),X3) )
| ~ spl22_75
| ~ spl22_290 ),
inference(resolution,[],[f3305,f667]) ).
fof(f667,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_75 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f66099,plain,
( spl22_1584
| ~ spl22_159
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3369,f3304,f1579,f66097]) ).
fof(f66097,plain,
( spl22_1584
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(X2,relation_rng(X0),X3),X3)
| sP2(X2,relation_rng(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1584])]) ).
fof(f1579,plain,
( spl22_159
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_159])]) ).
fof(f3369,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(X2,relation_rng(X0),X3),X3)
| sP2(X2,relation_rng(X0),X3) )
| ~ spl22_159
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1580]) ).
fof(f1580,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_159 ),
inference(avatar_component_clause,[],[f1579]) ).
fof(f66095,plain,
( spl22_1583
| ~ spl22_165
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3365,f3304,f1608,f66093]) ).
fof(f66093,plain,
( spl22_1583
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(X2,X3,relation_rng(X0)),X2)
| sP2(X2,X3,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1583])]) ).
fof(f1608,plain,
( spl22_165
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_165])]) ).
fof(f3365,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(X2,X3,relation_rng(X0)),X2)
| sP2(X2,X3,relation_rng(X0)) )
| ~ spl22_165
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1609]) ).
fof(f1609,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2) )
| ~ spl22_165 ),
inference(avatar_component_clause,[],[f1608]) ).
fof(f66091,plain,
( spl22_1582
| ~ spl22_161
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3364,f3304,f1587,f66089]) ).
fof(f66089,plain,
( spl22_1582
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(X2,X3,relation_rng(X0)),X3)
| sP2(X2,X3,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1582])]) ).
fof(f1587,plain,
( spl22_161
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_161])]) ).
fof(f3364,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK13(X2,X3,relation_rng(X0)),X3)
| sP2(X2,X3,relation_rng(X0)) )
| ~ spl22_161
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1588]) ).
fof(f1588,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2) )
| ~ spl22_161 ),
inference(avatar_component_clause,[],[f1587]) ).
fof(f66087,plain,
( spl22_1581
| ~ spl22_76
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3361,f3304,f670,f66085]) ).
fof(f66085,plain,
( spl22_1581
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_rng(X0)),X2)
| sP2(X2,X3,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1581])]) ).
fof(f3361,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_rng(X0)),X2)
| sP2(X2,X3,relation_rng(X0)) )
| ~ spl22_76
| ~ spl22_290 ),
inference(resolution,[],[f3305,f671]) ).
fof(f66083,plain,
( spl22_1580
| ~ spl22_75
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3360,f3304,f666,f66081]) ).
fof(f66081,plain,
( spl22_1580
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_rng(X0)),X3)
| sP2(X2,X3,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1580])]) ).
fof(f3360,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_rng(X0)),X3)
| sP2(X2,X3,relation_rng(X0)) )
| ~ spl22_75
| ~ spl22_290 ),
inference(resolution,[],[f3305,f667]) ).
fof(f66079,plain,
( spl22_1579
| ~ spl22_646
| ~ spl22_1040 ),
inference(avatar_split_clause,[],[f28074,f27948,f13295,f66077]) ).
fof(f27948,plain,
( spl22_1040
<=> ! [X0] : set_intersection2(relation_dom(sK19),X0) = relation_dom(relation_dom_restriction(sK19,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1040])]) ).
fof(f28074,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK19),X0))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) )
| ~ spl22_646
| ~ spl22_1040 ),
inference(superposition,[],[f13296,f27949]) ).
fof(f27949,plain,
( ! [X0] : set_intersection2(relation_dom(sK19),X0) = relation_dom(relation_dom_restriction(sK19,X0))
| ~ spl22_1040 ),
inference(avatar_component_clause,[],[f27948]) ).
fof(f66023,plain,
( spl22_1578
| ~ spl22_230
| ~ spl22_592 ),
inference(avatar_split_clause,[],[f11882,f11832,f2489,f66021]) ).
fof(f66021,plain,
( spl22_1578
<=> ! [X0,X3,X2,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)) = apply(sK5,sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1578])]) ).
fof(f2489,plain,
( spl22_230
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_230])]) ).
fof(f11832,plain,
( spl22_592
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_dom_restriction(X1,X2)))
| ~ sP1(relation_dom_restriction(X1,X2))
| apply(X1,sK9(relation_dom_restriction(X1,X2),X0)) = apply(relation_dom_restriction(X1,X2),sK9(relation_dom_restriction(X1,X2),X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_592])]) ).
fof(f11882,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)) = apply(sK5,sK13(relation_rng(relation_dom_restriction(X0,X1)),X2,X3)) )
| ~ spl22_230
| ~ spl22_592 ),
inference(resolution,[],[f11833,f2490]) ).
fof(f2490,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) )
| ~ spl22_230 ),
inference(avatar_component_clause,[],[f2489]) ).
fof(f11833,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_dom_restriction(X1,X2)))
| ~ sP1(relation_dom_restriction(X1,X2))
| apply(X1,sK9(relation_dom_restriction(X1,X2),X0)) = apply(relation_dom_restriction(X1,X2),sK9(relation_dom_restriction(X1,X2),X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_592 ),
inference(avatar_component_clause,[],[f11832]) ).
fof(f66019,plain,
( spl22_1577
| ~ spl22_228
| ~ spl22_592 ),
inference(avatar_split_clause,[],[f11875,f11832,f2447,f66017]) ).
fof(f66017,plain,
( spl22_1577
<=> ! [X0,X3,X2,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)) = apply(sK5,sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1577])]) ).
fof(f2447,plain,
( spl22_228
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_228])]) ).
fof(f11875,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)) = apply(sK5,sK13(X2,relation_rng(relation_dom_restriction(X0,X1)),X3)) )
| ~ spl22_228
| ~ spl22_592 ),
inference(resolution,[],[f11833,f2448]) ).
fof(f2448,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) )
| ~ spl22_228 ),
inference(avatar_component_clause,[],[f2447]) ).
fof(f66015,plain,
( spl22_1576
| ~ spl22_231
| ~ spl22_592 ),
inference(avatar_split_clause,[],[f11865,f11832,f2510,f66013]) ).
fof(f66013,plain,
( spl22_1576
<=> ! [X0,X3,X2,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1))))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))
| apply(sK5,sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1576])]) ).
fof(f2510,plain,
( spl22_231
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_231])]) ).
fof(f11865,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1))))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))
| apply(sK5,sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) )
| ~ spl22_231
| ~ spl22_592 ),
inference(resolution,[],[f11833,f2511]) ).
fof(f2511,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2)) )
| ~ spl22_231 ),
inference(avatar_component_clause,[],[f2510]) ).
fof(f66011,plain,
( spl22_1575
| ~ spl22_229
| ~ spl22_592 ),
inference(avatar_split_clause,[],[f11864,f11832,f2468,f66009]) ).
fof(f66009,plain,
( spl22_1575
<=> ! [X0,X3,X2,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1))))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))
| apply(sK5,sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1575])]) ).
fof(f2468,plain,
( spl22_229
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_229])]) ).
fof(f11864,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1))))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP2(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))
| apply(sK5,sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,relation_rng(relation_dom_restriction(X0,X1)))) )
| ~ spl22_229
| ~ spl22_592 ),
inference(resolution,[],[f11833,f2469]) ).
fof(f2469,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2)) )
| ~ spl22_229 ),
inference(avatar_component_clause,[],[f2468]) ).
fof(f65962,plain,
( spl22_1574
| ~ spl22_371
| ~ spl22_646 ),
inference(avatar_split_clause,[],[f13549,f13295,f4126,f65960]) ).
fof(f65960,plain,
( spl22_1574
<=> ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1574])]) ).
fof(f13549,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_371
| ~ spl22_646 ),
inference(superposition,[],[f13296,f4127]) ).
fof(f64338,plain,
( spl22_114
| spl22_1573
| ~ spl22_819
| ~ spl22_1551 ),
inference(avatar_split_clause,[],[f63527,f63357,f17777,f64336,f956]) ).
fof(f956,plain,
( spl22_114
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_114])]) ).
fof(f64336,plain,
( spl22_1573
<=> ! [X0] :
( ~ sP1(X0)
| ~ empty(X0)
| sP0(sK15,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1573])]) ).
fof(f17777,plain,
( spl22_819
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_819])]) ).
fof(f63357,plain,
( spl22_1551
<=> ! [X0,X1] :
( sP0(sK15,relation_rng(X0))
| ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1551])]) ).
fof(f63527,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| sP0(sK15,relation_rng(X0))
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_819
| ~ spl22_1551 ),
inference(duplicate_literal_removal,[],[f63450]) ).
fof(f63450,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| sP0(sK15,relation_rng(X0))
| ~ empty(X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_819
| ~ spl22_1551 ),
inference(resolution,[],[f63358,f17778]) ).
fof(f17778,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_819 ),
inference(avatar_component_clause,[],[f17777]) ).
fof(f63358,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| ~ sP1(X0)
| sP0(sK15,relation_rng(X0))
| ~ empty(X1) )
| ~ spl22_1551 ),
inference(avatar_component_clause,[],[f63357]) ).
fof(f63443,plain,
( spl22_1572
| ~ spl22_233
| ~ spl22_409 ),
inference(avatar_split_clause,[],[f5558,f5286,f2559,f63441]) ).
fof(f63441,plain,
( spl22_1572
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(relation_dom(X1),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1572])]) ).
fof(f5558,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(relation_dom(X1),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_409 ),
inference(resolution,[],[f5287,f2560]) ).
fof(f63439,plain,
( spl22_1571
| ~ spl22_233
| ~ spl22_408 ),
inference(avatar_split_clause,[],[f5521,f5282,f2559,f63437]) ).
fof(f63437,plain,
( spl22_1571
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,relation_dom(X2))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1571])]) ).
fof(f5521,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,relation_dom(X2))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_408 ),
inference(resolution,[],[f5283,f2560]) ).
fof(f63435,plain,
( spl22_1570
| ~ spl22_233
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5407,f5246,f2559,f63433]) ).
fof(f63433,plain,
( spl22_1570
<=> ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,relation_dom(X2))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1570])]) ).
fof(f5407,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,relation_dom(X2))),relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_401 ),
inference(resolution,[],[f5247,f2560]) ).
fof(f63431,plain,
( spl22_1569
| ~ spl22_233
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5357,f5242,f2559,f63429]) ).
fof(f63429,plain,
( spl22_1569
<=> ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(relation_dom(X1),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1569])]) ).
fof(f5357,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(relation_dom(X1),X2)),relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_400 ),
inference(resolution,[],[f5243,f2560]) ).
fof(f63427,plain,
( spl22_1568
| ~ spl22_119
| ~ spl22_397 ),
inference(avatar_split_clause,[],[f5179,f5130,f1064,f63425]) ).
fof(f63425,plain,
( spl22_1568
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| empty(sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1568])]) ).
fof(f1064,plain,
( spl22_119
<=> ! [X0] :
( empty(X0)
| in(sK10(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_119])]) ).
fof(f5130,plain,
( spl22_397
<=> ! [X2,X0,X1] :
( in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_397])]) ).
fof(f5179,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| empty(sK7(X0,powerset(X1))) )
| ~ spl22_119
| ~ spl22_397 ),
inference(resolution,[],[f5131,f1065]) ).
fof(f1065,plain,
( ! [X0] :
( in(sK10(X0),X0)
| empty(X0) )
| ~ spl22_119 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f5131,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0)) )
| ~ spl22_397 ),
inference(avatar_component_clause,[],[f5130]) ).
fof(f63423,plain,
( spl22_1567
| ~ spl22_45
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5050,f4944,f454,f63421]) ).
fof(f63421,plain,
( spl22_1567
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ in(X0,sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1567])]) ).
fof(f4944,plain,
( spl22_391
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| in(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_391])]) ).
fof(f5050,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ in(X0,sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) )
| ~ spl22_45
| ~ spl22_391 ),
inference(resolution,[],[f4945,f455]) ).
fof(f4945,plain,
( ! [X2,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0)
| sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)) )
| ~ spl22_391 ),
inference(avatar_component_clause,[],[f4944]) ).
fof(f63419,plain,
( spl22_1566
| ~ spl22_46
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5049,f4944,f458,f63417]) ).
fof(f63417,plain,
( spl22_1566
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| element(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1566])]) ).
fof(f458,plain,
( spl22_46
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_46])]) ).
fof(f5049,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| element(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0) )
| ~ spl22_46
| ~ spl22_391 ),
inference(resolution,[],[f4945,f459]) ).
fof(f459,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl22_46 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f63415,plain,
( spl22_1565
| ~ spl22_45
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5020,f4940,f454,f63413]) ).
fof(f63413,plain,
( spl22_1565
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ in(X1,sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1565])]) ).
fof(f4940,plain,
( spl22_390
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| in(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_390])]) ).
fof(f5020,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ in(X1,sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) )
| ~ spl22_45
| ~ spl22_390 ),
inference(resolution,[],[f4941,f455]) ).
fof(f4941,plain,
( ! [X2,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
| sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)) )
| ~ spl22_390 ),
inference(avatar_component_clause,[],[f4940]) ).
fof(f63411,plain,
( spl22_1564
| ~ spl22_46
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5019,f4940,f458,f63409]) ).
fof(f63409,plain,
( spl22_1564
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| element(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1564])]) ).
fof(f5019,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| element(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) )
| ~ spl22_46
| ~ spl22_390 ),
inference(resolution,[],[f4941,f459]) ).
fof(f63407,plain,
( spl22_1563
| ~ spl22_45
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4986,f4902,f454,f63405]) ).
fof(f63405,plain,
( spl22_1563
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ in(X1,sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1563])]) ).
fof(f4902,plain,
( spl22_388
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| in(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_388])]) ).
fof(f4986,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ in(X1,sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) )
| ~ spl22_45
| ~ spl22_388 ),
inference(resolution,[],[f4903,f455]) ).
fof(f4903,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1)
| sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)) )
| ~ spl22_388 ),
inference(avatar_component_clause,[],[f4902]) ).
fof(f63403,plain,
( spl22_1562
| ~ spl22_635
| ~ spl22_1299 ),
inference(avatar_split_clause,[],[f45991,f41554,f13056,f63401]) ).
fof(f63401,plain,
( spl22_1562
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,X0),sK15)
| sP0(sK15,set_intersection2(X0,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1562])]) ).
fof(f13056,plain,
( spl22_635
<=> ! [X1] :
( in(sK7(sK15,X1),X1)
| sP0(sK15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_635])]) ).
fof(f41554,plain,
( spl22_1299
<=> ! [X0,X1] :
( ~ in(X1,set_intersection2(X0,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1299])]) ).
fof(f45991,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,X0),sK15)
| sP0(sK15,set_intersection2(X0,relation_dom(sK5))) )
| ~ spl22_635
| ~ spl22_1299 ),
inference(resolution,[],[f41555,f13057]) ).
fof(f13057,plain,
( ! [X1] :
( in(sK7(sK15,X1),X1)
| sP0(sK15,X1) )
| ~ spl22_635 ),
inference(avatar_component_clause,[],[f13056]) ).
fof(f41555,plain,
( ! [X0,X1] :
( ~ in(X1,set_intersection2(X0,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_1299 ),
inference(avatar_component_clause,[],[f41554]) ).
fof(f63399,plain,
( spl22_1561
| ~ spl22_46
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4985,f4902,f458,f63397]) ).
fof(f63397,plain,
( spl22_1561
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| element(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1561])]) ).
fof(f4985,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| element(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1) )
| ~ spl22_46
| ~ spl22_388 ),
inference(resolution,[],[f4903,f459]) ).
fof(f63395,plain,
( spl22_1560
| ~ spl22_45
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4958,f4898,f454,f63393]) ).
fof(f63393,plain,
( spl22_1560
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ in(X2,sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1560])]) ).
fof(f4898,plain,
( spl22_387
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| in(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_387])]) ).
fof(f4958,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ in(X2,sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) )
| ~ spl22_45
| ~ spl22_387 ),
inference(resolution,[],[f4899,f455]) ).
fof(f4899,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2)
| sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)) )
| ~ spl22_387 ),
inference(avatar_component_clause,[],[f4898]) ).
fof(f63391,plain,
( spl22_1559
| ~ spl22_46
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4957,f4898,f458,f63389]) ).
fof(f63389,plain,
( spl22_1559
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| element(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1559])]) ).
fof(f4957,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| element(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2) )
| ~ spl22_46
| ~ spl22_387 ),
inference(resolution,[],[f4899,f459]) ).
fof(f63387,plain,
( spl22_1558
| ~ spl22_117
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4676,f4006,f1053,f63385]) ).
fof(f63385,plain,
( spl22_1558
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_dom(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1558])]) ).
fof(f1053,plain,
( spl22_117
<=> ! [X0] :
( relation_dom(X0) = sK15
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_117])]) ).
fof(f4676,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_dom(relation_rng(X0)) )
| ~ spl22_117
| ~ spl22_358 ),
inference(resolution,[],[f4007,f1054]) ).
fof(f1054,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK15 )
| ~ spl22_117 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f63383,plain,
( spl22_1557
| ~ spl22_116
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4675,f4006,f1049,f63381]) ).
fof(f63381,plain,
( spl22_1557
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_rng(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1557])]) ).
fof(f1049,plain,
( spl22_116
<=> ! [X0] :
( relation_rng(X0) = sK15
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_116])]) ).
fof(f4675,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| sK15 = relation_rng(relation_rng(X0)) )
| ~ spl22_116
| ~ spl22_358 ),
inference(resolution,[],[f4007,f1050]) ).
fof(f1050,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK15 )
| ~ spl22_116 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f63379,plain,
( spl22_1556
| ~ spl22_56
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4666,f4002,f545,f63377]) ).
fof(f63377,plain,
( spl22_1556
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,sK10(powerset(X2)))
| empty(X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1556])]) ).
fof(f4002,plain,
( spl22_357
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X0)
| element(sK13(X0,X1,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_357])]) ).
fof(f4666,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,sK10(powerset(X2)))
| empty(X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X2) )
| ~ spl22_56
| ~ spl22_357 ),
inference(resolution,[],[f4003,f546]) ).
fof(f4003,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| ~ empty(X0)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_357 ),
inference(avatar_component_clause,[],[f4002]) ).
fof(f63375,plain,
( spl22_1555
| ~ spl22_56
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f4593,f3986,f545,f63373]) ).
fof(f63373,plain,
( spl22_1555
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X1)),X2,X0)
| empty(X1)
| in(sK13(sK10(powerset(X1)),X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1555])]) ).
fof(f3986,plain,
( spl22_353
<=> ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| ~ empty(X2)
| element(sK13(sK10(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_353])]) ).
fof(f4593,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X1)),X2,X0)
| empty(X1)
| in(sK13(sK10(powerset(X1)),X2,X0),X1) )
| ~ spl22_56
| ~ spl22_353 ),
inference(resolution,[],[f3987,f546]) ).
fof(f3987,plain,
( ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X0)
| ~ empty(X2)
| sP2(sK10(powerset(X0)),X1,X2) )
| ~ spl22_353 ),
inference(avatar_component_clause,[],[f3986]) ).
fof(f63371,plain,
( spl22_1554
| ~ spl22_56
| ~ spl22_349 ),
inference(avatar_split_clause,[],[f4520,f3970,f545,f63369]) ).
fof(f63369,plain,
( spl22_1554
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,sK10(powerset(X2)))
| empty(X2)
| in(sK13(X1,X0,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1554])]) ).
fof(f3970,plain,
( spl22_349
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X1)
| element(sK13(X0,X1,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_349])]) ).
fof(f4520,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,sK10(powerset(X2)))
| empty(X2)
| in(sK13(X1,X0,sK10(powerset(X2))),X2) )
| ~ spl22_56
| ~ spl22_349 ),
inference(resolution,[],[f3971,f546]) ).
fof(f3971,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| ~ empty(X1)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_349 ),
inference(avatar_component_clause,[],[f3970]) ).
fof(f63367,plain,
( spl22_1553
| ~ spl22_56
| ~ spl22_345 ),
inference(avatar_split_clause,[],[f4451,f3954,f545,f63365]) ).
fof(f63365,plain,
( spl22_1553
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X2)),X0)
| empty(X2)
| in(sK13(X1,sK10(powerset(X2)),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1553])]) ).
fof(f3954,plain,
( spl22_345
<=> ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| ~ empty(X2)
| element(sK13(X0,sK10(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_345])]) ).
fof(f4451,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X2)),X0)
| empty(X2)
| in(sK13(X1,sK10(powerset(X2)),X0),X2) )
| ~ spl22_56
| ~ spl22_345 ),
inference(resolution,[],[f3955,f546]) ).
fof(f3955,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X1)
| ~ empty(X2)
| sP2(X0,sK10(powerset(X1)),X2) )
| ~ spl22_345 ),
inference(avatar_component_clause,[],[f3954]) ).
fof(f63363,plain,
( spl22_1552
| ~ spl22_119
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f4293,f3929,f1064,f63361]) ).
fof(f63361,plain,
( spl22_1552
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK10(apply(X1,X0)),X2)
| ~ sP0(X1,powerset(X2))
| empty(apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1552])]) ).
fof(f3929,plain,
( spl22_339
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| element(X3,X1)
| ~ in(X3,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_339])]) ).
fof(f4293,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK10(apply(X1,X0)),X2)
| ~ sP0(X1,powerset(X2))
| empty(apply(X1,X0)) )
| ~ spl22_119
| ~ spl22_339 ),
inference(resolution,[],[f3930,f1065]) ).
fof(f3930,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,apply(X0,X2))
| ~ in(X2,relation_dom(X0))
| element(X3,X1)
| ~ sP0(X0,powerset(X1)) )
| ~ spl22_339 ),
inference(avatar_component_clause,[],[f3929]) ).
fof(f63359,plain,
( spl22_1551
| ~ spl22_290
| ~ spl22_635 ),
inference(avatar_split_clause,[],[f13108,f13056,f3304,f63357]) ).
fof(f13108,plain,
( ! [X0,X1] :
( sP0(sK15,relation_rng(X0))
| ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_290
| ~ spl22_635 ),
inference(resolution,[],[f13057,f3305]) ).
fof(f63355,plain,
( spl22_1550
| ~ spl22_150
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3831,f3697,f1405,f63353]) ).
fof(f63353,plain,
( spl22_1550
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1550])]) ).
fof(f1405,plain,
( spl22_150
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_150])]) ).
fof(f3831,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,X4)
| ~ empty(X4) )
| ~ spl22_150
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1406]) ).
fof(f1406,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl22_150 ),
inference(avatar_component_clause,[],[f1405]) ).
fof(f63351,plain,
( spl22_1549
| ~ spl22_148
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3827,f3697,f1397,f63349]) ).
fof(f63349,plain,
( spl22_1549
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1549])]) ).
fof(f1397,plain,
( spl22_148
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_148])]) ).
fof(f3827,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),X4)
| ~ empty(X4) )
| ~ spl22_148
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1398]) ).
fof(f1398,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl22_148 ),
inference(avatar_component_clause,[],[f1397]) ).
fof(f63347,plain,
( spl22_1548
| ~ spl22_151
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3820,f3697,f1409,f63345]) ).
fof(f63345,plain,
( spl22_1548
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1548])]) ).
fof(f1409,plain,
( spl22_151
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_151])]) ).
fof(f3820,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| ~ empty(X3) )
| ~ spl22_151
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1410]) ).
fof(f1410,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X0) )
| ~ spl22_151 ),
inference(avatar_component_clause,[],[f1409]) ).
fof(f63343,plain,
( spl22_1547
| ~ spl22_149
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3819,f3697,f1401,f63341]) ).
fof(f63341,plain,
( spl22_1547
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1547])]) ).
fof(f1401,plain,
( spl22_149
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_149])]) ).
fof(f3819,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| ~ empty(X4) )
| ~ spl22_149
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1402]) ).
fof(f1402,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X1) )
| ~ spl22_149 ),
inference(avatar_component_clause,[],[f1401]) ).
fof(f63339,plain,
( spl22_1546
| ~ spl22_138
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3816,f3697,f1286,f63337]) ).
fof(f63337,plain,
( spl22_1546
<=> ! [X2,X0,X1,X3] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1546])]) ).
fof(f1286,plain,
( spl22_138
<=> ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_138])]) ).
fof(f3816,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),apply(X1,X0)) )
| ~ spl22_138
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1287]) ).
fof(f1287,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl22_138 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f63335,plain,
( spl22_1545
| ~ spl22_139
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3815,f3697,f1290,f63333]) ).
fof(f63333,plain,
( spl22_1545
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1545])]) ).
fof(f1290,plain,
( spl22_139
<=> ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_139])]) ).
fof(f3815,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,apply(X1,X0)) )
| ~ spl22_139
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1291]) ).
fof(f1291,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl22_139 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f63331,plain,
( spl22_1544
| ~ spl22_142
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3806,f3697,f1341,f63329]) ).
fof(f63329,plain,
( spl22_1544
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP0(X3,apply(X1,X0))
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1544])]) ).
fof(f1341,plain,
( spl22_142
<=> ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_142])]) ).
fof(f3806,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP0(X3,apply(X1,X0))
| ~ empty(relation_dom(X3)) )
| ~ spl22_142
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1342]) ).
fof(f1342,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ empty(relation_dom(X0)) )
| ~ spl22_142 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f63327,plain,
( spl22_1543
| ~ spl22_158
| ~ spl22_307 ),
inference(avatar_split_clause,[],[f3532,f3459,f1544,f63325]) ).
fof(f63325,plain,
( spl22_1543
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,relation_dom(X2))
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1543])]) ).
fof(f3459,plain,
( spl22_307
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(X2))
| ~ empty(X0)
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_307])]) ).
fof(f3532,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,relation_dom(X2))
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3) )
| ~ spl22_158
| ~ spl22_307 ),
inference(duplicate_literal_removal,[],[f3527]) ).
fof(f3527,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,relation_dom(X2))
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3)
| ~ empty(X3) )
| ~ spl22_158
| ~ spl22_307 ),
inference(resolution,[],[f3460,f1545]) ).
fof(f3460,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X3)
| ~ empty(X0)
| sP2(X0,X1,relation_dom(X2))
| ~ empty(X3) )
| ~ spl22_307 ),
inference(avatar_component_clause,[],[f3459]) ).
fof(f63323,plain,
( spl22_1542
| ~ spl22_158
| ~ spl22_303 ),
inference(avatar_split_clause,[],[f3521,f3442,f1544,f63321]) ).
fof(f63321,plain,
( spl22_1542
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,X0)
| ~ empty(X3)
| sK7(X1,X3) = apply(X1,sK8(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1542])]) ).
fof(f3442,plain,
( spl22_303
<=> ! [X0,X3,X2,X1] :
( sP2(relation_dom(X0),X1,X2)
| ~ empty(X2)
| ~ sP0(X0,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_303])]) ).
fof(f3521,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,X0)
| ~ empty(X3)
| sK7(X1,X3) = apply(X1,sK8(X1,X3)) )
| ~ spl22_158
| ~ spl22_303 ),
inference(duplicate_literal_removal,[],[f3516]) ).
fof(f3516,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,X0)
| ~ empty(X3)
| sK7(X1,X3) = apply(X1,sK8(X1,X3))
| ~ empty(X3) )
| ~ spl22_158
| ~ spl22_303 ),
inference(resolution,[],[f3443,f1545]) ).
fof(f3443,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X3)
| ~ empty(X2)
| sP2(relation_dom(X0),X1,X2)
| ~ empty(X3) )
| ~ spl22_303 ),
inference(avatar_component_clause,[],[f3442]) ).
fof(f63319,plain,
( spl22_1541
| ~ spl22_158
| ~ spl22_300 ),
inference(avatar_split_clause,[],[f3510,f3430,f1544,f63317]) ).
fof(f63317,plain,
( spl22_1541
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,relation_dom(X2))
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1541])]) ).
fof(f3430,plain,
( spl22_300
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(X2))
| ~ empty(X1)
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_300])]) ).
fof(f3510,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,relation_dom(X2))
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3) )
| ~ spl22_158
| ~ spl22_300 ),
inference(duplicate_literal_removal,[],[f3505]) ).
fof(f3505,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,relation_dom(X2))
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3)
| ~ empty(X3) )
| ~ spl22_158
| ~ spl22_300 ),
inference(resolution,[],[f3431,f1545]) ).
fof(f3431,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X3)
| ~ empty(X1)
| sP2(X0,X1,relation_dom(X2))
| ~ empty(X3) )
| ~ spl22_300 ),
inference(avatar_component_clause,[],[f3430]) ).
fof(f62853,plain,
( spl22_1540
| ~ spl22_158
| ~ spl22_297 ),
inference(avatar_split_clause,[],[f3494,f3418,f1544,f62851]) ).
fof(f62851,plain,
( spl22_1540
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),X0)
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1540])]) ).
fof(f3418,plain,
( spl22_297
<=> ! [X0,X3,X2,X1] :
( sP2(X0,relation_dom(X1),X2)
| ~ empty(X2)
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_297])]) ).
fof(f3494,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),X0)
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3) )
| ~ spl22_158
| ~ spl22_297 ),
inference(duplicate_literal_removal,[],[f3489]) ).
fof(f3489,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),X0)
| ~ empty(X3)
| apply(X2,sK8(X2,X3)) = sK7(X2,X3)
| ~ empty(X3) )
| ~ spl22_158
| ~ spl22_297 ),
inference(resolution,[],[f3419,f1545]) ).
fof(f3419,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X1,X3)
| ~ empty(X2)
| sP2(X0,relation_dom(X1),X2)
| ~ empty(X3) )
| ~ spl22_297 ),
inference(avatar_component_clause,[],[f3418]) ).
fof(f62849,plain,
( spl22_1539
| ~ spl22_158
| ~ spl22_292 ),
inference(avatar_split_clause,[],[f3478,f3390,f1544,f62847]) ).
fof(f62847,plain,
( spl22_1539
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1539])]) ).
fof(f3390,plain,
( spl22_292
<=> ! [X2,X0,X1] :
( sP0(X0,relation_dom(X1))
| ~ empty(relation_dom(X0))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_292])]) ).
fof(f3478,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2)) )
| ~ spl22_158
| ~ spl22_292 ),
inference(duplicate_literal_removal,[],[f3473]) ).
fof(f3473,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2))
| ~ empty(X2) )
| ~ spl22_158
| ~ spl22_292 ),
inference(resolution,[],[f3391,f1545]) ).
fof(f3391,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,X2)
| ~ empty(relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ empty(X2) )
| ~ spl22_292 ),
inference(avatar_component_clause,[],[f3390]) ).
fof(f62845,plain,
( spl22_1538
| ~ spl22_73
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3353,f3304,f652,f62843]) ).
fof(f62843,plain,
( spl22_1538
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK8(X2,relation_rng(X0)),relation_dom(X2))
| sP0(X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1538])]) ).
fof(f652,plain,
( spl22_73
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_73])]) ).
fof(f3353,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK8(X2,relation_rng(X0)),relation_dom(X2))
| sP0(X2,relation_rng(X0)) )
| ~ spl22_73
| ~ spl22_290 ),
inference(resolution,[],[f3305,f653]) ).
fof(f653,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_73 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f62841,plain,
( spl22_1537
| ~ spl22_154
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3350,f3304,f1527,f62839]) ).
fof(f62839,plain,
( spl22_1537
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK8(X2,relation_rng(X0)),relation_dom(X2))
| sP0(X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1537])]) ).
fof(f1527,plain,
( spl22_154
<=> ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| element(sK8(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_154])]) ).
fof(f3350,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| element(sK8(X2,relation_rng(X0)),relation_dom(X2))
| sP0(X2,relation_rng(X0)) )
| ~ spl22_154
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1528]) ).
fof(f1528,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_154 ),
inference(avatar_component_clause,[],[f1527]) ).
fof(f62837,plain,
( spl22_1536
| ~ spl22_44
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f3243,f2999,f450,f62835]) ).
fof(f62835,plain,
( spl22_1536
<=> ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| relation_dom_restriction(X0,X1) = relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X0,X1)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1536])]) ).
fof(f2999,plain,
( spl22_278
<=> ! [X0] :
( relation_dom_restriction(X0,relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_278])]) ).
fof(f3243,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| relation_dom_restriction(X0,X1) = relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X0,X1)))
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_278 ),
inference(resolution,[],[f3000,f451]) ).
fof(f3000,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation_dom_restriction(X0,relation_dom(X0)) = X0 )
| ~ spl22_278 ),
inference(avatar_component_clause,[],[f2999]) ).
fof(f62833,plain,
( spl22_1535
| ~ spl22_147
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3134,f2907,f1393,f62831]) ).
fof(f62831,plain,
( spl22_1535
<=> ! [X2,X0,X1] :
( empty(set_intersection2(X0,apply(X1,X2)))
| ~ sP0(X1,sK10(set_intersection2(X0,apply(X1,X2))))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1535])]) ).
fof(f1393,plain,
( spl22_147
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ in(X2,apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_147])]) ).
fof(f2907,plain,
( spl22_255
<=> ! [X0,X1] :
( in(sK10(set_intersection2(X0,X1)),X1)
| empty(set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_255])]) ).
fof(f3134,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(X0,apply(X1,X2)))
| ~ sP0(X1,sK10(set_intersection2(X0,apply(X1,X2))))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_255 ),
inference(resolution,[],[f2908,f1394]) ).
fof(f1394,plain,
( ! [X2,X0,X1] :
( ~ in(X2,apply(X1,X0))
| ~ sP0(X1,X2)
| ~ in(X0,relation_dom(X1)) )
| ~ spl22_147 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f2908,plain,
( ! [X0,X1] :
( in(sK10(set_intersection2(X0,X1)),X1)
| empty(set_intersection2(X0,X1)) )
| ~ spl22_255 ),
inference(avatar_component_clause,[],[f2907]) ).
fof(f62829,plain,
( spl22_1534
| ~ spl22_147
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3110,f2903,f1393,f62827]) ).
fof(f62827,plain,
( spl22_1534
<=> ! [X2,X0,X1] :
( empty(set_intersection2(apply(X0,X1),X2))
| ~ sP0(X0,sK10(set_intersection2(apply(X0,X1),X2)))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1534])]) ).
fof(f2903,plain,
( spl22_254
<=> ! [X0,X1] :
( in(sK10(set_intersection2(X0,X1)),X0)
| empty(set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_254])]) ).
fof(f3110,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(apply(X0,X1),X2))
| ~ sP0(X0,sK10(set_intersection2(apply(X0,X1),X2)))
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_147
| ~ spl22_254 ),
inference(resolution,[],[f2904,f1394]) ).
fof(f2904,plain,
( ! [X0,X1] :
( in(sK10(set_intersection2(X0,X1)),X0)
| empty(set_intersection2(X0,X1)) )
| ~ spl22_254 ),
inference(avatar_component_clause,[],[f2903]) ).
fof(f62825,plain,
( spl22_1533
| ~ spl22_147
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3089,f2895,f1393,f62823]) ).
fof(f62823,plain,
( spl22_1533
<=> ! [X2,X0,X1] :
( sP2(sK15,X0,apply(X1,X2))
| ~ sP0(X1,sK13(sK15,X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1533])]) ).
fof(f2895,plain,
( spl22_252
<=> ! [X0,X1] :
( in(sK13(sK15,X0,X1),X1)
| sP2(sK15,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_252])]) ).
fof(f3089,plain,
( ! [X2,X0,X1] :
( sP2(sK15,X0,apply(X1,X2))
| ~ sP0(X1,sK13(sK15,X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_252 ),
inference(resolution,[],[f2896,f1394]) ).
fof(f2896,plain,
( ! [X0,X1] :
( in(sK13(sK15,X0,X1),X1)
| sP2(sK15,X0,X1) )
| ~ spl22_252 ),
inference(avatar_component_clause,[],[f2895]) ).
fof(f62821,plain,
( spl22_1532
| ~ spl22_147
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3070,f2891,f1393,f62819]) ).
fof(f62819,plain,
( spl22_1532
<=> ! [X2,X0,X1] :
( sP2(X0,sK15,apply(X1,X2))
| ~ sP0(X1,sK13(X0,sK15,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1532])]) ).
fof(f2891,plain,
( spl22_251
<=> ! [X0,X1] :
( in(sK13(X0,sK15,X1),X1)
| sP2(X0,sK15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_251])]) ).
fof(f3070,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK15,apply(X1,X2))
| ~ sP0(X1,sK13(X0,sK15,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_251 ),
inference(resolution,[],[f2892,f1394]) ).
fof(f2892,plain,
( ! [X0,X1] :
( in(sK13(X0,sK15,X1),X1)
| sP2(X0,sK15,X1) )
| ~ spl22_251 ),
inference(avatar_component_clause,[],[f2891]) ).
fof(f62817,plain,
( spl22_1531
| ~ spl22_147
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3034,f2887,f1393,f62815]) ).
fof(f62815,plain,
( spl22_1531
<=> ! [X2,X0,X1] :
( sP2(X0,apply(X1,X2),sK15)
| ~ sP0(X1,sK13(X0,apply(X1,X2),sK15))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1531])]) ).
fof(f2887,plain,
( spl22_250
<=> ! [X0,X1] :
( in(sK13(X0,X1,sK15),X1)
| sP2(X0,X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_250])]) ).
fof(f3034,plain,
( ! [X2,X0,X1] :
( sP2(X0,apply(X1,X2),sK15)
| ~ sP0(X1,sK13(X0,apply(X1,X2),sK15))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_250 ),
inference(resolution,[],[f2888,f1394]) ).
fof(f2888,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,sK15),X1)
| sP2(X0,X1,sK15) )
| ~ spl22_250 ),
inference(avatar_component_clause,[],[f2887]) ).
fof(f62346,plain,
( spl22_1530
| ~ spl22_147
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3015,f2883,f1393,f62344]) ).
fof(f62344,plain,
( spl22_1530
<=> ! [X2,X0,X1] :
( sP2(apply(X0,X1),X2,sK15)
| ~ sP0(X0,sK13(apply(X0,X1),X2,sK15))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1530])]) ).
fof(f2883,plain,
( spl22_249
<=> ! [X0,X1] :
( in(sK13(X0,X1,sK15),X0)
| sP2(X0,X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_249])]) ).
fof(f3015,plain,
( ! [X2,X0,X1] :
( sP2(apply(X0,X1),X2,sK15)
| ~ sP0(X0,sK13(apply(X0,X1),X2,sK15))
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_147
| ~ spl22_249 ),
inference(resolution,[],[f2884,f1394]) ).
fof(f2884,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,sK15),X0)
| sP2(X0,X1,sK15) )
| ~ spl22_249 ),
inference(avatar_component_clause,[],[f2883]) ).
fof(f62342,plain,
( spl22_1529
| ~ spl22_77
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2583,f2559,f698,f62340]) ).
fof(f62340,plain,
( spl22_1529
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sK7(X1,relation_dom(X0)) = apply(X1,sK8(X1,relation_dom(X0)))
| sP0(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1529])]) ).
fof(f698,plain,
( spl22_77
<=> ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_77])]) ).
fof(f2583,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sK7(X1,relation_dom(X0)) = apply(X1,sK8(X1,relation_dom(X0)))
| sP0(X1,relation_dom(X0)) )
| ~ spl22_77
| ~ spl22_233 ),
inference(resolution,[],[f2560,f699]) ).
fof(f699,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1) )
| ~ spl22_77 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f62330,plain,
( ~ spl22_88
| ~ spl22_39
| spl22_1528
| ~ spl22_172
| ~ spl22_203 ),
inference(avatar_split_clause,[],[f2202,f2166,f1735,f62328,f410,f777]) ).
fof(f777,plain,
( spl22_88
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_88])]) ).
fof(f62328,plain,
( spl22_1528
<=> ! [X0] :
( sK15 = relation_dom_restriction(X0,sK15)
| ~ relation(X0)
| ~ function(X0)
| in(sK12(sK15,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1528])]) ).
fof(f1735,plain,
( spl22_172
<=> ! [X0,X1] :
( relation_dom_restriction(X0,sK15) = X1
| relation_dom(X1) != sK15
| in(sK12(X1,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_172])]) ).
fof(f2202,plain,
( ! [X0] :
( sK15 = relation_dom_restriction(X0,sK15)
| in(sK12(sK15,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_172
| ~ spl22_203 ),
inference(trivial_inequality_removal,[],[f2196]) ).
fof(f2196,plain,
( ! [X0] :
( sK15 != sK15
| sK15 = relation_dom_restriction(X0,sK15)
| in(sK12(sK15,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_172
| ~ spl22_203 ),
inference(superposition,[],[f1736,f2168]) ).
fof(f1736,plain,
( ! [X0,X1] :
( relation_dom(X1) != sK15
| relation_dom_restriction(X0,sK15) = X1
| in(sK12(X1,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_172 ),
inference(avatar_component_clause,[],[f1735]) ).
fof(f62069,plain,
( spl22_1527
| ~ spl22_216
| ~ spl22_592 ),
inference(avatar_split_clause,[],[f11840,f11832,f2344,f62067]) ).
fof(f62067,plain,
( spl22_1527
<=> ! [X2,X0,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK7(X2,relation_rng(relation_dom_restriction(X0,X1))))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK7(X2,relation_rng(relation_dom_restriction(X0,X1)))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP0(X2,relation_rng(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,relation_rng(relation_dom_restriction(X0,X1)))) = apply(sK5,sK8(X2,relation_rng(relation_dom_restriction(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1527])]) ).
fof(f2344,plain,
( spl22_216
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| sP0(X0,X1)
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_216])]) ).
fof(f11840,plain,
( ! [X2,X0,X1] :
( ~ sP1(relation_dom_restriction(X0,X1))
| apply(X0,sK9(relation_dom_restriction(X0,X1),sK7(X2,relation_rng(relation_dom_restriction(X0,X1))))) = apply(relation_dom_restriction(X0,X1),sK9(relation_dom_restriction(X0,X1),sK7(X2,relation_rng(relation_dom_restriction(X0,X1)))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sP0(X2,relation_rng(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,relation_rng(relation_dom_restriction(X0,X1)))) = apply(sK5,sK8(X2,relation_rng(relation_dom_restriction(X0,X1)))) )
| ~ spl22_216
| ~ spl22_592 ),
inference(resolution,[],[f11833,f2345]) ).
fof(f2345,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1)) )
| ~ spl22_216 ),
inference(avatar_component_clause,[],[f2344]) ).
fof(f62065,plain,
( spl22_1526
| ~ spl22_232
| ~ spl22_444 ),
inference(avatar_split_clause,[],[f7216,f6337,f2531,f62063]) ).
fof(f62063,plain,
( spl22_1526
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sP2(apply(X1,X0),X2,apply(X1,X0))
| sK7(X1,sK13(apply(X1,X0),X2,apply(X1,X0))) = apply(X1,sK8(X1,sK13(apply(X1,X0),X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(apply(X1,X0),X2,apply(X1,X0))),sK7(X1,sK13(apply(X1,X0),X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(apply(X1,X0),X2,apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1526])]) ).
fof(f2531,plain,
( spl22_232
<=> ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_232])]) ).
fof(f6337,plain,
( spl22_444
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| sP2(apply(X0,X1),X2,apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_444])]) ).
fof(f7216,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sP2(apply(X1,X0),X2,apply(X1,X0))
| sK7(X1,sK13(apply(X1,X0),X2,apply(X1,X0))) = apply(X1,sK8(X1,sK13(apply(X1,X0),X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(apply(X1,X0),X2,apply(X1,X0))),sK7(X1,sK13(apply(X1,X0),X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(apply(X1,X0),X2,apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_444 ),
inference(resolution,[],[f6338,f2532]) ).
fof(f2532,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1)) )
| ~ spl22_232 ),
inference(avatar_component_clause,[],[f2531]) ).
fof(f6338,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| sP2(apply(X0,X1),X2,apply(X0,X1)) )
| ~ spl22_444 ),
inference(avatar_component_clause,[],[f6337]) ).
fof(f62061,plain,
( spl22_1525
| ~ spl22_232
| ~ spl22_443 ),
inference(avatar_split_clause,[],[f7200,f6333,f2531,f62059]) ).
fof(f62059,plain,
( spl22_1525
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sP2(X2,apply(X1,X0),apply(X1,X0))
| sK7(X1,sK13(X2,apply(X1,X0),apply(X1,X0))) = apply(X1,sK8(X1,sK13(X2,apply(X1,X0),apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(X2,apply(X1,X0),apply(X1,X0))),sK7(X1,sK13(X2,apply(X1,X0),apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(X2,apply(X1,X0),apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1525])]) ).
fof(f6333,plain,
( spl22_443
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK13(X1,apply(X0,X2),apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP2(X1,apply(X0,X2),apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_443])]) ).
fof(f7200,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sP2(X2,apply(X1,X0),apply(X1,X0))
| sK7(X1,sK13(X2,apply(X1,X0),apply(X1,X0))) = apply(X1,sK8(X1,sK13(X2,apply(X1,X0),apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(X2,apply(X1,X0),apply(X1,X0))),sK7(X1,sK13(X2,apply(X1,X0),apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(X2,apply(X1,X0),apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_443 ),
inference(resolution,[],[f6334,f2532]) ).
fof(f6334,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK13(X1,apply(X0,X2),apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP2(X1,apply(X0,X2),apply(X0,X2)) )
| ~ spl22_443 ),
inference(avatar_component_clause,[],[f6333]) ).
fof(f62057,plain,
( spl22_1524
| ~ spl22_849
| ~ spl22_893 ),
inference(avatar_split_clause,[],[f21602,f20845,f19428,f62055]) ).
fof(f62055,plain,
( spl22_1524
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,sK10(powerset(X0))),X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1524])]) ).
fof(f19428,plain,
( spl22_849
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_849])]) ).
fof(f20845,plain,
( spl22_893
<=> ! [X0] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,sK10(powerset(X0))),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_893])]) ).
fof(f21602,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,sK10(powerset(X0))),X1)
| ~ empty(X1) )
| ~ spl22_849
| ~ spl22_893 ),
inference(resolution,[],[f20846,f19429]) ).
fof(f19429,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_849 ),
inference(avatar_component_clause,[],[f19428]) ).
fof(f20846,plain,
( ! [X0] :
( sP0(relation_dom_restriction(sK5,sK10(powerset(X0))),sK15)
| ~ empty(X0) )
| ~ spl22_893 ),
inference(avatar_component_clause,[],[f20845]) ).
fof(f60887,plain,
( spl22_1523
| ~ spl22_849
| ~ spl22_883 ),
inference(avatar_split_clause,[],[f21271,f20794,f19428,f60885]) ).
fof(f60885,plain,
( spl22_1523
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(relation_dom_restriction(sK5,relation_dom(X0)),X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1523])]) ).
fof(f20794,plain,
( spl22_883
<=> ! [X0] :
( ~ sP0(X0,sK15)
| sP0(relation_dom_restriction(sK5,relation_dom(X0)),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_883])]) ).
fof(f21271,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(relation_dom_restriction(sK5,relation_dom(X0)),X1)
| ~ empty(X1) )
| ~ spl22_849
| ~ spl22_883 ),
inference(resolution,[],[f20795,f19429]) ).
fof(f20795,plain,
( ! [X0] :
( sP0(relation_dom_restriction(sK5,relation_dom(X0)),sK15)
| ~ sP0(X0,sK15) )
| ~ spl22_883 ),
inference(avatar_component_clause,[],[f20794]) ).
fof(f58281,plain,
( spl22_1522
| ~ spl22_115
| ~ spl22_484 ),
inference(avatar_split_clause,[],[f8740,f8705,f959,f58279]) ).
fof(f58279,plain,
( spl22_1522
<=> ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,sK15)) = apply(sK15,sK8(X0,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1522])]) ).
fof(f8740,plain,
( ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,sK15)) = apply(sK15,sK8(X0,sK15)) )
| ~ spl22_115
| ~ spl22_484 ),
inference(resolution,[],[f8706,f960]) ).
fof(f58277,plain,
( spl22_1521
| ~ spl22_46
| ~ spl22_1477 ),
inference(avatar_split_clause,[],[f58007,f57398,f458,f58275]) ).
fof(f58275,plain,
( spl22_1521
<=> ! [X0] :
( sP0(X0,sK15)
| element(sK8(X0,sK15),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1521])]) ).
fof(f57398,plain,
( spl22_1477
<=> ! [X1] :
( sP0(X1,sK15)
| in(sK8(X1,sK15),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1477])]) ).
fof(f58007,plain,
( ! [X0] :
( sP0(X0,sK15)
| element(sK8(X0,sK15),relation_dom(X0)) )
| ~ spl22_46
| ~ spl22_1477 ),
inference(resolution,[],[f57399,f459]) ).
fof(f57399,plain,
( ! [X1] :
( in(sK8(X1,sK15),relation_dom(X1))
| sP0(X1,sK15) )
| ~ spl22_1477 ),
inference(avatar_component_clause,[],[f57398]) ).
fof(f58273,plain,
( spl22_1520
| ~ spl22_115
| ~ spl22_483 ),
inference(avatar_split_clause,[],[f8502,f8467,f959,f58271]) ).
fof(f58271,plain,
( spl22_1520
<=> ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,sK15)) = apply(sK20,sK8(X0,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1520])]) ).
fof(f8502,plain,
( ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,sK15)) = apply(sK20,sK8(X0,sK15)) )
| ~ spl22_115
| ~ spl22_483 ),
inference(resolution,[],[f8468,f960]) ).
fof(f58269,plain,
( spl22_1519
| ~ spl22_115
| ~ spl22_482 ),
inference(avatar_split_clause,[],[f8465,f8430,f959,f58267]) ).
fof(f58267,plain,
( spl22_1519
<=> ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,sK15)) = apply(sK19,sK8(X0,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1519])]) ).
fof(f8465,plain,
( ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,sK15)) = apply(sK19,sK8(X0,sK15)) )
| ~ spl22_115
| ~ spl22_482 ),
inference(resolution,[],[f8431,f960]) ).
fof(f58265,plain,
( spl22_1518
| ~ spl22_47
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5950,f5683,f462,f58263]) ).
fof(f58263,plain,
( spl22_1518
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = apply(X0,sK9(X0,apply(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1518])]) ).
fof(f5683,plain,
( spl22_420
<=> ! [X2,X0,X1] :
( apply(X1,X2) = apply(X0,sK9(X0,apply(X1,X2)))
| ~ sP1(X0)
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_420])]) ).
fof(f5950,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = apply(X0,sK9(X0,apply(X0,X1))) )
| ~ spl22_47
| ~ spl22_420 ),
inference(duplicate_literal_removal,[],[f5946]) ).
fof(f5946,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = apply(X0,sK9(X0,apply(X0,X1)))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_420 ),
inference(resolution,[],[f5684,f463]) ).
fof(f5684,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,relation_rng(X0))
| ~ sP1(X0)
| ~ in(X2,relation_dom(X1))
| apply(X1,X2) = apply(X0,sK9(X0,apply(X1,X2))) )
| ~ spl22_420 ),
inference(avatar_component_clause,[],[f5683]) ).
fof(f58261,plain,
( spl22_1517
| ~ spl22_26
| ~ spl22_403 ),
inference(avatar_split_clause,[],[f5441,f5254,f347,f58259]) ).
fof(f58259,plain,
( spl22_1517
<=> ! [X0,X1] :
( empty(powerset(X0))
| apply(X1,X0) = apply(relation_dom_restriction(X1,powerset(X0)),X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1517])]) ).
fof(f347,plain,
( spl22_26
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_26])]) ).
fof(f5254,plain,
( spl22_403
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| apply(X2,X1) = apply(relation_dom_restriction(X2,powerset(X0)),X1)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_403])]) ).
fof(f5441,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| apply(X1,X0) = apply(relation_dom_restriction(X1,powerset(X0)),X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_26
| ~ spl22_403 ),
inference(resolution,[],[f5255,f348]) ).
fof(f348,plain,
( ! [X0] : subset(X0,X0)
| ~ spl22_26 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f5255,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X0)
| empty(powerset(X0))
| apply(X2,X1) = apply(relation_dom_restriction(X2,powerset(X0)),X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_403 ),
inference(avatar_component_clause,[],[f5254]) ).
fof(f58257,plain,
( spl22_1516
| ~ spl22_133
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5392,f5246,f1246,f58255]) ).
fof(f58255,plain,
( spl22_1516
<=> ! [X0,X3,X2,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1516])]) ).
fof(f1246,plain,
( spl22_133
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_133])]) ).
fof(f5392,plain,
( ! [X2,X3,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_401 ),
inference(resolution,[],[f5247,f1247]) ).
fof(f1247,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133 ),
inference(avatar_component_clause,[],[f1246]) ).
fof(f58253,plain,
( spl22_1515
| ~ spl22_133
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5342,f5242,f1246,f58251]) ).
fof(f58251,plain,
( spl22_1515
<=> ! [X0,X3,X2,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1515])]) ).
fof(f5342,plain,
( ! [X2,X3,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_400 ),
inference(resolution,[],[f5243,f1247]) ).
fof(f58249,plain,
( spl22_1514
| ~ spl22_133
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5329,f5238,f1246,f58247]) ).
fof(f58247,plain,
( spl22_1514
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1)))
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1514])]) ).
fof(f5238,plain,
( spl22_399
<=> ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| in(sK8(X0,sK10(powerset(X1))),relation_dom(X0))
| sP0(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_399])]) ).
fof(f5329,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1)))
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_399 ),
inference(resolution,[],[f5239,f1247]) ).
fof(f5239,plain,
( ! [X0,X1] :
( in(sK8(X0,sK10(powerset(X1))),relation_dom(X0))
| element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl22_399 ),
inference(avatar_component_clause,[],[f5238]) ).
fof(f58245,plain,
( spl22_1513
| ~ spl22_133
| ~ spl22_394 ),
inference(avatar_split_clause,[],[f5136,f5118,f1246,f58243]) ).
fof(f58243,plain,
( spl22_1513
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1))
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1513])]) ).
fof(f5136,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1))
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_394 ),
inference(resolution,[],[f5119,f1247]) ).
fof(f58241,plain,
( spl22_1512
| ~ spl22_290
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5053,f4944,f3304,f58239]) ).
fof(f58239,plain,
( spl22_1512
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(relation_rng(X0),X1),X2,set_intersection2(relation_rng(X0),X1))
| ~ sP1(X0)
| ~ sP0(X0,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1512])]) ).
fof(f5053,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(relation_rng(X0),X1),X2,set_intersection2(relation_rng(X0),X1))
| ~ sP1(X0)
| ~ sP0(X0,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_391 ),
inference(resolution,[],[f4945,f3305]) ).
fof(f58237,plain,
( spl22_1511
| ~ spl22_290
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5023,f4940,f3304,f58235]) ).
fof(f58235,plain,
( spl22_1511
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,relation_rng(X1)),X2,set_intersection2(X0,relation_rng(X1)))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1511])]) ).
fof(f5023,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,relation_rng(X1)),X2,set_intersection2(X0,relation_rng(X1)))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_390 ),
inference(resolution,[],[f4941,f3305]) ).
fof(f58233,plain,
( spl22_1510
| ~ spl22_45
| ~ spl22_1477 ),
inference(avatar_split_clause,[],[f58006,f57398,f454,f58231]) ).
fof(f58231,plain,
( spl22_1510
<=> ! [X0] :
( sP0(X0,sK15)
| ~ in(relation_dom(X0),sK8(X0,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1510])]) ).
fof(f58006,plain,
( ! [X0] :
( sP0(X0,sK15)
| ~ in(relation_dom(X0),sK8(X0,sK15)) )
| ~ spl22_45
| ~ spl22_1477 ),
inference(resolution,[],[f57399,f455]) ).
fof(f58229,plain,
( spl22_1509
| ~ spl22_290
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4989,f4902,f3304,f58227]) ).
fof(f58227,plain,
( spl22_1509
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(relation_rng(X1),X2),set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1509])]) ).
fof(f4989,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(relation_rng(X1),X2),set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_388 ),
inference(resolution,[],[f4903,f3305]) ).
fof(f58225,plain,
( spl22_1508
| ~ spl22_290
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4961,f4898,f3304,f58223]) ).
fof(f58223,plain,
( spl22_1508
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,relation_rng(X2)),set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1508])]) ).
fof(f4961,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,relation_rng(X2)),set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_387 ),
inference(resolution,[],[f4899,f3305]) ).
fof(f58221,plain,
( spl22_1507
| ~ spl22_47
| ~ spl22_385 ),
inference(avatar_split_clause,[],[f4892,f4788,f462,f58219]) ).
fof(f58219,plain,
( spl22_1507
<=> ! [X2,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| element(sK13(X0,X1,relation_dom(X2)),X0)
| ~ empty(relation_rng(X2))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1507])]) ).
fof(f4788,plain,
( spl22_385
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,relation_dom(X2)),X0)
| sP2(X0,X1,relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_385])]) ).
fof(f4892,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| element(sK13(X0,X1,relation_dom(X2)),X0)
| ~ empty(relation_rng(X2))
| ~ sP1(X2) )
| ~ spl22_47
| ~ spl22_385 ),
inference(resolution,[],[f4789,f463]) ).
fof(f4789,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X3)
| sP2(X0,X1,relation_dom(X2))
| element(sK13(X0,X1,relation_dom(X2)),X0)
| ~ empty(X3) )
| ~ spl22_385 ),
inference(avatar_component_clause,[],[f4788]) ).
fof(f58217,plain,
( spl22_1506
| ~ spl22_47
| ~ spl22_384 ),
inference(avatar_split_clause,[],[f4885,f4784,f462,f58215]) ).
fof(f58215,plain,
( spl22_1506
<=> ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,X2)
| element(sK13(relation_dom(X0),X1,X2),X2)
| ~ empty(relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1506])]) ).
fof(f4784,plain,
( spl22_384
<=> ! [X0,X3,X2,X1] :
( element(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2)
| ~ sP0(X0,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_384])]) ).
fof(f4885,plain,
( ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,X2)
| element(sK13(relation_dom(X0),X1,X2),X2)
| ~ empty(relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_384 ),
inference(resolution,[],[f4785,f463]) ).
fof(f4785,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X3)
| sP2(relation_dom(X0),X1,X2)
| element(sK13(relation_dom(X0),X1,X2),X2)
| ~ empty(X3) )
| ~ spl22_384 ),
inference(avatar_component_clause,[],[f4784]) ).
fof(f58213,plain,
( spl22_1505
| ~ spl22_47
| ~ spl22_383 ),
inference(avatar_split_clause,[],[f4878,f4780,f462,f58211]) ).
fof(f58211,plain,
( spl22_1505
<=> ! [X2,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| element(sK13(X0,X1,relation_dom(X2)),X1)
| ~ empty(relation_rng(X2))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1505])]) ).
fof(f4780,plain,
( spl22_383
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,relation_dom(X2)),X1)
| sP2(X0,X1,relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_383])]) ).
fof(f4878,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| element(sK13(X0,X1,relation_dom(X2)),X1)
| ~ empty(relation_rng(X2))
| ~ sP1(X2) )
| ~ spl22_47
| ~ spl22_383 ),
inference(resolution,[],[f4781,f463]) ).
fof(f4781,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X3)
| sP2(X0,X1,relation_dom(X2))
| element(sK13(X0,X1,relation_dom(X2)),X1)
| ~ empty(X3) )
| ~ spl22_383 ),
inference(avatar_component_clause,[],[f4780]) ).
fof(f58209,plain,
( spl22_1504
| ~ spl22_47
| ~ spl22_382 ),
inference(avatar_split_clause,[],[f4871,f4776,f462,f58207]) ).
fof(f58207,plain,
( spl22_1504
<=> ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),X2)
| element(sK13(X0,relation_dom(X1),X2),X2)
| ~ empty(relation_rng(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1504])]) ).
fof(f4776,plain,
( spl22_382
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,relation_dom(X1),X2),X2)
| sP2(X0,relation_dom(X1),X2)
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_382])]) ).
fof(f4871,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),X2)
| element(sK13(X0,relation_dom(X1),X2),X2)
| ~ empty(relation_rng(X1))
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_382 ),
inference(resolution,[],[f4777,f463]) ).
fof(f4777,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X1,X3)
| sP2(X0,relation_dom(X1),X2)
| element(sK13(X0,relation_dom(X1),X2),X2)
| ~ empty(X3) )
| ~ spl22_382 ),
inference(avatar_component_clause,[],[f4776]) ).
fof(f58205,plain,
( spl22_1503
| ~ spl22_47
| ~ spl22_380 ),
inference(avatar_split_clause,[],[f4856,f4768,f462,f58203]) ).
fof(f58203,plain,
( spl22_1503
<=> ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1503])]) ).
fof(f4768,plain,
( spl22_380
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(relation_dom(X0),X2,X3),X3)
| sP2(relation_dom(X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_380])]) ).
fof(f4856,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2)
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_380 ),
inference(resolution,[],[f4769,f463]) ).
fof(f4769,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(relation_dom(X0),X2,X3),X3)
| sP2(relation_dom(X0),X2,X3) )
| ~ spl22_380 ),
inference(avatar_component_clause,[],[f4768]) ).
fof(f58201,plain,
( spl22_1502
| ~ spl22_47
| ~ spl22_379 ),
inference(avatar_split_clause,[],[f4849,f4764,f462,f58199]) ).
fof(f58199,plain,
( spl22_1502
<=> ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(X1,relation_dom(X0),X2),X2)
| sP2(X1,relation_dom(X0),X2)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1502])]) ).
fof(f4764,plain,
( spl22_379
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,relation_dom(X0),X3),X3)
| sP2(X2,relation_dom(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_379])]) ).
fof(f4849,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(X1,relation_dom(X0),X2),X2)
| sP2(X1,relation_dom(X0),X2)
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_379 ),
inference(resolution,[],[f4765,f463]) ).
fof(f4765,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,relation_dom(X0),X3),X3)
| sP2(X2,relation_dom(X0),X3) )
| ~ spl22_379 ),
inference(avatar_component_clause,[],[f4764]) ).
fof(f58197,plain,
( spl22_1501
| ~ spl22_47
| ~ spl22_377 ),
inference(avatar_split_clause,[],[f4842,f4756,f462,f58195]) ).
fof(f58195,plain,
( spl22_1501
<=> ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(X1,X2,relation_dom(X0)),X2)
| sP2(X1,X2,relation_dom(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1501])]) ).
fof(f4756,plain,
( spl22_377
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_dom(X0)),X3)
| sP2(X2,X3,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_377])]) ).
fof(f4842,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(X1,X2,relation_dom(X0)),X2)
| sP2(X1,X2,relation_dom(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_377 ),
inference(resolution,[],[f4757,f463]) ).
fof(f4757,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_dom(X0)),X3)
| sP2(X2,X3,relation_dom(X0)) )
| ~ spl22_377 ),
inference(avatar_component_clause,[],[f4756]) ).
fof(f58193,plain,
( spl22_1500
| ~ spl22_47
| ~ spl22_376 ),
inference(avatar_split_clause,[],[f4831,f4752,f462,f58191]) ).
fof(f58191,plain,
( spl22_1500
<=> ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(X1,X2,relation_dom(X0)),X1)
| sP2(X1,X2,relation_dom(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1500])]) ).
fof(f4752,plain,
( spl22_376
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_dom(X0)),X2)
| sP2(X2,X3,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_376])]) ).
fof(f4831,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK13(X1,X2,relation_dom(X0)),X1)
| sP2(X1,X2,relation_dom(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_376 ),
inference(resolution,[],[f4753,f463]) ).
fof(f4753,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_dom(X0)),X2)
| sP2(X2,X3,relation_dom(X0)) )
| ~ spl22_376 ),
inference(avatar_component_clause,[],[f4752]) ).
fof(f58111,plain,
( spl22_1499
| ~ spl22_113
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4674,f4006,f952,f58109]) ).
fof(f58109,plain,
( spl22_1499
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| relation_rng(X0) = sK15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1499])]) ).
fof(f952,plain,
( spl22_113
<=> ! [X0] :
( sK15 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_113])]) ).
fof(f4674,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| relation_rng(X0) = sK15 )
| ~ spl22_113
| ~ spl22_358 ),
inference(resolution,[],[f4007,f953]) ).
fof(f953,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = X0 )
| ~ spl22_113 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f58107,plain,
( spl22_1498
| ~ spl22_51
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4669,f4006,f503,f58105]) ).
fof(f58105,plain,
( spl22_1498
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1498])]) ).
fof(f503,plain,
( spl22_51
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_51])]) ).
fof(f4669,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| ~ relation(X0)
| empty(X0) )
| ~ spl22_51
| ~ spl22_358 ),
inference(resolution,[],[f4007,f504]) ).
fof(f504,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl22_51 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f58103,plain,
( spl22_1497
| ~ spl22_56
| ~ spl22_327 ),
inference(avatar_split_clause,[],[f3800,f3693,f545,f58101]) ).
fof(f58101,plain,
( spl22_1497
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK7(X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1497])]) ).
fof(f3800,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK7(X0,sK10(powerset(X1))),X1) )
| ~ spl22_56
| ~ spl22_327 ),
inference(resolution,[],[f3694,f546]) ).
fof(f58099,plain,
( spl22_1496
| ~ spl22_65
| ~ spl22_304 ),
inference(avatar_split_clause,[],[f3524,f3446,f604,f58097]) ).
fof(f58097,plain,
( spl22_1496
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1496])]) ).
fof(f604,plain,
( spl22_65
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_65])]) ).
fof(f3446,plain,
( spl22_304
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| element(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_304])]) ).
fof(f3524,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_304 ),
inference(resolution,[],[f3447,f605]) ).
fof(f605,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl22_65 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f3447,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| ~ empty(X0)
| sP2(X0,X1,X2) )
| ~ spl22_304 ),
inference(avatar_component_clause,[],[f3446]) ).
fof(f58095,plain,
( spl22_1495
| ~ spl22_65
| ~ spl22_301 ),
inference(avatar_split_clause,[],[f3513,f3434,f604,f58093]) ).
fof(f58093,plain,
( spl22_1495
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(powerset(X1),X2,X0)
| element(X3,X1)
| ~ in(X3,sK13(powerset(X1),X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1495])]) ).
fof(f3434,plain,
( spl22_301
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| element(sK13(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_301])]) ).
fof(f3513,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(powerset(X1),X2,X0)
| element(X3,X1)
| ~ in(X3,sK13(powerset(X1),X2,X0)) )
| ~ spl22_65
| ~ spl22_301 ),
inference(resolution,[],[f3435,f605]) ).
fof(f3435,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X0)
| ~ empty(X2)
| sP2(X0,X1,X2) )
| ~ spl22_301 ),
inference(avatar_component_clause,[],[f3434]) ).
fof(f58091,plain,
( spl22_1494
| ~ spl22_65
| ~ spl22_298 ),
inference(avatar_split_clause,[],[f3497,f3422,f604,f58089]) ).
fof(f58089,plain,
( spl22_1494
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X1,X0,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1494])]) ).
fof(f3422,plain,
( spl22_298
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| element(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_298])]) ).
fof(f3497,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X1,X0,powerset(X2))) )
| ~ spl22_65
| ~ spl22_298 ),
inference(resolution,[],[f3423,f605]) ).
fof(f3423,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| ~ empty(X1)
| sP2(X0,X1,X2) )
| ~ spl22_298 ),
inference(avatar_component_clause,[],[f3422]) ).
fof(f58087,plain,
( spl22_1493
| ~ spl22_65
| ~ spl22_295 ),
inference(avatar_split_clause,[],[f3486,f3410,f604,f58085]) ).
fof(f58085,plain,
( spl22_1493
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,powerset(X2),X0)
| element(X3,X2)
| ~ in(X3,sK13(X1,powerset(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1493])]) ).
fof(f3410,plain,
( spl22_295
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| element(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_295])]) ).
fof(f3486,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,powerset(X2),X0)
| element(X3,X2)
| ~ in(X3,sK13(X1,powerset(X2),X0)) )
| ~ spl22_65
| ~ spl22_295 ),
inference(resolution,[],[f3411,f605]) ).
fof(f3411,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X1)
| ~ empty(X2)
| sP2(X0,X1,X2) )
| ~ spl22_295 ),
inference(avatar_component_clause,[],[f3410]) ).
fof(f58083,plain,
( spl22_1492
| ~ spl22_158
| ~ spl22_283 ),
inference(avatar_split_clause,[],[f3322,f3272,f1544,f58081]) ).
fof(f58081,plain,
( spl22_1492
<=> ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ empty(X2)
| sK7(X0,X2) = apply(X0,sK8(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1492])]) ).
fof(f3272,plain,
( spl22_283
<=> ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_283])]) ).
fof(f3322,plain,
( ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ empty(X2)
| sK7(X0,X2) = apply(X0,sK8(X0,X2)) )
| ~ spl22_158
| ~ spl22_283 ),
inference(duplicate_literal_removal,[],[f3318]) ).
fof(f3318,plain,
( ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ empty(X2)
| sK7(X0,X2) = apply(X0,sK8(X0,X2))
| ~ empty(X2) )
| ~ spl22_158
| ~ spl22_283 ),
inference(resolution,[],[f3273,f1545]) ).
fof(f3273,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X2)
| sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ empty(X2) )
| ~ spl22_283 ),
inference(avatar_component_clause,[],[f3272]) ).
fof(f58079,plain,
( spl22_1491
| ~ spl22_158
| ~ spl22_282 ),
inference(avatar_split_clause,[],[f3316,f3268,f1544,f58077]) ).
fof(f58077,plain,
( spl22_1491
<=> ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1491])]) ).
fof(f3268,plain,
( spl22_282
<=> ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_282])]) ).
fof(f3316,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2)) )
| ~ spl22_158
| ~ spl22_282 ),
inference(duplicate_literal_removal,[],[f3312]) ).
fof(f3312,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2))
| ~ empty(X2) )
| ~ spl22_158
| ~ spl22_282 ),
inference(resolution,[],[f3269,f1545]) ).
fof(f3269,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,X2)
| sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ empty(X2) )
| ~ spl22_282 ),
inference(avatar_component_clause,[],[f3268]) ).
fof(f58075,plain,
( spl22_1490
| ~ spl22_65
| ~ spl22_263 ),
inference(avatar_split_clause,[],[f3179,f2939,f604,f58073]) ).
fof(f58073,plain,
( spl22_1490
<=> ! [X2,X0,X1] :
( sP2(powerset(X0),X1,powerset(X0))
| element(X2,X0)
| ~ in(X2,sK13(powerset(X0),X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1490])]) ).
fof(f2939,plain,
( spl22_263
<=> ! [X0,X1] :
( sP2(X0,X1,X0)
| element(sK13(X0,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_263])]) ).
fof(f3179,plain,
( ! [X2,X0,X1] :
( sP2(powerset(X0),X1,powerset(X0))
| element(X2,X0)
| ~ in(X2,sK13(powerset(X0),X1,powerset(X0))) )
| ~ spl22_65
| ~ spl22_263 ),
inference(resolution,[],[f2940,f605]) ).
fof(f2940,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl22_263 ),
inference(avatar_component_clause,[],[f2939]) ).
fof(f58071,plain,
( spl22_1489
| ~ spl22_133
| ~ spl22_1477 ),
inference(avatar_split_clause,[],[f57998,f57398,f1246,f58069]) ).
fof(f58069,plain,
( spl22_1489
<=> ! [X0,X1] :
( sP0(X0,sK15)
| ~ sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1489])]) ).
fof(f57998,plain,
( ! [X0,X1] :
( sP0(X0,sK15)
| ~ sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_133
| ~ spl22_1477 ),
inference(resolution,[],[f57399,f1247]) ).
fof(f58067,plain,
( spl22_1488
| ~ spl22_65
| ~ spl22_260 ),
inference(avatar_split_clause,[],[f3154,f2927,f604,f58065]) ).
fof(f58065,plain,
( spl22_1488
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1),powerset(X1))
| element(X2,X1)
| ~ in(X2,sK13(X0,powerset(X1),powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1488])]) ).
fof(f2927,plain,
( spl22_260
<=> ! [X0,X1] :
( sP2(X0,X1,X1)
| element(sK13(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_260])]) ).
fof(f3154,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1),powerset(X1))
| element(X2,X1)
| ~ in(X2,sK13(X0,powerset(X1),powerset(X1))) )
| ~ spl22_65
| ~ spl22_260 ),
inference(resolution,[],[f2928,f605]) ).
fof(f2928,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl22_260 ),
inference(avatar_component_clause,[],[f2927]) ).
fof(f58063,plain,
( spl22_1487
| ~ spl22_76
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2859,f2743,f670,f58061]) ).
fof(f58061,plain,
( spl22_1487
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1487])]) ).
fof(f2743,plain,
( spl22_248
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_248])]) ).
fof(f2859,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2) )
| ~ spl22_76
| ~ spl22_248 ),
inference(resolution,[],[f2744,f671]) ).
fof(f2744,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248 ),
inference(avatar_component_clause,[],[f2743]) ).
fof(f58059,plain,
( spl22_1486
| ~ spl22_163
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2857,f2743,f1600,f58057]) ).
fof(f58057,plain,
( spl22_1486
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1486])]) ).
fof(f2857,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2) )
| ~ spl22_163
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1601]) ).
fof(f58055,plain,
( spl22_1485
| ~ spl22_75
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2855,f2743,f666,f58053]) ).
fof(f58053,plain,
( spl22_1485
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(X1,relation_rng(X0),X2),X2)
| sP2(X1,relation_rng(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1485])]) ).
fof(f2855,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(X1,relation_rng(X0),X2),X2)
| sP2(X1,relation_rng(X0),X2) )
| ~ spl22_75
| ~ spl22_248 ),
inference(resolution,[],[f2744,f667]) ).
fof(f58051,plain,
( spl22_1484
| ~ spl22_159
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2853,f2743,f1579,f58049]) ).
fof(f58049,plain,
( spl22_1484
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(X1,relation_rng(X0),X2),X2)
| sP2(X1,relation_rng(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1484])]) ).
fof(f2853,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(X1,relation_rng(X0),X2),X2)
| sP2(X1,relation_rng(X0),X2) )
| ~ spl22_159
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1580]) ).
fof(f58047,plain,
( spl22_1483
| ~ spl22_165
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2849,f2743,f1608,f58045]) ).
fof(f58045,plain,
( spl22_1483
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(X1,X2,relation_rng(X0)),X1)
| sP2(X1,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1483])]) ).
fof(f2849,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(X1,X2,relation_rng(X0)),X1)
| sP2(X1,X2,relation_rng(X0)) )
| ~ spl22_165
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1609]) ).
fof(f58043,plain,
( spl22_1482
| ~ spl22_161
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2848,f2743,f1587,f58041]) ).
fof(f58041,plain,
( spl22_1482
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(X1,X2,relation_rng(X0)),X2)
| sP2(X1,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1482])]) ).
fof(f2848,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK13(X1,X2,relation_rng(X0)),X2)
| sP2(X1,X2,relation_rng(X0)) )
| ~ spl22_161
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1588]) ).
fof(f58039,plain,
( spl22_1481
| ~ spl22_76
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2845,f2743,f670,f58037]) ).
fof(f58037,plain,
( spl22_1481
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(X1,X2,relation_rng(X0)),X1)
| sP2(X1,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1481])]) ).
fof(f2845,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(X1,X2,relation_rng(X0)),X1)
| sP2(X1,X2,relation_rng(X0)) )
| ~ spl22_76
| ~ spl22_248 ),
inference(resolution,[],[f2744,f671]) ).
fof(f58035,plain,
( spl22_1480
| ~ spl22_75
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2844,f2743,f666,f58033]) ).
fof(f58033,plain,
( spl22_1480
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(X1,X2,relation_rng(X0)),X2)
| sP2(X1,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1480])]) ).
fof(f2844,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK13(X1,X2,relation_rng(X0)),X2)
| sP2(X1,X2,relation_rng(X0)) )
| ~ spl22_75
| ~ spl22_248 ),
inference(resolution,[],[f2744,f667]) ).
fof(f57983,plain,
( spl22_1479
| ~ spl22_184
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2537,f2531,f1959,f57981]) ).
fof(f57981,plain,
( spl22_1479
<=> ! [X0,X3,X2,X1] :
( sK7(X0,relation_dom(relation_dom_restriction(X1,X2))) = apply(X0,sK8(X0,relation_dom(relation_dom_restriction(X1,X2))))
| apply(relation_dom_restriction(sK5,relation_dom(relation_dom_restriction(X1,X2))),sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(sK5,sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| ~ in(X3,relation_dom(X0))
| apply(X1,apply(X0,X3)) = apply(relation_dom_restriction(X1,X2),apply(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1479])]) ).
fof(f1959,plain,
( spl22_184
<=> ! [X0,X3,X2,X1] :
( apply(X0,apply(X1,X2)) = apply(relation_dom_restriction(X0,X3),apply(X1,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,relation_dom(relation_dom_restriction(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_184])]) ).
fof(f2537,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,relation_dom(relation_dom_restriction(X1,X2))) = apply(X0,sK8(X0,relation_dom(relation_dom_restriction(X1,X2))))
| apply(relation_dom_restriction(sK5,relation_dom(relation_dom_restriction(X1,X2))),sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(sK5,sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| ~ in(X3,relation_dom(X0))
| apply(X1,apply(X0,X3)) = apply(relation_dom_restriction(X1,X2),apply(X0,X3)) )
| ~ spl22_184
| ~ spl22_232 ),
inference(resolution,[],[f2532,f1960]) ).
fof(f1960,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X1,relation_dom(relation_dom_restriction(X0,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| ~ in(X2,relation_dom(X1))
| apply(X0,apply(X1,X2)) = apply(relation_dom_restriction(X0,X3),apply(X1,X2)) )
| ~ spl22_184 ),
inference(avatar_component_clause,[],[f1959]) ).
fof(f57979,plain,
( spl22_1478
| ~ spl22_192
| ~ spl22_209 ),
inference(avatar_split_clause,[],[f2248,f2241,f2083,f57977]) ).
fof(f57977,plain,
( spl22_1478
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| apply(X0,apply(sK5,sK4)) = apply(relation_dom_restriction(X0,relation_dom(relation_dom_restriction(X1,X2))),apply(sK5,sK4))
| ~ function(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| sK7(sK5,relation_dom(relation_dom_restriction(X1,X2))) = apply(sK5,sK8(sK5,relation_dom(relation_dom_restriction(X1,X2))))
| apply(X1,sK7(sK5,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(sK5,relation_dom(relation_dom_restriction(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1478])]) ).
fof(f2083,plain,
( spl22_192
<=> ! [X2,X0,X1] :
( apply(X0,sK7(X1,relation_dom(relation_dom_restriction(X0,X2)))) = apply(relation_dom_restriction(X0,X2),sK7(X1,relation_dom(relation_dom_restriction(X0,X2))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| sK7(X1,relation_dom(relation_dom_restriction(X0,X2))) = apply(X1,sK8(X1,relation_dom(relation_dom_restriction(X0,X2))))
| sP0(X1,relation_dom(relation_dom_restriction(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_192])]) ).
fof(f2241,plain,
( spl22_209
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(sK5,sK4)) = apply(X0,apply(sK5,sK4))
| ~ sP0(sK5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_209])]) ).
fof(f2248,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| apply(X0,apply(sK5,sK4)) = apply(relation_dom_restriction(X0,relation_dom(relation_dom_restriction(X1,X2))),apply(sK5,sK4))
| ~ function(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| sK7(sK5,relation_dom(relation_dom_restriction(X1,X2))) = apply(sK5,sK8(sK5,relation_dom(relation_dom_restriction(X1,X2))))
| apply(X1,sK7(sK5,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(sK5,relation_dom(relation_dom_restriction(X1,X2)))) )
| ~ spl22_192
| ~ spl22_209 ),
inference(resolution,[],[f2242,f2084]) ).
fof(f2084,plain,
( ! [X2,X0,X1] :
( sP0(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| sK7(X1,relation_dom(relation_dom_restriction(X0,X2))) = apply(X1,sK8(X1,relation_dom(relation_dom_restriction(X0,X2))))
| apply(X0,sK7(X1,relation_dom(relation_dom_restriction(X0,X2)))) = apply(relation_dom_restriction(X0,X2),sK7(X1,relation_dom(relation_dom_restriction(X0,X2)))) )
| ~ spl22_192 ),
inference(avatar_component_clause,[],[f2083]) ).
fof(f2242,plain,
( ! [X0,X1] :
( ~ sP0(sK5,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(sK5,sK4)) = apply(X0,apply(sK5,sK4))
| ~ function(X0) )
| ~ spl22_209 ),
inference(avatar_component_clause,[],[f2241]) ).
fof(f57400,plain,
( spl22_114
| spl22_1477
| ~ spl22_53
| ~ spl22_112
| ~ spl22_334
| ~ spl22_371
| ~ spl22_478 ),
inference(avatar_split_clause,[],[f8595,f8381,f4126,f3909,f948,f511,f57398,f956]) ).
fof(f948,plain,
( spl22_112
<=> ! [X0] : sK15 = set_intersection2(sK15,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_112])]) ).
fof(f3909,plain,
( spl22_334
<=> ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK8(X2,relation_dom(X0)),relation_dom(X2))
| sP0(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_334])]) ).
fof(f8381,plain,
( spl22_478
<=> ! [X0] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,sK15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_478])]) ).
fof(f8595,plain,
( ! [X0,X1] :
( sP0(X1,sK15)
| in(sK8(X1,sK15),relation_dom(X1))
| ~ empty(X0) )
| ~ spl22_53
| ~ spl22_112
| ~ spl22_334
| ~ spl22_371
| ~ spl22_478 ),
inference(forward_demodulation,[],[f8594,f949]) ).
fof(f949,plain,
( ! [X0] : sK15 = set_intersection2(sK15,X0)
| ~ spl22_112 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f8594,plain,
( ! [X0,X1] :
( sP0(X1,set_intersection2(sK15,relation_dom(sK5)))
| in(sK8(X1,sK15),relation_dom(X1))
| ~ empty(X0) )
| ~ spl22_53
| ~ spl22_112
| ~ spl22_334
| ~ spl22_371
| ~ spl22_478 ),
inference(forward_demodulation,[],[f8593,f512]) ).
fof(f8593,plain,
( ! [X0,X1] :
( sP0(X1,set_intersection2(relation_dom(sK5),sK15))
| in(sK8(X1,sK15),relation_dom(X1))
| ~ empty(X0) )
| ~ spl22_53
| ~ spl22_112
| ~ spl22_334
| ~ spl22_371
| ~ spl22_478 ),
inference(forward_demodulation,[],[f8592,f4127]) ).
fof(f8592,plain,
( ! [X0,X1] :
( in(sK8(X1,sK15),relation_dom(X1))
| ~ empty(X0)
| sP0(X1,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_53
| ~ spl22_112
| ~ spl22_334
| ~ spl22_371
| ~ spl22_478 ),
inference(forward_demodulation,[],[f8591,f949]) ).
fof(f8591,plain,
( ! [X0,X1] :
( in(sK8(X1,set_intersection2(sK15,relation_dom(sK5))),relation_dom(X1))
| ~ empty(X0)
| sP0(X1,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_53
| ~ spl22_334
| ~ spl22_371
| ~ spl22_478 ),
inference(forward_demodulation,[],[f8590,f512]) ).
fof(f8590,plain,
( ! [X0,X1] :
( in(sK8(X1,set_intersection2(relation_dom(sK5),sK15)),relation_dom(X1))
| ~ empty(X0)
| sP0(X1,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_334
| ~ spl22_371
| ~ spl22_478 ),
inference(forward_demodulation,[],[f8554,f4127]) ).
fof(f8554,plain,
( ! [X0,X1] :
( ~ empty(X0)
| in(sK8(X1,relation_dom(relation_dom_restriction(sK5,sK15))),relation_dom(X1))
| sP0(X1,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_334
| ~ spl22_478 ),
inference(duplicate_literal_removal,[],[f8517]) ).
fof(f8517,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X0)
| in(sK8(X1,relation_dom(relation_dom_restriction(sK5,sK15))),relation_dom(X1))
| sP0(X1,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_334
| ~ spl22_478 ),
inference(resolution,[],[f8382,f3910]) ).
fof(f3910,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK8(X2,relation_dom(X0)),relation_dom(X2))
| sP0(X2,relation_dom(X0)) )
| ~ spl22_334 ),
inference(avatar_component_clause,[],[f3909]) ).
fof(f8382,plain,
( ! [X0] :
( sP0(relation_dom_restriction(sK5,sK15),X0)
| ~ empty(X0) )
| ~ spl22_478 ),
inference(avatar_component_clause,[],[f8381]) ).
fof(f57240,plain,
( spl22_1476
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_675 ),
inference(avatar_split_clause,[],[f14744,f14601,f4126,f935,f511,f15306,f57238]) ).
fof(f57238,plain,
( spl22_1476
<=> ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| ~ function(X0)
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1476])]) ).
fof(f15306,plain,
( spl22_700
<=> in(sK4,set_intersection2(sK3,relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_700])]) ).
fof(f935,plain,
( spl22_109
<=> apply(sK5,sK4) = apply(relation_dom_restriction(sK5,sK3),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_109])]) ).
fof(f14601,plain,
( spl22_675
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4))
| ~ sP0(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4)))
| ~ in(X4,relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_675])]) ).
fof(f14744,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))
| ~ function(X0) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_675 ),
inference(forward_demodulation,[],[f14743,f512]) ).
fof(f14743,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))
| ~ function(X0) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_675 ),
inference(forward_demodulation,[],[f14725,f4127]) ).
fof(f14725,plain,
( ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(sK5,sK4))
| ~ function(X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_675 ),
inference(superposition,[],[f14602,f937]) ).
fof(f937,plain,
( apply(sK5,sK4) = apply(relation_dom_restriction(sK5,sK3),sK4)
| ~ spl22_109 ),
inference(avatar_component_clause,[],[f935]) ).
fof(f14602,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4))
| ~ function(X0)
| ~ in(X4,relation_dom(X3)) )
| ~ spl22_675 ),
inference(avatar_component_clause,[],[f14601]) ).
fof(f57211,plain,
( spl22_1475
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_674 ),
inference(avatar_split_clause,[],[f14710,f14597,f4126,f935,f511,f15306,f57209]) ).
fof(f57209,plain,
( spl22_1475
<=> ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| ~ function(X1)
| sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1475])]) ).
fof(f14597,plain,
( spl22_674
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4))
| ~ sP0(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4)))
| ~ in(X4,relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_674])]) ).
fof(f14710,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))
| ~ function(X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_674 ),
inference(forward_demodulation,[],[f14709,f512]) ).
fof(f14709,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))
| ~ function(X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_674 ),
inference(forward_demodulation,[],[f14691,f4127]) ).
fof(f14691,plain,
( ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4)))
| sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),apply(sK5,sK4))
| ~ function(X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_674 ),
inference(superposition,[],[f14598,f937]) ).
fof(f14598,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4))
| ~ function(X0)
| ~ in(X4,relation_dom(X3)) )
| ~ spl22_674 ),
inference(avatar_component_clause,[],[f14597]) ).
fof(f57182,plain,
( spl22_1474
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_673 ),
inference(avatar_split_clause,[],[f14673,f14593,f4126,f935,f511,f15306,f57180]) ).
fof(f57180,plain,
( spl22_1474
<=> ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| sP2(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))
| apply(X1,sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1474])]) ).
fof(f14593,plain,
( spl22_673
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X3,sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X4,relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_673])]) ).
fof(f14673,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| sP2(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_673 ),
inference(forward_demodulation,[],[f14672,f512]) ).
fof(f14672,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| sP2(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_673 ),
inference(forward_demodulation,[],[f14654,f4127]) ).
fof(f14654,plain,
( ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2))))
| sP2(X0,apply(sK5,sK4),relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_673 ),
inference(superposition,[],[f14594,f937]) ).
fof(f14594,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ in(X4,relation_dom(X3)) )
| ~ spl22_673 ),
inference(avatar_component_clause,[],[f14593]) ).
fof(f57153,plain,
( spl22_1473
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_672 ),
inference(avatar_split_clause,[],[f14639,f14588,f4126,f935,f511,f15306,f57151]) ).
fof(f57151,plain,
( spl22_1473
<=> ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| sP2(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(X1,sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1473])]) ).
fof(f14588,plain,
( spl22_672
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X2,sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_672])]) ).
fof(f14639,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| sP2(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_672 ),
inference(forward_demodulation,[],[f14638,f512]) ).
fof(f14638,plain,
( ! [X2,X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| sP2(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_672 ),
inference(forward_demodulation,[],[f14620,f4127]) ).
fof(f14620,plain,
( ! [X2,X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| apply(X1,sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2))))
| sP2(apply(sK5,sK4),X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_672 ),
inference(superposition,[],[f14589,f937]) ).
fof(f14589,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_672 ),
inference(avatar_component_clause,[],[f14588]) ).
fof(f57149,plain,
( spl22_1472
| ~ spl22_232
| ~ spl22_507 ),
inference(avatar_split_clause,[],[f9469,f9264,f2531,f57147]) ).
fof(f57147,plain,
( spl22_1472
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| element(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1472])]) ).
fof(f9264,plain,
( spl22_507
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,apply(X2,X3)),X0)
| sP2(X0,X1,apply(X2,X3))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_507])]) ).
fof(f9469,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| element(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) )
| ~ spl22_232
| ~ spl22_507 ),
inference(resolution,[],[f9265,f2532]) ).
fof(f9265,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| sP2(X0,X1,apply(X2,X3))
| element(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_507 ),
inference(avatar_component_clause,[],[f9264]) ).
fof(f57138,plain,
( spl22_1471
| ~ spl22_232
| ~ spl22_506 ),
inference(avatar_split_clause,[],[f9449,f9260,f2531,f57136]) ).
fof(f57136,plain,
( spl22_1471
<=> ! [X0,X3,X2,X1] :
( sP2(apply(X0,X1),X2,X3)
| element(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0))
| sK7(X0,sK13(apply(X0,X1),X2,X3)) = apply(X0,sK8(X0,sK13(apply(X0,X1),X2,X3)))
| apply(relation_dom_restriction(sK5,sK13(apply(X0,X1),X2,X3)),sK7(X0,sK13(apply(X0,X1),X2,X3))) = apply(sK5,sK7(X0,sK13(apply(X0,X1),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1471])]) ).
fof(f9260,plain,
( spl22_506
<=> ! [X0,X3,X2,X1] :
( element(sK13(apply(X0,X1),X2,X3),X3)
| sP2(apply(X0,X1),X2,X3)
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_506])]) ).
fof(f9449,plain,
( ! [X2,X3,X0,X1] :
( sP2(apply(X0,X1),X2,X3)
| element(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0))
| sK7(X0,sK13(apply(X0,X1),X2,X3)) = apply(X0,sK8(X0,sK13(apply(X0,X1),X2,X3)))
| apply(relation_dom_restriction(sK5,sK13(apply(X0,X1),X2,X3)),sK7(X0,sK13(apply(X0,X1),X2,X3))) = apply(sK5,sK7(X0,sK13(apply(X0,X1),X2,X3))) )
| ~ spl22_232
| ~ spl22_506 ),
inference(resolution,[],[f9261,f2532]) ).
fof(f9261,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| sP2(apply(X0,X1),X2,X3)
| element(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_506 ),
inference(avatar_component_clause,[],[f9260]) ).
fof(f57134,plain,
( spl22_1470
| ~ spl22_232
| ~ spl22_505 ),
inference(avatar_split_clause,[],[f9425,f9256,f2531,f57132]) ).
fof(f57132,plain,
( spl22_1470
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| element(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1470])]) ).
fof(f9256,plain,
( spl22_505
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,apply(X2,X3)),X1)
| sP2(X0,X1,apply(X2,X3))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_505])]) ).
fof(f9425,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| element(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) )
| ~ spl22_232
| ~ spl22_505 ),
inference(resolution,[],[f9257,f2532]) ).
fof(f9257,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| sP2(X0,X1,apply(X2,X3))
| element(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_505 ),
inference(avatar_component_clause,[],[f9256]) ).
fof(f57130,plain,
( spl22_1469
| ~ spl22_232
| ~ spl22_504 ),
inference(avatar_split_clause,[],[f9405,f9252,f2531,f57128]) ).
fof(f57128,plain,
( spl22_1469
<=> ! [X0,X3,X2,X1] :
( sP2(X0,apply(X1,X2),X3)
| element(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1))
| sK7(X1,sK13(X0,apply(X1,X2),X3)) = apply(X1,sK8(X1,sK13(X0,apply(X1,X2),X3)))
| apply(relation_dom_restriction(sK5,sK13(X0,apply(X1,X2),X3)),sK7(X1,sK13(X0,apply(X1,X2),X3))) = apply(sK5,sK7(X1,sK13(X0,apply(X1,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1469])]) ).
fof(f9252,plain,
( spl22_504
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,apply(X1,X2),X3),X3)
| sP2(X0,apply(X1,X2),X3)
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_504])]) ).
fof(f9405,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,apply(X1,X2),X3)
| element(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1))
| sK7(X1,sK13(X0,apply(X1,X2),X3)) = apply(X1,sK8(X1,sK13(X0,apply(X1,X2),X3)))
| apply(relation_dom_restriction(sK5,sK13(X0,apply(X1,X2),X3)),sK7(X1,sK13(X0,apply(X1,X2),X3))) = apply(sK5,sK7(X1,sK13(X0,apply(X1,X2),X3))) )
| ~ spl22_232
| ~ spl22_504 ),
inference(resolution,[],[f9253,f2532]) ).
fof(f9253,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| sP2(X0,apply(X1,X2),X3)
| element(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_504 ),
inference(avatar_component_clause,[],[f9252]) ).
fof(f57126,plain,
( spl22_1468
| ~ spl22_232
| ~ spl22_499 ),
inference(avatar_split_clause,[],[f9333,f9232,f2531,f57124]) ).
fof(f57124,plain,
( spl22_1468
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(apply(X1,X0),X2,X3),X3)
| sP2(apply(X1,X0),X2,X3)
| sK7(X1,sK13(apply(X1,X0),X2,X3)) = apply(X1,sK8(X1,sK13(apply(X1,X0),X2,X3)))
| apply(relation_dom_restriction(sK5,sK13(apply(X1,X0),X2,X3)),sK7(X1,sK13(apply(X1,X0),X2,X3))) = apply(sK5,sK7(X1,sK13(apply(X1,X0),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1468])]) ).
fof(f9232,plain,
( spl22_499
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0))
| in(sK13(apply(X0,X1),X2,X3),X3)
| sP2(apply(X0,X1),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_499])]) ).
fof(f9333,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(apply(X1,X0),X2,X3),X3)
| sP2(apply(X1,X0),X2,X3)
| sK7(X1,sK13(apply(X1,X0),X2,X3)) = apply(X1,sK8(X1,sK13(apply(X1,X0),X2,X3)))
| apply(relation_dom_restriction(sK5,sK13(apply(X1,X0),X2,X3)),sK7(X1,sK13(apply(X1,X0),X2,X3))) = apply(sK5,sK7(X1,sK13(apply(X1,X0),X2,X3))) )
| ~ spl22_232
| ~ spl22_499 ),
inference(resolution,[],[f9233,f2532]) ).
fof(f9233,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0))
| in(sK13(apply(X0,X1),X2,X3),X3)
| sP2(apply(X0,X1),X2,X3) )
| ~ spl22_499 ),
inference(avatar_component_clause,[],[f9232]) ).
fof(f57122,plain,
( spl22_1467
| ~ spl22_232
| ~ spl22_498 ),
inference(avatar_split_clause,[],[f9313,f9228,f2531,f57120]) ).
fof(f57120,plain,
( spl22_1467
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(X2,apply(X1,X0),X3),X3)
| sP2(X2,apply(X1,X0),X3)
| sK7(X1,sK13(X2,apply(X1,X0),X3)) = apply(X1,sK8(X1,sK13(X2,apply(X1,X0),X3)))
| apply(relation_dom_restriction(sK5,sK13(X2,apply(X1,X0),X3)),sK7(X1,sK13(X2,apply(X1,X0),X3))) = apply(sK5,sK7(X1,sK13(X2,apply(X1,X0),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1467])]) ).
fof(f9228,plain,
( spl22_498
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,sK13(X1,apply(X0,X2),X3))
| ~ in(X2,relation_dom(X0))
| in(sK13(X1,apply(X0,X2),X3),X3)
| sP2(X1,apply(X0,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_498])]) ).
fof(f9313,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(X2,apply(X1,X0),X3),X3)
| sP2(X2,apply(X1,X0),X3)
| sK7(X1,sK13(X2,apply(X1,X0),X3)) = apply(X1,sK8(X1,sK13(X2,apply(X1,X0),X3)))
| apply(relation_dom_restriction(sK5,sK13(X2,apply(X1,X0),X3)),sK7(X1,sK13(X2,apply(X1,X0),X3))) = apply(sK5,sK7(X1,sK13(X2,apply(X1,X0),X3))) )
| ~ spl22_232
| ~ spl22_498 ),
inference(resolution,[],[f9229,f2532]) ).
fof(f9229,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(X1,apply(X0,X2),X3))
| ~ in(X2,relation_dom(X0))
| in(sK13(X1,apply(X0,X2),X3),X3)
| sP2(X1,apply(X0,X2),X3) )
| ~ spl22_498 ),
inference(avatar_component_clause,[],[f9228]) ).
fof(f57118,plain,
( spl22_1466
| ~ spl22_232
| ~ spl22_497 ),
inference(avatar_split_clause,[],[f9293,f9223,f2531,f57116]) ).
fof(f57116,plain,
( spl22_1466
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(X2,X3,apply(X1,X0)),X3)
| sP2(X2,X3,apply(X1,X0))
| sK7(X1,sK13(X2,X3,apply(X1,X0))) = apply(X1,sK8(X1,sK13(X2,X3,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(X2,X3,apply(X1,X0))),sK7(X1,sK13(X2,X3,apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(X2,X3,apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1466])]) ).
fof(f9223,plain,
( spl22_497
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,sK13(X1,X2,apply(X0,X3)))
| ~ in(X3,relation_dom(X0))
| in(sK13(X1,X2,apply(X0,X3)),X2)
| sP2(X1,X2,apply(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_497])]) ).
fof(f9293,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(X2,X3,apply(X1,X0)),X3)
| sP2(X2,X3,apply(X1,X0))
| sK7(X1,sK13(X2,X3,apply(X1,X0))) = apply(X1,sK8(X1,sK13(X2,X3,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(X2,X3,apply(X1,X0))),sK7(X1,sK13(X2,X3,apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(X2,X3,apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_497 ),
inference(resolution,[],[f9224,f2532]) ).
fof(f9224,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(X1,X2,apply(X0,X3)))
| ~ in(X3,relation_dom(X0))
| in(sK13(X1,X2,apply(X0,X3)),X2)
| sP2(X1,X2,apply(X0,X3)) )
| ~ spl22_497 ),
inference(avatar_component_clause,[],[f9223]) ).
fof(f57114,plain,
( spl22_1465
| ~ spl22_232
| ~ spl22_496 ),
inference(avatar_split_clause,[],[f9273,f9219,f2531,f57112]) ).
fof(f57112,plain,
( spl22_1465
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(X2,X3,apply(X1,X0)),X2)
| sP2(X2,X3,apply(X1,X0))
| sK7(X1,sK13(X2,X3,apply(X1,X0))) = apply(X1,sK8(X1,sK13(X2,X3,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(X2,X3,apply(X1,X0))),sK7(X1,sK13(X2,X3,apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(X2,X3,apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1465])]) ).
fof(f9219,plain,
( spl22_496
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,sK13(X1,X2,apply(X0,X3)))
| ~ in(X3,relation_dom(X0))
| in(sK13(X1,X2,apply(X0,X3)),X1)
| sP2(X1,X2,apply(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_496])]) ).
fof(f9273,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK13(X2,X3,apply(X1,X0)),X2)
| sP2(X2,X3,apply(X1,X0))
| sK7(X1,sK13(X2,X3,apply(X1,X0))) = apply(X1,sK8(X1,sK13(X2,X3,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK13(X2,X3,apply(X1,X0))),sK7(X1,sK13(X2,X3,apply(X1,X0)))) = apply(sK5,sK7(X1,sK13(X2,X3,apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_496 ),
inference(resolution,[],[f9220,f2532]) ).
fof(f9220,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(X1,X2,apply(X0,X3)))
| ~ in(X3,relation_dom(X0))
| in(sK13(X1,X2,apply(X0,X3)),X1)
| sP2(X1,X2,apply(X0,X3)) )
| ~ spl22_496 ),
inference(avatar_component_clause,[],[f9219]) ).
fof(f57079,plain,
( spl22_726
| ~ spl22_1464
| ~ spl22_1300
| ~ spl22_1460 ),
inference(avatar_split_clause,[],[f56541,f51486,f42444,f57076,f15781]) ).
fof(f15781,plain,
( spl22_726
<=> empty(apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_726])]) ).
fof(f57076,plain,
( spl22_1464
<=> sP0(sK5,sK6(apply(sK5,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1464])]) ).
fof(f42444,plain,
( spl22_1300
<=> ! [X0] :
( ~ sP0(sK5,sK6(X0))
| empty(X0)
| in(apply(sK5,sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1300])]) ).
fof(f51486,plain,
( spl22_1460
<=> ! [X0] :
( empty(X0)
| ~ sP0(sK5,sK6(X0))
| ~ in(X0,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1460])]) ).
fof(f56541,plain,
( ~ sP0(sK5,sK6(apply(sK5,sK4)))
| empty(apply(sK5,sK4))
| ~ spl22_1300
| ~ spl22_1460 ),
inference(duplicate_literal_removal,[],[f56326]) ).
fof(f56326,plain,
( ~ sP0(sK5,sK6(apply(sK5,sK4)))
| empty(apply(sK5,sK4))
| empty(apply(sK5,sK4))
| ~ sP0(sK5,sK6(apply(sK5,sK4)))
| ~ spl22_1300
| ~ spl22_1460 ),
inference(resolution,[],[f51487,f42445]) ).
fof(f42445,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| empty(X0)
| ~ sP0(sK5,sK6(X0)) )
| ~ spl22_1300 ),
inference(avatar_component_clause,[],[f42444]) ).
fof(f51487,plain,
( ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(sK5,sK6(X0))
| empty(X0) )
| ~ spl22_1460 ),
inference(avatar_component_clause,[],[f51486]) ).
fof(f51500,plain,
( spl22_1463
| ~ spl22_41
| ~ spl22_460 ),
inference(avatar_split_clause,[],[f8002,f6409,f419,f51498]) ).
fof(f51498,plain,
( spl22_1463
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1463])]) ).
fof(f8002,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_460 ),
inference(resolution,[],[f6410,f420]) ).
fof(f51496,plain,
( spl22_1462
| ~ spl22_41
| ~ spl22_459 ),
inference(avatar_split_clause,[],[f7952,f6405,f419,f51494]) ).
fof(f51494,plain,
( spl22_1462
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1462])]) ).
fof(f7952,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_459 ),
inference(resolution,[],[f6406,f420]) ).
fof(f51492,plain,
( spl22_1461
| ~ spl22_41
| ~ spl22_456 ),
inference(avatar_split_clause,[],[f7801,f6393,f419,f51490]) ).
fof(f51490,plain,
( spl22_1461
<=> ! [X0,X3,X2,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1461])]) ).
fof(f7801,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_456 ),
inference(resolution,[],[f6394,f420]) ).
fof(f51488,plain,
( spl22_1460
| ~ spl22_45
| ~ spl22_1300 ),
inference(avatar_split_clause,[],[f51083,f42444,f454,f51486]) ).
fof(f51083,plain,
( ! [X0] :
( empty(X0)
| ~ sP0(sK5,sK6(X0))
| ~ in(X0,apply(sK5,sK4)) )
| ~ spl22_45
| ~ spl22_1300 ),
inference(resolution,[],[f42445,f455]) ).
fof(f51484,plain,
( spl22_1459
| ~ spl22_41
| ~ spl22_455 ),
inference(avatar_split_clause,[],[f7750,f6389,f419,f51482]) ).
fof(f51482,plain,
( spl22_1459
<=> ! [X0,X3,X2,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1459])]) ).
fof(f7750,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_455 ),
inference(resolution,[],[f6390,f420]) ).
fof(f51480,plain,
( spl22_1458
| ~ spl22_41
| ~ spl22_452 ),
inference(avatar_split_clause,[],[f7601,f6369,f419,f51478]) ).
fof(f51478,plain,
( spl22_1458
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1458])]) ).
fof(f7601,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_452 ),
inference(resolution,[],[f6370,f420]) ).
fof(f51476,plain,
( spl22_1457
| ~ spl22_41
| ~ spl22_451 ),
inference(avatar_split_clause,[],[f7543,f6365,f419,f51474]) ).
fof(f51474,plain,
( spl22_1457
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1457])]) ).
fof(f7543,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_451 ),
inference(resolution,[],[f6366,f420]) ).
fof(f51472,plain,
( spl22_1456
| ~ spl22_41
| ~ spl22_448 ),
inference(avatar_split_clause,[],[f7398,f6353,f419,f51470]) ).
fof(f51470,plain,
( spl22_1456
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1456])]) ).
fof(f7398,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_448 ),
inference(resolution,[],[f6354,f420]) ).
fof(f51468,plain,
( spl22_1455
| ~ spl22_41
| ~ spl22_447 ),
inference(avatar_split_clause,[],[f7350,f6349,f419,f51466]) ).
fof(f51466,plain,
( spl22_1455
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1455])]) ).
fof(f7350,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_447 ),
inference(resolution,[],[f6350,f420]) ).
fof(f51464,plain,
( spl22_1454
| ~ spl22_41
| ~ spl22_442 ),
inference(avatar_split_clause,[],[f7156,f6309,f419,f51462]) ).
fof(f51462,plain,
( spl22_1454
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1454])]) ).
fof(f7156,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_442 ),
inference(resolution,[],[f6310,f420]) ).
fof(f51460,plain,
( spl22_1453
| ~ spl22_41
| ~ spl22_441 ),
inference(avatar_split_clause,[],[f7075,f6305,f419,f51458]) ).
fof(f51458,plain,
( spl22_1453
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1453])]) ).
fof(f7075,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_441 ),
inference(resolution,[],[f6306,f420]) ).
fof(f51456,plain,
( spl22_1452
| ~ spl22_41
| ~ spl22_440 ),
inference(avatar_split_clause,[],[f6969,f6301,f419,f51454]) ).
fof(f51454,plain,
( spl22_1452
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1452])]) ).
fof(f6969,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_440 ),
inference(resolution,[],[f6302,f420]) ).
fof(f51452,plain,
( spl22_1451
| ~ spl22_41
| ~ spl22_439 ),
inference(avatar_split_clause,[],[f6893,f6297,f419,f51450]) ).
fof(f51450,plain,
( spl22_1451
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1451])]) ).
fof(f6893,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_439 ),
inference(resolution,[],[f6298,f420]) ).
fof(f51448,plain,
( spl22_1450
| ~ spl22_41
| ~ spl22_438 ),
inference(avatar_split_clause,[],[f6841,f6293,f419,f51446]) ).
fof(f51446,plain,
( spl22_1450
<=> ! [X0,X3,X2,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1450])]) ).
fof(f6841,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_438 ),
inference(resolution,[],[f6294,f420]) ).
fof(f51444,plain,
( spl22_1449
| ~ spl22_53
| ~ spl22_1298 ),
inference(avatar_split_clause,[],[f45939,f40999,f511,f51442]) ).
fof(f51442,plain,
( spl22_1449
<=> ! [X0] :
( ~ sP0(sK5,set_intersection2(X0,relation_dom(sK20)))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1449])]) ).
fof(f40999,plain,
( spl22_1298
<=> ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK20),X0))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1298])]) ).
fof(f45939,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(X0,relation_dom(sK20)))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) )
| ~ spl22_53
| ~ spl22_1298 ),
inference(superposition,[],[f41000,f512]) ).
fof(f41000,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK20),X0))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) )
| ~ spl22_1298 ),
inference(avatar_component_clause,[],[f40999]) ).
fof(f51440,plain,
( spl22_1448
| ~ spl22_41
| ~ spl22_437 ),
inference(avatar_split_clause,[],[f6758,f6289,f419,f51438]) ).
fof(f51438,plain,
( spl22_1448
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1448])]) ).
fof(f6758,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_437 ),
inference(resolution,[],[f6290,f420]) ).
fof(f51436,plain,
( spl22_1447
| ~ spl22_41
| ~ spl22_436 ),
inference(avatar_split_clause,[],[f6646,f6285,f419,f51434]) ).
fof(f51434,plain,
( spl22_1447
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1447])]) ).
fof(f6646,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_436 ),
inference(resolution,[],[f6286,f420]) ).
fof(f51432,plain,
( spl22_1446
| ~ spl22_41
| ~ spl22_435 ),
inference(avatar_split_clause,[],[f6564,f6281,f419,f51430]) ).
fof(f51430,plain,
( spl22_1446
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1446])]) ).
fof(f6564,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_435 ),
inference(resolution,[],[f6282,f420]) ).
fof(f51428,plain,
( spl22_1445
| ~ spl22_47
| ~ spl22_359 ),
inference(avatar_split_clause,[],[f4697,f4010,f462,f51426]) ).
fof(f51426,plain,
( spl22_1445
<=> ! [X0,X1] :
( sP0(X0,relation_dom(X1))
| element(sK8(X0,relation_dom(X1)),relation_dom(X0))
| ~ empty(relation_rng(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1445])]) ).
fof(f4010,plain,
( spl22_359
<=> ! [X2,X0,X1] :
( element(sK8(X0,relation_dom(X1)),relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_359])]) ).
fof(f4697,plain,
( ! [X0,X1] :
( sP0(X0,relation_dom(X1))
| element(sK8(X0,relation_dom(X1)),relation_dom(X0))
| ~ empty(relation_rng(X1))
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_359 ),
inference(resolution,[],[f4011,f463]) ).
fof(f4011,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,X2)
| sP0(X0,relation_dom(X1))
| element(sK8(X0,relation_dom(X1)),relation_dom(X0))
| ~ empty(X2) )
| ~ spl22_359 ),
inference(avatar_component_clause,[],[f4010]) ).
fof(f51424,plain,
( spl22_1444
| ~ spl22_28
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4672,f4006,f355,f51422]) ).
fof(f51422,plain,
( spl22_1444
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1444])]) ).
fof(f355,plain,
( spl22_28
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_28])]) ).
fof(f4672,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| relation(relation_rng(X0)) )
| ~ spl22_28
| ~ spl22_358 ),
inference(resolution,[],[f4007,f356]) ).
fof(f356,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl22_28 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f51420,plain,
( spl22_1443
| ~ spl22_27
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4671,f4006,f351,f51418]) ).
fof(f51418,plain,
( spl22_1443
<=> ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1443])]) ).
fof(f351,plain,
( spl22_27
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_27])]) ).
fof(f4671,plain,
( ! [X0] :
( ~ sP1(X0)
| sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| function(relation_rng(X0)) )
| ~ spl22_27
| ~ spl22_358 ),
inference(resolution,[],[f4007,f352]) ).
fof(f352,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl22_27 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f51416,plain,
( spl22_1442
| ~ spl22_56
| ~ spl22_356 ),
inference(avatar_split_clause,[],[f4665,f3998,f545,f51414]) ).
fof(f51414,plain,
( spl22_1442
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,sK6(X2))
| empty(X2)
| in(sK13(X0,X1,sK6(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1442])]) ).
fof(f3998,plain,
( spl22_356
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| ~ empty(X0)
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_356])]) ).
fof(f4665,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,sK6(X2))
| empty(X2)
| in(sK13(X0,X1,sK6(X2)),X2) )
| ~ spl22_56
| ~ spl22_356 ),
inference(duplicate_literal_removal,[],[f4662]) ).
fof(f4662,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,sK6(X2))
| empty(X2)
| empty(X2)
| in(sK13(X0,X1,sK6(X2)),X2) )
| ~ spl22_56
| ~ spl22_356 ),
inference(resolution,[],[f3999,f546]) ).
fof(f3999,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| ~ empty(X0)
| sP2(X0,X1,sK6(X2))
| empty(X2) )
| ~ spl22_356 ),
inference(avatar_component_clause,[],[f3998]) ).
fof(f51412,plain,
( spl22_1441
| ~ spl22_290
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4637,f3994,f3304,f51410]) ).
fof(f51410,plain,
( spl22_1441
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1441])]) ).
fof(f3994,plain,
( spl22_355
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_355])]) ).
fof(f4637,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_355 ),
inference(resolution,[],[f3995,f3305]) ).
fof(f3995,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_355 ),
inference(avatar_component_clause,[],[f3994]) ).
fof(f51408,plain,
( spl22_1440
| ~ spl22_45
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4634,f3994,f454,f51406]) ).
fof(f51406,plain,
( spl22_1440
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ in(X2,sK13(X0,X1,set_intersection2(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1440])]) ).
fof(f4634,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ in(X2,sK13(X0,X1,set_intersection2(X2,X3))) )
| ~ spl22_45
| ~ spl22_355 ),
inference(resolution,[],[f3995,f455]) ).
fof(f51404,plain,
( spl22_1439
| ~ spl22_46
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4633,f3994,f458,f51402]) ).
fof(f51402,plain,
( spl22_1439
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| element(sK13(X0,X1,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1439])]) ).
fof(f4633,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| element(sK13(X0,X1,set_intersection2(X2,X3)),X2) )
| ~ spl22_46
| ~ spl22_355 ),
inference(resolution,[],[f3995,f459]) ).
fof(f51400,plain,
( spl22_1438
| ~ spl22_53
| ~ spl22_1297 ),
inference(avatar_split_clause,[],[f45664,f40614,f511,f51398]) ).
fof(f51398,plain,
( spl22_1438
<=> ! [X0] :
( ~ sP0(sK5,set_intersection2(X0,relation_dom(sK19)))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1438])]) ).
fof(f40614,plain,
( spl22_1297
<=> ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK19),X0))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1297])]) ).
fof(f45664,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(X0,relation_dom(sK19)))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) )
| ~ spl22_53
| ~ spl22_1297 ),
inference(superposition,[],[f40615,f512]) ).
fof(f40615,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK19),X0))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) )
| ~ spl22_1297 ),
inference(avatar_component_clause,[],[f40614]) ).
fof(f51396,plain,
( spl22_1437
| ~ spl22_290
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4603,f3990,f3304,f51394]) ).
fof(f51394,plain,
( spl22_1437
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1437])]) ).
fof(f3990,plain,
( spl22_354
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_354])]) ).
fof(f4603,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_354 ),
inference(resolution,[],[f3991,f3305]) ).
fof(f3991,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_354 ),
inference(avatar_component_clause,[],[f3990]) ).
fof(f51392,plain,
( spl22_1436
| ~ spl22_45
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4600,f3990,f454,f51390]) ).
fof(f51390,plain,
( spl22_1436
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ in(X3,sK13(X0,X1,set_intersection2(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1436])]) ).
fof(f4600,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ in(X3,sK13(X0,X1,set_intersection2(X2,X3))) )
| ~ spl22_45
| ~ spl22_354 ),
inference(resolution,[],[f3991,f455]) ).
fof(f51388,plain,
( spl22_1435
| ~ spl22_46
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4599,f3990,f458,f51386]) ).
fof(f51386,plain,
( spl22_1435
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| element(sK13(X0,X1,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1435])]) ).
fof(f4599,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| element(sK13(X0,X1,set_intersection2(X2,X3)),X3) )
| ~ spl22_46
| ~ spl22_354 ),
inference(resolution,[],[f3991,f459]) ).
fof(f51384,plain,
( spl22_1434
| ~ spl22_56
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f4592,f3982,f545,f51382]) ).
fof(f51382,plain,
( spl22_1434
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK6(X1),X2,X0)
| empty(X1)
| in(sK13(sK6(X1),X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1434])]) ).
fof(f3982,plain,
( spl22_352
<=> ! [X2,X0,X1] :
( sP2(sK6(X0),X1,X2)
| ~ empty(X2)
| element(sK13(sK6(X0),X1,X2),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_352])]) ).
fof(f4592,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK6(X1),X2,X0)
| empty(X1)
| in(sK13(sK6(X1),X2,X0),X1) )
| ~ spl22_56
| ~ spl22_352 ),
inference(duplicate_literal_removal,[],[f4589]) ).
fof(f4589,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK6(X1),X2,X0)
| empty(X1)
| empty(X1)
| in(sK13(sK6(X1),X2,X0),X1) )
| ~ spl22_56
| ~ spl22_352 ),
inference(resolution,[],[f3983,f546]) ).
fof(f3983,plain,
( ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,X2),X0)
| ~ empty(X2)
| sP2(sK6(X0),X1,X2)
| empty(X0) )
| ~ spl22_352 ),
inference(avatar_component_clause,[],[f3982]) ).
fof(f51380,plain,
( spl22_1433
| ~ spl22_290
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4563,f3978,f3304,f51378]) ).
fof(f51378,plain,
( spl22_1433
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(relation_rng(X1),X2),X3,X0)
| ~ sP1(X1)
| ~ sP0(X1,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1433])]) ).
fof(f3978,plain,
( spl22_351
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_351])]) ).
fof(f4563,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(set_intersection2(relation_rng(X1),X2),X3,X0)
| ~ sP1(X1)
| ~ sP0(X1,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_351 ),
inference(resolution,[],[f3979,f3305]) ).
fof(f3979,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X0)
| ~ empty(X3)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_351 ),
inference(avatar_component_clause,[],[f3978]) ).
fof(f51376,plain,
( spl22_1432
| ~ spl22_45
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4560,f3978,f454,f51374]) ).
fof(f51374,plain,
( spl22_1432
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ in(X1,sK13(set_intersection2(X1,X2),X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1432])]) ).
fof(f4560,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ in(X1,sK13(set_intersection2(X1,X2),X3,X0)) )
| ~ spl22_45
| ~ spl22_351 ),
inference(resolution,[],[f3979,f455]) ).
fof(f51372,plain,
( spl22_1431
| ~ spl22_46
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4559,f3978,f458,f51370]) ).
fof(f51370,plain,
( spl22_1431
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| element(sK13(set_intersection2(X1,X2),X3,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1431])]) ).
fof(f4559,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| element(sK13(set_intersection2(X1,X2),X3,X0),X1) )
| ~ spl22_46
| ~ spl22_351 ),
inference(resolution,[],[f3979,f459]) ).
fof(f51368,plain,
( spl22_1430
| ~ spl22_290
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4531,f3974,f3304,f51366]) ).
fof(f51366,plain,
( spl22_1430
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_rng(X2)),X3,X0)
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1430])]) ).
fof(f3974,plain,
( spl22_350
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_350])]) ).
fof(f4531,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_rng(X2)),X3,X0)
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_350 ),
inference(resolution,[],[f3975,f3305]) ).
fof(f3975,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X1)
| ~ empty(X3)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_350 ),
inference(avatar_component_clause,[],[f3974]) ).
fof(f51364,plain,
( spl22_1429
| ~ spl22_45
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4528,f3974,f454,f51362]) ).
fof(f51362,plain,
( spl22_1429
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ in(X2,sK13(set_intersection2(X1,X2),X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1429])]) ).
fof(f4528,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ in(X2,sK13(set_intersection2(X1,X2),X3,X0)) )
| ~ spl22_45
| ~ spl22_350 ),
inference(resolution,[],[f3975,f455]) ).
fof(f51360,plain,
( spl22_1428
| ~ spl22_46
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4527,f3974,f458,f51358]) ).
fof(f51358,plain,
( spl22_1428
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| element(sK13(set_intersection2(X1,X2),X3,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1428])]) ).
fof(f4527,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| element(sK13(set_intersection2(X1,X2),X3,X0),X2) )
| ~ spl22_46
| ~ spl22_350 ),
inference(resolution,[],[f3975,f459]) ).
fof(f51356,plain,
( spl22_1427
| ~ spl22_53
| ~ spl22_1292 ),
inference(avatar_split_clause,[],[f45065,f40374,f511,f51354]) ).
fof(f51354,plain,
( spl22_1427
<=> ! [X0] :
( ~ sP0(sK5,set_intersection2(X0,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1427])]) ).
fof(f40374,plain,
( spl22_1292
<=> ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1292])]) ).
fof(f45065,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(X0,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_53
| ~ spl22_1292 ),
inference(superposition,[],[f40375,f512]) ).
fof(f40375,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_1292 ),
inference(avatar_component_clause,[],[f40374]) ).
fof(f51352,plain,
( spl22_1426
| ~ spl22_56
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f4519,f3966,f545,f51350]) ).
fof(f51350,plain,
( spl22_1426
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,sK6(X2))
| empty(X2)
| in(sK13(X1,X0,sK6(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1426])]) ).
fof(f3966,plain,
( spl22_348
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| ~ empty(X1)
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_348])]) ).
fof(f4519,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,sK6(X2))
| empty(X2)
| in(sK13(X1,X0,sK6(X2)),X2) )
| ~ spl22_56
| ~ spl22_348 ),
inference(duplicate_literal_removal,[],[f4516]) ).
fof(f4516,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,sK6(X2))
| empty(X2)
| empty(X2)
| in(sK13(X1,X0,sK6(X2)),X2) )
| ~ spl22_56
| ~ spl22_348 ),
inference(resolution,[],[f3967,f546]) ).
fof(f3967,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| ~ empty(X1)
| sP2(X0,X1,sK6(X2))
| empty(X2) )
| ~ spl22_348 ),
inference(avatar_component_clause,[],[f3966]) ).
fof(f51348,plain,
( spl22_1425
| ~ spl22_290
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4491,f3962,f3304,f51346]) ).
fof(f51346,plain,
( spl22_1425
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1425])]) ).
fof(f3962,plain,
( spl22_347
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_347])]) ).
fof(f4491,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_347 ),
inference(resolution,[],[f3963,f3305]) ).
fof(f3963,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| ~ empty(X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_347 ),
inference(avatar_component_clause,[],[f3962]) ).
fof(f51344,plain,
( spl22_1424
| ~ spl22_45
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4488,f3962,f454,f51342]) ).
fof(f51342,plain,
( spl22_1424
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ in(X2,sK13(X1,X0,set_intersection2(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1424])]) ).
fof(f4488,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ in(X2,sK13(X1,X0,set_intersection2(X2,X3))) )
| ~ spl22_45
| ~ spl22_347 ),
inference(resolution,[],[f3963,f455]) ).
fof(f51340,plain,
( spl22_1423
| ~ spl22_46
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4487,f3962,f458,f51338]) ).
fof(f51338,plain,
( spl22_1423
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| element(sK13(X1,X0,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1423])]) ).
fof(f4487,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| element(sK13(X1,X0,set_intersection2(X2,X3)),X2) )
| ~ spl22_46
| ~ spl22_347 ),
inference(resolution,[],[f3963,f459]) ).
fof(f51336,plain,
( spl22_1422
| ~ spl22_290
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4461,f3958,f3304,f51334]) ).
fof(f51334,plain,
( spl22_1422
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1422])]) ).
fof(f3958,plain,
( spl22_346
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_346])]) ).
fof(f4461,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_346 ),
inference(resolution,[],[f3959,f3305]) ).
fof(f3959,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| ~ empty(X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_346 ),
inference(avatar_component_clause,[],[f3958]) ).
fof(f51332,plain,
( spl22_1421
| ~ spl22_45
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4458,f3958,f454,f51330]) ).
fof(f51330,plain,
( spl22_1421
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ in(X3,sK13(X1,X0,set_intersection2(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1421])]) ).
fof(f4458,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ in(X3,sK13(X1,X0,set_intersection2(X2,X3))) )
| ~ spl22_45
| ~ spl22_346 ),
inference(resolution,[],[f3959,f455]) ).
fof(f51328,plain,
( spl22_1420
| ~ spl22_46
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4457,f3958,f458,f51326]) ).
fof(f51326,plain,
( spl22_1420
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| element(sK13(X1,X0,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1420])]) ).
fof(f4457,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| element(sK13(X1,X0,set_intersection2(X2,X3)),X3) )
| ~ spl22_46
| ~ spl22_346 ),
inference(resolution,[],[f3959,f459]) ).
fof(f51324,plain,
( spl22_1419
| ~ spl22_56
| ~ spl22_344 ),
inference(avatar_split_clause,[],[f4405,f3950,f545,f51322]) ).
fof(f51322,plain,
( spl22_1419
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK6(X2),X0)
| empty(X2)
| in(sK13(X1,sK6(X2),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1419])]) ).
fof(f3950,plain,
( spl22_344
<=> ! [X2,X0,X1] :
( sP2(X0,sK6(X1),X2)
| ~ empty(X2)
| element(sK13(X0,sK6(X1),X2),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_344])]) ).
fof(f4405,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK6(X2),X0)
| empty(X2)
| in(sK13(X1,sK6(X2),X0),X2) )
| ~ spl22_56
| ~ spl22_344 ),
inference(duplicate_literal_removal,[],[f4402]) ).
fof(f4402,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK6(X2),X0)
| empty(X2)
| empty(X2)
| in(sK13(X1,sK6(X2),X0),X2) )
| ~ spl22_56
| ~ spl22_344 ),
inference(resolution,[],[f3951,f546]) ).
fof(f3951,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),X2),X1)
| ~ empty(X2)
| sP2(X0,sK6(X1),X2)
| empty(X1) )
| ~ spl22_344 ),
inference(avatar_component_clause,[],[f3950]) ).
fof(f51320,plain,
( spl22_1418
| ~ spl22_290
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4377,f3937,f3304,f51318]) ).
fof(f51318,plain,
( spl22_1418
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_rng(X2),X3),X0)
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1418])]) ).
fof(f3937,plain,
( spl22_341
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_341])]) ).
fof(f4377,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_rng(X2),X3),X0)
| ~ sP1(X2)
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_341 ),
inference(resolution,[],[f3938,f3305]) ).
fof(f3938,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X1)
| ~ empty(X3)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_341 ),
inference(avatar_component_clause,[],[f3937]) ).
fof(f51316,plain,
( spl22_1417
| ~ spl22_45
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4374,f3937,f454,f51314]) ).
fof(f51314,plain,
( spl22_1417
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ in(X2,sK13(X1,set_intersection2(X2,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1417])]) ).
fof(f4374,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ in(X2,sK13(X1,set_intersection2(X2,X3),X0)) )
| ~ spl22_45
| ~ spl22_341 ),
inference(resolution,[],[f3938,f455]) ).
fof(f51312,plain,
( spl22_1416
| ~ spl22_495
| ~ spl22_971 ),
inference(avatar_split_clause,[],[f24804,f23806,f9032,f51310]) ).
fof(f51310,plain,
( spl22_1416
<=> ! [X0] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP0(relation_dom_restriction(sK5,relation_rng(X0)),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1416])]) ).
fof(f9032,plain,
( spl22_495
<=> ! [X0] :
( ~ empty(set_intersection2(X0,relation_dom(sK5)))
| sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_495])]) ).
fof(f23806,plain,
( spl22_971
<=> ! [X0,X1] :
( empty(set_intersection2(relation_rng(X0),X1))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_971])]) ).
fof(f24804,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP0(relation_dom_restriction(sK5,relation_rng(X0)),sK15) )
| ~ spl22_495
| ~ spl22_971 ),
inference(resolution,[],[f23807,f9033]) ).
fof(f9033,plain,
( ! [X0] :
( ~ empty(set_intersection2(X0,relation_dom(sK5)))
| sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_495 ),
inference(avatar_component_clause,[],[f9032]) ).
fof(f23807,plain,
( ! [X0,X1] :
( empty(set_intersection2(relation_rng(X0),X1))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl22_971 ),
inference(avatar_component_clause,[],[f23806]) ).
fof(f51308,plain,
( spl22_1415
| ~ spl22_46
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4373,f3937,f458,f51306]) ).
fof(f51306,plain,
( spl22_1415
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| element(sK13(X1,set_intersection2(X2,X3),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1415])]) ).
fof(f4373,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| element(sK13(X1,set_intersection2(X2,X3),X0),X2) )
| ~ spl22_46
| ~ spl22_341 ),
inference(resolution,[],[f3938,f459]) ).
fof(f51304,plain,
( spl22_1414
| ~ spl22_290
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4347,f3933,f3304,f51302]) ).
fof(f51302,plain,
( spl22_1414
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_rng(X3)),X0)
| ~ sP1(X3)
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1414])]) ).
fof(f3933,plain,
( spl22_340
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_340])]) ).
fof(f4347,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_rng(X3)),X0)
| ~ sP1(X3)
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_290
| ~ spl22_340 ),
inference(resolution,[],[f3934,f3305]) ).
fof(f3934,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X2)
| ~ empty(X3)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_340 ),
inference(avatar_component_clause,[],[f3933]) ).
fof(f51300,plain,
( spl22_1413
| ~ spl22_45
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4344,f3933,f454,f51298]) ).
fof(f51298,plain,
( spl22_1413
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ in(X3,sK13(X1,set_intersection2(X2,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1413])]) ).
fof(f4344,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ in(X3,sK13(X1,set_intersection2(X2,X3),X0)) )
| ~ spl22_45
| ~ spl22_340 ),
inference(resolution,[],[f3934,f455]) ).
fof(f51296,plain,
( spl22_1412
| ~ spl22_46
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4343,f3933,f458,f51294]) ).
fof(f51294,plain,
( spl22_1412
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| element(sK13(X1,set_intersection2(X2,X3),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1412])]) ).
fof(f4343,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| element(sK13(X1,set_intersection2(X2,X3),X0),X3) )
| ~ spl22_46
| ~ spl22_340 ),
inference(resolution,[],[f3934,f459]) ).
fof(f51292,plain,
( spl22_1411
| ~ spl22_56
| ~ spl22_337 ),
inference(avatar_split_clause,[],[f4224,f3921,f545,f51290]) ).
fof(f51290,plain,
( spl22_1411
<=> ! [X0,X1] :
( sP2(sK6(X0),X1,sK6(X0))
| empty(X0)
| in(sK13(sK6(X0),X1,sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1411])]) ).
fof(f3921,plain,
( spl22_337
<=> ! [X0,X1] :
( sP2(sK6(X0),X1,sK6(X0))
| element(sK13(sK6(X0),X1,sK6(X0)),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_337])]) ).
fof(f4224,plain,
( ! [X0,X1] :
( sP2(sK6(X0),X1,sK6(X0))
| empty(X0)
| in(sK13(sK6(X0),X1,sK6(X0)),X0) )
| ~ spl22_56
| ~ spl22_337 ),
inference(duplicate_literal_removal,[],[f4221]) ).
fof(f4221,plain,
( ! [X0,X1] :
( sP2(sK6(X0),X1,sK6(X0))
| empty(X0)
| empty(X0)
| in(sK13(sK6(X0),X1,sK6(X0)),X0) )
| ~ spl22_56
| ~ spl22_337 ),
inference(resolution,[],[f3922,f546]) ).
fof(f3922,plain,
( ! [X0,X1] :
( element(sK13(sK6(X0),X1,sK6(X0)),X0)
| sP2(sK6(X0),X1,sK6(X0))
| empty(X0) )
| ~ spl22_337 ),
inference(avatar_component_clause,[],[f3921]) ).
fof(f51288,plain,
( spl22_1410
| ~ spl22_56
| ~ spl22_335 ),
inference(avatar_split_clause,[],[f4161,f3913,f545,f51286]) ).
fof(f51286,plain,
( spl22_1410
<=> ! [X0,X1] :
( sP2(X0,sK6(X1),sK6(X1))
| empty(X1)
| in(sK13(X0,sK6(X1),sK6(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1410])]) ).
fof(f3913,plain,
( spl22_335
<=> ! [X0,X1] :
( sP2(X0,sK6(X1),sK6(X1))
| element(sK13(X0,sK6(X1),sK6(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_335])]) ).
fof(f4161,plain,
( ! [X0,X1] :
( sP2(X0,sK6(X1),sK6(X1))
| empty(X1)
| in(sK13(X0,sK6(X1),sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_335 ),
inference(duplicate_literal_removal,[],[f4158]) ).
fof(f4158,plain,
( ! [X0,X1] :
( sP2(X0,sK6(X1),sK6(X1))
| empty(X1)
| empty(X1)
| in(sK13(X0,sK6(X1),sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_335 ),
inference(resolution,[],[f3914,f546]) ).
fof(f3914,plain,
( ! [X0,X1] :
( element(sK13(X0,sK6(X1),sK6(X1)),X1)
| sP2(X0,sK6(X1),sK6(X1))
| empty(X1) )
| ~ spl22_335 ),
inference(avatar_component_clause,[],[f3913]) ).
fof(f51284,plain,
( spl22_1409
| ~ spl22_47
| ~ spl22_334 ),
inference(avatar_split_clause,[],[f4153,f3909,f462,f51282]) ).
fof(f51282,plain,
( spl22_1409
<=> ! [X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK8(X1,relation_dom(X0)),relation_dom(X1))
| sP0(X1,relation_dom(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1409])]) ).
fof(f4153,plain,
( ! [X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK8(X1,relation_dom(X0)),relation_dom(X1))
| sP0(X1,relation_dom(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_334 ),
inference(resolution,[],[f3910,f463]) ).
fof(f51280,plain,
( spl22_1408
| ~ spl22_290
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f4136,f3905,f3304,f51278]) ).
fof(f51278,plain,
( spl22_1408
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_rng(X2))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1408])]) ).
fof(f3905,plain,
( spl22_333
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_333])]) ).
fof(f4136,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_rng(X2))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_333 ),
inference(resolution,[],[f3906,f3305]) ).
fof(f3906,plain,
( ! [X2,X0,X1] :
( in(sK13(sK10(powerset(X0)),X1,X2),X2)
| ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,X2) )
| ~ spl22_333 ),
inference(avatar_component_clause,[],[f3905]) ).
fof(f51276,plain,
( spl22_1407
| ~ spl22_45
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f4133,f3905,f454,f51274]) ).
fof(f51274,plain,
( spl22_1407
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,X2)
| ~ in(X2,sK13(sK10(powerset(X0)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1407])]) ).
fof(f4133,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,X2)
| ~ in(X2,sK13(sK10(powerset(X0)),X1,X2)) )
| ~ spl22_45
| ~ spl22_333 ),
inference(resolution,[],[f3906,f455]) ).
fof(f51272,plain,
( spl22_1406
| ~ spl22_290
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f4110,f3901,f3304,f51270]) ).
fof(f51270,plain,
( spl22_1406
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_rng(X2))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1406])]) ).
fof(f3901,plain,
( spl22_332
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(X1,sK10(powerset(X0)),X2),X2)
| sP2(X1,sK10(powerset(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_332])]) ).
fof(f4110,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_rng(X2))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_332 ),
inference(resolution,[],[f3902,f3305]) ).
fof(f3902,plain,
( ! [X2,X0,X1] :
( in(sK13(X1,sK10(powerset(X0)),X2),X2)
| ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),X2) )
| ~ spl22_332 ),
inference(avatar_component_clause,[],[f3901]) ).
fof(f51268,plain,
( spl22_1405
| ~ spl22_117
| ~ spl22_412 ),
inference(avatar_split_clause,[],[f6249,f5443,f1053,f51266]) ).
fof(f51266,plain,
( spl22_1405
<=> ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_dom(set_intersection2(X0,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1405])]) ).
fof(f5443,plain,
( spl22_412
<=> ! [X0] :
( empty(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_412])]) ).
fof(f6249,plain,
( ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_dom(set_intersection2(X0,relation_dom(sK5))) )
| ~ spl22_117
| ~ spl22_412 ),
inference(resolution,[],[f5444,f1054]) ).
fof(f5444,plain,
( ! [X0] :
( empty(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_412 ),
inference(avatar_component_clause,[],[f5443]) ).
fof(f51264,plain,
( spl22_1404
| ~ spl22_45
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f4107,f3901,f454,f51262]) ).
fof(f51262,plain,
( spl22_1404
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),X2)
| ~ in(X2,sK13(X1,sK10(powerset(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1404])]) ).
fof(f4107,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),X2)
| ~ in(X2,sK13(X1,sK10(powerset(X0)),X2)) )
| ~ spl22_45
| ~ spl22_332 ),
inference(resolution,[],[f3902,f455]) ).
fof(f51260,plain,
( spl22_1403
| ~ spl22_290
| ~ spl22_331 ),
inference(avatar_split_clause,[],[f4088,f3859,f3304,f51258]) ).
fof(f51258,plain,
( spl22_1403
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,relation_rng(X2),sK10(powerset(X0)))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1403])]) ).
fof(f3859,plain,
( spl22_331
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(X1,X2,sK10(powerset(X0))),X2)
| sP2(X1,X2,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_331])]) ).
fof(f4088,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_rng(X2),sK10(powerset(X0)))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_331 ),
inference(resolution,[],[f3860,f3305]) ).
fof(f3860,plain,
( ! [X2,X0,X1] :
( in(sK13(X1,X2,sK10(powerset(X0))),X2)
| ~ empty(X0)
| sP2(X1,X2,sK10(powerset(X0))) )
| ~ spl22_331 ),
inference(avatar_component_clause,[],[f3859]) ).
fof(f51256,plain,
( spl22_1402
| ~ spl22_45
| ~ spl22_331 ),
inference(avatar_split_clause,[],[f4085,f3859,f454,f51254]) ).
fof(f51254,plain,
( spl22_1402
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X2,sK10(powerset(X0)))
| ~ in(X2,sK13(X1,X2,sK10(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1402])]) ).
fof(f4085,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X2,sK10(powerset(X0)))
| ~ in(X2,sK13(X1,X2,sK10(powerset(X0)))) )
| ~ spl22_45
| ~ spl22_331 ),
inference(resolution,[],[f3860,f455]) ).
fof(f51252,plain,
( spl22_1401
| ~ spl22_290
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f4066,f3855,f3304,f51250]) ).
fof(f51250,plain,
( spl22_1401
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(relation_rng(X1),X2,sK10(powerset(X0)))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1401])]) ).
fof(f3855,plain,
( spl22_330
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(X1,X2,sK10(powerset(X0))),X1)
| sP2(X1,X2,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_330])]) ).
fof(f4066,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(relation_rng(X1),X2,sK10(powerset(X0)))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_330 ),
inference(resolution,[],[f3856,f3305]) ).
fof(f3856,plain,
( ! [X2,X0,X1] :
( in(sK13(X1,X2,sK10(powerset(X0))),X1)
| ~ empty(X0)
| sP2(X1,X2,sK10(powerset(X0))) )
| ~ spl22_330 ),
inference(avatar_component_clause,[],[f3855]) ).
fof(f51248,plain,
( spl22_1400
| ~ spl22_45
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f4063,f3855,f454,f51246]) ).
fof(f51246,plain,
( spl22_1400
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X2,sK10(powerset(X0)))
| ~ in(X1,sK13(X1,X2,sK10(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1400])]) ).
fof(f4063,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X2,sK10(powerset(X0)))
| ~ in(X1,sK13(X1,X2,sK10(powerset(X0)))) )
| ~ spl22_45
| ~ spl22_330 ),
inference(resolution,[],[f3856,f455]) ).
fof(f51244,plain,
( spl22_1399
| ~ spl22_252
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3840,f3697,f2895,f51242]) ).
fof(f51242,plain,
( spl22_1399
<=> ! [X2,X0,X1,X3] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(sK15,X3,apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1399])]) ).
fof(f3840,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(sK15,X3,apply(X1,X0)) )
| ~ spl22_252
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2896]) ).
fof(f51240,plain,
( spl22_1398
| ~ spl22_251
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3838,f3697,f2891,f51238]) ).
fof(f51238,plain,
( spl22_1398
<=> ! [X2,X0,X1,X3] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,sK15,apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1398])]) ).
fof(f3838,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,sK15,apply(X1,X0)) )
| ~ spl22_251
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2892]) ).
fof(f51236,plain,
( spl22_1397
| ~ spl22_250
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3836,f3697,f2887,f51234]) ).
fof(f51234,plain,
( spl22_1397
<=> ! [X2,X0,X1,X3] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1397])]) ).
fof(f3836,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),sK15) )
| ~ spl22_250
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2888]) ).
fof(f51232,plain,
( spl22_1396
| ~ spl22_249
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3835,f3697,f2883,f51230]) ).
fof(f51230,plain,
( spl22_1396
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1396])]) ).
fof(f3835,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,sK15) )
| ~ spl22_249
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2884]) ).
fof(f51228,plain,
( spl22_1395
| ~ spl22_255
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3814,f3697,f2907,f51226]) ).
fof(f51226,plain,
( spl22_1395
<=> ! [X2,X0,X1,X3] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| empty(set_intersection2(X3,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1395])]) ).
fof(f3814,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| empty(set_intersection2(X3,apply(X1,X0))) )
| ~ spl22_255
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2908]) ).
fof(f51224,plain,
( spl22_1394
| ~ spl22_116
| ~ spl22_412 ),
inference(avatar_split_clause,[],[f6248,f5443,f1049,f51222]) ).
fof(f51222,plain,
( spl22_1394
<=> ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_rng(set_intersection2(X0,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1394])]) ).
fof(f6248,plain,
( ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_rng(set_intersection2(X0,relation_dom(sK5))) )
| ~ spl22_116
| ~ spl22_412 ),
inference(resolution,[],[f5444,f1050]) ).
fof(f51220,plain,
( spl22_1393
| ~ spl22_254
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3813,f3697,f2903,f51218]) ).
fof(f51218,plain,
( spl22_1393
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| empty(set_intersection2(apply(X1,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1393])]) ).
fof(f3813,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| empty(set_intersection2(apply(X1,X0),X3)) )
| ~ spl22_254
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2904]) ).
fof(f51216,plain,
( spl22_1392
| ~ spl22_290
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3775,f3685,f3304,f51214]) ).
fof(f51214,plain,
( spl22_1392
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1392])]) ).
fof(f3775,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_325 ),
inference(resolution,[],[f3686,f3305]) ).
fof(f51212,plain,
( spl22_1391
| ~ spl22_290
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3750,f3681,f3304,f51210]) ).
fof(f51210,plain,
( spl22_1391
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1391])]) ).
fof(f3750,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_290
| ~ spl22_324 ),
inference(resolution,[],[f3682,f3305]) ).
fof(f51208,plain,
( spl22_1390
| ~ spl22_37
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3576,f3551,f402,f51206]) ).
fof(f51206,plain,
( spl22_1390
<=> ! [X0,X1] :
( ~ function(relation_dom(X0))
| set_intersection2(relation_dom(relation_dom(X0)),X1) = relation_dom(relation_dom_restriction(relation_dom(X0),X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1390])]) ).
fof(f402,plain,
( spl22_37
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_37])]) ).
fof(f3576,plain,
( ! [X0,X1] :
( ~ function(relation_dom(X0))
| set_intersection2(relation_dom(relation_dom(X0)),X1) = relation_dom(relation_dom_restriction(relation_dom(X0),X1))
| ~ empty(X0) )
| ~ spl22_37
| ~ spl22_313 ),
inference(resolution,[],[f3552,f403]) ).
fof(f403,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_37 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f51204,plain,
( spl22_1389
| ~ spl22_35
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3575,f3551,f394,f51202]) ).
fof(f51202,plain,
( spl22_1389
<=> ! [X0,X1] :
( ~ function(relation_rng(X0))
| set_intersection2(relation_dom(relation_rng(X0)),X1) = relation_dom(relation_dom_restriction(relation_rng(X0),X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1389])]) ).
fof(f394,plain,
( spl22_35
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_35])]) ).
fof(f3575,plain,
( ! [X0,X1] :
( ~ function(relation_rng(X0))
| set_intersection2(relation_dom(relation_rng(X0)),X1) = relation_dom(relation_dom_restriction(relation_rng(X0),X1))
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_313 ),
inference(resolution,[],[f3552,f395]) ).
fof(f395,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_35 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f51200,plain,
( spl22_1388
| ~ spl22_63
| ~ spl22_304 ),
inference(avatar_split_clause,[],[f3523,f3446,f586,f51198]) ).
fof(f51198,plain,
( spl22_1388
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1388])]) ).
fof(f3523,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_63
| ~ spl22_304 ),
inference(resolution,[],[f3447,f587]) ).
fof(f51196,plain,
( spl22_1387
| ~ spl22_63
| ~ spl22_301 ),
inference(avatar_split_clause,[],[f3512,f3434,f586,f51194]) ).
fof(f51194,plain,
( spl22_1387
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(powerset(X1),X2,X0)
| ~ empty(X1)
| ~ in(X3,sK13(powerset(X1),X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1387])]) ).
fof(f3512,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(powerset(X1),X2,X0)
| ~ empty(X1)
| ~ in(X3,sK13(powerset(X1),X2,X0)) )
| ~ spl22_63
| ~ spl22_301 ),
inference(resolution,[],[f3435,f587]) ).
fof(f51192,plain,
( spl22_1386
| ~ spl22_63
| ~ spl22_298 ),
inference(avatar_split_clause,[],[f3496,f3422,f586,f51190]) ).
fof(f51190,plain,
( spl22_1386
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,X0,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1386])]) ).
fof(f3496,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,powerset(X2))) )
| ~ spl22_63
| ~ spl22_298 ),
inference(resolution,[],[f3423,f587]) ).
fof(f51188,plain,
( spl22_1385
| ~ spl22_63
| ~ spl22_295 ),
inference(avatar_split_clause,[],[f3485,f3410,f586,f51186]) ).
fof(f51186,plain,
( spl22_1385
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,powerset(X2),X0)
| ~ empty(X2)
| ~ in(X3,sK13(X1,powerset(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1385])]) ).
fof(f3485,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,powerset(X2),X0)
| ~ empty(X2)
| ~ in(X3,sK13(X1,powerset(X2),X0)) )
| ~ spl22_63
| ~ spl22_295 ),
inference(resolution,[],[f3411,f587]) ).
fof(f51184,plain,
( spl22_1384
| ~ spl22_65
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3343,f3288,f604,f51182]) ).
fof(f51182,plain,
( spl22_1384
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1384])]) ).
fof(f3288,plain,
( spl22_286
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| element(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_286])]) ).
fof(f3343,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_286 ),
inference(resolution,[],[f3289,f605]) ).
fof(f3289,plain,
( ! [X0,X1] :
( element(sK7(X0,X1),X1)
| ~ empty(relation_dom(X0))
| sP0(X0,X1) )
| ~ spl22_286 ),
inference(avatar_component_clause,[],[f3288]) ).
fof(f51080,plain,
( spl22_1383
| ~ spl22_158
| ~ spl22_268 ),
inference(avatar_split_clause,[],[f3203,f2959,f1544,f51078]) ).
fof(f51078,plain,
( spl22_1383
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0)
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1383])]) ).
fof(f2959,plain,
( spl22_268
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_268])]) ).
fof(f3203,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0)
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2)) )
| ~ spl22_158
| ~ spl22_268 ),
inference(duplicate_literal_removal,[],[f3199]) ).
fof(f3199,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0)
| ~ empty(X2)
| sK7(X1,X2) = apply(X1,sK8(X1,X2))
| ~ empty(X2) )
| ~ spl22_158
| ~ spl22_268 ),
inference(resolution,[],[f2960,f1545]) ).
fof(f2960,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X2)
| ~ empty(X1)
| sP0(X0,X1)
| ~ empty(X2) )
| ~ spl22_268 ),
inference(avatar_component_clause,[],[f2959]) ).
fof(f51076,plain,
( spl22_1382
| ~ spl22_63
| ~ spl22_263 ),
inference(avatar_split_clause,[],[f3178,f2939,f586,f51074]) ).
fof(f51074,plain,
( spl22_1382
<=> ! [X2,X0,X1] :
( sP2(powerset(X0),X1,powerset(X0))
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1382])]) ).
fof(f3178,plain,
( ! [X2,X0,X1] :
( sP2(powerset(X0),X1,powerset(X0))
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,powerset(X0))) )
| ~ spl22_63
| ~ spl22_263 ),
inference(resolution,[],[f2940,f587]) ).
fof(f51072,plain,
( spl22_1381
| ~ spl22_63
| ~ spl22_260 ),
inference(avatar_split_clause,[],[f3153,f2927,f586,f51070]) ).
fof(f51070,plain,
( spl22_1381
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1),powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1381])]) ).
fof(f3153,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1),powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),powerset(X1))) )
| ~ spl22_63
| ~ spl22_260 ),
inference(resolution,[],[f2928,f587]) ).
fof(f51068,plain,
( spl22_1380
| ~ spl22_141
| ~ spl22_257 ),
inference(avatar_split_clause,[],[f3151,f2915,f1337,f51066]) ).
fof(f51066,plain,
( spl22_1380
<=> ! [X2,X0,X1] :
( ~ subset(set_intersection2(X0,X1),X2)
| empty(powerset(X2))
| ~ in(powerset(X2),X0)
| ~ in(powerset(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1380])]) ).
fof(f1337,plain,
( spl22_141
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_141])]) ).
fof(f2915,plain,
( spl22_257
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_257])]) ).
fof(f3151,plain,
( ! [X2,X0,X1] :
( ~ subset(set_intersection2(X0,X1),X2)
| empty(powerset(X2))
| ~ in(powerset(X2),X0)
| ~ in(powerset(X2),X1) )
| ~ spl22_141
| ~ spl22_257 ),
inference(resolution,[],[f2916,f1338]) ).
fof(f1338,plain,
( ! [X2,X0,X1] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) )
| ~ spl22_141 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f2916,plain,
( ! [X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(X1,X0)
| empty(powerset(X0)) )
| ~ spl22_257 ),
inference(avatar_component_clause,[],[f2915]) ).
fof(f51064,plain,
( spl22_1379
| ~ spl22_65
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f3148,f2911,f604,f51062]) ).
fof(f51062,plain,
( spl22_1379
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1379])]) ).
fof(f2911,plain,
( spl22_256
<=> ! [X0] :
( element(sK10(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_256])]) ).
fof(f3148,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) )
| ~ spl22_65
| ~ spl22_256 ),
inference(resolution,[],[f2912,f605]) ).
fof(f2912,plain,
( ! [X0] :
( element(sK10(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) )
| ~ spl22_256 ),
inference(avatar_component_clause,[],[f2911]) ).
fof(f51060,plain,
( spl22_1378
| ~ spl22_73
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2839,f2743,f652,f51058]) ).
fof(f51058,plain,
( spl22_1378
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK8(X1,relation_rng(X0)),relation_dom(X1))
| sP0(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1378])]) ).
fof(f2839,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| in(sK8(X1,relation_rng(X0)),relation_dom(X1))
| sP0(X1,relation_rng(X0)) )
| ~ spl22_73
| ~ spl22_248 ),
inference(resolution,[],[f2744,f653]) ).
fof(f51056,plain,
( spl22_1377
| ~ spl22_154
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2836,f2743,f1527,f51054]) ).
fof(f51054,plain,
( spl22_1377
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK8(X1,relation_rng(X0)),relation_dom(X1))
| sP0(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1377])]) ).
fof(f2836,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| element(sK8(X1,relation_rng(X0)),relation_dom(X1))
| sP0(X1,relation_rng(X0)) )
| ~ spl22_154
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1528]) ).
fof(f50889,plain,
( spl22_1376
| ~ spl22_232
| ~ spl22_528 ),
inference(avatar_split_clause,[],[f10327,f10230,f2531,f50887]) ).
fof(f50887,plain,
( spl22_1376
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sK7(X2,apply(X1,X0)) = apply(X2,sK8(X2,apply(X1,X0)))
| sP0(X2,apply(X1,X0))
| sK7(X1,sK7(X2,apply(X1,X0))) = apply(X1,sK8(X1,sK7(X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK7(X2,apply(X1,X0))),sK7(X1,sK7(X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK7(X2,apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1376])]) ).
fof(f10230,plain,
( spl22_528
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sK7(X1,apply(X0,X2)) = apply(X1,sK8(X1,apply(X0,X2)))
| sP0(X1,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_528])]) ).
fof(f10327,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sK7(X2,apply(X1,X0)) = apply(X2,sK8(X2,apply(X1,X0)))
| sP0(X2,apply(X1,X0))
| sK7(X1,sK7(X2,apply(X1,X0))) = apply(X1,sK8(X1,sK7(X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK7(X2,apply(X1,X0))),sK7(X1,sK7(X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK7(X2,apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_528 ),
inference(resolution,[],[f10231,f2532]) ).
fof(f10231,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sK7(X1,apply(X0,X2)) = apply(X1,sK8(X1,apply(X0,X2)))
| sP0(X1,apply(X0,X2)) )
| ~ spl22_528 ),
inference(avatar_component_clause,[],[f10230]) ).
fof(f50659,plain,
( spl22_1375
| ~ spl22_83
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2521,f2510,f742,f50657]) ).
fof(f50657,plain,
( spl22_1375
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(sK5,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1375])]) ).
fof(f742,plain,
( spl22_83
<=> ! [X4,X0,X2] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_83])]) ).
fof(f2521,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(sK5,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_231 ),
inference(resolution,[],[f2511,f743]) ).
fof(f743,plain,
( ! [X2,X0,X4] :
( ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) )
| ~ spl22_83 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f50655,plain,
( spl22_1374
| ~ spl22_83
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2500,f2489,f742,f50653]) ).
fof(f50653,plain,
( spl22_1374
<=> ! [X0,X3,X2,X1] :
( sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(sK5,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1374])]) ).
fof(f2500,plain,
( ! [X2,X3,X0,X1] :
( sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(sK5,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_230 ),
inference(resolution,[],[f2490,f743]) ).
fof(f50651,plain,
( spl22_1373
| ~ spl22_83
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2479,f2468,f742,f50649]) ).
fof(f50649,plain,
( spl22_1373
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(sK5,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1373])]) ).
fof(f2479,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(sK5,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_229 ),
inference(resolution,[],[f2469,f743]) ).
fof(f50647,plain,
( spl22_1372
| ~ spl22_83
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2458,f2447,f742,f50645]) ).
fof(f50645,plain,
( spl22_1372
<=> ! [X0,X3,X2,X1] :
( sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(sK5,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1372])]) ).
fof(f2458,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(sK5,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_228 ),
inference(resolution,[],[f2448,f743]) ).
fof(f47778,plain,
( spl22_1371
| spl22_81
| ~ spl22_1345 ),
inference(avatar_split_clause,[],[f46981,f46885,f726,f47775]) ).
fof(f47775,plain,
( spl22_1371
<=> apply(relation_dom_restriction(sK20,sK5),sK10(sK5)) = apply(sK20,sK10(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1371])]) ).
fof(f726,plain,
( spl22_81
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_81])]) ).
fof(f46885,plain,
( spl22_1345
<=> ! [X0] :
( apply(relation_dom_restriction(sK20,X0),sK10(X0)) = apply(sK20,sK10(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1345])]) ).
fof(f46981,plain,
( apply(relation_dom_restriction(sK20,sK5),sK10(sK5)) = apply(sK20,sK10(sK5))
| spl22_81
| ~ spl22_1345 ),
inference(resolution,[],[f46886,f728]) ).
fof(f728,plain,
( ~ empty(sK5)
| spl22_81 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f46886,plain,
( ! [X0] :
( empty(X0)
| apply(relation_dom_restriction(sK20,X0),sK10(X0)) = apply(sK20,sK10(X0)) )
| ~ spl22_1345 ),
inference(avatar_component_clause,[],[f46885]) ).
fof(f47222,plain,
( spl22_1370
| ~ spl22_41
| ~ spl22_409 ),
inference(avatar_split_clause,[],[f5548,f5286,f419,f47220]) ).
fof(f47220,plain,
( spl22_1370
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1370])]) ).
fof(f5548,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_409 ),
inference(resolution,[],[f5287,f420]) ).
fof(f47218,plain,
( spl22_1369
| spl22_49
| ~ spl22_1345 ),
inference(avatar_split_clause,[],[f46980,f46885,f487,f47215]) ).
fof(f47215,plain,
( spl22_1369
<=> apply(relation_dom_restriction(sK20,sK3),sK10(sK3)) = apply(sK20,sK10(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1369])]) ).
fof(f487,plain,
( spl22_49
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_49])]) ).
fof(f46980,plain,
( apply(relation_dom_restriction(sK20,sK3),sK10(sK3)) = apply(sK20,sK10(sK3))
| spl22_49
| ~ spl22_1345 ),
inference(resolution,[],[f46886,f489]) ).
fof(f489,plain,
( ~ empty(sK3)
| spl22_49 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f47213,plain,
( spl22_1368
| ~ spl22_41
| ~ spl22_408 ),
inference(avatar_split_clause,[],[f5511,f5282,f419,f47211]) ).
fof(f47211,plain,
( spl22_1368
<=> ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1368])]) ).
fof(f5511,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_408 ),
inference(resolution,[],[f5283,f420]) ).
fof(f47209,plain,
( spl22_1367
| ~ spl22_41
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5397,f5246,f419,f47207]) ).
fof(f47207,plain,
( spl22_1367
<=> ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1367])]) ).
fof(f5397,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_401 ),
inference(resolution,[],[f5247,f420]) ).
fof(f47205,plain,
( spl22_1366
| ~ spl22_233
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5390,f5246,f2559,f47203]) ).
fof(f47203,plain,
( spl22_1366
<=> ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1366])]) ).
fof(f5390,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_401 ),
inference(resolution,[],[f5247,f2560]) ).
fof(f47201,plain,
( spl22_1365
| ~ spl22_41
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5347,f5242,f419,f47199]) ).
fof(f47199,plain,
( spl22_1365
<=> ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1365])]) ).
fof(f5347,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_400 ),
inference(resolution,[],[f5243,f420]) ).
fof(f47197,plain,
( spl22_1364
| ~ spl22_233
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5340,f5242,f2559,f47195]) ).
fof(f47195,plain,
( spl22_1364
<=> ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1364])]) ).
fof(f5340,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| sP0(X0,set_intersection2(X1,X2))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_400 ),
inference(resolution,[],[f5243,f2560]) ).
fof(f47193,plain,
( spl22_1363
| ~ spl22_233
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5327,f5238,f2559,f47191]) ).
fof(f47191,plain,
( spl22_1363
<=> ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1)))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1363])]) ).
fof(f5327,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1)))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_399 ),
inference(resolution,[],[f5239,f2560]) ).
fof(f47189,plain,
( spl22_1362
| ~ spl22_233
| ~ spl22_394 ),
inference(avatar_split_clause,[],[f5134,f5118,f2559,f47187]) ).
fof(f47187,plain,
( spl22_1362
<=> ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1362])]) ).
fof(f5134,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_394 ),
inference(resolution,[],[f5119,f2560]) ).
fof(f47185,plain,
( spl22_1361
| ~ spl22_133
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5059,f4944,f1246,f47183]) ).
fof(f47183,plain,
( spl22_1361
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1361])]) ).
fof(f5059,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_391 ),
inference(resolution,[],[f4945,f1247]) ).
fof(f47181,plain,
( spl22_1360
| ~ spl22_248
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5054,f4944,f2743,f47179]) ).
fof(f47179,plain,
( spl22_1360
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(relation_rng(X0),X1),X2,set_intersection2(relation_rng(X0),X1))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1360])]) ).
fof(f5054,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(relation_rng(X0),X1),X2,set_intersection2(relation_rng(X0),X1))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl22_248
| ~ spl22_391 ),
inference(resolution,[],[f4945,f2744]) ).
fof(f47177,plain,
( spl22_1359
| ~ spl22_133
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5029,f4940,f1246,f47175]) ).
fof(f47175,plain,
( spl22_1359
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1359])]) ).
fof(f5029,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_390 ),
inference(resolution,[],[f4941,f1247]) ).
fof(f47173,plain,
( spl22_1358
| spl22_81
| ~ spl22_1344 ),
inference(avatar_split_clause,[],[f46879,f46783,f726,f47170]) ).
fof(f47170,plain,
( spl22_1358
<=> apply(relation_dom_restriction(sK19,sK5),sK10(sK5)) = apply(sK19,sK10(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1358])]) ).
fof(f46783,plain,
( spl22_1344
<=> ! [X0] :
( apply(relation_dom_restriction(sK19,X0),sK10(X0)) = apply(sK19,sK10(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1344])]) ).
fof(f46879,plain,
( apply(relation_dom_restriction(sK19,sK5),sK10(sK5)) = apply(sK19,sK10(sK5))
| spl22_81
| ~ spl22_1344 ),
inference(resolution,[],[f46784,f728]) ).
fof(f46784,plain,
( ! [X0] :
( empty(X0)
| apply(relation_dom_restriction(sK19,X0),sK10(X0)) = apply(sK19,sK10(X0)) )
| ~ spl22_1344 ),
inference(avatar_component_clause,[],[f46783]) ).
fof(f47168,plain,
( spl22_1357
| ~ spl22_248
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5024,f4940,f2743,f47166]) ).
fof(f47166,plain,
( spl22_1357
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,relation_rng(X1)),X2,set_intersection2(X0,relation_rng(X1)))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1357])]) ).
fof(f5024,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,relation_rng(X1)),X2,set_intersection2(X0,relation_rng(X1)))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_390 ),
inference(resolution,[],[f4941,f2744]) ).
fof(f47164,plain,
( spl22_1356
| ~ spl22_133
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4995,f4902,f1246,f47162]) ).
fof(f47162,plain,
( spl22_1356
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1356])]) ).
fof(f4995,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_388 ),
inference(resolution,[],[f4903,f1247]) ).
fof(f47160,plain,
( spl22_1355
| ~ spl22_248
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4990,f4902,f2743,f47158]) ).
fof(f47158,plain,
( spl22_1355
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(relation_rng(X1),X2),set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1355])]) ).
fof(f4990,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(relation_rng(X1),X2),set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_388 ),
inference(resolution,[],[f4903,f2744]) ).
fof(f47156,plain,
( spl22_1354
| ~ spl22_133
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4967,f4898,f1246,f47154]) ).
fof(f47154,plain,
( spl22_1354
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1354])]) ).
fof(f4967,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_387 ),
inference(resolution,[],[f4899,f1247]) ).
fof(f47152,plain,
( spl22_1353
| ~ spl22_248
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4962,f4898,f2743,f47150]) ).
fof(f47150,plain,
( spl22_1353
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,relation_rng(X2)),set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1353])]) ).
fof(f4962,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,relation_rng(X2)),set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_387 ),
inference(resolution,[],[f4899,f2744]) ).
fof(f47148,plain,
( spl22_1352
| ~ spl22_104
| ~ spl22_381 ),
inference(avatar_split_clause,[],[f4867,f4772,f902,f47146]) ).
fof(f47146,plain,
( spl22_1352
<=> ! [X0] :
( ~ empty(X0)
| relation_rng(sK20) = X0
| sK7(sK20,X0) = apply(sK20,sK8(sK20,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1352])]) ).
fof(f902,plain,
( spl22_104
<=> sP1(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_104])]) ).
fof(f4772,plain,
( spl22_381
<=> ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ empty(X1)
| relation_rng(X0) = X1
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_381])]) ).
fof(f4867,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(sK20) = X0
| sK7(sK20,X0) = apply(sK20,sK8(sK20,X0)) )
| ~ spl22_104
| ~ spl22_381 ),
inference(resolution,[],[f4773,f904]) ).
fof(f904,plain,
( sP1(sK20)
| ~ spl22_104 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f4773,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(X1)
| relation_rng(X0) = X1
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_381 ),
inference(avatar_component_clause,[],[f4772]) ).
fof(f47144,plain,
( spl22_1351
| ~ spl22_103
| ~ spl22_381 ),
inference(avatar_split_clause,[],[f4866,f4772,f897,f47142]) ).
fof(f47142,plain,
( spl22_1351
<=> ! [X0] :
( ~ empty(X0)
| relation_rng(sK19) = X0
| sK7(sK19,X0) = apply(sK19,sK8(sK19,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1351])]) ).
fof(f897,plain,
( spl22_103
<=> sP1(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_103])]) ).
fof(f4866,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(sK19) = X0
| sK7(sK19,X0) = apply(sK19,sK8(sK19,X0)) )
| ~ spl22_103
| ~ spl22_381 ),
inference(resolution,[],[f4773,f899]) ).
fof(f899,plain,
( sP1(sK19)
| ~ spl22_103 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f47140,plain,
( spl22_1350
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_375 ),
inference(avatar_split_clause,[],[f4824,f4748,f798,f254,f410,f47138]) ).
fof(f47138,plain,
( spl22_1350
<=> ! [X0] :
( apply(relation_dom_restriction(sK15,powerset(X0)),sK15) = apply(sK15,sK15)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1350])]) ).
fof(f4748,plain,
( spl22_375
<=> ! [X0,X1] :
( empty(powerset(X0))
| apply(relation_dom_restriction(X1,powerset(X0)),sK15) = apply(X1,sK15)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_375])]) ).
fof(f4824,plain,
( ! [X0] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,powerset(X0)),sK15) = apply(sK15,sK15)
| empty(powerset(X0)) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_375 ),
inference(forward_demodulation,[],[f4823,f800]) ).
fof(f4823,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK15,powerset(X0)),sK15) = apply(sK15,sK15)
| ~ function(empty_set)
| empty(powerset(X0)) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_375 ),
inference(forward_demodulation,[],[f4814,f800]) ).
fof(f4814,plain,
( ! [X0] :
( apply(relation_dom_restriction(empty_set,powerset(X0)),sK15) = apply(empty_set,sK15)
| ~ function(empty_set)
| empty(powerset(X0)) )
| ~ spl22_7
| ~ spl22_375 ),
inference(resolution,[],[f4749,f256]) ).
fof(f4749,plain,
( ! [X0,X1] :
( ~ relation(X1)
| apply(relation_dom_restriction(X1,powerset(X0)),sK15) = apply(X1,sK15)
| ~ function(X1)
| empty(powerset(X0)) )
| ~ spl22_375 ),
inference(avatar_component_clause,[],[f4748]) ).
fof(f47069,plain,
( ~ spl22_20
| spl22_1349
| ~ spl22_19
| ~ spl22_375 ),
inference(avatar_split_clause,[],[f4821,f4748,f314,f47067,f319]) ).
fof(f47067,plain,
( spl22_1349
<=> ! [X0] :
( apply(relation_dom_restriction(sK20,powerset(X0)),sK15) = apply(sK20,sK15)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1349])]) ).
fof(f4821,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK20,powerset(X0)),sK15) = apply(sK20,sK15)
| ~ function(sK20)
| empty(powerset(X0)) )
| ~ spl22_19
| ~ spl22_375 ),
inference(resolution,[],[f4749,f316]) ).
fof(f47065,plain,
( spl22_1348
| spl22_49
| ~ spl22_1344 ),
inference(avatar_split_clause,[],[f46878,f46783,f487,f47062]) ).
fof(f47062,plain,
( spl22_1348
<=> apply(relation_dom_restriction(sK19,sK3),sK10(sK3)) = apply(sK19,sK10(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1348])]) ).
fof(f46878,plain,
( apply(relation_dom_restriction(sK19,sK3),sK10(sK3)) = apply(sK19,sK10(sK3))
| spl22_49
| ~ spl22_1344 ),
inference(resolution,[],[f46784,f489]) ).
fof(f46993,plain,
( ~ spl22_18
| spl22_1347
| ~ spl22_17
| ~ spl22_375 ),
inference(avatar_split_clause,[],[f4820,f4748,f304,f46991,f309]) ).
fof(f46991,plain,
( spl22_1347
<=> ! [X0] :
( apply(relation_dom_restriction(sK19,powerset(X0)),sK15) = apply(sK19,sK15)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1347])]) ).
fof(f4820,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK19,powerset(X0)),sK15) = apply(sK19,sK15)
| ~ function(sK19)
| empty(powerset(X0)) )
| ~ spl22_17
| ~ spl22_375 ),
inference(resolution,[],[f4749,f306]) ).
fof(f46989,plain,
( spl22_1346
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_374 ),
inference(avatar_split_clause,[],[f4805,f4744,f798,f254,f410,f46987]) ).
fof(f46987,plain,
( spl22_1346
<=> ! [X0] :
( apply(relation_dom_restriction(sK15,X0),sK10(X0)) = apply(sK15,sK10(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1346])]) ).
fof(f4744,plain,
( spl22_374
<=> ! [X0,X1] :
( empty(X0)
| apply(relation_dom_restriction(X1,X0),sK10(X0)) = apply(X1,sK10(X0))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_374])]) ).
fof(f4805,plain,
( ! [X0] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X0),sK10(X0)) = apply(sK15,sK10(X0))
| empty(X0) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_374 ),
inference(forward_demodulation,[],[f4804,f800]) ).
fof(f4804,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK15,X0),sK10(X0)) = apply(sK15,sK10(X0))
| ~ function(empty_set)
| empty(X0) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_374 ),
inference(forward_demodulation,[],[f4795,f800]) ).
fof(f4795,plain,
( ! [X0] :
( apply(relation_dom_restriction(empty_set,X0),sK10(X0)) = apply(empty_set,sK10(X0))
| ~ function(empty_set)
| empty(X0) )
| ~ spl22_7
| ~ spl22_374 ),
inference(resolution,[],[f4745,f256]) ).
fof(f4745,plain,
( ! [X0,X1] :
( ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),sK10(X0)) = apply(X1,sK10(X0))
| ~ function(X1)
| empty(X0) )
| ~ spl22_374 ),
inference(avatar_component_clause,[],[f4744]) ).
fof(f46887,plain,
( ~ spl22_20
| spl22_1345
| ~ spl22_19
| ~ spl22_374 ),
inference(avatar_split_clause,[],[f4802,f4744,f314,f46885,f319]) ).
fof(f4802,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK20,X0),sK10(X0)) = apply(sK20,sK10(X0))
| ~ function(sK20)
| empty(X0) )
| ~ spl22_19
| ~ spl22_374 ),
inference(resolution,[],[f4745,f316]) ).
fof(f46785,plain,
( ~ spl22_18
| spl22_1344
| ~ spl22_17
| ~ spl22_374 ),
inference(avatar_split_clause,[],[f4801,f4744,f304,f46783,f309]) ).
fof(f4801,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK19,X0),sK10(X0)) = apply(sK19,sK10(X0))
| ~ function(sK19)
| empty(X0) )
| ~ spl22_17
| ~ spl22_374 ),
inference(resolution,[],[f4745,f306]) ).
fof(f46781,plain,
( spl22_1343
| ~ spl22_56
| ~ spl22_326 ),
inference(avatar_split_clause,[],[f3799,f3689,f545,f46779]) ).
fof(f46779,plain,
( spl22_1343
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK6(X1))
| empty(X1)
| in(sK7(X0,sK6(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1343])]) ).
fof(f3689,plain,
( spl22_326
<=> ! [X0,X1] :
( sP0(X0,sK6(X1))
| ~ empty(relation_dom(X0))
| element(sK7(X0,sK6(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_326])]) ).
fof(f3799,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK6(X1))
| empty(X1)
| in(sK7(X0,sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_326 ),
inference(duplicate_literal_removal,[],[f3796]) ).
fof(f3796,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK6(X1))
| empty(X1)
| empty(X1)
| in(sK7(X0,sK6(X1)),X1) )
| ~ spl22_56
| ~ spl22_326 ),
inference(resolution,[],[f3690,f546]) ).
fof(f3690,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| ~ empty(relation_dom(X0))
| sP0(X0,sK6(X1))
| empty(X1) )
| ~ spl22_326 ),
inference(avatar_component_clause,[],[f3689]) ).
fof(f46777,plain,
( spl22_1342
| ~ spl22_45
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3772,f3685,f454,f46775]) ).
fof(f46775,plain,
( spl22_1342
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ in(X1,sK7(X0,set_intersection2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1342])]) ).
fof(f3772,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ in(X1,sK7(X0,set_intersection2(X1,X2))) )
| ~ spl22_45
| ~ spl22_325 ),
inference(resolution,[],[f3686,f455]) ).
fof(f46773,plain,
( spl22_1341
| ~ spl22_46
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3771,f3685,f458,f46771]) ).
fof(f46771,plain,
( spl22_1341
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| element(sK7(X0,set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1341])]) ).
fof(f3771,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| element(sK7(X0,set_intersection2(X1,X2)),X1) )
| ~ spl22_46
| ~ spl22_325 ),
inference(resolution,[],[f3686,f459]) ).
fof(f46744,plain,
( spl22_1340
| ~ spl22_45
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3747,f3681,f454,f46742]) ).
fof(f46742,plain,
( spl22_1340
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ in(X2,sK7(X0,set_intersection2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1340])]) ).
fof(f3747,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ in(X2,sK7(X0,set_intersection2(X1,X2))) )
| ~ spl22_45
| ~ spl22_324 ),
inference(resolution,[],[f3682,f455]) ).
fof(f46740,plain,
( spl22_1339
| ~ spl22_46
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3746,f3681,f458,f46738]) ).
fof(f46738,plain,
( spl22_1339
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| element(sK7(X0,set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1339])]) ).
fof(f3746,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| element(sK7(X0,set_intersection2(X1,X2)),X2) )
| ~ spl22_46
| ~ spl22_324 ),
inference(resolution,[],[f3682,f459]) ).
fof(f46736,plain,
( spl22_1338
| ~ spl22_56
| ~ spl22_323 ),
inference(avatar_split_clause,[],[f3741,f3677,f545,f46734]) ).
fof(f46734,plain,
( spl22_1338
<=> ! [X2,X0,X1] :
( empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,sK6(X0))
| in(apply(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1338])]) ).
fof(f3741,plain,
( ! [X2,X0,X1] :
( empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,sK6(X0))
| in(apply(X2,X1),X0) )
| ~ spl22_56
| ~ spl22_323 ),
inference(duplicate_literal_removal,[],[f3729]) ).
fof(f3729,plain,
( ! [X2,X0,X1] :
( empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,sK6(X0))
| empty(X0)
| in(apply(X2,X1),X0) )
| ~ spl22_56
| ~ spl22_323 ),
inference(resolution,[],[f3678,f546]) ).
fof(f46732,plain,
( spl22_1337
| ~ spl22_45
| ~ spl22_322 ),
inference(avatar_split_clause,[],[f3727,f3673,f454,f46730]) ).
fof(f46730,plain,
( spl22_1337
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(relation_dom(X1),sK8(X1,sK10(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1337])]) ).
fof(f3673,plain,
( spl22_322
<=> ! [X0,X1] :
( ~ empty(X0)
| in(sK8(X1,sK10(powerset(X0))),relation_dom(X1))
| sP0(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_322])]) ).
fof(f3727,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(relation_dom(X1),sK8(X1,sK10(powerset(X0)))) )
| ~ spl22_45
| ~ spl22_322 ),
inference(resolution,[],[f3674,f455]) ).
fof(f3674,plain,
( ! [X0,X1] :
( in(sK8(X1,sK10(powerset(X0))),relation_dom(X1))
| ~ empty(X0)
| sP0(X1,sK10(powerset(X0))) )
| ~ spl22_322 ),
inference(avatar_component_clause,[],[f3673]) ).
fof(f46728,plain,
( spl22_1336
| ~ spl22_61
| ~ spl22_291 ),
inference(avatar_split_clause,[],[f3462,f3386,f578,f46726]) ).
fof(f46726,plain,
( spl22_1336
<=> ! [X0] :
( sK7(X0,sK15) = apply(X0,sK8(X0,sK15))
| relation_rng(X0) = sK15
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1336])]) ).
fof(f3386,plain,
( spl22_291
<=> ! [X0] :
( sK7(X0,sK15) = apply(X0,sK8(X0,sK15))
| sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_291])]) ).
fof(f3462,plain,
( ! [X0] :
( sK7(X0,sK15) = apply(X0,sK8(X0,sK15))
| relation_rng(X0) = sK15
| ~ sP1(X0) )
| ~ spl22_61
| ~ spl22_291 ),
inference(resolution,[],[f3387,f579]) ).
fof(f3387,plain,
( ! [X0] :
( sP0(X0,sK15)
| sK7(X0,sK15) = apply(X0,sK8(X0,sK15)) )
| ~ spl22_291 ),
inference(avatar_component_clause,[],[f3386]) ).
fof(f46724,plain,
( spl22_1335
| ~ spl22_69
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3348,f3304,f628,f46722]) ).
fof(f46722,plain,
( spl22_1335
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1335])]) ).
fof(f3348,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,relation_rng(X0)) )
| ~ spl22_69
| ~ spl22_290 ),
inference(resolution,[],[f3305,f629]) ).
fof(f46720,plain,
( spl22_1334
| ~ spl22_63
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3342,f3288,f586,f46718]) ).
fof(f46718,plain,
( spl22_1334
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1334])]) ).
fof(f3342,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_63
| ~ spl22_286 ),
inference(resolution,[],[f3289,f587]) ).
fof(f46716,plain,
( spl22_1333
| ~ spl22_65
| ~ spl22_277 ),
inference(avatar_split_clause,[],[f3239,f2995,f604,f46714]) ).
fof(f46714,plain,
( spl22_1333
<=> ! [X2,X0,X1] :
( sP2(powerset(X0),X1,sK15)
| element(X2,X0)
| ~ in(X2,sK13(powerset(X0),X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1333])]) ).
fof(f2995,plain,
( spl22_277
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK15),X0)
| sP2(X0,X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_277])]) ).
fof(f3239,plain,
( ! [X2,X0,X1] :
( sP2(powerset(X0),X1,sK15)
| element(X2,X0)
| ~ in(X2,sK13(powerset(X0),X1,sK15)) )
| ~ spl22_65
| ~ spl22_277 ),
inference(resolution,[],[f2996,f605]) ).
fof(f2996,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK15),X0)
| sP2(X0,X1,sK15) )
| ~ spl22_277 ),
inference(avatar_component_clause,[],[f2995]) ).
fof(f46712,plain,
( spl22_1332
| ~ spl22_65
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f3236,f2991,f604,f46710]) ).
fof(f46710,plain,
( spl22_1332
<=> ! [X2,X0,X1] :
( sP2(sK15,X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK13(sK15,X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1332])]) ).
fof(f2991,plain,
( spl22_276
<=> ! [X0,X1] :
( element(sK13(sK15,X0,X1),X1)
| sP2(sK15,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_276])]) ).
fof(f3236,plain,
( ! [X2,X0,X1] :
( sP2(sK15,X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK13(sK15,X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_276 ),
inference(resolution,[],[f2992,f605]) ).
fof(f2992,plain,
( ! [X0,X1] :
( element(sK13(sK15,X0,X1),X1)
| sP2(sK15,X0,X1) )
| ~ spl22_276 ),
inference(avatar_component_clause,[],[f2991]) ).
fof(f46708,plain,
( spl22_1331
| ~ spl22_65
| ~ spl22_275 ),
inference(avatar_split_clause,[],[f3233,f2987,f604,f46706]) ).
fof(f46706,plain,
( spl22_1331
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1),sK15)
| element(X2,X1)
| ~ in(X2,sK13(X0,powerset(X1),sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1331])]) ).
fof(f2987,plain,
( spl22_275
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK15),X1)
| sP2(X0,X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_275])]) ).
fof(f3233,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1),sK15)
| element(X2,X1)
| ~ in(X2,sK13(X0,powerset(X1),sK15)) )
| ~ spl22_65
| ~ spl22_275 ),
inference(resolution,[],[f2988,f605]) ).
fof(f2988,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK15),X1)
| sP2(X0,X1,sK15) )
| ~ spl22_275 ),
inference(avatar_component_clause,[],[f2987]) ).
fof(f46704,plain,
( spl22_1330
| ~ spl22_119
| ~ spl22_1299 ),
inference(avatar_split_clause,[],[f46017,f41554,f1064,f46702]) ).
fof(f46702,plain,
( spl22_1330
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,X0),sK15)
| empty(set_intersection2(X0,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1330])]) ).
fof(f46017,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,X0),sK15)
| empty(set_intersection2(X0,relation_dom(sK5))) )
| ~ spl22_119
| ~ spl22_1299 ),
inference(resolution,[],[f41555,f1065]) ).
fof(f46700,plain,
( spl22_1329
| ~ spl22_65
| ~ spl22_274 ),
inference(avatar_split_clause,[],[f3230,f2983,f604,f46698]) ).
fof(f46698,plain,
( spl22_1329
<=> ! [X2,X0,X1] :
( sP2(X0,sK15,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK13(X0,sK15,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1329])]) ).
fof(f2983,plain,
( spl22_274
<=> ! [X0,X1] :
( element(sK13(X0,sK15,X1),X1)
| sP2(X0,sK15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_274])]) ).
fof(f3230,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK15,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK13(X0,sK15,powerset(X1))) )
| ~ spl22_65
| ~ spl22_274 ),
inference(resolution,[],[f2984,f605]) ).
fof(f2984,plain,
( ! [X0,X1] :
( element(sK13(X0,sK15,X1),X1)
| sP2(X0,sK15,X1) )
| ~ spl22_274 ),
inference(avatar_component_clause,[],[f2983]) ).
fof(f46696,plain,
( spl22_1328
| ~ spl22_63
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f3147,f2911,f586,f46694]) ).
fof(f46694,plain,
( spl22_1328
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1328])]) ).
fof(f3147,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) )
| ~ spl22_63
| ~ spl22_256 ),
inference(resolution,[],[f2912,f587]) ).
fof(f46692,plain,
( spl22_1327
| ~ spl22_65
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f3097,f2899,f604,f46690]) ).
fof(f46690,plain,
( spl22_1327
<=> ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1327])]) ).
fof(f2899,plain,
( spl22_253
<=> ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_253])]) ).
fof(f3097,plain,
( ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) )
| ~ spl22_65
| ~ spl22_253 ),
inference(resolution,[],[f2900,f605]) ).
fof(f2900,plain,
( ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) )
| ~ spl22_253 ),
inference(avatar_component_clause,[],[f2899]) ).
fof(f46688,plain,
( spl22_1326
| ~ spl22_76
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2610,f2559,f670,f46686]) ).
fof(f46686,plain,
( spl22_1326
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1326])]) ).
fof(f2610,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2) )
| ~ spl22_76
| ~ spl22_233 ),
inference(resolution,[],[f2560,f671]) ).
fof(f46684,plain,
( spl22_1325
| ~ spl22_163
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2608,f2559,f1600,f46682]) ).
fof(f46682,plain,
( spl22_1325
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1325])]) ).
fof(f2608,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2) )
| ~ spl22_163
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1601]) ).
fof(f46680,plain,
( spl22_1324
| ~ spl22_75
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2606,f2559,f666,f46678]) ).
fof(f46678,plain,
( spl22_1324
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(X1,relation_dom(X0),X2),X2)
| sP2(X1,relation_dom(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1324])]) ).
fof(f2606,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(X1,relation_dom(X0),X2),X2)
| sP2(X1,relation_dom(X0),X2) )
| ~ spl22_75
| ~ spl22_233 ),
inference(resolution,[],[f2560,f667]) ).
fof(f46676,plain,
( spl22_1323
| ~ spl22_159
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2604,f2559,f1579,f46674]) ).
fof(f46674,plain,
( spl22_1323
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(X1,relation_dom(X0),X2),X2)
| sP2(X1,relation_dom(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1323])]) ).
fof(f2604,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(X1,relation_dom(X0),X2),X2)
| sP2(X1,relation_dom(X0),X2) )
| ~ spl22_159
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1580]) ).
fof(f46672,plain,
( spl22_1322
| ~ spl22_165
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2600,f2559,f1608,f46670]) ).
fof(f46670,plain,
( spl22_1322
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(X1,X2,relation_dom(X0)),X1)
| sP2(X1,X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1322])]) ).
fof(f2600,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(X1,X2,relation_dom(X0)),X1)
| sP2(X1,X2,relation_dom(X0)) )
| ~ spl22_165
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1609]) ).
fof(f46668,plain,
( spl22_1321
| ~ spl22_161
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2599,f2559,f1587,f46666]) ).
fof(f46666,plain,
( spl22_1321
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(X1,X2,relation_dom(X0)),X2)
| sP2(X1,X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1321])]) ).
fof(f2599,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| element(sK13(X1,X2,relation_dom(X0)),X2)
| sP2(X1,X2,relation_dom(X0)) )
| ~ spl22_161
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1588]) ).
fof(f46664,plain,
( spl22_1320
| ~ spl22_76
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2596,f2559,f670,f46662]) ).
fof(f46662,plain,
( spl22_1320
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(X1,X2,relation_dom(X0)),X1)
| sP2(X1,X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1320])]) ).
fof(f2596,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(X1,X2,relation_dom(X0)),X1)
| sP2(X1,X2,relation_dom(X0)) )
| ~ spl22_76
| ~ spl22_233 ),
inference(resolution,[],[f2560,f671]) ).
fof(f46641,plain,
( spl22_1319
| ~ spl22_75
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2595,f2559,f666,f46639]) ).
fof(f46639,plain,
( spl22_1319
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(X1,X2,relation_dom(X0)),X2)
| sP2(X1,X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1319])]) ).
fof(f2595,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| in(sK13(X1,X2,relation_dom(X0)),X2)
| sP2(X1,X2,relation_dom(X0)) )
| ~ spl22_75
| ~ spl22_233 ),
inference(resolution,[],[f2560,f667]) ).
fof(f46616,plain,
( spl22_1318
| ~ spl22_232
| ~ spl22_609 ),
inference(avatar_split_clause,[],[f12530,f12515,f2531,f46614]) ).
fof(f46614,plain,
( spl22_1318
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| sK7(X3,relation_dom(X2)) = apply(X3,sK8(X3,relation_dom(X2)))
| sP0(X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1318])]) ).
fof(f12515,plain,
( spl22_609
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| sK7(X3,relation_dom(X2)) = apply(X3,sK8(X3,relation_dom(X2)))
| sP0(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_609])]) ).
fof(f12530,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| sK7(X3,relation_dom(X2)) = apply(X3,sK8(X3,relation_dom(X2)))
| sP0(X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_609 ),
inference(resolution,[],[f12516,f2532]) ).
fof(f12516,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| sK7(X3,relation_dom(X2)) = apply(X3,sK8(X3,relation_dom(X2)))
| sP0(X3,relation_dom(X2)) )
| ~ spl22_609 ),
inference(avatar_component_clause,[],[f12515]) ).
fof(f46465,plain,
( ~ spl22_1317
| ~ spl22_700
| ~ spl22_1299 ),
inference(avatar_split_clause,[],[f45990,f41554,f15306,f46462]) ).
fof(f46462,plain,
( spl22_1317
<=> sP0(relation_dom_restriction(sK5,sK3),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1317])]) ).
fof(f45990,plain,
( ~ sP0(relation_dom_restriction(sK5,sK3),sK15)
| ~ spl22_700
| ~ spl22_1299 ),
inference(resolution,[],[f41555,f15307]) ).
fof(f15307,plain,
( in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_700 ),
inference(avatar_component_clause,[],[f15306]) ).
fof(f46204,plain,
( spl22_1316
| ~ spl22_232
| ~ spl22_602 ),
inference(avatar_split_clause,[],[f12434,f11988,f2531,f46202]) ).
fof(f46202,plain,
( spl22_1316
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| in(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1316])]) ).
fof(f11988,plain,
( spl22_602
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ sP0(X2,X1)
| in(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_602])]) ).
fof(f12434,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| in(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_602 ),
inference(resolution,[],[f11989,f2532]) ).
fof(f11989,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| in(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4) )
| ~ spl22_602 ),
inference(avatar_component_clause,[],[f11988]) ).
fof(f46200,plain,
( spl22_1315
| ~ spl22_232
| ~ spl22_601 ),
inference(avatar_split_clause,[],[f12393,f11984,f2531,f46198]) ).
fof(f46198,plain,
( spl22_1315
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| element(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1315])]) ).
fof(f11984,plain,
( spl22_601
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ sP0(X2,X1)
| element(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_601])]) ).
fof(f12393,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| element(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_601 ),
inference(resolution,[],[f11985,f2532]) ).
fof(f11985,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| element(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4) )
| ~ spl22_601 ),
inference(avatar_component_clause,[],[f11984]) ).
fof(f46196,plain,
( spl22_1314
| ~ spl22_232
| ~ spl22_600 ),
inference(avatar_split_clause,[],[f12352,f11980,f2531,f46194]) ).
fof(f46194,plain,
( spl22_1314
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| in(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1314])]) ).
fof(f11980,plain,
( spl22_600
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ sP0(X2,X1)
| in(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_600])]) ).
fof(f12352,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| in(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_600 ),
inference(resolution,[],[f11981,f2532]) ).
fof(f11981,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| in(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4) )
| ~ spl22_600 ),
inference(avatar_component_clause,[],[f11980]) ).
fof(f45984,plain,
( spl22_1313
| ~ spl22_232
| ~ spl22_599 ),
inference(avatar_split_clause,[],[f12311,f11976,f2531,f45982]) ).
fof(f45982,plain,
( spl22_1313
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| element(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1313])]) ).
fof(f11976,plain,
( spl22_599
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ sP0(X2,X1)
| element(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_599])]) ).
fof(f12311,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| element(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_599 ),
inference(resolution,[],[f11977,f2532]) ).
fof(f11977,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| element(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4) )
| ~ spl22_599 ),
inference(avatar_component_clause,[],[f11976]) ).
fof(f45980,plain,
( spl22_1312
| ~ spl22_232
| ~ spl22_598 ),
inference(avatar_split_clause,[],[f12270,f11972,f2531,f45978]) ).
fof(f45978,plain,
( spl22_1312
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| in(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1312])]) ).
fof(f11972,plain,
( spl22_598
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| in(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_598])]) ).
fof(f12270,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| in(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_598 ),
inference(resolution,[],[f11973,f2532]) ).
fof(f11973,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| in(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_598 ),
inference(avatar_component_clause,[],[f11972]) ).
fof(f45976,plain,
( spl22_1311
| ~ spl22_232
| ~ spl22_597 ),
inference(avatar_split_clause,[],[f12229,f11968,f2531,f45974]) ).
fof(f45974,plain,
( spl22_1311
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| in(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1311])]) ).
fof(f11968,plain,
( spl22_597
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| in(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_597])]) ).
fof(f12229,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| in(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_597 ),
inference(resolution,[],[f11969,f2532]) ).
fof(f11969,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| in(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_597 ),
inference(avatar_component_clause,[],[f11968]) ).
fof(f45972,plain,
( spl22_1310
| ~ spl22_232
| ~ spl22_596 ),
inference(avatar_split_clause,[],[f12188,f11964,f2531,f45970]) ).
fof(f45970,plain,
( spl22_1310
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| element(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1310])]) ).
fof(f11964,plain,
( spl22_596
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| element(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_596])]) ).
fof(f12188,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| element(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_596 ),
inference(resolution,[],[f11965,f2532]) ).
fof(f11965,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| element(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_596 ),
inference(avatar_component_clause,[],[f11964]) ).
fof(f45968,plain,
( spl22_1309
| ~ spl22_232
| ~ spl22_594 ),
inference(avatar_split_clause,[],[f12147,f11955,f2531,f45966]) ).
fof(f45966,plain,
( spl22_1309
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| element(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1309])]) ).
fof(f11955,plain,
( spl22_594
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| element(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_594])]) ).
fof(f12147,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| element(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_594 ),
inference(resolution,[],[f11956,f2532]) ).
fof(f11956,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| element(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_594 ),
inference(avatar_component_clause,[],[f11955]) ).
fof(f45964,plain,
( spl22_1308
| ~ spl22_232
| ~ spl22_476 ),
inference(avatar_split_clause,[],[f8875,f8373,f2531,f45962]) ).
fof(f45962,plain,
( spl22_1308
<=> ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| element(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| sK7(X1,sK7(X0,apply(X1,X2))) = apply(X1,sK8(X1,sK7(X0,apply(X1,X2))))
| apply(relation_dom_restriction(sK5,sK7(X0,apply(X1,X2))),sK7(X1,sK7(X0,apply(X1,X2)))) = apply(sK5,sK7(X1,sK7(X0,apply(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1308])]) ).
fof(f8373,plain,
( spl22_476
<=> ! [X2,X0,X1] :
( element(sK8(X0,apply(X1,X2)),relation_dom(X0))
| sP0(X0,apply(X1,X2))
| ~ sP0(X1,sK7(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_476])]) ).
fof(f8875,plain,
( ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| element(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| sK7(X1,sK7(X0,apply(X1,X2))) = apply(X1,sK8(X1,sK7(X0,apply(X1,X2))))
| apply(relation_dom_restriction(sK5,sK7(X0,apply(X1,X2))),sK7(X1,sK7(X0,apply(X1,X2)))) = apply(sK5,sK7(X1,sK7(X0,apply(X1,X2)))) )
| ~ spl22_232
| ~ spl22_476 ),
inference(resolution,[],[f8374,f2532]) ).
fof(f8374,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,sK7(X0,apply(X1,X2)))
| sP0(X0,apply(X1,X2))
| element(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_476 ),
inference(avatar_component_clause,[],[f8373]) ).
fof(f45960,plain,
( spl22_1307
| ~ spl22_232
| ~ spl22_471 ),
inference(avatar_split_clause,[],[f8835,f8353,f2531,f45958]) ).
fof(f45958,plain,
( spl22_1307
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK8(X2,apply(X1,X0)),relation_dom(X2))
| sP0(X2,apply(X1,X0))
| sK7(X1,sK7(X2,apply(X1,X0))) = apply(X1,sK8(X1,sK7(X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK7(X2,apply(X1,X0))),sK7(X1,sK7(X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK7(X2,apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1307])]) ).
fof(f8353,plain,
( spl22_471
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| in(sK8(X1,apply(X0,X2)),relation_dom(X1))
| sP0(X1,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_471])]) ).
fof(f8835,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(sK8(X2,apply(X1,X0)),relation_dom(X2))
| sP0(X2,apply(X1,X0))
| sK7(X1,sK7(X2,apply(X1,X0))) = apply(X1,sK8(X1,sK7(X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK7(X2,apply(X1,X0))),sK7(X1,sK7(X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK7(X2,apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_471 ),
inference(resolution,[],[f8354,f2532]) ).
fof(f8354,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| in(sK8(X1,apply(X0,X2)),relation_dom(X1))
| sP0(X1,apply(X0,X2)) )
| ~ spl22_471 ),
inference(avatar_component_clause,[],[f8353]) ).
fof(f45956,plain,
( spl22_1306
| ~ spl22_232
| ~ spl22_407 ),
inference(avatar_split_clause,[],[f5494,f5270,f2531,f45954]) ).
fof(f45954,plain,
( spl22_1306
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,apply(X2,X3))
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1306])]) ).
fof(f5270,plain,
( spl22_407
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| ~ empty(X0)
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_407])]) ).
fof(f5494,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,apply(X2,X3))
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) )
| ~ spl22_232
| ~ spl22_407 ),
inference(resolution,[],[f5271,f2532]) ).
fof(f5271,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ empty(X0)
| sP2(X0,X1,apply(X2,X3))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_407 ),
inference(avatar_component_clause,[],[f5270]) ).
fof(f45952,plain,
( spl22_1305
| ~ spl22_232
| ~ spl22_406 ),
inference(avatar_split_clause,[],[f5478,f5266,f2531,f45950]) ).
fof(f45950,plain,
( spl22_1305
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(apply(X1,X2),X3,X0)
| ~ in(X2,relation_dom(X1))
| sK7(X1,sK13(apply(X1,X2),X3,X0)) = apply(X1,sK8(X1,sK13(apply(X1,X2),X3,X0)))
| apply(relation_dom_restriction(sK5,sK13(apply(X1,X2),X3,X0)),sK7(X1,sK13(apply(X1,X2),X3,X0))) = apply(sK5,sK7(X1,sK13(apply(X1,X2),X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1305])]) ).
fof(f5266,plain,
( spl22_406
<=> ! [X0,X3,X2,X1] :
( sP2(apply(X0,X1),X2,X3)
| ~ empty(X3)
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_406])]) ).
fof(f5478,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(apply(X1,X2),X3,X0)
| ~ in(X2,relation_dom(X1))
| sK7(X1,sK13(apply(X1,X2),X3,X0)) = apply(X1,sK8(X1,sK13(apply(X1,X2),X3,X0)))
| apply(relation_dom_restriction(sK5,sK13(apply(X1,X2),X3,X0)),sK7(X1,sK13(apply(X1,X2),X3,X0))) = apply(sK5,sK7(X1,sK13(apply(X1,X2),X3,X0))) )
| ~ spl22_232
| ~ spl22_406 ),
inference(resolution,[],[f5267,f2532]) ).
fof(f5267,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ empty(X3)
| sP2(apply(X0,X1),X2,X3)
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_406 ),
inference(avatar_component_clause,[],[f5266]) ).
fof(f45948,plain,
( spl22_1304
| ~ spl22_232
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5462,f5262,f2531,f45946]) ).
fof(f45946,plain,
( spl22_1304
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,apply(X2,X3))
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X1,X0,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X1,X0,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X1,X0,apply(X2,X3))),sK7(X2,sK13(X1,X0,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X1,X0,apply(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1304])]) ).
fof(f5262,plain,
( spl22_405
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| ~ empty(X1)
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_405])]) ).
fof(f5462,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,apply(X2,X3))
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X1,X0,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X1,X0,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X1,X0,apply(X2,X3))),sK7(X2,sK13(X1,X0,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X1,X0,apply(X2,X3)))) )
| ~ spl22_232
| ~ spl22_405 ),
inference(resolution,[],[f5263,f2532]) ).
fof(f5263,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ empty(X1)
| sP2(X0,X1,apply(X2,X3))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_405 ),
inference(avatar_component_clause,[],[f5262]) ).
fof(f45924,plain,
( spl22_1303
| ~ spl22_232
| ~ spl22_404 ),
inference(avatar_split_clause,[],[f5446,f5258,f2531,f45922]) ).
fof(f45922,plain,
( spl22_1303
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X1,apply(X2,X3),X0)) = apply(X2,sK8(X2,sK13(X1,apply(X2,X3),X0)))
| apply(relation_dom_restriction(sK5,sK13(X1,apply(X2,X3),X0)),sK7(X2,sK13(X1,apply(X2,X3),X0))) = apply(sK5,sK7(X2,sK13(X1,apply(X2,X3),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1303])]) ).
fof(f5258,plain,
( spl22_404
<=> ! [X0,X3,X2,X1] :
( sP2(X0,apply(X1,X2),X3)
| ~ empty(X3)
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_404])]) ).
fof(f5446,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| sK7(X2,sK13(X1,apply(X2,X3),X0)) = apply(X2,sK8(X2,sK13(X1,apply(X2,X3),X0)))
| apply(relation_dom_restriction(sK5,sK13(X1,apply(X2,X3),X0)),sK7(X2,sK13(X1,apply(X2,X3),X0))) = apply(sK5,sK7(X2,sK13(X1,apply(X2,X3),X0))) )
| ~ spl22_232
| ~ spl22_404 ),
inference(resolution,[],[f5259,f2532]) ).
fof(f5259,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| ~ empty(X3)
| sP2(X0,apply(X1,X2),X3)
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_404 ),
inference(avatar_component_clause,[],[f5258]) ).
fof(f45769,plain,
( spl22_1302
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_647 ),
inference(avatar_split_clause,[],[f13356,f13327,f4126,f935,f511,f15306,f45767]) ).
fof(f45767,plain,
( spl22_1302
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| ~ function(X0)
| sP0(relation_dom_restriction(X0,X1),apply(sK5,sK4))
| apply(X0,sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1302])]) ).
fof(f13327,plain,
( spl22_647
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),apply(X2,X3))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),apply(X2,X3)))
| sP0(relation_dom_restriction(X0,X1),apply(X2,X3))
| ~ sP0(X2,sK7(relation_dom_restriction(X0,X1),apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_647])]) ).
fof(f13356,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| sP0(relation_dom_restriction(X0,X1),apply(sK5,sK4))
| ~ function(X0) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_647 ),
inference(forward_demodulation,[],[f13355,f512]) ).
fof(f13355,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| sP0(relation_dom_restriction(X0,X1),apply(sK5,sK4))
| ~ function(X0) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_647 ),
inference(forward_demodulation,[],[f13340,f4127]) ).
fof(f13340,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),apply(sK5,sK4)))
| sP0(relation_dom_restriction(X0,X1),apply(sK5,sK4))
| ~ function(X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_647 ),
inference(superposition,[],[f13328,f937]) ).
fof(f13328,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,sK7(relation_dom_restriction(X0,X1),apply(X2,X3)))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),apply(X2,X3))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),apply(X2,X3)))
| sP0(relation_dom_restriction(X0,X1),apply(X2,X3))
| ~ function(X0)
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_647 ),
inference(avatar_component_clause,[],[f13327]) ).
fof(f45765,plain,
( spl22_1301
| ~ spl22_83
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2354,f2344,f742,f45763]) ).
fof(f45763,plain,
( spl22_1301
<=> ! [X2,X0,X1] :
( sP0(X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(sK5,sK8(X0,relation_dom(relation_dom_restriction(X1,X2))))
| apply(X1,sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1301])]) ).
fof(f2354,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(sK5,sK8(X0,relation_dom(relation_dom_restriction(X1,X2))))
| apply(X1,sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_216 ),
inference(resolution,[],[f2345,f743]) ).
fof(f42446,plain,
( spl22_1300
| ~ spl22_56
| ~ spl22_1186 ),
inference(avatar_split_clause,[],[f40200,f37143,f545,f42444]) ).
fof(f37143,plain,
( spl22_1186
<=> ! [X0] :
( ~ sP0(sK5,sK6(X0))
| element(apply(sK5,sK4),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1186])]) ).
fof(f40200,plain,
( ! [X0] :
( ~ sP0(sK5,sK6(X0))
| empty(X0)
| in(apply(sK5,sK4),X0) )
| ~ spl22_56
| ~ spl22_1186 ),
inference(duplicate_literal_removal,[],[f40197]) ).
fof(f40197,plain,
( ! [X0] :
( ~ sP0(sK5,sK6(X0))
| empty(X0)
| empty(X0)
| in(apply(sK5,sK4),X0) )
| ~ spl22_56
| ~ spl22_1186 ),
inference(resolution,[],[f37144,f546]) ).
fof(f37144,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(sK5,sK6(X0))
| empty(X0) )
| ~ spl22_1186 ),
inference(avatar_component_clause,[],[f37143]) ).
fof(f41556,plain,
( spl22_1299
| ~ spl22_53
| ~ spl22_1018 ),
inference(avatar_split_clause,[],[f37978,f27680,f511,f41554]) ).
fof(f27680,plain,
( spl22_1018
<=> ! [X0,X1] :
( ~ in(X1,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1018])]) ).
fof(f37978,plain,
( ! [X0,X1] :
( ~ in(X1,set_intersection2(X0,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_53
| ~ spl22_1018 ),
inference(superposition,[],[f27681,f512]) ).
fof(f27681,plain,
( ! [X0,X1] :
( ~ in(X1,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_1018 ),
inference(avatar_component_clause,[],[f27680]) ).
fof(f41001,plain,
( spl22_1298
| ~ spl22_776
| ~ spl22_1041 ),
inference(avatar_split_clause,[],[f28242,f28111,f16658,f40999]) ).
fof(f16658,plain,
( spl22_776
<=> ! [X0] :
( ~ sP0(sK5,relation_dom(X0))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_776])]) ).
fof(f28242,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK20),X0))
| ~ sP0(relation_dom_restriction(sK20,X0),sK15) )
| ~ spl22_776
| ~ spl22_1041 ),
inference(superposition,[],[f16659,f28112]) ).
fof(f16659,plain,
( ! [X0] :
( ~ sP0(sK5,relation_dom(X0))
| ~ sP0(X0,sK15) )
| ~ spl22_776 ),
inference(avatar_component_clause,[],[f16658]) ).
fof(f40616,plain,
( spl22_1297
| ~ spl22_776
| ~ spl22_1040 ),
inference(avatar_split_clause,[],[f28079,f27948,f16658,f40614]) ).
fof(f28079,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK19),X0))
| ~ sP0(relation_dom_restriction(sK19,X0),sK15) )
| ~ spl22_776
| ~ spl22_1040 ),
inference(superposition,[],[f16659,f27949]) ).
fof(f40392,plain,
( spl22_1296
| ~ spl22_461 ),
inference(avatar_split_clause,[],[f8059,f6413,f40390]) ).
fof(f40390,plain,
( spl22_1296
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X0))),X0)
| sP2(X0,X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1296])]) ).
fof(f6413,plain,
( spl22_461
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2)))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_461])]) ).
fof(f8059,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X0))),X0)
| sP2(X0,X1,sK10(powerset(X0))) )
| ~ spl22_461 ),
inference(factoring,[],[f6414]) ).
fof(f6414,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| element(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_461 ),
inference(avatar_component_clause,[],[f6413]) ).
fof(f40388,plain,
( spl22_1295
| ~ spl22_457 ),
inference(avatar_split_clause,[],[f7858,f6397,f40386]) ).
fof(f40386,plain,
( spl22_1295
<=> ! [X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X0),X0)
| sP2(sK10(powerset(X0)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1295])]) ).
fof(f6397,plain,
( spl22_457
<=> ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2)
| element(sK13(sK10(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_457])]) ).
fof(f7858,plain,
( ! [X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X0),X0)
| sP2(sK10(powerset(X0)),X1,X0) )
| ~ spl22_457 ),
inference(factoring,[],[f6398]) ).
fof(f6398,plain,
( ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X2)
| element(sK13(sK10(powerset(X0)),X1,X2),X0)
| sP2(sK10(powerset(X0)),X1,X2) )
| ~ spl22_457 ),
inference(avatar_component_clause,[],[f6397]) ).
fof(f40384,plain,
( spl22_1294
| ~ spl22_453 ),
inference(avatar_split_clause,[],[f7657,f6381,f40382]) ).
fof(f40382,plain,
( spl22_1294
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X1))),X1)
| sP2(X0,X1,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1294])]) ).
fof(f6381,plain,
( spl22_453
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2)))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_453])]) ).
fof(f7657,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X1))),X1)
| sP2(X0,X1,sK10(powerset(X1))) )
| ~ spl22_453 ),
inference(factoring,[],[f6382]) ).
fof(f6382,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| element(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_453 ),
inference(avatar_component_clause,[],[f6381]) ).
fof(f40380,plain,
( spl22_1293
| ~ spl22_449 ),
inference(avatar_split_clause,[],[f7453,f6357,f40378]) ).
fof(f40378,plain,
( spl22_1293
<=> ! [X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X1),X1)
| sP2(X0,sK10(powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1293])]) ).
fof(f6357,plain,
( spl22_449
<=> ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X2)
| sP2(X0,sK10(powerset(X1)),X2)
| element(sK13(X0,sK10(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_449])]) ).
fof(f7453,plain,
( ! [X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X1),X1)
| sP2(X0,sK10(powerset(X1)),X1) )
| ~ spl22_449 ),
inference(factoring,[],[f6358]) ).
fof(f6358,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X2)
| element(sK13(X0,sK10(powerset(X1)),X2),X1)
| sP2(X0,sK10(powerset(X1)),X2) )
| ~ spl22_449 ),
inference(avatar_component_clause,[],[f6357]) ).
fof(f40376,plain,
( spl22_1292
| ~ spl22_371
| ~ spl22_776 ),
inference(avatar_split_clause,[],[f16860,f16658,f4126,f40374]) ).
fof(f16860,plain,
( ! [X0] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_371
| ~ spl22_776 ),
inference(superposition,[],[f16659,f4127]) ).
fof(f40372,plain,
( spl22_1291
| ~ spl22_442 ),
inference(avatar_split_clause,[],[f7183,f6309,f40370]) ).
fof(f40370,plain,
( spl22_1291
<=> ! [X2,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X1),X1)
| sP2(set_intersection2(X0,X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1291])]) ).
fof(f7183,plain,
( ! [X2,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X1),X1)
| sP2(set_intersection2(X0,X1),X2,X1) )
| ~ spl22_442 ),
inference(factoring,[],[f6310]) ).
fof(f40368,plain,
( spl22_1290
| ~ spl22_441 ),
inference(avatar_split_clause,[],[f7102,f6305,f40366]) ).
fof(f40366,plain,
( spl22_1290
<=> ! [X2,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X2),X2)
| sP2(X0,set_intersection2(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1290])]) ).
fof(f7102,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X2),X2)
| sP2(X0,set_intersection2(X1,X2),X2) )
| ~ spl22_441 ),
inference(factoring,[],[f6306]) ).
fof(f40364,plain,
( spl22_1289
| ~ spl22_440 ),
inference(avatar_split_clause,[],[f7026,f6301,f40362]) ).
fof(f40362,plain,
( spl22_1289
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X1)),X1)
| sP2(X0,X1,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1289])]) ).
fof(f7026,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X1)),X1)
| sP2(X0,X1,set_intersection2(X2,X1)) )
| ~ spl22_440 ),
inference(factoring,[],[f6302]) ).
fof(f40360,plain,
( spl22_1288
| ~ spl22_439 ),
inference(avatar_split_clause,[],[f6950,f6297,f40358]) ).
fof(f40358,plain,
( spl22_1288
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X0)),X0)
| sP2(X0,X1,set_intersection2(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1288])]) ).
fof(f6950,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X0)),X0)
| sP2(X0,X1,set_intersection2(X2,X0)) )
| ~ spl22_439 ),
inference(factoring,[],[f6298]) ).
fof(f40356,plain,
( spl22_1287
| ~ spl22_438 ),
inference(avatar_split_clause,[],[f6868,f6293,f40354]) ).
fof(f40354,plain,
( spl22_1287
<=> ! [X2,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X0),X0)
| sP2(set_intersection2(X0,X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1287])]) ).
fof(f6868,plain,
( ! [X2,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X0),X0)
| sP2(set_intersection2(X0,X1),X2,X0) )
| ~ spl22_438 ),
inference(factoring,[],[f6294]) ).
fof(f40352,plain,
( spl22_1286
| ~ spl22_437 ),
inference(avatar_split_clause,[],[f6785,f6289,f40350]) ).
fof(f40350,plain,
( spl22_1286
<=> ! [X2,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X1),X1)
| sP2(X0,set_intersection2(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1286])]) ).
fof(f6785,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X1),X1)
| sP2(X0,set_intersection2(X1,X2),X1) )
| ~ spl22_437 ),
inference(factoring,[],[f6290]) ).
fof(f40348,plain,
( spl22_1285
| ~ spl22_436 ),
inference(avatar_split_clause,[],[f6703,f6285,f40346]) ).
fof(f40346,plain,
( spl22_1285
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X1,X2)),X1)
| sP2(X0,X1,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1285])]) ).
fof(f6703,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X1,X2)),X1)
| sP2(X0,X1,set_intersection2(X1,X2)) )
| ~ spl22_436 ),
inference(factoring,[],[f6286]) ).
fof(f40344,plain,
( spl22_1284
| ~ spl22_435 ),
inference(avatar_split_clause,[],[f6621,f6281,f40342]) ).
fof(f40342,plain,
( spl22_1284
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X0,X2)),X0)
| sP2(X0,X1,set_intersection2(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1284])]) ).
fof(f6621,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X0,X2)),X0)
| sP2(X0,X1,set_intersection2(X0,X2)) )
| ~ spl22_435 ),
inference(factoring,[],[f6282]) ).
fof(f40340,plain,
( spl22_1283
| ~ spl22_429 ),
inference(avatar_split_clause,[],[f6233,f5719,f40338]) ).
fof(f40338,plain,
( spl22_1283
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK6(X0)),X0)
| sP2(X0,X1,sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1283])]) ).
fof(f5719,plain,
( spl22_429
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X0)
| sP2(X0,X1,sK6(X2))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_429])]) ).
fof(f6233,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK6(X0)),X0)
| sP2(X0,X1,sK6(X0))
| empty(X0) )
| ~ spl22_429 ),
inference(factoring,[],[f5720]) ).
fof(f5720,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| element(sK13(X0,X1,sK6(X2)),X0)
| sP2(X0,X1,sK6(X2))
| empty(X2) )
| ~ spl22_429 ),
inference(avatar_component_clause,[],[f5719]) ).
fof(f40336,plain,
( spl22_1282
| ~ spl22_427 ),
inference(avatar_split_clause,[],[f6163,f5711,f40334]) ).
fof(f40334,plain,
( spl22_1282
<=> ! [X0,X1] :
( element(sK13(sK6(X0),X1,X0),X0)
| sP2(sK6(X0),X1,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1282])]) ).
fof(f5711,plain,
( spl22_427
<=> ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,X2),X2)
| sP2(sK6(X0),X1,X2)
| element(sK13(sK6(X0),X1,X2),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_427])]) ).
fof(f6163,plain,
( ! [X0,X1] :
( element(sK13(sK6(X0),X1,X0),X0)
| sP2(sK6(X0),X1,X0)
| empty(X0) )
| ~ spl22_427 ),
inference(factoring,[],[f5712]) ).
fof(f5712,plain,
( ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,X2),X2)
| element(sK13(sK6(X0),X1,X2),X0)
| sP2(sK6(X0),X1,X2)
| empty(X0) )
| ~ spl22_427 ),
inference(avatar_component_clause,[],[f5711]) ).
fof(f40332,plain,
( spl22_1281
| ~ spl22_117
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4911,f4627,f1053,f40330]) ).
fof(f40330,plain,
( spl22_1281
<=> ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_dom(set_intersection2(relation_dom(sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1281])]) ).
fof(f4627,plain,
( spl22_372
<=> ! [X0] :
( empty(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_372])]) ).
fof(f4911,plain,
( ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_dom(set_intersection2(relation_dom(sK5),X0)) )
| ~ spl22_117
| ~ spl22_372 ),
inference(resolution,[],[f4628,f1054]) ).
fof(f4628,plain,
( ! [X0] :
( empty(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_372 ),
inference(avatar_component_clause,[],[f4627]) ).
fof(f40328,plain,
( spl22_1280
| ~ spl22_424 ),
inference(avatar_split_clause,[],[f6093,f5699,f40326]) ).
fof(f40326,plain,
( spl22_1280
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK6(X1)),X1)
| sP2(X0,X1,sK6(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1280])]) ).
fof(f5699,plain,
( spl22_424
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X1)
| sP2(X0,X1,sK6(X2))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_424])]) ).
fof(f6093,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK6(X1)),X1)
| sP2(X0,X1,sK6(X1))
| empty(X1) )
| ~ spl22_424 ),
inference(factoring,[],[f5700]) ).
fof(f5700,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| element(sK13(X0,X1,sK6(X2)),X1)
| sP2(X0,X1,sK6(X2))
| empty(X2) )
| ~ spl22_424 ),
inference(avatar_component_clause,[],[f5699]) ).
fof(f40324,plain,
( spl22_1279
| ~ spl22_422 ),
inference(avatar_split_clause,[],[f6023,f5691,f40322]) ).
fof(f40322,plain,
( spl22_1279
<=> ! [X0,X1] :
( element(sK13(X0,sK6(X1),X1),X1)
| sP2(X0,sK6(X1),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1279])]) ).
fof(f5691,plain,
( spl22_422
<=> ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),X2),X2)
| sP2(X0,sK6(X1),X2)
| element(sK13(X0,sK6(X1),X2),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_422])]) ).
fof(f6023,plain,
( ! [X0,X1] :
( element(sK13(X0,sK6(X1),X1),X1)
| sP2(X0,sK6(X1),X1)
| empty(X1) )
| ~ spl22_422 ),
inference(factoring,[],[f5692]) ).
fof(f5692,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),X2),X2)
| element(sK13(X0,sK6(X1),X2),X1)
| sP2(X0,sK6(X1),X2)
| empty(X1) )
| ~ spl22_422 ),
inference(avatar_component_clause,[],[f5691]) ).
fof(f40320,plain,
( spl22_1278
| ~ spl22_112
| ~ spl22_408 ),
inference(avatar_split_clause,[],[f5538,f5282,f948,f40318]) ).
fof(f40318,plain,
( spl22_1278
<=> ! [X0,X1] :
( element(sK8(X1,sK15),relation_dom(X1))
| in(sK7(X1,sK15),X0)
| sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1278])]) ).
fof(f5538,plain,
( ! [X0,X1] :
( element(sK8(X1,sK15),relation_dom(X1))
| in(sK7(X1,sK15),X0)
| sP0(X1,sK15) )
| ~ spl22_112
| ~ spl22_408 ),
inference(superposition,[],[f5283,f949]) ).
fof(f40316,plain,
( spl22_1277
| ~ spl22_31
| ~ spl22_92
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5385,f5242,f798,f378,f40314]) ).
fof(f40314,plain,
( spl22_1277
<=> ! [X0,X1] :
( sP0(X1,sK15)
| in(sK7(X1,sK15),X0)
| in(sK8(X1,sK15),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1277])]) ).
fof(f378,plain,
( spl22_31
<=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_31])]) ).
fof(f5385,plain,
( ! [X0,X1] :
( sP0(X1,sK15)
| in(sK7(X1,sK15),X0)
| in(sK8(X1,sK15),relation_dom(X1)) )
| ~ spl22_31
| ~ spl22_92
| ~ spl22_400 ),
inference(forward_demodulation,[],[f5384,f800]) ).
fof(f5384,plain,
( ! [X0,X1] :
( in(sK7(X1,sK15),X0)
| in(sK8(X1,sK15),relation_dom(X1))
| sP0(X1,empty_set) )
| ~ spl22_31
| ~ spl22_92
| ~ spl22_400 ),
inference(forward_demodulation,[],[f5383,f800]) ).
fof(f5383,plain,
( ! [X0,X1] :
( in(sK8(X1,sK15),relation_dom(X1))
| in(sK7(X1,empty_set),X0)
| sP0(X1,empty_set) )
| ~ spl22_31
| ~ spl22_92
| ~ spl22_400 ),
inference(forward_demodulation,[],[f5372,f800]) ).
fof(f5372,plain,
( ! [X0,X1] :
( in(sK8(X1,empty_set),relation_dom(X1))
| in(sK7(X1,empty_set),X0)
| sP0(X1,empty_set) )
| ~ spl22_31
| ~ spl22_400 ),
inference(superposition,[],[f5243,f379]) ).
fof(f379,plain,
( ! [X0] : empty_set = set_intersection2(X0,empty_set)
| ~ spl22_31 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f40312,plain,
( spl22_1276
| ~ spl22_121
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5066,f4944,f1110,f40310]) ).
fof(f40310,plain,
( spl22_1276
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(sK10(powerset(X0)),X1),X2,set_intersection2(sK10(powerset(X0)),X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1276])]) ).
fof(f5066,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(sK10(powerset(X0)),X1),X2,set_intersection2(sK10(powerset(X0)),X1))
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_391 ),
inference(resolution,[],[f4945,f1111]) ).
fof(f40308,plain,
( spl22_1275
| ~ spl22_121
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5036,f4940,f1110,f40306]) ).
fof(f40306,plain,
( spl22_1275
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,sK10(powerset(X1))),X2,set_intersection2(X0,sK10(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1275])]) ).
fof(f5036,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,sK10(powerset(X1))),X2,set_intersection2(X0,sK10(powerset(X1))))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_390 ),
inference(resolution,[],[f4941,f1111]) ).
fof(f40304,plain,
( spl22_1274
| ~ spl22_121
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f5002,f4902,f1110,f40302]) ).
fof(f40302,plain,
( spl22_1274
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(sK10(powerset(X1)),X2),set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1274])]) ).
fof(f5002,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(sK10(powerset(X1)),X2),set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_388 ),
inference(resolution,[],[f4903,f1111]) ).
fof(f40300,plain,
( spl22_1273
| ~ spl22_121
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4974,f4898,f1110,f40298]) ).
fof(f40298,plain,
( spl22_1273
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,sK10(powerset(X2))),set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1273])]) ).
fof(f4974,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,sK10(powerset(X2))),set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_387 ),
inference(resolution,[],[f4899,f1111]) ).
fof(f40296,plain,
( spl22_1272
| ~ spl22_133
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4643,f3994,f1246,f40294]) ).
fof(f40294,plain,
( spl22_1272
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1272])]) ).
fof(f4643,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_355 ),
inference(resolution,[],[f3995,f1247]) ).
fof(f40292,plain,
( spl22_1271
| ~ spl22_248
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4638,f3994,f2743,f40290]) ).
fof(f40290,plain,
( spl22_1271
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1271])]) ).
fof(f4638,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_355 ),
inference(resolution,[],[f3995,f2744]) ).
fof(f40288,plain,
( spl22_1270
| ~ spl22_116
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4910,f4627,f1049,f40286]) ).
fof(f40286,plain,
( spl22_1270
<=> ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_rng(set_intersection2(relation_dom(sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1270])]) ).
fof(f4910,plain,
( ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = relation_rng(set_intersection2(relation_dom(sK5),X0)) )
| ~ spl22_116
| ~ spl22_372 ),
inference(resolution,[],[f4628,f1050]) ).
fof(f40284,plain,
( spl22_1269
| ~ spl22_133
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4609,f3990,f1246,f40282]) ).
fof(f40282,plain,
( spl22_1269
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1269])]) ).
fof(f4609,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_354 ),
inference(resolution,[],[f3991,f1247]) ).
fof(f40280,plain,
( spl22_1268
| ~ spl22_248
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4604,f3990,f2743,f40278]) ).
fof(f40278,plain,
( spl22_1268
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1268])]) ).
fof(f4604,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ empty(relation_dom(X3)) )
| ~ spl22_248
| ~ spl22_354 ),
inference(resolution,[],[f3991,f2744]) ).
fof(f40276,plain,
( spl22_1267
| ~ spl22_133
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4569,f3978,f1246,f40274]) ).
fof(f40274,plain,
( spl22_1267
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(relation_dom(X1),X2),X3,X0)
| ~ sP0(X1,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1267])]) ).
fof(f4569,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(set_intersection2(relation_dom(X1),X2),X3,X0)
| ~ sP0(X1,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_351 ),
inference(resolution,[],[f3979,f1247]) ).
fof(f40272,plain,
( spl22_1266
| ~ spl22_248
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4564,f3978,f2743,f40270]) ).
fof(f40270,plain,
( spl22_1266
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(relation_rng(X1),X2),X3,X0)
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1266])]) ).
fof(f4564,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(relation_rng(X1),X2),X3,X0)
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_351 ),
inference(resolution,[],[f3979,f2744]) ).
fof(f40268,plain,
( spl22_1265
| ~ spl22_133
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4537,f3974,f1246,f40266]) ).
fof(f40266,plain,
( spl22_1265
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_dom(X2)),X3,X0)
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1265])]) ).
fof(f4537,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_dom(X2)),X3,X0)
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_350 ),
inference(resolution,[],[f3975,f1247]) ).
fof(f40264,plain,
( spl22_1264
| ~ spl22_248
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4532,f3974,f2743,f40262]) ).
fof(f40262,plain,
( spl22_1264
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_rng(X2)),X3,X0)
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1264])]) ).
fof(f4532,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_rng(X2)),X3,X0)
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_350 ),
inference(resolution,[],[f3975,f2744]) ).
fof(f40260,plain,
( spl22_1263
| ~ spl22_133
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4497,f3962,f1246,f40258]) ).
fof(f40258,plain,
( spl22_1263
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1263])]) ).
fof(f4497,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_347 ),
inference(resolution,[],[f3963,f1247]) ).
fof(f40256,plain,
( spl22_1262
| ~ spl22_248
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4492,f3962,f2743,f40254]) ).
fof(f40254,plain,
( spl22_1262
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1262])]) ).
fof(f4492,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_rng(X2),X3))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_347 ),
inference(resolution,[],[f3963,f2744]) ).
fof(f40252,plain,
( spl22_1261
| ~ spl22_133
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4467,f3958,f1246,f40250]) ).
fof(f40250,plain,
( spl22_1261
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1261])]) ).
fof(f4467,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_346 ),
inference(resolution,[],[f3959,f1247]) ).
fof(f40248,plain,
( spl22_1260
| ~ spl22_248
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4462,f3958,f2743,f40246]) ).
fof(f40246,plain,
( spl22_1260
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1260])]) ).
fof(f4462,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_rng(X3)))
| ~ sP1(X3)
| ~ empty(relation_dom(X3)) )
| ~ spl22_248
| ~ spl22_346 ),
inference(resolution,[],[f3959,f2744]) ).
fof(f40244,plain,
( spl22_1259
| ~ spl22_266
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4905,f4627,f2951,f40242]) ).
fof(f40242,plain,
( spl22_1259
<=> ! [X0,X1] :
( ~ empty(relation_dom_restriction(sK5,X0))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1259])]) ).
fof(f2951,plain,
( spl22_266
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ empty(set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_266])]) ).
fof(f4905,plain,
( ! [X0,X1] :
( ~ empty(relation_dom_restriction(sK5,X0))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(sK5)) )
| ~ spl22_266
| ~ spl22_372 ),
inference(resolution,[],[f4628,f2952]) ).
fof(f2952,plain,
( ! [X2,X0,X1] :
( ~ empty(set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) )
| ~ spl22_266 ),
inference(avatar_component_clause,[],[f2951]) ).
fof(f40240,plain,
( spl22_1258
| ~ spl22_133
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4383,f3937,f1246,f40238]) ).
fof(f40238,plain,
( spl22_1258
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_dom(X2),X3),X0)
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1258])]) ).
fof(f4383,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_dom(X2),X3),X0)
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_341 ),
inference(resolution,[],[f3938,f1247]) ).
fof(f40236,plain,
( spl22_1257
| ~ spl22_248
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4378,f3937,f2743,f40234]) ).
fof(f40234,plain,
( spl22_1257
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_rng(X2),X3),X0)
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1257])]) ).
fof(f4378,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_rng(X2),X3),X0)
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_341 ),
inference(resolution,[],[f3938,f2744]) ).
fof(f40232,plain,
( spl22_1256
| ~ spl22_133
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4353,f3933,f1246,f40230]) ).
fof(f40230,plain,
( spl22_1256
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_dom(X3)),X0)
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1256])]) ).
fof(f4353,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_dom(X3)),X0)
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_340 ),
inference(resolution,[],[f3934,f1247]) ).
fof(f40228,plain,
( spl22_1255
| ~ spl22_248
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4348,f3933,f2743,f40226]) ).
fof(f40226,plain,
( spl22_1255
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_rng(X3)),X0)
| ~ sP1(X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1255])]) ).
fof(f4348,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_rng(X3)),X0)
| ~ sP1(X3)
| ~ empty(relation_dom(X3)) )
| ~ spl22_248
| ~ spl22_340 ),
inference(resolution,[],[f3934,f2744]) ).
fof(f40224,plain,
( spl22_1254
| ~ spl22_133
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f4142,f3905,f1246,f40222]) ).
fof(f40222,plain,
( spl22_1254
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1254])]) ).
fof(f4142,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_333 ),
inference(resolution,[],[f3906,f1247]) ).
fof(f40220,plain,
( spl22_1253
| ~ spl22_248
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f4137,f3905,f2743,f40218]) ).
fof(f40218,plain,
( spl22_1253
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_rng(X2))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1253])]) ).
fof(f4137,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_rng(X2))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_333 ),
inference(resolution,[],[f3906,f2744]) ).
fof(f40216,plain,
( spl22_1252
| ~ spl22_133
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f4116,f3901,f1246,f40214]) ).
fof(f40214,plain,
( spl22_1252
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1252])]) ).
fof(f4116,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_332 ),
inference(resolution,[],[f3902,f1247]) ).
fof(f40212,plain,
( spl22_1251
| ~ spl22_248
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f4111,f3901,f2743,f40210]) ).
fof(f40210,plain,
( spl22_1251
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_rng(X2))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1251])]) ).
fof(f4111,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_rng(X2))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_332 ),
inference(resolution,[],[f3902,f2744]) ).
fof(f40208,plain,
( spl22_1250
| ~ spl22_133
| ~ spl22_331 ),
inference(avatar_split_clause,[],[f4094,f3859,f1246,f40206]) ).
fof(f40206,plain,
( spl22_1250
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),sK10(powerset(X0)))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1250])]) ).
fof(f4094,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),sK10(powerset(X0)))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_331 ),
inference(resolution,[],[f3860,f1247]) ).
fof(f40204,plain,
( spl22_1249
| ~ spl22_248
| ~ spl22_331 ),
inference(avatar_split_clause,[],[f4089,f3859,f2743,f40202]) ).
fof(f40202,plain,
( spl22_1249
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_rng(X2),sK10(powerset(X0)))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1249])]) ).
fof(f4089,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_rng(X2),sK10(powerset(X0)))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_331 ),
inference(resolution,[],[f3860,f2744]) ).
fof(f40196,plain,
( spl22_1248
| ~ spl22_133
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f4072,f3855,f1246,f40194]) ).
fof(f40194,plain,
( spl22_1248
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,sK10(powerset(X0)))
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1248])]) ).
fof(f4072,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,sK10(powerset(X0)))
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_330 ),
inference(resolution,[],[f3856,f1247]) ).
fof(f40192,plain,
( spl22_1247
| ~ spl22_248
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f4067,f3855,f2743,f40190]) ).
fof(f40190,plain,
( spl22_1247
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(relation_rng(X1),X2,sK10(powerset(X0)))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1247])]) ).
fof(f4067,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(relation_rng(X1),X2,sK10(powerset(X0)))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_330 ),
inference(resolution,[],[f3856,f2744]) ).
fof(f40188,plain,
( spl22_1246
| ~ spl22_119
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3812,f3697,f1064,f40186]) ).
fof(f40186,plain,
( spl22_1246
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| empty(apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1246])]) ).
fof(f3812,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| empty(apply(X1,X0)) )
| ~ spl22_119
| ~ spl22_328 ),
inference(resolution,[],[f3698,f1065]) ).
fof(f40184,plain,
( spl22_1245
| ~ spl22_133
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3781,f3685,f1246,f40182]) ).
fof(f40182,plain,
( spl22_1245
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1245])]) ).
fof(f3781,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_325 ),
inference(resolution,[],[f3686,f1247]) ).
fof(f40180,plain,
( spl22_1244
| ~ spl22_248
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3776,f3685,f2743,f40178]) ).
fof(f40178,plain,
( spl22_1244
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1244])]) ).
fof(f3776,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_rng(X1),X2))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_325 ),
inference(resolution,[],[f3686,f2744]) ).
fof(f40176,plain,
( spl22_1243
| ~ spl22_133
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3756,f3681,f1246,f40174]) ).
fof(f40174,plain,
( spl22_1243
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1243])]) ).
fof(f3756,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_324 ),
inference(resolution,[],[f3682,f1247]) ).
fof(f40172,plain,
( spl22_1242
| ~ spl22_248
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3751,f3681,f2743,f40170]) ).
fof(f40170,plain,
( spl22_1242
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1242])]) ).
fof(f3751,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_rng(X2)))
| ~ sP1(X2)
| ~ empty(relation_dom(X2)) )
| ~ spl22_248
| ~ spl22_324 ),
inference(resolution,[],[f3682,f2744]) ).
fof(f40168,plain,
( spl22_1241
| ~ spl22_150
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3374,f3304,f1405,f40166]) ).
fof(f40166,plain,
( spl22_1241
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1241])]) ).
fof(f3374,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,X3)
| ~ empty(X3) )
| ~ spl22_150
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1406]) ).
fof(f40164,plain,
( spl22_1240
| ~ spl22_148
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3370,f3304,f1397,f40162]) ).
fof(f40162,plain,
( spl22_1240
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1240])]) ).
fof(f3370,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),X3)
| ~ empty(X3) )
| ~ spl22_148
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1398]) ).
fof(f40160,plain,
( spl22_1239
| ~ spl22_151
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3363,f3304,f1409,f40158]) ).
fof(f40158,plain,
( spl22_1239
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1239])]) ).
fof(f3363,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| ~ empty(X2) )
| ~ spl22_151
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1410]) ).
fof(f40135,plain,
( spl22_1238
| ~ spl22_149
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3362,f3304,f1401,f40133]) ).
fof(f40133,plain,
( spl22_1238
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1238])]) ).
fof(f3362,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| ~ empty(X3) )
| ~ spl22_149
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1402]) ).
fof(f40131,plain,
( spl22_1237
| ~ spl22_142
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3351,f3304,f1341,f40129]) ).
fof(f40129,plain,
( spl22_1237
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP0(X2,relation_rng(X0))
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1237])]) ).
fof(f3351,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP0(X2,relation_rng(X0))
| ~ empty(relation_dom(X2)) )
| ~ spl22_142
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1342]) ).
fof(f40127,plain,
( spl22_1236
| ~ spl22_37
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f3242,f2999,f402,f40125]) ).
fof(f40125,plain,
( spl22_1236
<=> ! [X0] :
( ~ function(relation_dom(X0))
| relation_dom(X0) = relation_dom_restriction(relation_dom(X0),relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1236])]) ).
fof(f3242,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| relation_dom(X0) = relation_dom_restriction(relation_dom(X0),relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl22_37
| ~ spl22_278 ),
inference(resolution,[],[f3000,f403]) ).
fof(f40123,plain,
( spl22_1235
| ~ spl22_35
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f3241,f2999,f394,f40121]) ).
fof(f40121,plain,
( spl22_1235
<=> ! [X0] :
( ~ function(relation_rng(X0))
| relation_rng(X0) = relation_dom_restriction(relation_rng(X0),relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1235])]) ).
fof(f3241,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| relation_rng(X0) = relation_dom_restriction(relation_rng(X0),relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_278 ),
inference(resolution,[],[f3000,f395]) ).
fof(f40119,plain,
( spl22_1234
| ~ spl22_63
| ~ spl22_277 ),
inference(avatar_split_clause,[],[f3238,f2995,f586,f40117]) ).
fof(f40117,plain,
( spl22_1234
<=> ! [X2,X0,X1] :
( sP2(powerset(X0),X1,sK15)
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1234])]) ).
fof(f3238,plain,
( ! [X2,X0,X1] :
( sP2(powerset(X0),X1,sK15)
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,sK15)) )
| ~ spl22_63
| ~ spl22_277 ),
inference(resolution,[],[f2996,f587]) ).
fof(f40115,plain,
( spl22_1233
| ~ spl22_63
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f3235,f2991,f586,f40113]) ).
fof(f40113,plain,
( spl22_1233
<=> ! [X2,X0,X1] :
( sP2(sK15,X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(sK15,X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1233])]) ).
fof(f3235,plain,
( ! [X2,X0,X1] :
( sP2(sK15,X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(sK15,X0,powerset(X1))) )
| ~ spl22_63
| ~ spl22_276 ),
inference(resolution,[],[f2992,f587]) ).
fof(f40111,plain,
( spl22_1232
| ~ spl22_63
| ~ spl22_275 ),
inference(avatar_split_clause,[],[f3232,f2987,f586,f40109]) ).
fof(f40109,plain,
( spl22_1232
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1),sK15)
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1232])]) ).
fof(f3232,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1),sK15)
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),sK15)) )
| ~ spl22_63
| ~ spl22_275 ),
inference(resolution,[],[f2988,f587]) ).
fof(f40107,plain,
( spl22_1231
| ~ spl22_63
| ~ spl22_274 ),
inference(avatar_split_clause,[],[f3229,f2983,f586,f40105]) ).
fof(f40105,plain,
( spl22_1231
<=> ! [X2,X0,X1] :
( sP2(X0,sK15,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK15,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1231])]) ).
fof(f3229,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK15,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK15,powerset(X1))) )
| ~ spl22_63
| ~ spl22_274 ),
inference(resolution,[],[f2984,f587]) ).
fof(f40103,plain,
( spl22_1230
| ~ spl22_136
| ~ spl22_257 ),
inference(avatar_split_clause,[],[f3150,f2915,f1278,f40101]) ).
fof(f40101,plain,
( spl22_1230
<=> ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1230])]) ).
fof(f1278,plain,
( spl22_136
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_136])]) ).
fof(f3150,plain,
( ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) )
| ~ spl22_136
| ~ spl22_257 ),
inference(resolution,[],[f2916,f1279]) ).
fof(f1279,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl22_136 ),
inference(avatar_component_clause,[],[f1278]) ).
fof(f40099,plain,
( spl22_1229
| ~ spl22_128
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3136,f2907,f1151,f40097]) ).
fof(f40097,plain,
( spl22_1229
<=> ! [X0,X1] :
( empty(set_intersection2(X0,sK10(powerset(X1))))
| element(sK10(set_intersection2(X0,sK10(powerset(X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1229])]) ).
fof(f3136,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,sK10(powerset(X1))))
| element(sK10(set_intersection2(X0,sK10(powerset(X1)))),X1) )
| ~ spl22_128
| ~ spl22_255 ),
inference(resolution,[],[f2908,f1152]) ).
fof(f39950,plain,
( spl22_1228
| ~ spl22_132
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3135,f2907,f1242,f39948]) ).
fof(f39948,plain,
( spl22_1228
<=> ! [X0,X1] :
( empty(set_intersection2(X0,sK6(X1)))
| element(sK10(set_intersection2(X0,sK6(X1))),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1228])]) ).
fof(f3135,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,sK6(X1)))
| element(sK10(set_intersection2(X0,sK6(X1))),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_255 ),
inference(resolution,[],[f2908,f1243]) ).
fof(f39946,plain,
( spl22_1227
| ~ spl22_129
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3127,f2907,f1155,f39944]) ).
fof(f39944,plain,
( spl22_1227
<=> ! [X2,X0,X1] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK10(set_intersection2(X0,set_intersection2(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1227])]) ).
fof(f3127,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK10(set_intersection2(X0,set_intersection2(X1,X2))),X1) )
| ~ spl22_129
| ~ spl22_255 ),
inference(resolution,[],[f2908,f1156]) ).
fof(f39942,plain,
( spl22_1226
| ~ spl22_130
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3126,f2907,f1159,f39940]) ).
fof(f39940,plain,
( spl22_1226
<=> ! [X2,X0,X1] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK10(set_intersection2(X0,set_intersection2(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1226])]) ).
fof(f3126,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK10(set_intersection2(X0,set_intersection2(X1,X2))),X2) )
| ~ spl22_130
| ~ spl22_255 ),
inference(resolution,[],[f2908,f1160]) ).
fof(f39938,plain,
( spl22_1225
| ~ spl22_128
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3112,f2903,f1151,f39936]) ).
fof(f39936,plain,
( spl22_1225
<=> ! [X0,X1] :
( empty(set_intersection2(sK10(powerset(X0)),X1))
| element(sK10(set_intersection2(sK10(powerset(X0)),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1225])]) ).
fof(f3112,plain,
( ! [X0,X1] :
( empty(set_intersection2(sK10(powerset(X0)),X1))
| element(sK10(set_intersection2(sK10(powerset(X0)),X1)),X0) )
| ~ spl22_128
| ~ spl22_254 ),
inference(resolution,[],[f2904,f1152]) ).
fof(f39934,plain,
( spl22_1224
| ~ spl22_132
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3111,f2903,f1242,f39932]) ).
fof(f39932,plain,
( spl22_1224
<=> ! [X0,X1] :
( empty(set_intersection2(sK6(X0),X1))
| element(sK10(set_intersection2(sK6(X0),X1)),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1224])]) ).
fof(f3111,plain,
( ! [X0,X1] :
( empty(set_intersection2(sK6(X0),X1))
| element(sK10(set_intersection2(sK6(X0),X1)),X0)
| empty(X0) )
| ~ spl22_132
| ~ spl22_254 ),
inference(resolution,[],[f2904,f1243]) ).
fof(f39930,plain,
( spl22_1223
| ~ spl22_129
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3103,f2903,f1155,f39928]) ).
fof(f39928,plain,
( spl22_1223
<=> ! [X2,X0,X1] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK10(set_intersection2(set_intersection2(X0,X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1223])]) ).
fof(f3103,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK10(set_intersection2(set_intersection2(X0,X1),X2)),X0) )
| ~ spl22_129
| ~ spl22_254 ),
inference(resolution,[],[f2904,f1156]) ).
fof(f39926,plain,
( spl22_1222
| ~ spl22_130
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3102,f2903,f1159,f39924]) ).
fof(f39924,plain,
( spl22_1222
<=> ! [X2,X0,X1] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK10(set_intersection2(set_intersection2(X0,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1222])]) ).
fof(f3102,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK10(set_intersection2(set_intersection2(X0,X1),X2)),X1) )
| ~ spl22_130
| ~ spl22_254 ),
inference(resolution,[],[f2904,f1160]) ).
fof(f39922,plain,
( spl22_1221
| ~ spl22_63
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f3096,f2899,f586,f39920]) ).
fof(f39920,plain,
( spl22_1221
<=> ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1221])]) ).
fof(f3096,plain,
( ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) )
| ~ spl22_63
| ~ spl22_253 ),
inference(resolution,[],[f2900,f587]) ).
fof(f39918,plain,
( spl22_1220
| ~ spl22_128
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3091,f2895,f1151,f39916]) ).
fof(f39916,plain,
( spl22_1220
<=> ! [X0,X1] :
( sP2(sK15,X0,sK10(powerset(X1)))
| element(sK13(sK15,X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1220])]) ).
fof(f3091,plain,
( ! [X0,X1] :
( sP2(sK15,X0,sK10(powerset(X1)))
| element(sK13(sK15,X0,sK10(powerset(X1))),X1) )
| ~ spl22_128
| ~ spl22_252 ),
inference(resolution,[],[f2896,f1152]) ).
fof(f39914,plain,
( spl22_1219
| ~ spl22_132
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3090,f2895,f1242,f39912]) ).
fof(f39912,plain,
( spl22_1219
<=> ! [X0,X1] :
( sP2(sK15,X0,sK6(X1))
| element(sK13(sK15,X0,sK6(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1219])]) ).
fof(f3090,plain,
( ! [X0,X1] :
( sP2(sK15,X0,sK6(X1))
| element(sK13(sK15,X0,sK6(X1)),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_252 ),
inference(resolution,[],[f2896,f1243]) ).
fof(f39765,plain,
( spl22_1218
| ~ spl22_129
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3082,f2895,f1155,f39763]) ).
fof(f39763,plain,
( spl22_1218
<=> ! [X2,X0,X1] :
( sP2(sK15,X0,set_intersection2(X1,X2))
| in(sK13(sK15,X0,set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1218])]) ).
fof(f3082,plain,
( ! [X2,X0,X1] :
( sP2(sK15,X0,set_intersection2(X1,X2))
| in(sK13(sK15,X0,set_intersection2(X1,X2)),X1) )
| ~ spl22_129
| ~ spl22_252 ),
inference(resolution,[],[f2896,f1156]) ).
fof(f39761,plain,
( spl22_1217
| ~ spl22_130
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3081,f2895,f1159,f39759]) ).
fof(f39759,plain,
( spl22_1217
<=> ! [X2,X0,X1] :
( sP2(sK15,X0,set_intersection2(X1,X2))
| in(sK13(sK15,X0,set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1217])]) ).
fof(f3081,plain,
( ! [X2,X0,X1] :
( sP2(sK15,X0,set_intersection2(X1,X2))
| in(sK13(sK15,X0,set_intersection2(X1,X2)),X2) )
| ~ spl22_130
| ~ spl22_252 ),
inference(resolution,[],[f2896,f1160]) ).
fof(f39757,plain,
( spl22_1216
| ~ spl22_128
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3072,f2891,f1151,f39755]) ).
fof(f39755,plain,
( spl22_1216
<=> ! [X0,X1] :
( sP2(X0,sK15,sK10(powerset(X1)))
| element(sK13(X0,sK15,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1216])]) ).
fof(f3072,plain,
( ! [X0,X1] :
( sP2(X0,sK15,sK10(powerset(X1)))
| element(sK13(X0,sK15,sK10(powerset(X1))),X1) )
| ~ spl22_128
| ~ spl22_251 ),
inference(resolution,[],[f2892,f1152]) ).
fof(f39753,plain,
( spl22_1215
| ~ spl22_132
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3071,f2891,f1242,f39751]) ).
fof(f39751,plain,
( spl22_1215
<=> ! [X0,X1] :
( sP2(X0,sK15,sK6(X1))
| element(sK13(X0,sK15,sK6(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1215])]) ).
fof(f3071,plain,
( ! [X0,X1] :
( sP2(X0,sK15,sK6(X1))
| element(sK13(X0,sK15,sK6(X1)),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_251 ),
inference(resolution,[],[f2892,f1243]) ).
fof(f39749,plain,
( spl22_1214
| ~ spl22_129
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3063,f2891,f1155,f39747]) ).
fof(f39747,plain,
( spl22_1214
<=> ! [X2,X0,X1] :
( sP2(X0,sK15,set_intersection2(X1,X2))
| in(sK13(X0,sK15,set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1214])]) ).
fof(f3063,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK15,set_intersection2(X1,X2))
| in(sK13(X0,sK15,set_intersection2(X1,X2)),X1) )
| ~ spl22_129
| ~ spl22_251 ),
inference(resolution,[],[f2892,f1156]) ).
fof(f39745,plain,
( spl22_1213
| ~ spl22_130
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3062,f2891,f1159,f39743]) ).
fof(f39743,plain,
( spl22_1213
<=> ! [X2,X0,X1] :
( sP2(X0,sK15,set_intersection2(X1,X2))
| in(sK13(X0,sK15,set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1213])]) ).
fof(f3062,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK15,set_intersection2(X1,X2))
| in(sK13(X0,sK15,set_intersection2(X1,X2)),X2) )
| ~ spl22_130
| ~ spl22_251 ),
inference(resolution,[],[f2892,f1160]) ).
fof(f39741,plain,
( spl22_1212
| ~ spl22_128
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3036,f2887,f1151,f39739]) ).
fof(f39739,plain,
( spl22_1212
<=> ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK15)
| element(sK13(X0,sK10(powerset(X1)),sK15),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1212])]) ).
fof(f3036,plain,
( ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK15)
| element(sK13(X0,sK10(powerset(X1)),sK15),X1) )
| ~ spl22_128
| ~ spl22_250 ),
inference(resolution,[],[f2888,f1152]) ).
fof(f39737,plain,
( spl22_1211
| ~ spl22_132
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3035,f2887,f1242,f39735]) ).
fof(f39735,plain,
( spl22_1211
<=> ! [X0,X1] :
( sP2(X0,sK6(X1),sK15)
| element(sK13(X0,sK6(X1),sK15),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1211])]) ).
fof(f3035,plain,
( ! [X0,X1] :
( sP2(X0,sK6(X1),sK15)
| element(sK13(X0,sK6(X1),sK15),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_250 ),
inference(resolution,[],[f2888,f1243]) ).
fof(f39733,plain,
( spl22_1210
| ~ spl22_129
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3027,f2887,f1155,f39731]) ).
fof(f39731,plain,
( spl22_1210
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK15)
| in(sK13(X0,set_intersection2(X1,X2),sK15),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1210])]) ).
fof(f3027,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK15)
| in(sK13(X0,set_intersection2(X1,X2),sK15),X1) )
| ~ spl22_129
| ~ spl22_250 ),
inference(resolution,[],[f2888,f1156]) ).
fof(f39729,plain,
( spl22_1209
| ~ spl22_130
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3026,f2887,f1159,f39727]) ).
fof(f39727,plain,
( spl22_1209
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK15)
| in(sK13(X0,set_intersection2(X1,X2),sK15),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1209])]) ).
fof(f3026,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),sK15)
| in(sK13(X0,set_intersection2(X1,X2),sK15),X2) )
| ~ spl22_130
| ~ spl22_250 ),
inference(resolution,[],[f2888,f1160]) ).
fof(f39580,plain,
( spl22_1208
| ~ spl22_128
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3017,f2883,f1151,f39578]) ).
fof(f39578,plain,
( spl22_1208
<=> ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK15)
| element(sK13(sK10(powerset(X0)),X1,sK15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1208])]) ).
fof(f3017,plain,
( ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK15)
| element(sK13(sK10(powerset(X0)),X1,sK15),X0) )
| ~ spl22_128
| ~ spl22_249 ),
inference(resolution,[],[f2884,f1152]) ).
fof(f39576,plain,
( spl22_1207
| ~ spl22_132
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3016,f2883,f1242,f39574]) ).
fof(f39574,plain,
( spl22_1207
<=> ! [X0,X1] :
( sP2(sK6(X0),X1,sK15)
| element(sK13(sK6(X0),X1,sK15),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1207])]) ).
fof(f3016,plain,
( ! [X0,X1] :
( sP2(sK6(X0),X1,sK15)
| element(sK13(sK6(X0),X1,sK15),X0)
| empty(X0) )
| ~ spl22_132
| ~ spl22_249 ),
inference(resolution,[],[f2884,f1243]) ).
fof(f39572,plain,
( spl22_1206
| ~ spl22_129
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3008,f2883,f1155,f39570]) ).
fof(f39570,plain,
( spl22_1206
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK15)
| in(sK13(set_intersection2(X0,X1),X2,sK15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1206])]) ).
fof(f3008,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK15)
| in(sK13(set_intersection2(X0,X1),X2,sK15),X0) )
| ~ spl22_129
| ~ spl22_249 ),
inference(resolution,[],[f2884,f1156]) ).
fof(f39568,plain,
( spl22_1205
| ~ spl22_130
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3007,f2883,f1159,f39566]) ).
fof(f39566,plain,
( spl22_1205
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK15)
| in(sK13(set_intersection2(X0,X1),X2,sK15),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1205])]) ).
fof(f3007,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,sK15)
| in(sK13(set_intersection2(X0,X1),X2,sK15),X1) )
| ~ spl22_130
| ~ spl22_249 ),
inference(resolution,[],[f2884,f1160]) ).
fof(f39564,plain,
( spl22_1204
| ~ spl22_158
| ~ spl22_239 ),
inference(avatar_split_clause,[],[f2713,f2690,f1544,f39562]) ).
fof(f39562,plain,
( spl22_1204
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(relation_dom(X1))
| sK7(X1,X0) = apply(X1,sK8(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1204])]) ).
fof(f2690,plain,
( spl22_239
<=> ! [X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_239])]) ).
fof(f2713,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(relation_dom(X1))
| sK7(X1,X0) = apply(X1,sK8(X1,X0)) )
| ~ spl22_158
| ~ spl22_239 ),
inference(duplicate_literal_removal,[],[f2711]) ).
fof(f2711,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(relation_dom(X1))
| sK7(X1,X0) = apply(X1,sK8(X1,X0))
| ~ empty(X0) )
| ~ spl22_158
| ~ spl22_239 ),
inference(resolution,[],[f2691,f1545]) ).
fof(f2691,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| empty(relation_dom(X0)) )
| ~ spl22_239 ),
inference(avatar_component_clause,[],[f2690]) ).
fof(f39560,plain,
( spl22_1203
| ~ spl22_73
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2584,f2559,f652,f39558]) ).
fof(f39558,plain,
( spl22_1203
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| in(sK8(X1,relation_dom(X0)),relation_dom(X1))
| sP0(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1203])]) ).
fof(f2584,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| in(sK8(X1,relation_dom(X0)),relation_dom(X1))
| sP0(X1,relation_dom(X0)) )
| ~ spl22_73
| ~ spl22_233 ),
inference(resolution,[],[f2560,f653]) ).
fof(f39556,plain,
( spl22_1202
| ~ spl22_154
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2581,f2559,f1527,f39554]) ).
fof(f39554,plain,
( spl22_1202
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| element(sK8(X1,relation_dom(X0)),relation_dom(X1))
| sP0(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1202])]) ).
fof(f2581,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| element(sK8(X1,relation_dom(X0)),relation_dom(X1))
| sP0(X1,relation_dom(X0)) )
| ~ spl22_154
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1528]) ).
fof(f38867,plain,
( spl22_1201
| ~ spl22_232
| ~ spl22_585 ),
inference(avatar_split_clause,[],[f11606,f11544,f2531,f38865]) ).
fof(f38865,plain,
( spl22_1201
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| in(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1201])]) ).
fof(f11544,plain,
( spl22_585
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| in(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_585])]) ).
fof(f11606,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| in(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_585 ),
inference(resolution,[],[f11545,f2532]) ).
fof(f11545,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| in(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2)) )
| ~ spl22_585 ),
inference(avatar_component_clause,[],[f11544]) ).
fof(f38863,plain,
( spl22_1200
| ~ spl22_232
| ~ spl22_584 ),
inference(avatar_split_clause,[],[f11570,f11540,f2531,f38861]) ).
fof(f38861,plain,
( spl22_1200
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| element(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1200])]) ).
fof(f11540,plain,
( spl22_584
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| element(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_584])]) ).
fof(f11570,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| element(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_584 ),
inference(resolution,[],[f11541,f2532]) ).
fof(f11541,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| element(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2)) )
| ~ spl22_584 ),
inference(avatar_component_clause,[],[f11540]) ).
fof(f38859,plain,
( spl22_1199
| ~ spl22_230
| ~ spl22_549 ),
inference(avatar_split_clause,[],[f10731,f10647,f2489,f38857]) ).
fof(f38857,plain,
( spl22_1199
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(relation_rng(X2),X3,X4)))) = apply(X0,apply(X2,sK9(X2,sK13(relation_rng(X2),X3,X4))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(relation_rng(X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(relation_rng(X2),X3,X4)) = apply(sK5,sK13(relation_rng(X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1199])]) ).
fof(f10647,plain,
( spl22_549
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,X3))) = apply(X0,apply(X2,sK9(X2,X3)))
| ~ sP0(X2,X1)
| ~ in(X3,relation_rng(X2))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_549])]) ).
fof(f10731,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(relation_rng(X2),X3,X4)))) = apply(X0,apply(X2,sK9(X2,sK13(relation_rng(X2),X3,X4))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(relation_rng(X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(relation_rng(X2),X3,X4)) = apply(sK5,sK13(relation_rng(X2),X3,X4)) )
| ~ spl22_230
| ~ spl22_549 ),
inference(resolution,[],[f10648,f2490]) ).
fof(f10648,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,relation_rng(X2))
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,X3))) = apply(X0,apply(X2,sK9(X2,X3)))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2) )
| ~ spl22_549 ),
inference(avatar_component_clause,[],[f10647]) ).
fof(f38855,plain,
( spl22_1198
| ~ spl22_228
| ~ spl22_549 ),
inference(avatar_split_clause,[],[f10724,f10647,f2447,f38853]) ).
fof(f38853,plain,
( spl22_1198
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(X3,relation_rng(X2),X4)))) = apply(X0,apply(X2,sK9(X2,sK13(X3,relation_rng(X2),X4))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(X3,relation_rng(X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,relation_rng(X2),X4)) = apply(sK5,sK13(X3,relation_rng(X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1198])]) ).
fof(f10724,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(X3,relation_rng(X2),X4)))) = apply(X0,apply(X2,sK9(X2,sK13(X3,relation_rng(X2),X4))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(X3,relation_rng(X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,relation_rng(X2),X4)) = apply(sK5,sK13(X3,relation_rng(X2),X4)) )
| ~ spl22_228
| ~ spl22_549 ),
inference(resolution,[],[f10648,f2448]) ).
fof(f38851,plain,
( spl22_1197
| ~ spl22_231
| ~ spl22_549 ),
inference(avatar_split_clause,[],[f10714,f10647,f2510,f38849]) ).
fof(f38849,plain,
( spl22_1197
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2))))) = apply(X0,apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2)))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(X3,X4,relation_rng(X2))
| apply(sK5,sK13(X3,X4,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,relation_rng(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1197])]) ).
fof(f10714,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2))))) = apply(X0,apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2)))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(X3,X4,relation_rng(X2))
| apply(sK5,sK13(X3,X4,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,relation_rng(X2))) )
| ~ spl22_231
| ~ spl22_549 ),
inference(resolution,[],[f10648,f2511]) ).
fof(f38847,plain,
( spl22_1196
| ~ spl22_229
| ~ spl22_549 ),
inference(avatar_split_clause,[],[f10713,f10647,f2468,f38845]) ).
fof(f38845,plain,
( spl22_1196
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2))))) = apply(X0,apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2)))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(X3,X4,relation_rng(X2))
| apply(sK5,sK13(X3,X4,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,relation_rng(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1196])]) ).
fof(f10713,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2))))) = apply(X0,apply(X2,sK9(X2,sK13(X3,X4,relation_rng(X2)))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP2(X3,X4,relation_rng(X2))
| apply(sK5,sK13(X3,X4,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,relation_rng(X2))) )
| ~ spl22_229
| ~ spl22_549 ),
inference(resolution,[],[f10648,f2469]) ).
fof(f38562,plain,
( spl22_1195
| ~ spl22_232
| ~ spl22_582 ),
inference(avatar_split_clause,[],[f11507,f11386,f2531,f38560]) ).
fof(f38560,plain,
( spl22_1195
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2)))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2))))
| ~ function(X0)
| sP2(relation_dom(X2),X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1195])]) ).
fof(f11386,plain,
( spl22_582
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2)))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(relation_dom(X2),X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_582])]) ).
fof(f11507,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2)))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2))))
| ~ function(X0)
| sP2(relation_dom(X2),X3,relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_582 ),
inference(resolution,[],[f11387,f2532]) ).
fof(f11387,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2)))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2))))
| ~ function(X0)
| sP2(relation_dom(X2),X3,relation_dom(X2)) )
| ~ spl22_582 ),
inference(avatar_component_clause,[],[f11386]) ).
fof(f38558,plain,
( spl22_1194
| ~ spl22_232
| ~ spl22_581 ),
inference(avatar_split_clause,[],[f11477,f11382,f2531,f38556]) ).
fof(f38556,plain,
( spl22_1194
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2))))
| ~ function(X0)
| sP2(X3,relation_dom(X2),relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1194])]) ).
fof(f11382,plain,
( spl22_581
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(X3,relation_dom(X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_581])]) ).
fof(f11477,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2))))
| ~ function(X0)
| sP2(X3,relation_dom(X2),relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_581 ),
inference(resolution,[],[f11383,f2532]) ).
fof(f11383,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2))))
| ~ function(X0)
| sP2(X3,relation_dom(X2),relation_dom(X2)) )
| ~ spl22_581 ),
inference(avatar_component_clause,[],[f11382]) ).
fof(f38554,plain,
( spl22_1193
| ~ spl22_232
| ~ spl22_550 ),
inference(avatar_split_clause,[],[f10862,f10798,f2531,f38552]) ).
fof(f38552,plain,
( spl22_1193
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,apply(X3,X4))) = apply(X0,apply(X2,apply(X3,X4)))
| ~ sP0(X2,X1)
| ~ in(X4,relation_dom(X3))
| ~ function(X0)
| sK7(X3,relation_dom(X2)) = apply(X3,sK8(X3,relation_dom(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK7(X3,relation_dom(X2))) = apply(sK5,sK7(X3,relation_dom(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1193])]) ).
fof(f10798,plain,
( spl22_550
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,apply(X3,X4))) = apply(X0,apply(X2,apply(X3,X4)))
| ~ sP0(X2,X1)
| ~ in(X4,relation_dom(X3))
| ~ sP0(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_550])]) ).
fof(f10862,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,apply(X3,X4))) = apply(X0,apply(X2,apply(X3,X4)))
| ~ sP0(X2,X1)
| ~ in(X4,relation_dom(X3))
| ~ function(X0)
| sK7(X3,relation_dom(X2)) = apply(X3,sK8(X3,relation_dom(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK7(X3,relation_dom(X2))) = apply(sK5,sK7(X3,relation_dom(X2))) )
| ~ spl22_232
| ~ spl22_550 ),
inference(resolution,[],[f10799,f2532]) ).
fof(f10799,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X3,relation_dom(X2))
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,apply(X3,X4))) = apply(X0,apply(X2,apply(X3,X4)))
| ~ sP0(X2,X1)
| ~ in(X4,relation_dom(X3))
| ~ function(X0) )
| ~ spl22_550 ),
inference(avatar_component_clause,[],[f10798]) ).
fof(f38346,plain,
( spl22_1192
| ~ spl22_119
| ~ spl22_1018 ),
inference(avatar_split_clause,[],[f37831,f27680,f1064,f38344]) ).
fof(f38344,plain,
( spl22_1192
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,X0),sK15)
| empty(set_intersection2(relation_dom(sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1192])]) ).
fof(f37831,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,X0),sK15)
| empty(set_intersection2(relation_dom(sK5),X0)) )
| ~ spl22_119
| ~ spl22_1018 ),
inference(resolution,[],[f27681,f1065]) ).
fof(f38342,plain,
( spl22_1191
| ~ spl22_232
| ~ spl22_573 ),
inference(avatar_split_clause,[],[f11330,f11146,f2531,f38340]) ).
fof(f38340,plain,
( spl22_1191
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| sP2(relation_dom(X2),X3,X4)
| ~ empty(X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1191])]) ).
fof(f11146,plain,
( spl22_573
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ sP0(X2,X1)
| sP2(relation_dom(X2),X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_573])]) ).
fof(f11330,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| sP2(relation_dom(X2),X3,X4)
| ~ empty(X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_573 ),
inference(resolution,[],[f11147,f2532]) ).
fof(f11147,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ function(X0)
| sP2(relation_dom(X2),X3,X4)
| ~ empty(X4) )
| ~ spl22_573 ),
inference(avatar_component_clause,[],[f11146]) ).
fof(f38338,plain,
( spl22_1190
| ~ spl22_232
| ~ spl22_572 ),
inference(avatar_split_clause,[],[f11301,f11142,f2531,f38336]) ).
fof(f38336,plain,
( spl22_1190
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| sP2(X3,relation_dom(X2),X4)
| ~ empty(X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1190])]) ).
fof(f11142,plain,
( spl22_572
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ sP0(X2,X1)
| sP2(X3,relation_dom(X2),X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_572])]) ).
fof(f11301,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| sP2(X3,relation_dom(X2),X4)
| ~ empty(X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_572 ),
inference(resolution,[],[f11143,f2532]) ).
fof(f11143,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ function(X0)
| sP2(X3,relation_dom(X2),X4)
| ~ empty(X4) )
| ~ spl22_572 ),
inference(avatar_component_clause,[],[f11142]) ).
fof(f38334,plain,
( spl22_1189
| ~ spl22_232
| ~ spl22_571 ),
inference(avatar_split_clause,[],[f11272,f11138,f2531,f38332]) ).
fof(f38332,plain,
( spl22_1189
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1189])]) ).
fof(f11138,plain,
( spl22_571
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_571])]) ).
fof(f11272,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X4)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_571 ),
inference(resolution,[],[f11139,f2532]) ).
fof(f11139,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X4) )
| ~ spl22_571 ),
inference(avatar_component_clause,[],[f11138]) ).
fof(f38330,plain,
( spl22_1188
| ~ spl22_232
| ~ spl22_570 ),
inference(avatar_split_clause,[],[f11243,f11134,f2531,f38328]) ).
fof(f38328,plain,
( spl22_1188
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1188])]) ).
fof(f11134,plain,
( spl22_570
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_570])]) ).
fof(f11243,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_570 ),
inference(resolution,[],[f11135,f2532]) ).
fof(f11135,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ function(X0)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X3) )
| ~ spl22_570 ),
inference(avatar_component_clause,[],[f11134]) ).
fof(f38326,plain,
( spl22_1187
| ~ spl22_232
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5147,f5122,f2531,f38324]) ).
fof(f38324,plain,
( spl22_1187
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sP0(X2,apply(X1,X0))
| ~ empty(relation_dom(X2))
| sK7(X1,sK7(X2,apply(X1,X0))) = apply(X1,sK8(X1,sK7(X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK7(X2,apply(X1,X0))),sK7(X1,sK7(X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK7(X2,apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1187])]) ).
fof(f5122,plain,
( spl22_395
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP0(X1,apply(X0,X2))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_395])]) ).
fof(f5147,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| sP0(X2,apply(X1,X0))
| ~ empty(relation_dom(X2))
| sK7(X1,sK7(X2,apply(X1,X0))) = apply(X1,sK8(X1,sK7(X2,apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK7(X2,apply(X1,X0))),sK7(X1,sK7(X2,apply(X1,X0)))) = apply(sK5,sK7(X1,sK7(X2,apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_395 ),
inference(resolution,[],[f5123,f2532]) ).
fof(f5123,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP0(X1,apply(X0,X2))
| ~ empty(relation_dom(X1)) )
| ~ spl22_395 ),
inference(avatar_component_clause,[],[f5122]) ).
fof(f37145,plain,
( spl22_1186
| ~ spl22_132
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15707,f15680,f1242,f37143]) ).
fof(f15680,plain,
( spl22_718
<=> ! [X0] :
( ~ sP0(sK5,X0)
| in(apply(sK5,sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_718])]) ).
fof(f15707,plain,
( ! [X0] :
( ~ sP0(sK5,sK6(X0))
| element(apply(sK5,sK4),X0)
| empty(X0) )
| ~ spl22_132
| ~ spl22_718 ),
inference(resolution,[],[f15681,f1243]) ).
fof(f15681,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(sK5,X0) )
| ~ spl22_718 ),
inference(avatar_component_clause,[],[f15680]) ).
fof(f37075,plain,
( spl22_1185
| ~ spl22_230
| ~ spl22_458 ),
inference(avatar_split_clause,[],[f7889,f6401,f2489,f37073]) ).
fof(f37073,plain,
( spl22_1185
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| element(sK13(sK13(powerset(X0),X1,X2),X3,X4),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(sK13(powerset(X0),X1,X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(powerset(X0),X1,X2),X3,X4)) = apply(sK5,sK13(sK13(powerset(X0),X1,X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1185])]) ).
fof(f6401,plain,
( spl22_458
<=> ! [X0,X3,X2,X1] :
( in(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_458])]) ).
fof(f7889,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| element(sK13(sK13(powerset(X0),X1,X2),X3,X4),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(sK13(powerset(X0),X1,X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(powerset(X0),X1,X2),X3,X4)) = apply(sK5,sK13(sK13(powerset(X0),X1,X2),X3,X4)) )
| ~ spl22_230
| ~ spl22_458 ),
inference(resolution,[],[f6402,f2490]) ).
fof(f6402,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(powerset(X0),X1,X2))
| sP2(powerset(X0),X1,X2)
| element(X3,X0)
| in(sK13(powerset(X0),X1,X2),X2) )
| ~ spl22_458 ),
inference(avatar_component_clause,[],[f6401]) ).
fof(f37071,plain,
( spl22_1184
| ~ spl22_228
| ~ spl22_458 ),
inference(avatar_split_clause,[],[f7885,f6401,f2447,f37069]) ).
fof(f37069,plain,
( spl22_1184
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| element(sK13(X3,sK13(powerset(X0),X1,X2),X4),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,sK13(powerset(X0),X1,X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(powerset(X0),X1,X2),X4)) = apply(sK5,sK13(X3,sK13(powerset(X0),X1,X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1184])]) ).
fof(f7885,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| element(sK13(X3,sK13(powerset(X0),X1,X2),X4),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,sK13(powerset(X0),X1,X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(powerset(X0),X1,X2),X4)) = apply(sK5,sK13(X3,sK13(powerset(X0),X1,X2),X4)) )
| ~ spl22_228
| ~ spl22_458 ),
inference(resolution,[],[f6402,f2448]) ).
fof(f37067,plain,
( spl22_1183
| ~ spl22_231
| ~ spl22_458 ),
inference(avatar_split_clause,[],[f7884,f6401,f2510,f37065]) ).
fof(f37065,plain,
( spl22_1183
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| element(sK13(X3,X4,sK13(powerset(X0),X1,X2)),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(powerset(X0),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1183])]) ).
fof(f7884,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| element(sK13(X3,X4,sK13(powerset(X0),X1,X2)),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(powerset(X0),X1,X2))) )
| ~ spl22_231
| ~ spl22_458 ),
inference(resolution,[],[f6402,f2511]) ).
fof(f37063,plain,
( spl22_1182
| ~ spl22_229
| ~ spl22_458 ),
inference(avatar_split_clause,[],[f7883,f6401,f2468,f37061]) ).
fof(f37061,plain,
( spl22_1182
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| element(sK13(X3,X4,sK13(powerset(X0),X1,X2)),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(powerset(X0),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1182])]) ).
fof(f7883,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| element(sK13(X3,X4,sK13(powerset(X0),X1,X2)),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(powerset(X0),X1,X2))) )
| ~ spl22_229
| ~ spl22_458 ),
inference(resolution,[],[f6402,f2469]) ).
fof(f37059,plain,
( spl22_1181
| ~ spl22_230
| ~ spl22_454 ),
inference(avatar_split_clause,[],[f7688,f6385,f2489,f37057]) ).
fof(f37057,plain,
( spl22_1181
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(sK13(X0,X1,powerset(X2)),X3,X4),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1181])]) ).
fof(f6385,plain,
( spl22_454
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_454])]) ).
fof(f7688,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(sK13(X0,X1,powerset(X2)),X3,X4),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) )
| ~ spl22_230
| ~ spl22_454 ),
inference(resolution,[],[f6386,f2490]) ).
fof(f6386,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,X1,powerset(X2)))
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| in(sK13(X0,X1,powerset(X2)),X0) )
| ~ spl22_454 ),
inference(avatar_component_clause,[],[f6385]) ).
fof(f37055,plain,
( spl22_1180
| ~ spl22_228
| ~ spl22_454 ),
inference(avatar_split_clause,[],[f7684,f6385,f2447,f37053]) ).
fof(f37053,plain,
( spl22_1180
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,sK13(X0,X1,powerset(X2)),X4),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1180])]) ).
fof(f7684,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,sK13(X0,X1,powerset(X2)),X4),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) )
| ~ spl22_228
| ~ spl22_454 ),
inference(resolution,[],[f6386,f2448]) ).
fof(f37051,plain,
( spl22_1179
| ~ spl22_231
| ~ spl22_454 ),
inference(avatar_split_clause,[],[f7683,f6385,f2510,f37049]) ).
fof(f37049,plain,
( spl22_1179
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1179])]) ).
fof(f7683,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_231
| ~ spl22_454 ),
inference(resolution,[],[f6386,f2511]) ).
fof(f37047,plain,
( spl22_1178
| ~ spl22_229
| ~ spl22_454 ),
inference(avatar_split_clause,[],[f7682,f6385,f2468,f37045]) ).
fof(f37045,plain,
( spl22_1178
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1178])]) ).
fof(f7682,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_229
| ~ spl22_454 ),
inference(resolution,[],[f6386,f2469]) ).
fof(f37043,plain,
( spl22_1177
| ~ spl22_230
| ~ spl22_450 ),
inference(avatar_split_clause,[],[f7484,f6361,f2489,f37041]) ).
fof(f37041,plain,
( spl22_1177
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| element(sK13(sK13(X0,powerset(X1),X2),X3,X4),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(sK13(X0,powerset(X1),X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,powerset(X1),X2),X3,X4)) = apply(sK5,sK13(sK13(X0,powerset(X1),X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1177])]) ).
fof(f6361,plain,
( spl22_450
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_450])]) ).
fof(f7484,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| element(sK13(sK13(X0,powerset(X1),X2),X3,X4),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(sK13(X0,powerset(X1),X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,powerset(X1),X2),X3,X4)) = apply(sK5,sK13(sK13(X0,powerset(X1),X2),X3,X4)) )
| ~ spl22_230
| ~ spl22_450 ),
inference(resolution,[],[f6362,f2490]) ).
fof(f6362,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,powerset(X1),X2))
| sP2(X0,powerset(X1),X2)
| element(X3,X1)
| in(sK13(X0,powerset(X1),X2),X2) )
| ~ spl22_450 ),
inference(avatar_component_clause,[],[f6361]) ).
fof(f37039,plain,
( spl22_1176
| ~ spl22_290
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15693,f15680,f3304,f37037]) ).
fof(f37037,plain,
( spl22_1176
<=> ! [X0,X1] :
( ~ sP0(sK5,relation_rng(X0))
| ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1176])]) ).
fof(f15693,plain,
( ! [X0,X1] :
( ~ sP0(sK5,relation_rng(X0))
| ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_290
| ~ spl22_718 ),
inference(resolution,[],[f15681,f3305]) ).
fof(f37035,plain,
( spl22_1175
| ~ spl22_228
| ~ spl22_450 ),
inference(avatar_split_clause,[],[f7480,f6361,f2447,f37033]) ).
fof(f37033,plain,
( spl22_1175
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| element(sK13(X3,sK13(X0,powerset(X1),X2),X4),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,sK13(X0,powerset(X1),X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,powerset(X1),X2),X4)) = apply(sK5,sK13(X3,sK13(X0,powerset(X1),X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1175])]) ).
fof(f7480,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| element(sK13(X3,sK13(X0,powerset(X1),X2),X4),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,sK13(X0,powerset(X1),X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,powerset(X1),X2),X4)) = apply(sK5,sK13(X3,sK13(X0,powerset(X1),X2),X4)) )
| ~ spl22_228
| ~ spl22_450 ),
inference(resolution,[],[f6362,f2448]) ).
fof(f37031,plain,
( spl22_1174
| ~ spl22_231
| ~ spl22_450 ),
inference(avatar_split_clause,[],[f7479,f6361,f2510,f37029]) ).
fof(f37029,plain,
( spl22_1174
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| element(sK13(X3,X4,sK13(X0,powerset(X1),X2)),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,powerset(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1174])]) ).
fof(f7479,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| element(sK13(X3,X4,sK13(X0,powerset(X1),X2)),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,powerset(X1),X2))) )
| ~ spl22_231
| ~ spl22_450 ),
inference(resolution,[],[f6362,f2511]) ).
fof(f37027,plain,
( spl22_1173
| ~ spl22_229
| ~ spl22_450 ),
inference(avatar_split_clause,[],[f7478,f6361,f2468,f37025]) ).
fof(f37025,plain,
( spl22_1173
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| element(sK13(X3,X4,sK13(X0,powerset(X1),X2)),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,powerset(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1173])]) ).
fof(f7478,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| element(sK13(X3,X4,sK13(X0,powerset(X1),X2)),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,powerset(X1),X2))) )
| ~ spl22_229
| ~ spl22_450 ),
inference(resolution,[],[f6362,f2469]) ).
fof(f37023,plain,
( spl22_1172
| ~ spl22_230
| ~ spl22_446 ),
inference(avatar_split_clause,[],[f7293,f6345,f2489,f37021]) ).
fof(f37021,plain,
( spl22_1172
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(sK13(X0,X1,powerset(X2)),X3,X4),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1172])]) ).
fof(f6345,plain,
( spl22_446
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_446])]) ).
fof(f7293,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(sK13(X0,X1,powerset(X2)),X3,X4),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) )
| ~ spl22_230
| ~ spl22_446 ),
inference(resolution,[],[f6346,f2490]) ).
fof(f6346,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,X1,powerset(X2)))
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| in(sK13(X0,X1,powerset(X2)),X1) )
| ~ spl22_446 ),
inference(avatar_component_clause,[],[f6345]) ).
fof(f37019,plain,
( spl22_1171
| ~ spl22_228
| ~ spl22_446 ),
inference(avatar_split_clause,[],[f7289,f6345,f2447,f37017]) ).
fof(f37017,plain,
( spl22_1171
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,sK13(X0,X1,powerset(X2)),X4),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1171])]) ).
fof(f7289,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,sK13(X0,X1,powerset(X2)),X4),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) )
| ~ spl22_228
| ~ spl22_446 ),
inference(resolution,[],[f6346,f2448]) ).
fof(f37015,plain,
( spl22_1170
| ~ spl22_231
| ~ spl22_446 ),
inference(avatar_split_clause,[],[f7288,f6345,f2510,f37013]) ).
fof(f37013,plain,
( spl22_1170
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1170])]) ).
fof(f7288,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_231
| ~ spl22_446 ),
inference(resolution,[],[f6346,f2511]) ).
fof(f37011,plain,
( spl22_1169
| ~ spl22_229
| ~ spl22_446 ),
inference(avatar_split_clause,[],[f7287,f6345,f2468,f37009]) ).
fof(f37009,plain,
( spl22_1169
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1169])]) ).
fof(f7287,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| element(sK13(X3,X4,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_229
| ~ spl22_446 ),
inference(resolution,[],[f6346,f2469]) ).
fof(f36430,plain,
( spl22_1168
| ~ spl22_27
| ~ spl22_726 ),
inference(avatar_split_clause,[],[f35932,f15781,f351,f36427]) ).
fof(f36427,plain,
( spl22_1168
<=> function(apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1168])]) ).
fof(f35932,plain,
( function(apply(sK5,sK4))
| ~ spl22_27
| ~ spl22_726 ),
inference(resolution,[],[f15783,f352]) ).
fof(f15783,plain,
( empty(apply(sK5,sK4))
| ~ spl22_726 ),
inference(avatar_component_clause,[],[f15781]) ).
fof(f35931,plain,
( spl22_726
| ~ spl22_119
| ~ spl22_739 ),
inference(avatar_split_clause,[],[f35725,f15881,f1064,f15781]) ).
fof(f15881,plain,
( spl22_739
<=> ! [X0] : ~ in(X0,apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_739])]) ).
fof(f35725,plain,
( empty(apply(sK5,sK4))
| ~ spl22_119
| ~ spl22_739 ),
inference(resolution,[],[f15882,f1065]) ).
fof(f15882,plain,
( ! [X0] : ~ in(X0,apply(sK5,sK4))
| ~ spl22_739 ),
inference(avatar_component_clause,[],[f15881]) ).
fof(f35891,plain,
( spl22_1167
| ~ spl22_233
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5057,f4944,f2559,f35889]) ).
fof(f35889,plain,
( spl22_1167
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1167])]) ).
fof(f5057,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_391 ),
inference(resolution,[],[f4945,f2560]) ).
fof(f35887,plain,
( spl22_1166
| ~ spl22_233
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5027,f4940,f2559,f35885]) ).
fof(f35885,plain,
( spl22_1166
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1166])]) ).
fof(f5027,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_390 ),
inference(resolution,[],[f4941,f2560]) ).
fof(f35883,plain,
( spl22_1165
| ~ spl22_233
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4993,f4902,f2559,f35881]) ).
fof(f35881,plain,
( spl22_1165
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1165])]) ).
fof(f4993,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_388 ),
inference(resolution,[],[f4903,f2560]) ).
fof(f35879,plain,
( spl22_1164
| ~ spl22_233
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4965,f4898,f2559,f35877]) ).
fof(f35877,plain,
( spl22_1164
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1164])]) ).
fof(f4965,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_387 ),
inference(resolution,[],[f4899,f2560]) ).
fof(f35875,plain,
( spl22_1163
| ~ spl22_47
| ~ spl22_311 ),
inference(avatar_split_clause,[],[f3567,f3543,f462,f35873]) ).
fof(f35873,plain,
( spl22_1163
<=> ! [X0,X1] :
( sP0(X0,X1)
| element(sK7(X0,X1),X1)
| ~ empty(relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1163])]) ).
fof(f3567,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| element(sK7(X0,X1),X1)
| ~ empty(relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_311 ),
inference(resolution,[],[f3544,f463]) ).
fof(f35871,plain,
( spl22_1162
| ~ spl22_47
| ~ spl22_310 ),
inference(avatar_split_clause,[],[f3560,f3538,f462,f35869]) ).
fof(f35869,plain,
( spl22_1162
<=> ! [X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1162])]) ).
fof(f3560,plain,
( ! [X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_310 ),
inference(resolution,[],[f3539,f463]) ).
fof(f35867,plain,
( spl22_1161
| ~ spl22_138
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3359,f3304,f1286,f35865]) ).
fof(f35865,plain,
( spl22_1161
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1161])]) ).
fof(f3359,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),relation_rng(X0)) )
| ~ spl22_138
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1287]) ).
fof(f35863,plain,
( spl22_1160
| ~ spl22_139
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3358,f3304,f1290,f35861]) ).
fof(f35861,plain,
( spl22_1160
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1160])]) ).
fof(f3358,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,relation_rng(X0)) )
| ~ spl22_139
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1291]) ).
fof(f35697,plain,
( spl22_739
| spl22_1159
| ~ spl22_63
| ~ spl22_716 ),
inference(avatar_split_clause,[],[f15672,f15668,f586,f35695,f15881]) ).
fof(f35695,plain,
( spl22_1159
<=> ! [X0] :
( ~ sP0(sK5,powerset(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1159])]) ).
fof(f15668,plain,
( spl22_716
<=> ! [X0] :
( ~ sP0(sK5,X0)
| element(apply(sK5,sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_716])]) ).
fof(f15672,plain,
( ! [X0,X1] :
( ~ sP0(sK5,powerset(X0))
| ~ empty(X0)
| ~ in(X1,apply(sK5,sK4)) )
| ~ spl22_63
| ~ spl22_716 ),
inference(resolution,[],[f15669,f587]) ).
fof(f15669,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(sK5,X0) )
| ~ spl22_716 ),
inference(avatar_component_clause,[],[f15668]) ).
fof(f35693,plain,
( spl22_1158
| ~ spl22_61
| ~ spl22_267 ),
inference(avatar_split_clause,[],[f3195,f2955,f578,f35691]) ).
fof(f35691,plain,
( spl22_1158
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ empty(X1)
| relation_rng(X0) = sK10(powerset(X1))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1158])]) ).
fof(f2955,plain,
( spl22_267
<=> ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| ~ empty(relation_dom(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_267])]) ).
fof(f3195,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ empty(X1)
| relation_rng(X0) = sK10(powerset(X1))
| ~ sP1(X0) )
| ~ spl22_61
| ~ spl22_267 ),
inference(resolution,[],[f2956,f579]) ).
fof(f2956,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| ~ empty(relation_dom(X0))
| ~ empty(X1) )
| ~ spl22_267 ),
inference(avatar_component_clause,[],[f2955]) ).
fof(f35689,plain,
( spl22_1157
| ~ spl22_69
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2834,f2743,f628,f35687]) ).
fof(f35687,plain,
( spl22_1157
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1157])]) ).
fof(f2834,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,relation_rng(X0)) )
| ~ spl22_69
| ~ spl22_248 ),
inference(resolution,[],[f2744,f629]) ).
fof(f35539,plain,
( spl22_1156
| ~ spl22_232
| ~ spl22_565 ),
inference(avatar_split_clause,[],[f10952,f10946,f2531,f35537]) ).
fof(f35537,plain,
( spl22_1156
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| sP0(X3,relation_dom(X2))
| ~ empty(relation_dom(X3))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1156])]) ).
fof(f10946,plain,
( spl22_565
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP0(X3,relation_dom(X2))
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_565])]) ).
fof(f10952,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| sP0(X3,relation_dom(X2))
| ~ empty(relation_dom(X3))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_565 ),
inference(resolution,[],[f10947,f2532]) ).
fof(f10947,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ function(X0)
| sP0(X3,relation_dom(X2))
| ~ empty(relation_dom(X3)) )
| ~ spl22_565 ),
inference(avatar_component_clause,[],[f10946]) ).
fof(f35535,plain,
( spl22_1155
| ~ spl22_216
| ~ spl22_549 ),
inference(avatar_split_clause,[],[f10689,f10647,f2344,f35533]) ).
fof(f35533,plain,
( spl22_1155
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK7(X3,relation_rng(X2))))) = apply(X0,apply(X2,sK9(X2,sK7(X3,relation_rng(X2)))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP0(X3,relation_rng(X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,relation_rng(X2))) = apply(sK5,sK8(X3,relation_rng(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1155])]) ).
fof(f10689,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,sK7(X3,relation_rng(X2))))) = apply(X0,apply(X2,sK9(X2,sK7(X3,relation_rng(X2)))))
| ~ sP0(X2,X1)
| ~ function(X0)
| ~ sP1(X2)
| sP0(X3,relation_rng(X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,relation_rng(X2))) = apply(sK5,sK8(X3,relation_rng(X2))) )
| ~ spl22_216
| ~ spl22_549 ),
inference(resolution,[],[f10648,f2345]) ).
fof(f35531,plain,
( spl22_1154
| spl22_11
| ~ spl22_696 ),
inference(avatar_split_clause,[],[f15266,f15221,f274,f35528]) ).
fof(f35528,plain,
( spl22_1154
<=> apply(relation_dom_restriction(sK5,sK16),sK10(sK16)) = apply(sK5,sK10(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1154])]) ).
fof(f274,plain,
( spl22_11
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_11])]) ).
fof(f15221,plain,
( spl22_696
<=> ! [X0] :
( apply(relation_dom_restriction(sK5,X0),sK10(X0)) = apply(sK5,sK10(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_696])]) ).
fof(f15266,plain,
( apply(relation_dom_restriction(sK5,sK16),sK10(sK16)) = apply(sK5,sK10(sK16))
| spl22_11
| ~ spl22_696 ),
inference(resolution,[],[f15222,f276]) ).
fof(f276,plain,
( ~ empty(sK16)
| spl22_11 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f15222,plain,
( ! [X0] :
( empty(X0)
| apply(relation_dom_restriction(sK5,X0),sK10(X0)) = apply(sK5,sK10(X0)) )
| ~ spl22_696 ),
inference(avatar_component_clause,[],[f15221]) ).
fof(f35526,plain,
( spl22_1153
| ~ spl22_230
| ~ spl22_477 ),
inference(avatar_split_clause,[],[f8928,f8377,f2489,f35524]) ).
fof(f35524,plain,
( spl22_1153
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(sK7(X0,powerset(X1)),X2,X3),X1)
| sP0(X0,powerset(X1))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1153])]) ).
fof(f8377,plain,
( spl22_477
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_477])]) ).
fof(f8928,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(sK7(X0,powerset(X1)),X2,X3),X1)
| sP0(X0,powerset(X1))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) )
| ~ spl22_230
| ~ spl22_477 ),
inference(resolution,[],[f8378,f2490]) ).
fof(f8378,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(X2,X1)
| sP0(X0,powerset(X1)) )
| ~ spl22_477 ),
inference(avatar_component_clause,[],[f8377]) ).
fof(f35522,plain,
( spl22_1152
| ~ spl22_228
| ~ spl22_477 ),
inference(avatar_split_clause,[],[f8924,f8377,f2447,f35520]) ).
fof(f35520,plain,
( spl22_1152
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(X2,sK7(X0,powerset(X1)),X3),X1)
| sP0(X0,powerset(X1))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1152])]) ).
fof(f8924,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(X2,sK7(X0,powerset(X1)),X3),X1)
| sP0(X0,powerset(X1))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) )
| ~ spl22_228
| ~ spl22_477 ),
inference(resolution,[],[f8378,f2448]) ).
fof(f35518,plain,
( spl22_1151
| ~ spl22_231
| ~ spl22_477 ),
inference(avatar_split_clause,[],[f8923,f8377,f2510,f35516]) ).
fof(f35516,plain,
( spl22_1151
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1151])]) ).
fof(f8923,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_231
| ~ spl22_477 ),
inference(resolution,[],[f8378,f2511]) ).
fof(f35514,plain,
( spl22_1150
| ~ spl22_229
| ~ spl22_477 ),
inference(avatar_split_clause,[],[f8922,f8377,f2468,f35512]) ).
fof(f35512,plain,
( spl22_1150
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1150])]) ).
fof(f8922,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_229
| ~ spl22_477 ),
inference(resolution,[],[f8378,f2469]) ).
fof(f35069,plain,
( spl22_1149
| ~ spl22_228
| ~ spl22_591 ),
inference(avatar_split_clause,[],[f11815,f11741,f2447,f35067]) ).
fof(f35067,plain,
( spl22_1149
<=> ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X1)
| sP2(X0,X1,set_intersection2(X2,X1))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X1)),sK13(X0,X1,set_intersection2(X2,X1))) = apply(sK5,sK13(X0,X1,set_intersection2(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1149])]) ).
fof(f11741,plain,
( spl22_591
<=> ! [X0,X3,X2,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_591])]) ).
fof(f11815,plain,
( ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X1)
| sP2(X0,X1,set_intersection2(X2,X1))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X1)),sK13(X0,X1,set_intersection2(X2,X1))) = apply(sK5,sK13(X0,X1,set_intersection2(X2,X1))) )
| ~ spl22_228
| ~ spl22_591 ),
inference(duplicate_literal_removal,[],[f11763]) ).
fof(f11763,plain,
( ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X1)),X1)
| sP2(X0,X1,set_intersection2(X2,X1))
| sP2(X0,X1,set_intersection2(X2,X1))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X1)),sK13(X0,X1,set_intersection2(X2,X1))) = apply(sK5,sK13(X0,X1,set_intersection2(X2,X1))) )
| ~ spl22_228
| ~ spl22_591 ),
inference(resolution,[],[f11742,f2448]) ).
fof(f11742,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_591 ),
inference(avatar_component_clause,[],[f11741]) ).
fof(f35065,plain,
( spl22_1148
| spl22_9
| ~ spl22_696 ),
inference(avatar_split_clause,[],[f15265,f15221,f264,f35062]) ).
fof(f35062,plain,
( spl22_1148
<=> apply(relation_dom_restriction(sK5,sK14),sK10(sK14)) = apply(sK5,sK10(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1148])]) ).
fof(f264,plain,
( spl22_9
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_9])]) ).
fof(f15265,plain,
( apply(relation_dom_restriction(sK5,sK14),sK10(sK14)) = apply(sK5,sK10(sK14))
| spl22_9
| ~ spl22_696 ),
inference(resolution,[],[f15222,f266]) ).
fof(f266,plain,
( ~ empty(sK14)
| spl22_9 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f35060,plain,
( spl22_1147
| ~ spl22_230
| ~ spl22_591 ),
inference(avatar_split_clause,[],[f11810,f11741,f2489,f35058]) ).
fof(f35058,plain,
( spl22_1147
<=> ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X1)
| sP2(X0,X1,set_intersection2(X2,X0))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X0)),sK13(X0,X1,set_intersection2(X2,X0))) = apply(sK5,sK13(X0,X1,set_intersection2(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1147])]) ).
fof(f11810,plain,
( ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X1)
| sP2(X0,X1,set_intersection2(X2,X0))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X0)),sK13(X0,X1,set_intersection2(X2,X0))) = apply(sK5,sK13(X0,X1,set_intersection2(X2,X0))) )
| ~ spl22_230
| ~ spl22_591 ),
inference(duplicate_literal_removal,[],[f11770]) ).
fof(f11770,plain,
( ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X0)),X1)
| sP2(X0,X1,set_intersection2(X2,X0))
| sP2(X0,X1,set_intersection2(X2,X0))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X0)),sK13(X0,X1,set_intersection2(X2,X0))) = apply(sK5,sK13(X0,X1,set_intersection2(X2,X0))) )
| ~ spl22_230
| ~ spl22_591 ),
inference(resolution,[],[f11742,f2490]) ).
fof(f35056,plain,
( spl22_1146
| ~ spl22_232
| ~ spl22_552 ),
inference(avatar_split_clause,[],[f10887,f10806,f2531,f35054]) ).
fof(f35054,plain,
( spl22_1146
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1146])]) ).
fof(f10806,plain,
( spl22_552
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ sP0(X2,X1)
| in(sK7(X2,X3),X3)
| sP0(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_552])]) ).
fof(f10887,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_552 ),
inference(resolution,[],[f10807,f2532]) ).
fof(f10807,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| in(sK7(X2,X3),X3)
| sP0(X2,X3) )
| ~ spl22_552 ),
inference(avatar_component_clause,[],[f10806]) ).
fof(f35052,plain,
( spl22_1145
| ~ spl22_232
| ~ spl22_551 ),
inference(avatar_split_clause,[],[f10873,f10802,f2531,f35050]) ).
fof(f35050,plain,
( spl22_1145
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| element(sK7(X2,X3),X3)
| sP0(X2,X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1145])]) ).
fof(f10802,plain,
( spl22_551
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ sP0(X2,X1)
| element(sK7(X2,X3),X3)
| sP0(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_551])]) ).
fof(f10873,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| element(sK7(X2,X3),X3)
| sP0(X2,X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_551 ),
inference(resolution,[],[f10803,f2532]) ).
fof(f10803,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| element(sK7(X2,X3),X3)
| sP0(X2,X3) )
| ~ spl22_551 ),
inference(avatar_component_clause,[],[f10802]) ).
fof(f35048,plain,
( spl22_1144
| ~ spl22_83
| ~ spl22_215 ),
inference(avatar_split_clause,[],[f2319,f2316,f742,f35046]) ).
fof(f35046,plain,
( spl22_1144
<=> ! [X2,X0,X1] :
( sP0(relation_dom_restriction(X0,X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK7(relation_dom_restriction(X0,X1),X2)) = apply(sK5,sK7(relation_dom_restriction(X0,X1),X2))
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1144])]) ).
fof(f2316,plain,
( spl22_215
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK5,X0),sK7(X1,X0)) = apply(sK5,sK7(X1,X0))
| sP0(X1,X0)
| in(sK8(X1,X0),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_215])]) ).
fof(f2319,plain,
( ! [X2,X0,X1] :
( sP0(relation_dom_restriction(X0,X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK7(relation_dom_restriction(X0,X1),X2)) = apply(sK5,sK7(relation_dom_restriction(X0,X1),X2))
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_215 ),
inference(resolution,[],[f2317,f743]) ).
fof(f2317,plain,
( ! [X0,X1] :
( in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0)
| apply(relation_dom_restriction(sK5,X0),sK7(X1,X0)) = apply(sK5,sK7(X1,X0)) )
| ~ spl22_215 ),
inference(avatar_component_clause,[],[f2316]) ).
fof(f33922,plain,
( spl22_1143
| ~ spl22_230
| ~ spl22_470 ),
inference(avatar_split_clause,[],[f8774,f8349,f2489,f33920]) ).
fof(f33920,plain,
( spl22_1143
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(relation_rng(X0),X2,X3))) = apply(X1,sK9(X0,sK13(relation_rng(X0),X2,X3)))
| ~ function(X1)
| ~ relation(X1)
| sP2(relation_rng(X0),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_rng(X0),X2,X3)) = apply(sK5,sK13(relation_rng(X0),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1143])]) ).
fof(f8349,plain,
( spl22_470
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| apply(relation_dom_restriction(X2,relation_dom(X1)),sK9(X1,X0)) = apply(X2,sK9(X1,X0))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_470])]) ).
fof(f8774,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(relation_rng(X0),X2,X3))) = apply(X1,sK9(X0,sK13(relation_rng(X0),X2,X3)))
| ~ function(X1)
| ~ relation(X1)
| sP2(relation_rng(X0),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_rng(X0),X2,X3)) = apply(sK5,sK13(relation_rng(X0),X2,X3)) )
| ~ spl22_230
| ~ spl22_470 ),
inference(resolution,[],[f8350,f2490]) ).
fof(f8350,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| apply(relation_dom_restriction(X2,relation_dom(X1)),sK9(X1,X0)) = apply(X2,sK9(X1,X0))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_470 ),
inference(avatar_component_clause,[],[f8349]) ).
fof(f33918,plain,
( spl22_1142
| ~ spl22_228
| ~ spl22_470 ),
inference(avatar_split_clause,[],[f8770,f8349,f2447,f33916]) ).
fof(f33916,plain,
( spl22_1142
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(X2,relation_rng(X0),X3))) = apply(X1,sK9(X0,sK13(X2,relation_rng(X0),X3)))
| ~ function(X1)
| ~ relation(X1)
| sP2(X2,relation_rng(X0),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,relation_rng(X0),X3)) = apply(sK5,sK13(X2,relation_rng(X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1142])]) ).
fof(f8770,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(X2,relation_rng(X0),X3))) = apply(X1,sK9(X0,sK13(X2,relation_rng(X0),X3)))
| ~ function(X1)
| ~ relation(X1)
| sP2(X2,relation_rng(X0),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,relation_rng(X0),X3)) = apply(sK5,sK13(X2,relation_rng(X0),X3)) )
| ~ spl22_228
| ~ spl22_470 ),
inference(resolution,[],[f8350,f2448]) ).
fof(f33914,plain,
( spl22_1141
| ~ spl22_231
| ~ spl22_470 ),
inference(avatar_split_clause,[],[f8769,f8349,f2510,f33912]) ).
fof(f33912,plain,
( spl22_1141
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(X2,X3,relation_rng(X0)))) = apply(X1,sK9(X0,sK13(X2,X3,relation_rng(X0))))
| ~ function(X1)
| ~ relation(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1141])]) ).
fof(f8769,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(X2,X3,relation_rng(X0)))) = apply(X1,sK9(X0,sK13(X2,X3,relation_rng(X0))))
| ~ function(X1)
| ~ relation(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,relation_rng(X0))) )
| ~ spl22_231
| ~ spl22_470 ),
inference(resolution,[],[f8350,f2511]) ).
fof(f33910,plain,
( spl22_1140
| ~ spl22_229
| ~ spl22_470 ),
inference(avatar_split_clause,[],[f8768,f8349,f2468,f33908]) ).
fof(f33908,plain,
( spl22_1140
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(X2,X3,relation_rng(X0)))) = apply(X1,sK9(X0,sK13(X2,X3,relation_rng(X0))))
| ~ function(X1)
| ~ relation(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1140])]) ).
fof(f8768,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK13(X2,X3,relation_rng(X0)))) = apply(X1,sK9(X0,sK13(X2,X3,relation_rng(X0))))
| ~ function(X1)
| ~ relation(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,relation_rng(X0))) )
| ~ spl22_229
| ~ spl22_470 ),
inference(resolution,[],[f8350,f2469]) ).
fof(f33700,plain,
( spl22_1139
| ~ spl22_216
| ~ spl22_458 ),
inference(avatar_split_clause,[],[f7860,f6401,f2344,f33698]) ).
fof(f33698,plain,
( spl22_1139
<=> ! [X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| element(sK7(X3,sK13(powerset(X0),X1,X2)),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP0(X3,sK13(powerset(X0),X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(powerset(X0),X1,X2))) = apply(sK5,sK8(X3,sK13(powerset(X0),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1139])]) ).
fof(f7860,plain,
( ! [X2,X3,X0,X1] :
( sP2(powerset(X0),X1,X2)
| element(sK7(X3,sK13(powerset(X0),X1,X2)),X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP0(X3,sK13(powerset(X0),X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(powerset(X0),X1,X2))) = apply(sK5,sK8(X3,sK13(powerset(X0),X1,X2))) )
| ~ spl22_216
| ~ spl22_458 ),
inference(resolution,[],[f6402,f2345]) ).
fof(f33696,plain,
( spl22_1138
| ~ spl22_216
| ~ spl22_454 ),
inference(avatar_split_clause,[],[f7659,f6385,f2344,f33694]) ).
fof(f33694,plain,
( spl22_1138
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK7(X3,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1138])]) ).
fof(f7659,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK7(X3,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_216
| ~ spl22_454 ),
inference(resolution,[],[f6386,f2345]) ).
fof(f33692,plain,
( spl22_1137
| ~ spl22_216
| ~ spl22_450 ),
inference(avatar_split_clause,[],[f7455,f6361,f2344,f33690]) ).
fof(f33690,plain,
( spl22_1137
<=> ! [X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| element(sK7(X3,sK13(X0,powerset(X1),X2)),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP0(X3,sK13(X0,powerset(X1),X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,powerset(X1),X2))) = apply(sK5,sK8(X3,sK13(X0,powerset(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1137])]) ).
fof(f7455,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,powerset(X1),X2)
| element(sK7(X3,sK13(X0,powerset(X1),X2)),X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP0(X3,sK13(X0,powerset(X1),X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,powerset(X1),X2))) = apply(sK5,sK8(X3,sK13(X0,powerset(X1),X2))) )
| ~ spl22_216
| ~ spl22_450 ),
inference(resolution,[],[f6362,f2345]) ).
fof(f33688,plain,
( spl22_1136
| ~ spl22_216
| ~ spl22_446 ),
inference(avatar_split_clause,[],[f7264,f6345,f2344,f33686]) ).
fof(f33686,plain,
( spl22_1136
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK7(X3,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1136])]) ).
fof(f7264,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,powerset(X2))
| element(sK7(X3,sK13(X0,X1,powerset(X2))),X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_216
| ~ spl22_446 ),
inference(resolution,[],[f6346,f2345]) ).
fof(f33684,plain,
( spl22_1135
| ~ spl22_173
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2522,f2510,f1739,f33682]) ).
fof(f33682,plain,
( spl22_1135
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_dom(X2)))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK13(X0,X1,relation_dom(X2)))) = apply(X3,apply(X2,sK13(X0,X1,relation_dom(X2))))
| ~ sP0(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1135])]) ).
fof(f1739,plain,
( spl22_173
<=> ! [X0,X3,X2,X1] :
( apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_173])]) ).
fof(f2522,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_dom(X2)))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK13(X0,X1,relation_dom(X2)))) = apply(X3,apply(X2,sK13(X0,X1,relation_dom(X2))))
| ~ sP0(X2,X4) )
| ~ spl22_173
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1740]) ).
fof(f1740,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom(X2))
| ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3))
| ~ sP0(X2,X1) )
| ~ spl22_173 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f33680,plain,
( spl22_1134
| ~ spl22_173
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2501,f2489,f1739,f33678]) ).
fof(f33678,plain,
( spl22_1134
<=> ! [X4,X0,X3,X2,X1] :
( sP2(relation_dom(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_dom(X0),X1,X2)) = apply(sK5,sK13(relation_dom(X0),X1,X2))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X0,sK13(relation_dom(X0),X1,X2))) = apply(X3,apply(X0,sK13(relation_dom(X0),X1,X2)))
| ~ sP0(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1134])]) ).
fof(f2501,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(relation_dom(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_dom(X0),X1,X2)) = apply(sK5,sK13(relation_dom(X0),X1,X2))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X0,sK13(relation_dom(X0),X1,X2))) = apply(X3,apply(X0,sK13(relation_dom(X0),X1,X2)))
| ~ sP0(X0,X4) )
| ~ spl22_173
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1740]) ).
fof(f33676,plain,
( spl22_1133
| ~ spl22_173
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2480,f2468,f1739,f33674]) ).
fof(f33674,plain,
( spl22_1133
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_dom(X2)))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK13(X0,X1,relation_dom(X2)))) = apply(X3,apply(X2,sK13(X0,X1,relation_dom(X2))))
| ~ sP0(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1133])]) ).
fof(f2480,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_dom(X2)))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK13(X0,X1,relation_dom(X2)))) = apply(X3,apply(X2,sK13(X0,X1,relation_dom(X2))))
| ~ sP0(X2,X4) )
| ~ spl22_173
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1740]) ).
fof(f33672,plain,
( spl22_1132
| ~ spl22_173
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2459,f2447,f1739,f33670]) ).
fof(f33670,plain,
( spl22_1132
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,relation_dom(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,relation_dom(X1),X2)) = apply(sK5,sK13(X0,relation_dom(X1),X2))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X1,sK13(X0,relation_dom(X1),X2))) = apply(X3,apply(X1,sK13(X0,relation_dom(X1),X2)))
| ~ sP0(X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1132])]) ).
fof(f2459,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,relation_dom(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,relation_dom(X1),X2)) = apply(sK5,sK13(X0,relation_dom(X1),X2))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X1,sK13(X0,relation_dom(X1),X2))) = apply(X3,apply(X1,sK13(X0,relation_dom(X1),X2)))
| ~ sP0(X1,X4) )
| ~ spl22_173
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1740]) ).
fof(f33665,plain,
( spl22_1131
| ~ spl22_216
| ~ spl22_477 ),
inference(avatar_split_clause,[],[f8900,f8377,f2344,f33663]) ).
fof(f33663,plain,
( spl22_1131
<=> ! [X2,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK7(X2,sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1131])]) ).
fof(f8900,plain,
( ! [X2,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(sK7(X2,sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) )
| ~ spl22_216
| ~ spl22_477 ),
inference(resolution,[],[f8378,f2345]) ).
fof(f33661,plain,
( spl22_1130
| ~ spl22_53
| ~ spl22_1128 ),
inference(avatar_split_clause,[],[f33280,f31830,f511,f33659]) ).
fof(f33659,plain,
( spl22_1130
<=> ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK20)))
| ~ empty(relation_dom_restriction(sK20,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1130])]) ).
fof(f31830,plain,
( spl22_1128
<=> ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK20),X0))
| ~ empty(relation_dom_restriction(sK20,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1128])]) ).
fof(f33280,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK20)))
| ~ empty(relation_dom_restriction(sK20,X0)) )
| ~ spl22_53
| ~ spl22_1128 ),
inference(superposition,[],[f31831,f512]) ).
fof(f31831,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK20),X0))
| ~ empty(relation_dom_restriction(sK20,X0)) )
| ~ spl22_1128 ),
inference(avatar_component_clause,[],[f31830]) ).
fof(f33525,plain,
( spl22_1129
| ~ spl22_53
| ~ spl22_1121 ),
inference(avatar_split_clause,[],[f32567,f31696,f511,f33523]) ).
fof(f33523,plain,
( spl22_1129
<=> ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK19)))
| ~ empty(relation_dom_restriction(sK19,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1129])]) ).
fof(f31696,plain,
( spl22_1121
<=> ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK19),X0))
| ~ empty(relation_dom_restriction(sK19,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1121])]) ).
fof(f32567,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK19)))
| ~ empty(relation_dom_restriction(sK19,X0)) )
| ~ spl22_53
| ~ spl22_1121 ),
inference(superposition,[],[f31697,f512]) ).
fof(f31697,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK19),X0))
| ~ empty(relation_dom_restriction(sK19,X0)) )
| ~ spl22_1121 ),
inference(avatar_component_clause,[],[f31696]) ).
fof(f31832,plain,
( spl22_1128
| ~ spl22_809
| ~ spl22_1041 ),
inference(avatar_split_clause,[],[f28247,f28111,f17544,f31830]) ).
fof(f28247,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK20),X0))
| ~ empty(relation_dom_restriction(sK20,X0)) )
| ~ spl22_809
| ~ spl22_1041 ),
inference(superposition,[],[f17545,f28112]) ).
fof(f31722,plain,
( spl22_1127
| ~ spl22_121
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4650,f3994,f1110,f31720]) ).
fof(f31720,plain,
( spl22_1127
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(sK10(powerset(X2)),X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1127])]) ).
fof(f4650,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(sK10(powerset(X2)),X3))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_355 ),
inference(resolution,[],[f3995,f1111]) ).
fof(f31718,plain,
( spl22_1126
| ~ spl22_233
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4641,f3994,f2559,f31716]) ).
fof(f31716,plain,
( spl22_1126
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1126])]) ).
fof(f4641,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_355 ),
inference(resolution,[],[f3995,f2560]) ).
fof(f31714,plain,
( spl22_1125
| ~ spl22_121
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4616,f3990,f1110,f31712]) ).
fof(f31712,plain,
( spl22_1125
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,sK10(powerset(X3))))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1125])]) ).
fof(f4616,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,sK10(powerset(X3))))
| ~ empty(X3) )
| ~ spl22_121
| ~ spl22_354 ),
inference(resolution,[],[f3991,f1111]) ).
fof(f31710,plain,
( spl22_1124
| ~ spl22_233
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4607,f3990,f2559,f31708]) ).
fof(f31708,plain,
( spl22_1124
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1124])]) ).
fof(f4607,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_354 ),
inference(resolution,[],[f3991,f2560]) ).
fof(f31706,plain,
( spl22_1123
| ~ spl22_121
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4576,f3978,f1110,f31704]) ).
fof(f31704,plain,
( spl22_1123
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(sK10(powerset(X1)),X2),X3,X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1123])]) ).
fof(f4576,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(sK10(powerset(X1)),X2),X3,X0)
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_351 ),
inference(resolution,[],[f3979,f1111]) ).
fof(f31702,plain,
( spl22_1122
| ~ spl22_233
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4567,f3978,f2559,f31700]) ).
fof(f31700,plain,
( spl22_1122
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(relation_dom(X1),X2),X3,X0)
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1122])]) ).
fof(f4567,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(relation_dom(X1),X2),X3,X0)
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_351 ),
inference(resolution,[],[f3979,f2560]) ).
fof(f31698,plain,
( spl22_1121
| ~ spl22_809
| ~ spl22_1040 ),
inference(avatar_split_clause,[],[f28084,f27948,f17544,f31696]) ).
fof(f28084,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK19),X0))
| ~ empty(relation_dom_restriction(sK19,X0)) )
| ~ spl22_809
| ~ spl22_1040 ),
inference(superposition,[],[f17545,f27949]) ).
fof(f31694,plain,
( spl22_1120
| ~ spl22_121
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4544,f3974,f1110,f31692]) ).
fof(f31692,plain,
( spl22_1120
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,sK10(powerset(X2))),X3,X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1120])]) ).
fof(f4544,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,sK10(powerset(X2))),X3,X0)
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_350 ),
inference(resolution,[],[f3975,f1111]) ).
fof(f31690,plain,
( spl22_1119
| ~ spl22_233
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4535,f3974,f2559,f31688]) ).
fof(f31688,plain,
( spl22_1119
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_dom(X2)),X3,X0)
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1119])]) ).
fof(f4535,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,relation_dom(X2)),X3,X0)
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_350 ),
inference(resolution,[],[f3975,f2560]) ).
fof(f31686,plain,
( spl22_1118
| ~ spl22_121
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4504,f3962,f1110,f31684]) ).
fof(f31684,plain,
( spl22_1118
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(sK10(powerset(X2)),X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1118])]) ).
fof(f4504,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(sK10(powerset(X2)),X3))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_347 ),
inference(resolution,[],[f3963,f1111]) ).
fof(f31682,plain,
( spl22_1117
| ~ spl22_233
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4495,f3962,f2559,f31680]) ).
fof(f31680,plain,
( spl22_1117
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1117])]) ).
fof(f4495,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(relation_dom(X2),X3))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_347 ),
inference(resolution,[],[f3963,f2560]) ).
fof(f31678,plain,
( spl22_1116
| ~ spl22_121
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4474,f3958,f1110,f31676]) ).
fof(f31676,plain,
( spl22_1116
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,sK10(powerset(X3))))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1116])]) ).
fof(f4474,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,sK10(powerset(X3))))
| ~ empty(X3) )
| ~ spl22_121
| ~ spl22_346 ),
inference(resolution,[],[f3959,f1111]) ).
fof(f31674,plain,
( spl22_1115
| ~ spl22_233
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4465,f3958,f2559,f31672]) ).
fof(f31672,plain,
( spl22_1115
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1115])]) ).
fof(f4465,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,relation_dom(X3)))
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_346 ),
inference(resolution,[],[f3959,f2560]) ).
fof(f31670,plain,
( spl22_1114
| ~ spl22_121
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4390,f3937,f1110,f31668]) ).
fof(f31668,plain,
( spl22_1114
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(sK10(powerset(X2)),X3),X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1114])]) ).
fof(f4390,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(sK10(powerset(X2)),X3),X0)
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_341 ),
inference(resolution,[],[f3938,f1111]) ).
fof(f31666,plain,
( spl22_1113
| ~ spl22_233
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4381,f3937,f2559,f31664]) ).
fof(f31664,plain,
( spl22_1113
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_dom(X2),X3),X0)
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1113])]) ).
fof(f4381,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(relation_dom(X2),X3),X0)
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_341 ),
inference(resolution,[],[f3938,f2560]) ).
fof(f31662,plain,
( spl22_1112
| ~ spl22_121
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4360,f3933,f1110,f31660]) ).
fof(f31660,plain,
( spl22_1112
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,sK10(powerset(X3))),X0)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1112])]) ).
fof(f4360,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,sK10(powerset(X3))),X0)
| ~ empty(X3) )
| ~ spl22_121
| ~ spl22_340 ),
inference(resolution,[],[f3934,f1111]) ).
fof(f31658,plain,
( spl22_1111
| ~ spl22_233
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4351,f3933,f2559,f31656]) ).
fof(f31656,plain,
( spl22_1111
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_dom(X3)),X0)
| ~ sP0(X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1111])]) ).
fof(f4351,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,relation_dom(X3)),X0)
| ~ sP0(X3,sK15) )
| ~ spl22_233
| ~ spl22_340 ),
inference(resolution,[],[f3934,f2560]) ).
fof(f31654,plain,
( spl22_1110
| ~ spl22_233
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f4140,f3905,f2559,f31652]) ).
fof(f31652,plain,
( spl22_1110
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_dom(X2))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1110])]) ).
fof(f4140,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X0)),X1,relation_dom(X2))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_333 ),
inference(resolution,[],[f3906,f2560]) ).
fof(f31650,plain,
( spl22_1109
| ~ spl22_233
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f4114,f3901,f2559,f31648]) ).
fof(f31648,plain,
( spl22_1109
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_dom(X2))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1109])]) ).
fof(f4114,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X0)),relation_dom(X2))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_332 ),
inference(resolution,[],[f3902,f2560]) ).
fof(f31646,plain,
( spl22_1108
| ~ spl22_121
| ~ spl22_331 ),
inference(avatar_split_clause,[],[f4100,f3859,f1110,f31644]) ).
fof(f31644,plain,
( spl22_1108
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X2)),sK10(powerset(X0)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1108])]) ).
fof(f4100,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(X2)),sK10(powerset(X0)))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_331 ),
inference(resolution,[],[f3860,f1111]) ).
fof(f31642,plain,
( spl22_1107
| ~ spl22_233
| ~ spl22_331 ),
inference(avatar_split_clause,[],[f4092,f3859,f2559,f31640]) ).
fof(f31640,plain,
( spl22_1107
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),sK10(powerset(X0)))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1107])]) ).
fof(f4092,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),sK10(powerset(X0)))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_331 ),
inference(resolution,[],[f3860,f2560]) ).
fof(f31638,plain,
( spl22_1106
| ~ spl22_121
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f4078,f3855,f1110,f31636]) ).
fof(f31636,plain,
( spl22_1106
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X1)),X2,sK10(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1106])]) ).
fof(f4078,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(X1)),X2,sK10(powerset(X0)))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_330 ),
inference(resolution,[],[f3856,f1111]) ).
fof(f31634,plain,
( spl22_1105
| ~ spl22_233
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f4070,f3855,f2559,f31632]) ).
fof(f31632,plain,
( spl22_1105
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,sK10(powerset(X0)))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1105])]) ).
fof(f4070,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,sK10(powerset(X0)))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_330 ),
inference(resolution,[],[f3856,f2560]) ).
fof(f31630,plain,
( spl22_1104
| ~ spl22_121
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3785,f3685,f1110,f31628]) ).
fof(f31628,plain,
( spl22_1104
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1104])]) ).
fof(f3785,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(sK10(powerset(X1)),X2))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_325 ),
inference(resolution,[],[f3686,f1111]) ).
fof(f31626,plain,
( spl22_1103
| ~ spl22_233
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3779,f3685,f2559,f31624]) ).
fof(f31624,plain,
( spl22_1103
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1103])]) ).
fof(f3779,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(relation_dom(X1),X2))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_325 ),
inference(resolution,[],[f3686,f2560]) ).
fof(f31622,plain,
( spl22_1102
| ~ spl22_121
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3760,f3681,f1110,f31620]) ).
fof(f31620,plain,
( spl22_1102
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1102])]) ).
fof(f3760,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_324 ),
inference(resolution,[],[f3682,f1111]) ).
fof(f31618,plain,
( spl22_1101
| ~ spl22_233
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3754,f3681,f2559,f31616]) ).
fof(f31616,plain,
( spl22_1101
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1101])]) ).
fof(f3754,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,relation_dom(X2)))
| ~ sP0(X2,sK15) )
| ~ spl22_233
| ~ spl22_324 ),
inference(resolution,[],[f3682,f2560]) ).
fof(f31614,plain,
( ~ spl22_1100
| ~ spl22_3
| ~ spl22_141
| spl22_1043 ),
inference(avatar_split_clause,[],[f28790,f28695,f1337,f234,f31611]) ).
fof(f31611,plain,
( spl22_1100
<=> in(sK4,relation_dom(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1100])]) ).
fof(f234,plain,
( spl22_3
<=> in(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_3])]) ).
fof(f28695,plain,
( spl22_1043
<=> in(sK4,set_intersection2(sK3,relation_dom(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1043])]) ).
fof(f28790,plain,
( ~ in(sK4,sK3)
| ~ in(sK4,relation_dom(sK20))
| ~ spl22_141
| spl22_1043 ),
inference(resolution,[],[f28697,f1338]) ).
fof(f28697,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK20)))
| spl22_1043 ),
inference(avatar_component_clause,[],[f28695]) ).
fof(f31609,plain,
( spl22_1099
| ~ spl22_133
| ~ spl22_322 ),
inference(avatar_split_clause,[],[f3723,f3673,f1246,f31607]) ).
fof(f31607,plain,
( spl22_1099
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1099])]) ).
fof(f3723,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_322 ),
inference(resolution,[],[f3674,f1247]) ).
fof(f31605,plain,
( spl22_1098
| ~ spl22_47
| ~ spl22_307 ),
inference(avatar_split_clause,[],[f3528,f3459,f462,f31603]) ).
fof(f31603,plain,
( spl22_1098
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,relation_dom(X2))
| ~ empty(relation_rng(X2))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1098])]) ).
fof(f3528,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,relation_dom(X2))
| ~ empty(relation_rng(X2))
| ~ sP1(X2) )
| ~ spl22_47
| ~ spl22_307 ),
inference(resolution,[],[f3460,f463]) ).
fof(f31601,plain,
( spl22_1097
| ~ spl22_47
| ~ spl22_303 ),
inference(avatar_split_clause,[],[f3517,f3442,f462,f31599]) ).
fof(f31599,plain,
( spl22_1097
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,X0)
| ~ empty(relation_rng(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1097])]) ).
fof(f3517,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(relation_dom(X1),X2,X0)
| ~ empty(relation_rng(X1))
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_303 ),
inference(resolution,[],[f3443,f463]) ).
fof(f31597,plain,
( spl22_1096
| ~ spl22_47
| ~ spl22_300 ),
inference(avatar_split_clause,[],[f3506,f3430,f462,f31595]) ).
fof(f31595,plain,
( spl22_1096
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,relation_dom(X2))
| ~ empty(relation_rng(X2))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1096])]) ).
fof(f3506,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,relation_dom(X2))
| ~ empty(relation_rng(X2))
| ~ sP1(X2) )
| ~ spl22_47
| ~ spl22_300 ),
inference(resolution,[],[f3431,f463]) ).
fof(f31593,plain,
( spl22_1095
| ~ spl22_47
| ~ spl22_297 ),
inference(avatar_split_clause,[],[f3490,f3418,f462,f31591]) ).
fof(f31591,plain,
( spl22_1095
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),X0)
| ~ empty(relation_rng(X2))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1095])]) ).
fof(f3490,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_dom(X2),X0)
| ~ empty(relation_rng(X2))
| ~ sP1(X2) )
| ~ spl22_47
| ~ spl22_297 ),
inference(resolution,[],[f3419,f463]) ).
fof(f31589,plain,
( spl22_1094
| ~ spl22_47
| ~ spl22_292 ),
inference(avatar_split_clause,[],[f3474,f3390,f462,f31587]) ).
fof(f31587,plain,
( spl22_1094
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ empty(relation_rng(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1094])]) ).
fof(f3474,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ empty(relation_rng(X1))
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_292 ),
inference(resolution,[],[f3391,f463]) ).
fof(f31585,plain,
( spl22_1093
| ~ spl22_252
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3383,f3304,f2895,f31583]) ).
fof(f31583,plain,
( spl22_1093
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(sK15,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1093])]) ).
fof(f3383,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(sK15,X2,relation_rng(X0)) )
| ~ spl22_252
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2896]) ).
fof(f31581,plain,
( spl22_1092
| ~ spl22_251
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3381,f3304,f2891,f31579]) ).
fof(f31579,plain,
( spl22_1092
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,sK15,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1092])]) ).
fof(f3381,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,sK15,relation_rng(X0)) )
| ~ spl22_251
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2892]) ).
fof(f31577,plain,
( spl22_1091
| ~ spl22_250
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3379,f3304,f2887,f31575]) ).
fof(f31575,plain,
( spl22_1091
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1091])]) ).
fof(f3379,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),sK15) )
| ~ spl22_250
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2888]) ).
fof(f31573,plain,
( spl22_1090
| ~ spl22_249
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3378,f3304,f2883,f31571]) ).
fof(f31571,plain,
( spl22_1090
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1090])]) ).
fof(f3378,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,sK15) )
| ~ spl22_249
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2884]) ).
fof(f31569,plain,
( spl22_1089
| ~ spl22_255
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3357,f3304,f2907,f31567]) ).
fof(f31567,plain,
( spl22_1089
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| empty(set_intersection2(X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1089])]) ).
fof(f3357,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| empty(set_intersection2(X2,relation_rng(X0))) )
| ~ spl22_255
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2908]) ).
fof(f31565,plain,
( spl22_1088
| ~ spl22_254
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3356,f3304,f2903,f31563]) ).
fof(f31563,plain,
( spl22_1088
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| empty(set_intersection2(relation_rng(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1088])]) ).
fof(f3356,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| empty(set_intersection2(relation_rng(X0),X2)) )
| ~ spl22_254
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2904]) ).
fof(f31561,plain,
( spl22_1087
| ~ spl22_56
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f3095,f2899,f545,f31559]) ).
fof(f31559,plain,
( spl22_1087
<=> ! [X0] :
( empty(sK10(powerset(X0)))
| empty(X0)
| in(sK10(sK10(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1087])]) ).
fof(f3095,plain,
( ! [X0] :
( empty(sK10(powerset(X0)))
| empty(X0)
| in(sK10(sK10(powerset(X0))),X0) )
| ~ spl22_56
| ~ spl22_253 ),
inference(resolution,[],[f2900,f546]) ).
fof(f31557,plain,
( spl22_1086
| ~ spl22_150
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2858,f2743,f1405,f31555]) ).
fof(f31555,plain,
( spl22_1086
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(relation_rng(X0),X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1086])]) ).
fof(f2858,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(relation_rng(X0),X1,X2)
| ~ empty(X2) )
| ~ spl22_150
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1406]) ).
fof(f31553,plain,
( spl22_1085
| ~ spl22_148
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2854,f2743,f1397,f31551]) ).
fof(f31551,plain,
( spl22_1085
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0),X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1085])]) ).
fof(f2854,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0),X2)
| ~ empty(X2) )
| ~ spl22_148
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1398]) ).
fof(f31549,plain,
( spl22_1084
| ~ spl22_151
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2847,f2743,f1409,f31547]) ).
fof(f31547,plain,
( spl22_1084
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1084])]) ).
fof(f2847,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X1) )
| ~ spl22_151
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1410]) ).
fof(f31545,plain,
( spl22_1083
| ~ spl22_149
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2846,f2743,f1401,f31543]) ).
fof(f31543,plain,
( spl22_1083
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1083])]) ).
fof(f2846,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X2) )
| ~ spl22_149
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1402]) ).
fof(f31541,plain,
( spl22_1082
| ~ spl22_142
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2837,f2743,f1341,f31539]) ).
fof(f31539,plain,
( spl22_1082
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP0(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1082])]) ).
fof(f2837,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP0(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) )
| ~ spl22_142
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1342]) ).
fof(f31484,plain,
( ~ spl22_1081
| ~ spl22_3
| ~ spl22_141
| spl22_1042 ),
inference(avatar_split_clause,[],[f28749,f28414,f1337,f234,f31481]) ).
fof(f31481,plain,
( spl22_1081
<=> in(sK4,relation_dom(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1081])]) ).
fof(f28414,plain,
( spl22_1042
<=> in(sK4,set_intersection2(sK3,relation_dom(sK19))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1042])]) ).
fof(f28749,plain,
( ~ in(sK4,sK3)
| ~ in(sK4,relation_dom(sK19))
| ~ spl22_141
| spl22_1042 ),
inference(resolution,[],[f28416,f1338]) ).
fof(f28416,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK19)))
| spl22_1042 ),
inference(avatar_component_clause,[],[f28414]) ).
fof(f31383,plain,
( spl22_1080
| ~ spl22_232
| ~ spl22_541 ),
inference(avatar_split_clause,[],[f10607,f10284,f2531,f31381]) ).
fof(f31381,plain,
( spl22_1080
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| sP0(X2,X3)
| ~ empty(X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1080])]) ).
fof(f10284,plain,
( spl22_541
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ sP0(X2,X1)
| sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_541])]) ).
fof(f10607,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| sP0(X2,X3)
| ~ empty(X3)
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_541 ),
inference(resolution,[],[f10285,f2532]) ).
fof(f10285,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ function(X0)
| sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_541 ),
inference(avatar_component_clause,[],[f10284]) ).
fof(f31379,plain,
( spl22_1079
| ~ spl22_230
| ~ spl22_411 ),
inference(avatar_split_clause,[],[f5626,f5294,f2489,f31377]) ).
fof(f31377,plain,
( spl22_1079
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| element(sK13(sK7(X0,powerset(X1)),X2,X3),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1079])]) ).
fof(f5294,plain,
( spl22_411
<=> ! [X2,X0,X1] :
( in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_411])]) ).
fof(f5626,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| element(sK13(sK7(X0,powerset(X1)),X2,X3),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) )
| ~ spl22_230
| ~ spl22_411 ),
inference(resolution,[],[f5295,f2490]) ).
fof(f5295,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| sP0(X0,powerset(X1))
| element(X2,X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0)) )
| ~ spl22_411 ),
inference(avatar_component_clause,[],[f5294]) ).
fof(f31375,plain,
( spl22_1078
| ~ spl22_228
| ~ spl22_411 ),
inference(avatar_split_clause,[],[f5622,f5294,f2447,f31373]) ).
fof(f31373,plain,
( spl22_1078
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| element(sK13(X2,sK7(X0,powerset(X1)),X3),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1078])]) ).
fof(f5622,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| element(sK13(X2,sK7(X0,powerset(X1)),X3),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) )
| ~ spl22_228
| ~ spl22_411 ),
inference(resolution,[],[f5295,f2448]) ).
fof(f31371,plain,
( spl22_1077
| ~ spl22_231
| ~ spl22_411 ),
inference(avatar_split_clause,[],[f5621,f5294,f2510,f31369]) ).
fof(f31369,plain,
( spl22_1077
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1077])]) ).
fof(f5621,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_231
| ~ spl22_411 ),
inference(resolution,[],[f5295,f2511]) ).
fof(f31367,plain,
( spl22_1076
| ~ spl22_229
| ~ spl22_411 ),
inference(avatar_split_clause,[],[f5620,f5294,f2468,f31365]) ).
fof(f31365,plain,
( spl22_1076
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1076])]) ).
fof(f5620,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| element(sK13(X2,X3,sK7(X0,powerset(X1))),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_229
| ~ spl22_411 ),
inference(resolution,[],[f5295,f2469]) ).
fof(f30062,plain,
( spl22_1075
| ~ spl22_232
| ~ spl22_509 ),
inference(avatar_split_clause,[],[f10203,f9490,f2531,f30060]) ).
fof(f30060,plain,
( spl22_1075
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK10(relation_dom(X2)))) = apply(X0,apply(X2,sK10(relation_dom(X2))))
| ~ function(X0)
| empty(relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1075])]) ).
fof(f9490,plain,
( spl22_509
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK10(relation_dom(X2)))) = apply(X0,apply(X2,sK10(relation_dom(X2))))
| ~ sP0(X2,X1)
| empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_509])]) ).
fof(f10203,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK10(relation_dom(X2)))) = apply(X0,apply(X2,sK10(relation_dom(X2))))
| ~ function(X0)
| empty(relation_dom(X2))
| sK7(X2,X1) = apply(X2,sK8(X2,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X2,X1)) = apply(sK5,sK7(X2,X1)) )
| ~ spl22_232
| ~ spl22_509 ),
inference(resolution,[],[f9491,f2532]) ).
fof(f9491,plain,
( ! [X2,X0,X1] :
( ~ sP0(X2,X1)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK10(relation_dom(X2)))) = apply(X0,apply(X2,sK10(relation_dom(X2))))
| ~ function(X0)
| empty(relation_dom(X2)) )
| ~ spl22_509 ),
inference(avatar_component_clause,[],[f9490]) ).
fof(f30058,plain,
( spl22_1074
| ~ spl22_216
| ~ spl22_470 ),
inference(avatar_split_clause,[],[f8746,f8349,f2344,f30056]) ).
fof(f30056,plain,
( spl22_1074
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK7(X2,relation_rng(X0)))) = apply(X1,sK9(X0,sK7(X2,relation_rng(X0))))
| ~ function(X1)
| ~ relation(X1)
| sP0(X2,relation_rng(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,relation_rng(X0))) = apply(sK5,sK8(X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1074])]) ).
fof(f8746,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| apply(relation_dom_restriction(X1,relation_dom(X0)),sK9(X0,sK7(X2,relation_rng(X0)))) = apply(X1,sK9(X0,sK7(X2,relation_rng(X0))))
| ~ function(X1)
| ~ relation(X1)
| sP0(X2,relation_rng(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,relation_rng(X0))) = apply(sK5,sK8(X2,relation_rng(X0))) )
| ~ spl22_216
| ~ spl22_470 ),
inference(resolution,[],[f8350,f2345]) ).
fof(f30054,plain,
( spl22_1073
| ~ spl22_230
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5913,f5679,f2489,f30052]) ).
fof(f30052,plain,
( spl22_1073
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(X4,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X4,set_intersection2(X3,X0)),sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1073])]) ).
fof(f5679,plain,
( spl22_419
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| apply(relation_dom_restriction(X3,set_intersection2(X1,X2)),X0) = apply(X3,X0)
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_419])]) ).
fof(f5913,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(X4,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X4,set_intersection2(X3,X0)),sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) )
| ~ spl22_230
| ~ spl22_419 ),
inference(resolution,[],[f5680,f2490]) ).
fof(f5680,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| apply(relation_dom_restriction(X3,set_intersection2(X1,X2)),X0) = apply(X3,X0)
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_419 ),
inference(avatar_component_clause,[],[f5679]) ).
fof(f30050,plain,
( spl22_1072
| ~ spl22_228
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5909,f5679,f2447,f30048]) ).
fof(f30048,plain,
( spl22_1072
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(X4,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X4,set_intersection2(X3,X1)),sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1072])]) ).
fof(f5909,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(X4,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X4,set_intersection2(X3,X1)),sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2)) )
| ~ spl22_228
| ~ spl22_419 ),
inference(resolution,[],[f5680,f2448]) ).
fof(f30046,plain,
( spl22_1071
| ~ spl22_231
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5908,f5679,f2510,f30044]) ).
fof(f30044,plain,
( spl22_1071
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(relation_dom_restriction(X4,set_intersection2(X3,X2)),sK13(X0,X1,X2)) = apply(X4,sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1071])]) ).
fof(f5908,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(relation_dom_restriction(X4,set_intersection2(X3,X2)),sK13(X0,X1,X2)) = apply(X4,sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2)) )
| ~ spl22_231
| ~ spl22_419 ),
inference(resolution,[],[f5680,f2511]) ).
fof(f30041,plain,
( spl22_1070
| ~ spl22_229
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5907,f5679,f2468,f30039]) ).
fof(f30039,plain,
( spl22_1070
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(relation_dom_restriction(X4,set_intersection2(X3,X2)),sK13(X0,X1,X2)) = apply(X4,sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1070])]) ).
fof(f5907,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK13(X0,X1,X2),X3)
| apply(relation_dom_restriction(X4,set_intersection2(X3,X2)),sK13(X0,X1,X2)) = apply(X4,sK13(X0,X1,X2))
| ~ function(X4)
| ~ relation(X4)
| sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2)) )
| ~ spl22_229
| ~ spl22_419 ),
inference(resolution,[],[f5680,f2469]) ).
fof(f30037,plain,
( spl22_1069
| ~ spl22_173
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2355,f2344,f1739,f30035]) ).
fof(f30035,plain,
( spl22_1069
<=> ! [X0,X3,X2,X1] :
( sP0(X0,relation_dom(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_dom(X1))) = apply(sK5,sK8(X0,relation_dom(X1)))
| ~ function(X2)
| ~ relation(X2)
| apply(relation_dom_restriction(X2,X3),apply(X1,sK7(X0,relation_dom(X1)))) = apply(X2,apply(X1,sK7(X0,relation_dom(X1))))
| ~ sP0(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1069])]) ).
fof(f2355,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,relation_dom(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_dom(X1))) = apply(sK5,sK8(X0,relation_dom(X1)))
| ~ function(X2)
| ~ relation(X2)
| apply(relation_dom_restriction(X2,X3),apply(X1,sK7(X0,relation_dom(X1)))) = apply(X2,apply(X1,sK7(X0,relation_dom(X1))))
| ~ sP0(X1,X3) )
| ~ spl22_173
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1740]) ).
fof(f29777,plain,
( ~ spl22_1068
| spl22_721
| ~ spl22_1041 ),
inference(avatar_split_clause,[],[f28116,f28111,f15759,f29774]) ).
fof(f29774,plain,
( spl22_1068
<=> in(sK4,set_intersection2(relation_dom(sK20),relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1068])]) ).
fof(f15759,plain,
( spl22_721
<=> in(sK4,relation_dom(relation_dom_restriction(sK20,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_721])]) ).
fof(f28116,plain,
( ~ in(sK4,set_intersection2(relation_dom(sK20),relation_dom(sK5)))
| spl22_721
| ~ spl22_1041 ),
inference(superposition,[],[f15761,f28112]) ).
fof(f15761,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK20,relation_dom(sK5))))
| spl22_721 ),
inference(avatar_component_clause,[],[f15759]) ).
fof(f29172,plain,
( ~ spl22_1067
| spl22_719
| ~ spl22_1040 ),
inference(avatar_split_clause,[],[f27953,f27948,f15751,f29169]) ).
fof(f29169,plain,
( spl22_1067
<=> in(sK4,set_intersection2(relation_dom(sK19),relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1067])]) ).
fof(f15751,plain,
( spl22_719
<=> in(sK4,relation_dom(relation_dom_restriction(sK19,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_719])]) ).
fof(f27953,plain,
( ~ in(sK4,set_intersection2(relation_dom(sK19),relation_dom(sK5)))
| spl22_719
| ~ spl22_1040 ),
inference(superposition,[],[f15753,f27949]) ).
fof(f15753,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK19,relation_dom(sK5))))
| spl22_719 ),
inference(avatar_component_clause,[],[f15751]) ).
fof(f28810,plain,
( spl22_1066
| ~ spl22_230
| ~ spl22_469 ),
inference(avatar_split_clause,[],[f8288,f8086,f2489,f28808]) ).
fof(f28808,plain,
( spl22_1066
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1066])]) ).
fof(f8086,plain,
( spl22_469
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_469])]) ).
fof(f8288,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) )
| ~ spl22_230
| ~ spl22_469 ),
inference(resolution,[],[f8087,f2490]) ).
fof(f8087,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1)) )
| ~ spl22_469 ),
inference(avatar_component_clause,[],[f8086]) ).
fof(f28806,plain,
( spl22_1065
| ~ spl22_228
| ~ spl22_469 ),
inference(avatar_split_clause,[],[f8284,f8086,f2447,f28804]) ).
fof(f28804,plain,
( spl22_1065
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1065])]) ).
fof(f8284,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) )
| ~ spl22_228
| ~ spl22_469 ),
inference(resolution,[],[f8087,f2448]) ).
fof(f28802,plain,
( spl22_1064
| ~ spl22_231
| ~ spl22_469 ),
inference(avatar_split_clause,[],[f8283,f8086,f2510,f28800]) ).
fof(f28800,plain,
( spl22_1064
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1064])]) ).
fof(f8283,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_231
| ~ spl22_469 ),
inference(resolution,[],[f8087,f2511]) ).
fof(f28798,plain,
( spl22_1063
| ~ spl22_229
| ~ spl22_469 ),
inference(avatar_split_clause,[],[f8282,f8086,f2468,f28796]) ).
fof(f28796,plain,
( spl22_1063
<=> ! [X0,X3,X2,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1063])]) ).
fof(f8282,plain,
( ! [X2,X3,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_229
| ~ spl22_469 ),
inference(resolution,[],[f8087,f2469]) ).
fof(f28794,plain,
( spl22_1062
| ~ spl22_230
| ~ spl22_428 ),
inference(avatar_split_clause,[],[f6195,f5715,f2489,f28792]) ).
fof(f28792,plain,
( spl22_1062
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(sK13(powerset(X0),X1,X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(powerset(X0),X1,X2),X3,X4)) = apply(sK5,sK13(sK13(powerset(X0),X1,X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1062])]) ).
fof(f5715,plain,
( spl22_428
<=> ! [X2,X0,X1,X3] :
( in(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_428])]) ).
fof(f6195,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(sK13(powerset(X0),X1,X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(powerset(X0),X1,X2),X3,X4)) = apply(sK5,sK13(sK13(powerset(X0),X1,X2),X3,X4)) )
| ~ spl22_230
| ~ spl22_428 ),
inference(resolution,[],[f5716,f2490]) ).
fof(f5716,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(powerset(X0),X1,X2))
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2) )
| ~ spl22_428 ),
inference(avatar_component_clause,[],[f5715]) ).
fof(f28789,plain,
( spl22_1061
| ~ spl22_228
| ~ spl22_428 ),
inference(avatar_split_clause,[],[f6191,f5715,f2447,f28787]) ).
fof(f28787,plain,
( spl22_1061
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,sK13(powerset(X0),X1,X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(powerset(X0),X1,X2),X4)) = apply(sK5,sK13(X3,sK13(powerset(X0),X1,X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1061])]) ).
fof(f6191,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,sK13(powerset(X0),X1,X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(powerset(X0),X1,X2),X4)) = apply(sK5,sK13(X3,sK13(powerset(X0),X1,X2),X4)) )
| ~ spl22_228
| ~ spl22_428 ),
inference(resolution,[],[f5716,f2448]) ).
fof(f28785,plain,
( spl22_1060
| ~ spl22_231
| ~ spl22_428 ),
inference(avatar_split_clause,[],[f6190,f5715,f2510,f28783]) ).
fof(f28783,plain,
( spl22_1060
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(powerset(X0),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1060])]) ).
fof(f6190,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(powerset(X0),X1,X2))) )
| ~ spl22_231
| ~ spl22_428 ),
inference(resolution,[],[f5716,f2511]) ).
fof(f28781,plain,
( spl22_1059
| ~ spl22_229
| ~ spl22_428 ),
inference(avatar_split_clause,[],[f6189,f5715,f2468,f28779]) ).
fof(f28779,plain,
( spl22_1059
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(powerset(X0),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1059])]) ).
fof(f6189,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP2(X3,X4,sK13(powerset(X0),X1,X2))
| apply(sK5,sK13(X3,X4,sK13(powerset(X0),X1,X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(powerset(X0),X1,X2))) )
| ~ spl22_229
| ~ spl22_428 ),
inference(resolution,[],[f5716,f2469]) ).
fof(f28777,plain,
( spl22_1058
| ~ spl22_230
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f6125,f5703,f2489,f28775]) ).
fof(f28775,plain,
( spl22_1058
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1058])]) ).
fof(f5703,plain,
( spl22_425
<=> ! [X2,X0,X1,X3] :
( in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_425])]) ).
fof(f6125,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) )
| ~ spl22_230
| ~ spl22_425 ),
inference(resolution,[],[f5704,f2490]) ).
fof(f5704,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,X1,powerset(X2)))
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0) )
| ~ spl22_425 ),
inference(avatar_component_clause,[],[f5703]) ).
fof(f28773,plain,
( spl22_1057
| ~ spl22_228
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f6121,f5703,f2447,f28771]) ).
fof(f28771,plain,
( spl22_1057
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1057])]) ).
fof(f6121,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) )
| ~ spl22_228
| ~ spl22_425 ),
inference(resolution,[],[f5704,f2448]) ).
fof(f28769,plain,
( spl22_1056
| ~ spl22_231
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f6120,f5703,f2510,f28767]) ).
fof(f28767,plain,
( spl22_1056
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1056])]) ).
fof(f6120,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_231
| ~ spl22_425 ),
inference(resolution,[],[f5704,f2511]) ).
fof(f28765,plain,
( spl22_1055
| ~ spl22_229
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f6119,f5703,f2468,f28763]) ).
fof(f28763,plain,
( spl22_1055
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1055])]) ).
fof(f6119,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_229
| ~ spl22_425 ),
inference(resolution,[],[f5704,f2469]) ).
fof(f28761,plain,
( spl22_1054
| ~ spl22_230
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f6055,f5695,f2489,f28759]) ).
fof(f28759,plain,
( spl22_1054
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(sK13(X0,powerset(X1),X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,powerset(X1),X2),X3,X4)) = apply(sK5,sK13(sK13(X0,powerset(X1),X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1054])]) ).
fof(f5695,plain,
( spl22_423
<=> ! [X2,X0,X1,X3] :
( in(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_423])]) ).
fof(f6055,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(sK13(X0,powerset(X1),X2),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,powerset(X1),X2),X3,X4)) = apply(sK5,sK13(sK13(X0,powerset(X1),X2),X3,X4)) )
| ~ spl22_230
| ~ spl22_423 ),
inference(resolution,[],[f5696,f2490]) ).
fof(f5696,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,powerset(X1),X2))
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2) )
| ~ spl22_423 ),
inference(avatar_component_clause,[],[f5695]) ).
fof(f28757,plain,
( spl22_1053
| ~ spl22_228
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f6051,f5695,f2447,f28755]) ).
fof(f28755,plain,
( spl22_1053
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,sK13(X0,powerset(X1),X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,powerset(X1),X2),X4)) = apply(sK5,sK13(X3,sK13(X0,powerset(X1),X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1053])]) ).
fof(f6051,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,sK13(X0,powerset(X1),X2),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,powerset(X1),X2),X4)) = apply(sK5,sK13(X3,sK13(X0,powerset(X1),X2),X4)) )
| ~ spl22_228
| ~ spl22_423 ),
inference(resolution,[],[f5696,f2448]) ).
fof(f28753,plain,
( spl22_1052
| ~ spl22_231
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f6050,f5695,f2510,f28751]) ).
fof(f28751,plain,
( spl22_1052
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,powerset(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1052])]) ).
fof(f6050,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,powerset(X1),X2))) )
| ~ spl22_231
| ~ spl22_423 ),
inference(resolution,[],[f5696,f2511]) ).
fof(f28748,plain,
( spl22_1051
| ~ spl22_229
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f6049,f5695,f2468,f28746]) ).
fof(f28746,plain,
( spl22_1051
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,powerset(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1051])]) ).
fof(f6049,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP2(X3,X4,sK13(X0,powerset(X1),X2))
| apply(sK5,sK13(X3,X4,sK13(X0,powerset(X1),X2))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,powerset(X1),X2))) )
| ~ spl22_229
| ~ spl22_423 ),
inference(resolution,[],[f5696,f2469]) ).
fof(f28744,plain,
( spl22_1050
| ~ spl22_230
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5985,f5687,f2489,f28742]) ).
fof(f28742,plain,
( spl22_1050
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1050])]) ).
fof(f5687,plain,
( spl22_421
<=> ! [X2,X0,X1,X3] :
( in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_421])]) ).
fof(f5985,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(sK13(X0,X1,powerset(X2)),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(sK13(X0,X1,powerset(X2)),X3,X4)) = apply(sK5,sK13(sK13(X0,X1,powerset(X2)),X3,X4)) )
| ~ spl22_230
| ~ spl22_421 ),
inference(resolution,[],[f5688,f2490]) ).
fof(f5688,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,X1,powerset(X2)))
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1) )
| ~ spl22_421 ),
inference(avatar_component_clause,[],[f5687]) ).
fof(f28740,plain,
( spl22_1049
| ~ spl22_228
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5981,f5687,f2447,f28738]) ).
fof(f28738,plain,
( spl22_1049
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1049])]) ).
fof(f5981,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,sK13(X0,X1,powerset(X2)),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,sK13(X0,X1,powerset(X2)),X4)) = apply(sK5,sK13(X3,sK13(X0,X1,powerset(X2)),X4)) )
| ~ spl22_228
| ~ spl22_421 ),
inference(resolution,[],[f5688,f2448]) ).
fof(f28736,plain,
( spl22_1048
| ~ spl22_231
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5980,f5687,f2510,f28734]) ).
fof(f28734,plain,
( spl22_1048
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1048])]) ).
fof(f5980,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_231
| ~ spl22_421 ),
inference(resolution,[],[f5688,f2511]) ).
fof(f28732,plain,
( spl22_1047
| ~ spl22_229
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5979,f5687,f2468,f28730]) ).
fof(f28730,plain,
( spl22_1047
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1047])]) ).
fof(f5979,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X3,X4,sK13(X0,X1,powerset(X2)))
| apply(sK5,sK13(X3,X4,sK13(X0,X1,powerset(X2)))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_229
| ~ spl22_421 ),
inference(resolution,[],[f5688,f2469]) ).
fof(f28728,plain,
( spl22_1046
| ~ spl22_216
| ~ spl22_411 ),
inference(avatar_split_clause,[],[f5597,f5294,f2344,f28726]) ).
fof(f28726,plain,
( spl22_1046
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(sK7(X2,sK7(X0,powerset(X1))),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1046])]) ).
fof(f5597,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(sK7(X2,sK7(X0,powerset(X1))),X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) )
| ~ spl22_216
| ~ spl22_411 ),
inference(resolution,[],[f5295,f2345]) ).
fof(f28724,plain,
( spl22_1045
| ~ spl22_232
| ~ spl22_393 ),
inference(avatar_split_clause,[],[f5101,f4952,f2531,f28722]) ).
fof(f28722,plain,
( spl22_1045
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ in(X2,relation_dom(X3))
| ~ sP0(X1,apply(X3,X2))
| sK7(X3,apply(X1,X0)) = apply(X3,sK8(X3,apply(X1,X0)))
| apply(relation_dom_restriction(sK5,apply(X1,X0)),sK7(X3,apply(X1,X0))) = apply(sK5,sK7(X3,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1045])]) ).
fof(f4952,plain,
( spl22_393
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,apply(X1,X2))
| ~ in(X3,relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,apply(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_393])]) ).
fof(f5101,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ in(X2,relation_dom(X3))
| ~ sP0(X1,apply(X3,X2))
| sK7(X3,apply(X1,X0)) = apply(X3,sK8(X3,apply(X1,X0)))
| apply(relation_dom_restriction(sK5,apply(X1,X0)),sK7(X3,apply(X1,X0))) = apply(sK5,sK7(X3,apply(X1,X0))) )
| ~ spl22_232
| ~ spl22_393 ),
inference(resolution,[],[f4953,f2532]) ).
fof(f4953,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X1,apply(X0,X3))
| ~ in(X3,relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X0,apply(X1,X2)) )
| ~ spl22_393 ),
inference(avatar_component_clause,[],[f4952]) ).
fof(f28720,plain,
( spl22_1044
| ~ spl22_232
| ~ spl22_317 ),
inference(avatar_split_clause,[],[f3649,f3614,f2531,f28718]) ).
fof(f28718,plain,
( spl22_1044
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| empty(apply(X1,X0))
| sK7(X1,sK10(apply(X1,X0))) = apply(X1,sK8(X1,sK10(apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK10(apply(X1,X0))),sK7(X1,sK10(apply(X1,X0)))) = apply(sK5,sK7(X1,sK10(apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1044])]) ).
fof(f3614,plain,
( spl22_317
<=> ! [X0,X1] :
( ~ sP0(X0,sK10(apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| empty(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_317])]) ).
fof(f3649,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| empty(apply(X1,X0))
| sK7(X1,sK10(apply(X1,X0))) = apply(X1,sK8(X1,sK10(apply(X1,X0))))
| apply(relation_dom_restriction(sK5,sK10(apply(X1,X0))),sK7(X1,sK10(apply(X1,X0)))) = apply(sK5,sK7(X1,sK10(apply(X1,X0)))) )
| ~ spl22_232
| ~ spl22_317 ),
inference(resolution,[],[f3615,f2532]) ).
fof(f3615,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK10(apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| empty(apply(X0,X1)) )
| ~ spl22_317 ),
inference(avatar_component_clause,[],[f3614]) ).
fof(f28698,plain,
( ~ spl22_1043
| ~ spl22_53
| spl22_705
| ~ spl22_1041 ),
inference(avatar_split_clause,[],[f28272,f28111,f15328,f511,f28695]) ).
fof(f15328,plain,
( spl22_705
<=> in(sK4,relation_dom(relation_dom_restriction(sK20,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_705])]) ).
fof(f28272,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK20)))
| ~ spl22_53
| spl22_705
| ~ spl22_1041 ),
inference(forward_demodulation,[],[f28115,f512]) ).
fof(f28115,plain,
( ~ in(sK4,set_intersection2(relation_dom(sK20),sK3))
| spl22_705
| ~ spl22_1041 ),
inference(superposition,[],[f15330,f28112]) ).
fof(f15330,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK20,sK3)))
| spl22_705 ),
inference(avatar_component_clause,[],[f15328]) ).
fof(f28417,plain,
( ~ spl22_1042
| ~ spl22_53
| spl22_701
| ~ spl22_1040 ),
inference(avatar_split_clause,[],[f28109,f27948,f15312,f511,f28414]) ).
fof(f15312,plain,
( spl22_701
<=> in(sK4,relation_dom(relation_dom_restriction(sK19,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_701])]) ).
fof(f28109,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK19)))
| ~ spl22_53
| spl22_701
| ~ spl22_1040 ),
inference(forward_demodulation,[],[f27952,f512]) ).
fof(f27952,plain,
( ~ in(sK4,set_intersection2(relation_dom(sK19),sK3))
| spl22_701
| ~ spl22_1040 ),
inference(superposition,[],[f15314,f27949]) ).
fof(f15314,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK19,sK3)))
| spl22_701 ),
inference(avatar_component_clause,[],[f15312]) ).
fof(f28113,plain,
( spl22_1041
| ~ spl22_20
| ~ spl22_19
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3585,f3551,f314,f319,f28111]) ).
fof(f3585,plain,
( ! [X0] :
( ~ function(sK20)
| set_intersection2(relation_dom(sK20),X0) = relation_dom(relation_dom_restriction(sK20,X0)) )
| ~ spl22_19
| ~ spl22_313 ),
inference(resolution,[],[f3552,f316]) ).
fof(f27950,plain,
( spl22_1040
| ~ spl22_18
| ~ spl22_17
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3584,f3551,f304,f309,f27948]) ).
fof(f3584,plain,
( ! [X0] :
( ~ function(sK19)
| set_intersection2(relation_dom(sK19),X0) = relation_dom(relation_dom_restriction(sK19,X0)) )
| ~ spl22_17
| ~ spl22_313 ),
inference(resolution,[],[f3552,f306]) ).
fof(f27946,plain,
( spl22_1039
| ~ spl22_47
| ~ spl22_283 ),
inference(avatar_split_clause,[],[f3319,f3272,f462,f27944]) ).
fof(f27944,plain,
( spl22_1039
<=> ! [X0,X1] :
( sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ empty(relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1039])]) ).
fof(f3319,plain,
( ! [X0,X1] :
( sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ empty(relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_283 ),
inference(resolution,[],[f3273,f463]) ).
fof(f27942,plain,
( spl22_1038
| spl22_81
| ~ spl22_696 ),
inference(avatar_split_clause,[],[f15262,f15221,f726,f27939]) ).
fof(f27939,plain,
( spl22_1038
<=> apply(relation_dom_restriction(sK5,sK5),sK10(sK5)) = apply(sK5,sK10(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1038])]) ).
fof(f15262,plain,
( apply(relation_dom_restriction(sK5,sK5),sK10(sK5)) = apply(sK5,sK10(sK5))
| spl22_81
| ~ spl22_696 ),
inference(resolution,[],[f15222,f728]) ).
fof(f27937,plain,
( spl22_1037
| ~ spl22_47
| ~ spl22_282 ),
inference(avatar_split_clause,[],[f3313,f3268,f462,f27935]) ).
fof(f27935,plain,
( spl22_1037
<=> ! [X0,X1] :
( sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ empty(relation_rng(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1037])]) ).
fof(f3313,plain,
( ! [X0,X1] :
( sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ empty(relation_rng(X1))
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_282 ),
inference(resolution,[],[f3269,f463]) ).
fof(f27933,plain,
( spl22_1036
| ~ spl22_62
| ~ spl22_273 ),
inference(avatar_split_clause,[],[f3227,f2979,f582,f27931]) ).
fof(f27931,plain,
( spl22_1036
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| sK10(powerset(X1)) = set_intersection2(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1036])]) ).
fof(f582,plain,
( spl22_62
<=> ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_62])]) ).
fof(f2979,plain,
( spl22_273
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_273])]) ).
fof(f3227,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| sK10(powerset(X1)) = set_intersection2(X2,X0) )
| ~ spl22_62
| ~ spl22_273 ),
inference(resolution,[],[f2980,f583]) ).
fof(f583,plain,
( ! [X2,X0,X1] :
( ~ sP2(X1,X0,X2)
| set_intersection2(X0,X1) = X2 )
| ~ spl22_62 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f2980,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl22_273 ),
inference(avatar_component_clause,[],[f2979]) ).
fof(f27929,plain,
( spl22_1035
| ~ spl22_62
| ~ spl22_272 ),
inference(avatar_split_clause,[],[f3215,f2975,f582,f27927]) ).
fof(f27927,plain,
( spl22_1035
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(X2,sK10(powerset(X1))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1035])]) ).
fof(f2975,plain,
( spl22_272
<=> ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_272])]) ).
fof(f3215,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(X2,sK10(powerset(X1))) = X0 )
| ~ spl22_62
| ~ spl22_272 ),
inference(resolution,[],[f2976,f583]) ).
fof(f2976,plain,
( ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl22_272 ),
inference(avatar_component_clause,[],[f2975]) ).
fof(f27925,plain,
( spl22_1034
| ~ spl22_62
| ~ spl22_271 ),
inference(avatar_split_clause,[],[f3211,f2971,f582,f27923]) ).
fof(f27923,plain,
( spl22_1034
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| sK10(powerset(X1)) = set_intersection2(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1034])]) ).
fof(f2971,plain,
( spl22_271
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_271])]) ).
fof(f3211,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| sK10(powerset(X1)) = set_intersection2(X0,X2) )
| ~ spl22_62
| ~ spl22_271 ),
inference(resolution,[],[f2972,f583]) ).
fof(f2972,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X1)
| ~ empty(X2) )
| ~ spl22_271 ),
inference(avatar_component_clause,[],[f2971]) ).
fof(f27921,plain,
( spl22_1033
| ~ spl22_62
| ~ spl22_269 ),
inference(avatar_split_clause,[],[f3207,f2963,f582,f27919]) ).
fof(f27919,plain,
( spl22_1033
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(sK10(powerset(X1)),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1033])]) ).
fof(f2963,plain,
( spl22_269
<=> ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_269])]) ).
fof(f3207,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(sK10(powerset(X1)),X2) = X0 )
| ~ spl22_62
| ~ spl22_269 ),
inference(resolution,[],[f2964,f583]) ).
fof(f2964,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl22_269 ),
inference(avatar_component_clause,[],[f2963]) ).
fof(f27917,plain,
( spl22_1032
| ~ spl22_62
| ~ spl22_265 ),
inference(avatar_split_clause,[],[f3184,f2947,f582,f27915]) ).
fof(f27915,plain,
( spl22_1032
<=> ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = set_intersection2(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1032])]) ).
fof(f2947,plain,
( spl22_265
<=> ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK10(powerset(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_265])]) ).
fof(f3184,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = set_intersection2(X1,sK10(powerset(X0))) )
| ~ spl22_62
| ~ spl22_265 ),
inference(resolution,[],[f2948,f583]) ).
fof(f2948,plain,
( ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_265 ),
inference(avatar_component_clause,[],[f2947]) ).
fof(f27913,plain,
( spl22_1031
| ~ spl22_62
| ~ spl22_262 ),
inference(avatar_split_clause,[],[f3176,f2935,f582,f27911]) ).
fof(f27911,plain,
( spl22_1031
<=> ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = set_intersection2(sK10(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1031])]) ).
fof(f2935,plain,
( spl22_262
<=> ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK10(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_262])]) ).
fof(f3176,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = set_intersection2(sK10(powerset(X0)),X1) )
| ~ spl22_62
| ~ spl22_262 ),
inference(resolution,[],[f2936,f583]) ).
fof(f2936,plain,
( ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK10(powerset(X1)))
| ~ empty(X1) )
| ~ spl22_262 ),
inference(avatar_component_clause,[],[f2935]) ).
fof(f27909,plain,
( spl22_1030
| ~ spl22_138
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2843,f2743,f1286,f27907]) ).
fof(f27907,plain,
( spl22_1030
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1030])]) ).
fof(f2843,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0),relation_rng(X0)) )
| ~ spl22_138
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1287]) ).
fof(f27905,plain,
( spl22_1029
| ~ spl22_139
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2842,f2743,f1290,f27903]) ).
fof(f27903,plain,
( spl22_1029
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(relation_rng(X0),X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1029])]) ).
fof(f2842,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(relation_rng(X0),X1,relation_rng(X0)) )
| ~ spl22_139
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1291]) ).
fof(f27901,plain,
( spl22_1028
| ~ spl22_218
| ~ spl22_247 ),
inference(avatar_split_clause,[],[f2815,f2739,f2367,f27899]) ).
fof(f27899,plain,
( spl22_1028
<=> ! [X0,X1] :
( relation_dom(relation_dom(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1028])]) ).
fof(f2367,plain,
( spl22_218
<=> ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_218])]) ).
fof(f2739,plain,
( spl22_247
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_247])]) ).
fof(f2815,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_247 ),
inference(resolution,[],[f2740,f2368]) ).
fof(f2368,plain,
( ! [X0] :
( empty(sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_218 ),
inference(avatar_component_clause,[],[f2367]) ).
fof(f2740,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl22_247 ),
inference(avatar_component_clause,[],[f2739]) ).
fof(f27897,plain,
( spl22_1027
| spl22_49
| ~ spl22_696 ),
inference(avatar_split_clause,[],[f15261,f15221,f487,f27894]) ).
fof(f27894,plain,
( spl22_1027
<=> apply(relation_dom_restriction(sK5,sK3),sK10(sK3)) = apply(sK5,sK10(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1027])]) ).
fof(f15261,plain,
( apply(relation_dom_restriction(sK5,sK3),sK10(sK3)) = apply(sK5,sK10(sK3))
| spl22_49
| ~ spl22_696 ),
inference(resolution,[],[f15222,f489]) ).
fof(f27892,plain,
( spl22_1026
| ~ spl22_218
| ~ spl22_246 ),
inference(avatar_split_clause,[],[f2793,f2735,f2367,f27890]) ).
fof(f27890,plain,
( spl22_1026
<=> ! [X0,X1] :
( relation_dom(relation_rng(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1026])]) ).
fof(f2735,plain,
( spl22_246
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_246])]) ).
fof(f2793,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_246 ),
inference(resolution,[],[f2736,f2368]) ).
fof(f2736,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl22_246 ),
inference(avatar_component_clause,[],[f2735]) ).
fof(f27888,plain,
( spl22_1025
| ~ spl22_218
| ~ spl22_245 ),
inference(avatar_split_clause,[],[f2771,f2731,f2367,f27886]) ).
fof(f27886,plain,
( spl22_1025
<=> ! [X0,X1] :
( relation_rng(relation_dom(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1025])]) ).
fof(f2731,plain,
( spl22_245
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_245])]) ).
fof(f2771,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_245 ),
inference(resolution,[],[f2732,f2368]) ).
fof(f2732,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl22_245 ),
inference(avatar_component_clause,[],[f2731]) ).
fof(f27884,plain,
( spl22_1024
| ~ spl22_218
| ~ spl22_244 ),
inference(avatar_split_clause,[],[f2749,f2727,f2367,f27882]) ).
fof(f27882,plain,
( spl22_1024
<=> ! [X0,X1] :
( relation_rng(relation_rng(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1024])]) ).
fof(f2727,plain,
( spl22_244
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_244])]) ).
fof(f2749,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(sK10(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_244 ),
inference(resolution,[],[f2728,f2368]) ).
fof(f2728,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl22_244 ),
inference(avatar_component_clause,[],[f2727]) ).
fof(f27880,plain,
( spl22_1023
| ~ spl22_73
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2589,f2559,f652,f27878]) ).
fof(f27878,plain,
( spl22_1023
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| in(sK7(X0,X1),X1)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1023])]) ).
fof(f2589,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_73
| ~ spl22_233 ),
inference(resolution,[],[f2560,f653]) ).
fof(f27876,plain,
( spl22_1022
| ~ spl22_156
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2587,f2559,f1535,f27874]) ).
fof(f27874,plain,
( spl22_1022
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| element(sK7(X0,X1),X1)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1022])]) ).
fof(f1535,plain,
( spl22_156
<=> ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_156])]) ).
fof(f2587,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| element(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_156
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1536]) ).
fof(f1536,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| element(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_156 ),
inference(avatar_component_clause,[],[f1535]) ).
fof(f27872,plain,
( spl22_1021
| ~ spl22_69
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2578,f2559,f628,f27870]) ).
fof(f27870,plain,
( spl22_1021
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1021])]) ).
fof(f2578,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,relation_dom(X0)) )
| ~ spl22_69
| ~ spl22_233 ),
inference(resolution,[],[f2560,f629]) ).
fof(f27690,plain,
( spl22_1020
| ~ spl22_209
| ~ spl22_548 ),
inference(avatar_split_clause,[],[f10679,f10643,f2241,f27688]) ).
fof(f27688,plain,
( spl22_1020
<=> ! [X0,X1] :
( ~ sP1(X0)
| sK7(sK5,relation_rng(X0)) = apply(sK5,sK8(sK5,relation_rng(X0)))
| sK7(sK5,relation_rng(X0)) = apply(X0,sK9(X0,sK7(sK5,relation_rng(X0))))
| ~ relation(X1)
| apply(X1,apply(sK5,sK4)) = apply(relation_dom_restriction(X1,relation_rng(X0)),apply(sK5,sK4))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1020])]) ).
fof(f10643,plain,
( spl22_548
<=> ! [X0,X1] :
( sK7(X1,relation_rng(X0)) = apply(X0,sK9(X0,sK7(X1,relation_rng(X0))))
| ~ sP1(X0)
| sK7(X1,relation_rng(X0)) = apply(X1,sK8(X1,relation_rng(X0)))
| sP0(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_548])]) ).
fof(f10679,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| sK7(sK5,relation_rng(X0)) = apply(sK5,sK8(sK5,relation_rng(X0)))
| sK7(sK5,relation_rng(X0)) = apply(X0,sK9(X0,sK7(sK5,relation_rng(X0))))
| ~ relation(X1)
| apply(X1,apply(sK5,sK4)) = apply(relation_dom_restriction(X1,relation_rng(X0)),apply(sK5,sK4))
| ~ function(X1) )
| ~ spl22_209
| ~ spl22_548 ),
inference(resolution,[],[f10644,f2242]) ).
fof(f10644,plain,
( ! [X0,X1] :
( sP0(X1,relation_rng(X0))
| ~ sP1(X0)
| sK7(X1,relation_rng(X0)) = apply(X1,sK8(X1,relation_rng(X0)))
| sK7(X1,relation_rng(X0)) = apply(X0,sK9(X0,sK7(X1,relation_rng(X0)))) )
| ~ spl22_548 ),
inference(avatar_component_clause,[],[f10643]) ).
fof(f27686,plain,
( spl22_1019
| ~ spl22_232
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5947,f5683,f2531,f27684]) ).
fof(f27684,plain,
( spl22_1019
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ in(X1,relation_dom(X2))
| apply(X2,X1) = apply(X0,sK9(X0,apply(X2,X1)))
| sK7(X2,relation_rng(X0)) = apply(X2,sK8(X2,relation_rng(X0)))
| apply(relation_dom_restriction(sK5,relation_rng(X0)),sK7(X2,relation_rng(X0))) = apply(sK5,sK7(X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1019])]) ).
fof(f5947,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ in(X1,relation_dom(X2))
| apply(X2,X1) = apply(X0,sK9(X0,apply(X2,X1)))
| sK7(X2,relation_rng(X0)) = apply(X2,sK8(X2,relation_rng(X0)))
| apply(relation_dom_restriction(sK5,relation_rng(X0)),sK7(X2,relation_rng(X0))) = apply(sK5,sK7(X2,relation_rng(X0))) )
| ~ spl22_232
| ~ spl22_420 ),
inference(resolution,[],[f5684,f2532]) ).
fof(f27682,plain,
( spl22_1018
| ~ spl22_233
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4439,f4126,f2559,f27680]) ).
fof(f4439,plain,
( ! [X0,X1] :
( ~ in(X1,set_intersection2(relation_dom(sK5),X0))
| ~ sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_233
| ~ spl22_371 ),
inference(superposition,[],[f2560,f4127]) ).
fof(f26952,plain,
( spl22_1017
| ~ spl22_216
| ~ spl22_469 ),
inference(avatar_split_clause,[],[f8259,f8086,f2344,f26950]) ).
fof(f26950,plain,
( spl22_1017
<=> ! [X2,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1017])]) ).
fof(f8259,plain,
( ! [X2,X0,X1] :
( sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) )
| ~ spl22_216
| ~ spl22_469 ),
inference(resolution,[],[f8087,f2345]) ).
fof(f26948,plain,
( spl22_1016
| ~ spl22_216
| ~ spl22_428 ),
inference(avatar_split_clause,[],[f6166,f5715,f2344,f26946]) ).
fof(f26946,plain,
( spl22_1016
<=> ! [X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP0(X3,sK13(powerset(X0),X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(powerset(X0),X1,X2))) = apply(sK5,sK8(X3,sK13(powerset(X0),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1016])]) ).
fof(f6166,plain,
( ! [X2,X3,X0,X1] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| sP0(X3,sK13(powerset(X0),X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(powerset(X0),X1,X2))) = apply(sK5,sK8(X3,sK13(powerset(X0),X1,X2))) )
| ~ spl22_216
| ~ spl22_428 ),
inference(resolution,[],[f5716,f2345]) ).
fof(f26944,plain,
( spl22_1015
| ~ spl22_216
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f6096,f5703,f2344,f26942]) ).
fof(f26942,plain,
( spl22_1015
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1015])]) ).
fof(f6096,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_216
| ~ spl22_425 ),
inference(resolution,[],[f5704,f2345]) ).
fof(f26940,plain,
( spl22_1014
| ~ spl22_216
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f6026,f5695,f2344,f26938]) ).
fof(f26938,plain,
( spl22_1014
<=> ! [X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP0(X3,sK13(X0,powerset(X1),X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,powerset(X1),X2))) = apply(sK5,sK8(X3,sK13(X0,powerset(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1014])]) ).
fof(f6026,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| sP0(X3,sK13(X0,powerset(X1),X2))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,powerset(X1),X2))) = apply(sK5,sK8(X3,sK13(X0,powerset(X1),X2))) )
| ~ spl22_216
| ~ spl22_423 ),
inference(resolution,[],[f5696,f2345]) ).
fof(f26936,plain,
( spl22_1013
| ~ spl22_216
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5956,f5687,f2344,f26934]) ).
fof(f26934,plain,
( spl22_1013
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1013])]) ).
fof(f5956,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| sP0(X3,sK13(X0,X1,powerset(X2)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,sK13(X0,X1,powerset(X2)))) = apply(sK5,sK8(X3,sK13(X0,X1,powerset(X2)))) )
| ~ spl22_216
| ~ spl22_421 ),
inference(resolution,[],[f5688,f2345]) ).
fof(f26440,plain,
( spl22_1012
| ~ spl22_53
| ~ spl22_998 ),
inference(avatar_split_clause,[],[f26059,f25920,f511,f26438]) ).
fof(f26438,plain,
( spl22_1012
<=> ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1012])]) ).
fof(f25920,plain,
( spl22_998
<=> ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_998])]) ).
fof(f26059,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_53
| ~ spl22_998 ),
inference(superposition,[],[f25921,f512]) ).
fof(f25921,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_998 ),
inference(avatar_component_clause,[],[f25920]) ).
fof(f26205,plain,
( spl22_1011
| ~ spl22_215
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5884,f5679,f2316,f26203]) ).
fof(f26203,plain,
( spl22_1011
<=> ! [X0,X3,X2,X1] :
( ~ in(sK8(X0,X1),X2)
| apply(relation_dom_restriction(X3,set_intersection2(X2,relation_dom(X0))),sK8(X0,X1)) = apply(X3,sK8(X0,X1))
| ~ function(X3)
| ~ relation(X3)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1011])]) ).
fof(f5884,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK8(X0,X1),X2)
| apply(relation_dom_restriction(X3,set_intersection2(X2,relation_dom(X0))),sK8(X0,X1)) = apply(X3,sK8(X0,X1))
| ~ function(X3)
| ~ relation(X3)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1)) )
| ~ spl22_215
| ~ spl22_419 ),
inference(resolution,[],[f5680,f2317]) ).
fof(f26201,plain,
( spl22_1010
| ~ spl22_216
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5872,f5679,f2344,f26199]) ).
fof(f26199,plain,
( spl22_1010
<=> ! [X0,X3,X2,X1] :
( ~ in(sK7(X0,X1),X2)
| apply(relation_dom_restriction(X3,set_intersection2(X2,X1)),sK7(X0,X1)) = apply(X3,sK7(X0,X1))
| ~ function(X3)
| ~ relation(X3)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1010])]) ).
fof(f5872,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK7(X0,X1),X2)
| apply(relation_dom_restriction(X3,set_intersection2(X2,X1)),sK7(X0,X1)) = apply(X3,sK7(X0,X1))
| ~ function(X3)
| ~ relation(X3)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1)) )
| ~ spl22_216
| ~ spl22_419 ),
inference(resolution,[],[f5680,f2345]) ).
fof(f26197,plain,
( spl22_1009
| ~ spl22_230
| ~ spl22_397 ),
inference(avatar_split_clause,[],[f5196,f5130,f2489,f26195]) ).
fof(f26195,plain,
( spl22_1009
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1009])]) ).
fof(f5196,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(sK7(X0,powerset(X1)),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(sK7(X0,powerset(X1)),X2,X3)) = apply(sK5,sK13(sK7(X0,powerset(X1)),X2,X3)) )
| ~ spl22_230
| ~ spl22_397 ),
inference(resolution,[],[f5131,f2490]) ).
fof(f26193,plain,
( spl22_1008
| ~ spl22_228
| ~ spl22_397 ),
inference(avatar_split_clause,[],[f5192,f5130,f2447,f26191]) ).
fof(f26191,plain,
( spl22_1008
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1008])]) ).
fof(f5192,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,sK7(X0,powerset(X1)),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,sK7(X0,powerset(X1)),X3)) = apply(sK5,sK13(X2,sK7(X0,powerset(X1)),X3)) )
| ~ spl22_228
| ~ spl22_397 ),
inference(resolution,[],[f5131,f2448]) ).
fof(f26189,plain,
( spl22_1007
| ~ spl22_231
| ~ spl22_397 ),
inference(avatar_split_clause,[],[f5191,f5130,f2510,f26187]) ).
fof(f26187,plain,
( spl22_1007
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1007])]) ).
fof(f5191,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_231
| ~ spl22_397 ),
inference(resolution,[],[f5131,f2511]) ).
fof(f26185,plain,
( spl22_1006
| ~ spl22_229
| ~ spl22_397 ),
inference(avatar_split_clause,[],[f5190,f5130,f2468,f26183]) ).
fof(f26183,plain,
( spl22_1006
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1006])]) ).
fof(f5190,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP2(X2,X3,sK7(X0,powerset(X1)))
| apply(sK5,sK13(X2,X3,sK7(X0,powerset(X1)))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,sK7(X0,powerset(X1)))) )
| ~ spl22_229
| ~ spl22_397 ),
inference(resolution,[],[f5131,f2469]) ).
fof(f26181,plain,
( spl22_1005
| ~ spl22_230
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f4310,f3929,f2489,f26179]) ).
fof(f26179,plain,
( spl22_1005
<=> ! [X2,X4,X0,X3,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK13(apply(X1,X0),X2,X3),X4)
| ~ sP0(X1,powerset(X4))
| sP2(apply(X1,X0),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(apply(X1,X0),X2,X3)) = apply(sK5,sK13(apply(X1,X0),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1005])]) ).
fof(f4310,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| element(sK13(apply(X1,X0),X2,X3),X4)
| ~ sP0(X1,powerset(X4))
| sP2(apply(X1,X0),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(apply(X1,X0),X2,X3)) = apply(sK5,sK13(apply(X1,X0),X2,X3)) )
| ~ spl22_230
| ~ spl22_339 ),
inference(resolution,[],[f3930,f2490]) ).
fof(f25988,plain,
( spl22_1004
| ~ spl22_228
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f4306,f3929,f2447,f25986]) ).
fof(f25986,plain,
( spl22_1004
<=> ! [X2,X4,X0,X3,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK13(X2,apply(X1,X0),X3),X4)
| ~ sP0(X1,powerset(X4))
| sP2(X2,apply(X1,X0),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,apply(X1,X0),X3)) = apply(sK5,sK13(X2,apply(X1,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1004])]) ).
fof(f4306,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| element(sK13(X2,apply(X1,X0),X3),X4)
| ~ sP0(X1,powerset(X4))
| sP2(X2,apply(X1,X0),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,apply(X1,X0),X3)) = apply(sK5,sK13(X2,apply(X1,X0),X3)) )
| ~ spl22_228
| ~ spl22_339 ),
inference(resolution,[],[f3930,f2448]) ).
fof(f25984,plain,
( spl22_1003
| ~ spl22_231
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f4305,f3929,f2510,f25982]) ).
fof(f25982,plain,
( spl22_1003
<=> ! [X2,X4,X0,X3,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK13(X2,X3,apply(X1,X0)),X4)
| ~ sP0(X1,powerset(X4))
| sP2(X2,X3,apply(X1,X0))
| apply(sK5,sK13(X2,X3,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1003])]) ).
fof(f4305,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| element(sK13(X2,X3,apply(X1,X0)),X4)
| ~ sP0(X1,powerset(X4))
| sP2(X2,X3,apply(X1,X0))
| apply(sK5,sK13(X2,X3,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,apply(X1,X0))) )
| ~ spl22_231
| ~ spl22_339 ),
inference(resolution,[],[f3930,f2511]) ).
fof(f25980,plain,
( spl22_1002
| ~ spl22_229
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f4304,f3929,f2468,f25978]) ).
fof(f25978,plain,
( spl22_1002
<=> ! [X2,X4,X0,X3,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK13(X2,X3,apply(X1,X0)),X4)
| ~ sP0(X1,powerset(X4))
| sP2(X2,X3,apply(X1,X0))
| apply(sK5,sK13(X2,X3,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1002])]) ).
fof(f4304,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| element(sK13(X2,X3,apply(X1,X0)),X4)
| ~ sP0(X1,powerset(X4))
| sP2(X2,X3,apply(X1,X0))
| apply(sK5,sK13(X2,X3,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,apply(X1,X0))) )
| ~ spl22_229
| ~ spl22_339 ),
inference(resolution,[],[f3930,f2469]) ).
fof(f25976,plain,
( spl22_1001
| ~ spl22_232
| ~ spl22_316 ),
inference(avatar_split_clause,[],[f3641,f3610,f2531,f25974]) ).
fof(f25974,plain,
( spl22_1001
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| in(apply(X1,X0),X2)
| sK7(X1,set_intersection2(X3,X2)) = apply(X1,sK8(X1,set_intersection2(X3,X2)))
| apply(relation_dom_restriction(sK5,set_intersection2(X3,X2)),sK7(X1,set_intersection2(X3,X2))) = apply(sK5,sK7(X1,set_intersection2(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1001])]) ).
fof(f3610,plain,
( spl22_316
<=> ! [X0,X3,X2,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_316])]) ).
fof(f3641,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(apply(X1,X0),X2)
| sK7(X1,set_intersection2(X3,X2)) = apply(X1,sK8(X1,set_intersection2(X3,X2)))
| apply(relation_dom_restriction(sK5,set_intersection2(X3,X2)),sK7(X1,set_intersection2(X3,X2))) = apply(sK5,sK7(X1,set_intersection2(X3,X2))) )
| ~ spl22_232
| ~ spl22_316 ),
inference(resolution,[],[f3611,f2532]) ).
fof(f3611,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,set_intersection2(X3,X2))
| ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),X2) )
| ~ spl22_316 ),
inference(avatar_component_clause,[],[f3610]) ).
fof(f25972,plain,
( spl22_1000
| ~ spl22_232
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3632,f3606,f2531,f25970]) ).
fof(f25970,plain,
( spl22_1000
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| in(apply(X1,X0),X2)
| sK7(X1,set_intersection2(X2,X3)) = apply(X1,sK8(X1,set_intersection2(X2,X3)))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X3)),sK7(X1,set_intersection2(X2,X3))) = apply(sK5,sK7(X1,set_intersection2(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1000])]) ).
fof(f3606,plain,
( spl22_315
<=> ! [X0,X3,X2,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_315])]) ).
fof(f3632,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| in(apply(X1,X0),X2)
| sK7(X1,set_intersection2(X2,X3)) = apply(X1,sK8(X1,set_intersection2(X2,X3)))
| apply(relation_dom_restriction(sK5,set_intersection2(X2,X3)),sK7(X1,set_intersection2(X2,X3))) = apply(sK5,sK7(X1,set_intersection2(X2,X3))) )
| ~ spl22_232
| ~ spl22_315 ),
inference(resolution,[],[f3607,f2532]) ).
fof(f3607,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,set_intersection2(X2,X3))
| ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),X2) )
| ~ spl22_315 ),
inference(avatar_component_clause,[],[f3606]) ).
fof(f25968,plain,
( spl22_999
| ~ spl22_232
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3630,f3602,f2531,f25966]) ).
fof(f25966,plain,
( spl22_999
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| element(apply(X1,X0),X2)
| sK7(X1,sK10(powerset(X2))) = apply(X1,sK8(X1,sK10(powerset(X2))))
| apply(relation_dom_restriction(sK5,sK10(powerset(X2))),sK7(X1,sK10(powerset(X2)))) = apply(sK5,sK7(X1,sK10(powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_999])]) ).
fof(f3602,plain,
( spl22_314
<=> ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK10(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_314])]) ).
fof(f3630,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| element(apply(X1,X0),X2)
| sK7(X1,sK10(powerset(X2))) = apply(X1,sK8(X1,sK10(powerset(X2))))
| apply(relation_dom_restriction(sK5,sK10(powerset(X2))),sK7(X1,sK10(powerset(X2)))) = apply(sK5,sK7(X1,sK10(powerset(X2)))) )
| ~ spl22_232
| ~ spl22_314 ),
inference(resolution,[],[f3603,f2532]) ).
fof(f3603,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK10(powerset(X2)))
| ~ in(X1,relation_dom(X0))
| element(apply(X0,X1),X2) )
| ~ spl22_314 ),
inference(avatar_component_clause,[],[f3602]) ).
fof(f25922,plain,
( spl22_998
| ~ spl22_371
| ~ spl22_809 ),
inference(avatar_split_clause,[],[f17662,f17544,f4126,f25920]) ).
fof(f17662,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_371
| ~ spl22_809 ),
inference(superposition,[],[f17545,f4127]) ).
fof(f24872,plain,
( spl22_997
| ~ spl22_53
| ~ spl22_996 ),
inference(avatar_split_clause,[],[f24452,f24177,f511,f24870]) ).
fof(f24870,plain,
( spl22_997
<=> ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK5)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_997])]) ).
fof(f24177,plain,
( spl22_996
<=> ! [X1] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_996])]) ).
fof(f24452,plain,
( ! [X0] :
( sP0(sK15,set_intersection2(X0,relation_dom(sK5)))
| ~ empty(X0) )
| ~ spl22_53
| ~ spl22_996 ),
inference(superposition,[],[f24178,f512]) ).
fof(f24178,plain,
( ! [X1] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X1))
| ~ empty(X1) )
| ~ spl22_996 ),
inference(avatar_component_clause,[],[f24177]) ).
fof(f24179,plain,
( spl22_114
| spl22_996
| ~ spl22_371
| ~ spl22_684
| ~ spl22_877 ),
inference(avatar_split_clause,[],[f20528,f20196,f14820,f4126,f24177,f956]) ).
fof(f14820,plain,
( spl22_684
<=> ! [X0,X1] :
( sP0(sK15,relation_dom(X0))
| ~ sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_684])]) ).
fof(f20196,plain,
( spl22_877
<=> ! [X0,X1] :
( sP0(relation_dom_restriction(sK5,X0),X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_877])]) ).
fof(f20528,plain,
( ! [X0,X1] :
( sP0(sK15,set_intersection2(relation_dom(sK5),X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl22_371
| ~ spl22_684
| ~ spl22_877 ),
inference(forward_demodulation,[],[f20426,f4127]) ).
fof(f20426,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| sP0(sK15,relation_dom(relation_dom_restriction(sK5,X1))) )
| ~ spl22_684
| ~ spl22_877 ),
inference(duplicate_literal_removal,[],[f20364]) ).
fof(f20364,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| sP0(sK15,relation_dom(relation_dom_restriction(sK5,X1)))
| ~ empty(X0) )
| ~ spl22_684
| ~ spl22_877 ),
inference(resolution,[],[f20197,f14821]) ).
fof(f14821,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| sP0(sK15,relation_dom(X0))
| ~ empty(X1) )
| ~ spl22_684 ),
inference(avatar_component_clause,[],[f14820]) ).
fof(f20197,plain,
( ! [X0,X1] :
( sP0(relation_dom_restriction(sK5,X0),X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_877 ),
inference(avatar_component_clause,[],[f20196]) ).
fof(f23931,plain,
( spl22_995
| ~ spl22_41
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f5047,f4944,f419,f23929]) ).
fof(f23929,plain,
( spl22_995
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_995])]) ).
fof(f5047,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_391 ),
inference(resolution,[],[f4945,f420]) ).
fof(f23927,plain,
( spl22_994
| ~ spl22_41
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f5017,f4940,f419,f23925]) ).
fof(f23925,plain,
( spl22_994
<=> ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_994])]) ).
fof(f5017,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_390 ),
inference(resolution,[],[f4941,f420]) ).
fof(f23923,plain,
( spl22_993
| ~ spl22_41
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4983,f4902,f419,f23921]) ).
fof(f23921,plain,
( spl22_993
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_993])]) ).
fof(f4983,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_388 ),
inference(resolution,[],[f4903,f420]) ).
fof(f23919,plain,
( spl22_992
| ~ spl22_41
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4955,f4898,f419,f23917]) ).
fof(f23917,plain,
( spl22_992
<=> ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_992])]) ).
fof(f4955,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_387 ),
inference(resolution,[],[f4899,f420]) ).
fof(f23915,plain,
( spl22_991
| ~ spl22_41
| ~ spl22_355 ),
inference(avatar_split_clause,[],[f4631,f3994,f419,f23913]) ).
fof(f23913,plain,
( spl22_991
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_991])]) ).
fof(f4631,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_355 ),
inference(resolution,[],[f3995,f420]) ).
fof(f23911,plain,
( spl22_990
| ~ spl22_41
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4597,f3990,f419,f23909]) ).
fof(f23909,plain,
( spl22_990
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_990])]) ).
fof(f4597,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_354 ),
inference(resolution,[],[f3991,f420]) ).
fof(f23907,plain,
( spl22_989
| ~ spl22_41
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f4557,f3978,f419,f23905]) ).
fof(f23905,plain,
( spl22_989
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_989])]) ).
fof(f4557,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_351 ),
inference(resolution,[],[f3979,f420]) ).
fof(f23903,plain,
( spl22_988
| ~ spl22_41
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f4525,f3974,f419,f23901]) ).
fof(f23901,plain,
( spl22_988
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_988])]) ).
fof(f4525,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(set_intersection2(X1,X2),X3,X0)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_350 ),
inference(resolution,[],[f3975,f420]) ).
fof(f23899,plain,
( spl22_987
| ~ spl22_41
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f4485,f3962,f419,f23897]) ).
fof(f23897,plain,
( spl22_987
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_987])]) ).
fof(f4485,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_347 ),
inference(resolution,[],[f3963,f420]) ).
fof(f23895,plain,
( spl22_986
| ~ spl22_41
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f4455,f3958,f419,f23893]) ).
fof(f23893,plain,
( spl22_986
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_986])]) ).
fof(f4455,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,set_intersection2(X2,X3))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_346 ),
inference(resolution,[],[f3959,f420]) ).
fof(f23877,plain,
( spl22_985
| ~ spl22_41
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f4371,f3937,f419,f23875]) ).
fof(f23875,plain,
( spl22_985
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_985])]) ).
fof(f4371,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_341 ),
inference(resolution,[],[f3938,f420]) ).
fof(f23873,plain,
( spl22_984
| ~ spl22_41
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4341,f3933,f419,f23871]) ).
fof(f23871,plain,
( spl22_984
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_984])]) ).
fof(f4341,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,set_intersection2(X2,X3),X0)
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_340 ),
inference(resolution,[],[f3934,f420]) ).
fof(f23869,plain,
( spl22_983
| ~ spl22_138
| ~ spl22_336 ),
inference(avatar_split_clause,[],[f4219,f3917,f1286,f23867]) ).
fof(f23867,plain,
( spl22_983
<=> ! [X0,X1] :
( ~ in(sK13(X0,X1,X1),X0)
| sP2(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_983])]) ).
fof(f3917,plain,
( spl22_336
<=> ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(sK13(X0,X1,X1),X0)
| ~ in(sK13(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_336])]) ).
fof(f4219,plain,
( ! [X0,X1] :
( ~ in(sK13(X0,X1,X1),X0)
| sP2(X0,X1,X1) )
| ~ spl22_138
| ~ spl22_336 ),
inference(duplicate_literal_removal,[],[f4163]) ).
fof(f4163,plain,
( ! [X0,X1] :
( ~ in(sK13(X0,X1,X1),X0)
| sP2(X0,X1,X1)
| sP2(X0,X1,X1) )
| ~ spl22_138
| ~ spl22_336 ),
inference(resolution,[],[f3918,f1287]) ).
fof(f3918,plain,
( ! [X0,X1] :
( ~ in(sK13(X0,X1,X1),X1)
| ~ in(sK13(X0,X1,X1),X0)
| sP2(X0,X1,X1) )
| ~ spl22_336 ),
inference(avatar_component_clause,[],[f3917]) ).
fof(f23865,plain,
( spl22_982
| ~ spl22_41
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3769,f3685,f419,f23863]) ).
fof(f23863,plain,
( spl22_982
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_982])]) ).
fof(f3769,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_325 ),
inference(resolution,[],[f3686,f420]) ).
fof(f23861,plain,
( spl22_981
| ~ spl22_41
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3744,f3681,f419,f23859]) ).
fof(f23859,plain,
( spl22_981
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_981])]) ).
fof(f3744,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_324 ),
inference(resolution,[],[f3682,f420]) ).
fof(f23857,plain,
( spl22_980
| ~ spl22_233
| ~ spl22_322 ),
inference(avatar_split_clause,[],[f3721,f3673,f2559,f23855]) ).
fof(f23855,plain,
( spl22_980
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_980])]) ).
fof(f3721,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_322 ),
inference(resolution,[],[f3674,f2560]) ).
fof(f23853,plain,
( spl22_979
| ~ spl22_119
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3355,f3304,f1064,f23851]) ).
fof(f23851,plain,
( spl22_979
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_979])]) ).
fof(f3355,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| empty(relation_rng(X0)) )
| ~ spl22_119
| ~ spl22_290 ),
inference(resolution,[],[f3305,f1065]) ).
fof(f23849,plain,
( spl22_978
| ~ spl22_47
| ~ spl22_268 ),
inference(avatar_split_clause,[],[f3200,f2959,f462,f23847]) ).
fof(f23847,plain,
( spl22_978
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,X0)
| ~ empty(relation_rng(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_978])]) ).
fof(f3200,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,X0)
| ~ empty(relation_rng(X1))
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_268 ),
inference(resolution,[],[f2960,f463]) ).
fof(f23845,plain,
( spl22_977
| ~ spl22_56
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f3149,f2911,f545,f23843]) ).
fof(f23843,plain,
( spl22_977
<=> ! [X0] :
( empty(X0)
| empty(sK6(X0))
| in(sK10(sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_977])]) ).
fof(f3149,plain,
( ! [X0] :
( empty(X0)
| empty(sK6(X0))
| in(sK10(sK6(X0)),X0) )
| ~ spl22_56
| ~ spl22_256 ),
inference(duplicate_literal_removal,[],[f3146]) ).
fof(f3146,plain,
( ! [X0] :
( empty(X0)
| empty(sK6(X0))
| empty(X0)
| in(sK10(sK6(X0)),X0) )
| ~ spl22_56
| ~ spl22_256 ),
inference(resolution,[],[f2912,f546]) ).
fof(f23841,plain,
( spl22_976
| ~ spl22_133
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3133,f2907,f1246,f23839]) ).
fof(f23839,plain,
( spl22_976
<=> ! [X2,X0,X1] :
( empty(set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_976])]) ).
fof(f3133,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_255 ),
inference(resolution,[],[f2908,f1247]) ).
fof(f23824,plain,
( spl22_975
| ~ spl22_248
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3128,f2907,f2743,f23822]) ).
fof(f23822,plain,
( spl22_975
<=> ! [X0,X1] :
( empty(set_intersection2(X0,relation_rng(X1)))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_975])]) ).
fof(f3128,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,relation_rng(X1)))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_255 ),
inference(resolution,[],[f2908,f2744]) ).
fof(f23820,plain,
( spl22_974
| ~ spl22_45
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3125,f2907,f454,f23818]) ).
fof(f23818,plain,
( spl22_974
<=> ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ in(X1,sK10(set_intersection2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_974])]) ).
fof(f3125,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ in(X1,sK10(set_intersection2(X0,X1))) )
| ~ spl22_45
| ~ spl22_255 ),
inference(resolution,[],[f2908,f455]) ).
fof(f23816,plain,
( spl22_973
| ~ spl22_46
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3124,f2907,f458,f23814]) ).
fof(f23814,plain,
( spl22_973
<=> ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| element(sK10(set_intersection2(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_973])]) ).
fof(f3124,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| element(sK10(set_intersection2(X0,X1)),X1) )
| ~ spl22_46
| ~ spl22_255 ),
inference(resolution,[],[f2908,f459]) ).
fof(f23812,plain,
( spl22_972
| ~ spl22_133
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3109,f2903,f1246,f23810]) ).
fof(f23810,plain,
( spl22_972
<=> ! [X2,X0,X1] :
( empty(set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_972])]) ).
fof(f3109,plain,
( ! [X2,X0,X1] :
( empty(set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_254 ),
inference(resolution,[],[f2904,f1247]) ).
fof(f23808,plain,
( spl22_971
| ~ spl22_248
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3104,f2903,f2743,f23806]) ).
fof(f3104,plain,
( ! [X0,X1] :
( empty(set_intersection2(relation_rng(X0),X1))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl22_248
| ~ spl22_254 ),
inference(resolution,[],[f2904,f2744]) ).
fof(f23804,plain,
( spl22_970
| ~ spl22_45
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3101,f2903,f454,f23802]) ).
fof(f23802,plain,
( spl22_970
<=> ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK10(set_intersection2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_970])]) ).
fof(f3101,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK10(set_intersection2(X0,X1))) )
| ~ spl22_45
| ~ spl22_254 ),
inference(resolution,[],[f2904,f455]) ).
fof(f23800,plain,
( spl22_969
| ~ spl22_46
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3100,f2903,f458,f23798]) ).
fof(f23798,plain,
( spl22_969
<=> ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| element(sK10(set_intersection2(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_969])]) ).
fof(f3100,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| element(sK10(set_intersection2(X0,X1)),X0) )
| ~ spl22_46
| ~ spl22_254 ),
inference(resolution,[],[f2904,f459]) ).
fof(f23796,plain,
( spl22_968
| ~ spl22_133
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3088,f2895,f1246,f23794]) ).
fof(f23794,plain,
( spl22_968
<=> ! [X2,X0,X1] :
( sP2(sK15,X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_968])]) ).
fof(f3088,plain,
( ! [X2,X0,X1] :
( sP2(sK15,X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_252 ),
inference(resolution,[],[f2896,f1247]) ).
fof(f23792,plain,
( spl22_967
| ~ spl22_248
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3083,f2895,f2743,f23790]) ).
fof(f23790,plain,
( spl22_967
<=> ! [X0,X1] :
( sP2(sK15,X0,relation_rng(X1))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_967])]) ).
fof(f3083,plain,
( ! [X0,X1] :
( sP2(sK15,X0,relation_rng(X1))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_252 ),
inference(resolution,[],[f2896,f2744]) ).
fof(f23788,plain,
( spl22_966
| ~ spl22_45
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3080,f2895,f454,f23786]) ).
fof(f23786,plain,
( spl22_966
<=> ! [X0,X1] :
( sP2(sK15,X0,X1)
| ~ in(X1,sK13(sK15,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_966])]) ).
fof(f3080,plain,
( ! [X0,X1] :
( sP2(sK15,X0,X1)
| ~ in(X1,sK13(sK15,X0,X1)) )
| ~ spl22_45
| ~ spl22_252 ),
inference(resolution,[],[f2896,f455]) ).
fof(f23705,plain,
( spl22_965
| ~ spl22_133
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3069,f2891,f1246,f23703]) ).
fof(f23703,plain,
( spl22_965
<=> ! [X2,X0,X1] :
( sP2(X0,sK15,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_965])]) ).
fof(f3069,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK15,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_251 ),
inference(resolution,[],[f2892,f1247]) ).
fof(f23701,plain,
( spl22_964
| ~ spl22_248
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3064,f2891,f2743,f23699]) ).
fof(f23699,plain,
( spl22_964
<=> ! [X0,X1] :
( sP2(X0,sK15,relation_rng(X1))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_964])]) ).
fof(f3064,plain,
( ! [X0,X1] :
( sP2(X0,sK15,relation_rng(X1))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_251 ),
inference(resolution,[],[f2892,f2744]) ).
fof(f23697,plain,
( spl22_963
| ~ spl22_45
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3061,f2891,f454,f23695]) ).
fof(f23695,plain,
( spl22_963
<=> ! [X0,X1] :
( sP2(X0,sK15,X1)
| ~ in(X1,sK13(X0,sK15,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_963])]) ).
fof(f3061,plain,
( ! [X0,X1] :
( sP2(X0,sK15,X1)
| ~ in(X1,sK13(X0,sK15,X1)) )
| ~ spl22_45
| ~ spl22_251 ),
inference(resolution,[],[f2892,f455]) ).
fof(f23693,plain,
( spl22_962
| ~ spl22_133
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3033,f2887,f1246,f23691]) ).
fof(f23691,plain,
( spl22_962
<=> ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),sK15)
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_962])]) ).
fof(f3033,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),sK15)
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_250 ),
inference(resolution,[],[f2888,f1247]) ).
fof(f23689,plain,
( spl22_961
| ~ spl22_248
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3028,f2887,f2743,f23687]) ).
fof(f23687,plain,
( spl22_961
<=> ! [X0,X1] :
( sP2(X0,relation_rng(X1),sK15)
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_961])]) ).
fof(f3028,plain,
( ! [X0,X1] :
( sP2(X0,relation_rng(X1),sK15)
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_248
| ~ spl22_250 ),
inference(resolution,[],[f2888,f2744]) ).
fof(f23685,plain,
( spl22_960
| ~ spl22_45
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3025,f2887,f454,f23683]) ).
fof(f23683,plain,
( spl22_960
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ in(X1,sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_960])]) ).
fof(f3025,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ in(X1,sK13(X0,X1,sK15)) )
| ~ spl22_45
| ~ spl22_250 ),
inference(resolution,[],[f2888,f455]) ).
fof(f23681,plain,
( spl22_959
| ~ spl22_133
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3014,f2883,f1246,f23679]) ).
fof(f23679,plain,
( spl22_959
<=> ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,sK15)
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_959])]) ).
fof(f3014,plain,
( ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,sK15)
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_249 ),
inference(resolution,[],[f2884,f1247]) ).
fof(f23677,plain,
( spl22_958
| ~ spl22_248
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3009,f2883,f2743,f23675]) ).
fof(f23675,plain,
( spl22_958
<=> ! [X0,X1] :
( sP2(relation_rng(X0),X1,sK15)
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_958])]) ).
fof(f3009,plain,
( ! [X0,X1] :
( sP2(relation_rng(X0),X1,sK15)
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl22_248
| ~ spl22_249 ),
inference(resolution,[],[f2884,f2744]) ).
fof(f23673,plain,
( spl22_957
| ~ spl22_45
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3006,f2883,f454,f23671]) ).
fof(f23671,plain,
( spl22_957
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ in(X0,sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_957])]) ).
fof(f3006,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ in(X0,sK13(X0,X1,sK15)) )
| ~ spl22_45
| ~ spl22_249 ),
inference(resolution,[],[f2884,f455]) ).
fof(f23669,plain,
( spl22_956
| ~ spl22_36
| ~ spl22_247 ),
inference(avatar_split_clause,[],[f2813,f2739,f398,f23667]) ).
fof(f23667,plain,
( spl22_956
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_956])]) ).
fof(f398,plain,
( spl22_36
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_36])]) ).
fof(f2813,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_247 ),
inference(resolution,[],[f2740,f399]) ).
fof(f399,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_36 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f23665,plain,
( spl22_955
| ~ spl22_128
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15719,f15680,f1151,f23663]) ).
fof(f23663,plain,
( spl22_955
<=> ! [X0] :
( ~ sP0(sK5,sK10(powerset(X0)))
| element(apply(sK5,sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_955])]) ).
fof(f15719,plain,
( ! [X0] :
( ~ sP0(sK5,sK10(powerset(X0)))
| element(apply(sK5,sK4),X0) )
| ~ spl22_128
| ~ spl22_718 ),
inference(resolution,[],[f15681,f1152]) ).
fof(f23661,plain,
( spl22_954
| ~ spl22_34
| ~ spl22_247 ),
inference(avatar_split_clause,[],[f2812,f2739,f390,f23659]) ).
fof(f23659,plain,
( spl22_954
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_954])]) ).
fof(f390,plain,
( spl22_34
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_34])]) ).
fof(f2812,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_247 ),
inference(resolution,[],[f2740,f391]) ).
fof(f391,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_34 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f23657,plain,
( spl22_953
| ~ spl22_36
| ~ spl22_246 ),
inference(avatar_split_clause,[],[f2791,f2735,f398,f23655]) ).
fof(f23655,plain,
( spl22_953
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_953])]) ).
fof(f2791,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_246 ),
inference(resolution,[],[f2736,f399]) ).
fof(f23653,plain,
( spl22_952
| ~ spl22_34
| ~ spl22_246 ),
inference(avatar_split_clause,[],[f2790,f2735,f390,f23651]) ).
fof(f23651,plain,
( spl22_952
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_952])]) ).
fof(f2790,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_246 ),
inference(resolution,[],[f2736,f391]) ).
fof(f23649,plain,
( spl22_951
| ~ spl22_36
| ~ spl22_245 ),
inference(avatar_split_clause,[],[f2769,f2731,f398,f23647]) ).
fof(f23647,plain,
( spl22_951
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_951])]) ).
fof(f2769,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_245 ),
inference(resolution,[],[f2732,f399]) ).
fof(f23645,plain,
( spl22_950
| ~ spl22_34
| ~ spl22_245 ),
inference(avatar_split_clause,[],[f2768,f2731,f390,f23643]) ).
fof(f23643,plain,
( spl22_950
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_950])]) ).
fof(f2768,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_245 ),
inference(resolution,[],[f2732,f391]) ).
fof(f23641,plain,
( spl22_949
| ~ spl22_36
| ~ spl22_244 ),
inference(avatar_split_clause,[],[f2747,f2727,f398,f23639]) ).
fof(f23639,plain,
( spl22_949
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_949])]) ).
fof(f2747,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_244 ),
inference(resolution,[],[f2728,f399]) ).
fof(f23637,plain,
( spl22_948
| ~ spl22_34
| ~ spl22_244 ),
inference(avatar_split_clause,[],[f2746,f2727,f390,f23635]) ).
fof(f23635,plain,
( spl22_948
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_948])]) ).
fof(f2746,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_244 ),
inference(resolution,[],[f2728,f391]) ).
fof(f23633,plain,
( spl22_947
| ~ spl22_150
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2609,f2559,f1405,f23631]) ).
fof(f23631,plain,
( spl22_947
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(relation_dom(X0),X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_947])]) ).
fof(f2609,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(relation_dom(X0),X1,X2)
| ~ empty(X2) )
| ~ spl22_150
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1406]) ).
fof(f23629,plain,
( spl22_946
| ~ spl22_148
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2605,f2559,f1397,f23627]) ).
fof(f23627,plain,
( spl22_946
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,relation_dom(X0),X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_946])]) ).
fof(f2605,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,relation_dom(X0),X2)
| ~ empty(X2) )
| ~ spl22_148
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1398]) ).
fof(f23625,plain,
( spl22_945
| ~ spl22_151
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2598,f2559,f1409,f23623]) ).
fof(f23623,plain,
( spl22_945
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_945])]) ).
fof(f2598,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| ~ empty(X1) )
| ~ spl22_151
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1410]) ).
fof(f23621,plain,
( spl22_944
| ~ spl22_129
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15690,f15680,f1155,f23619]) ).
fof(f23619,plain,
( spl22_944
<=> ! [X0,X1] :
( ~ sP0(sK5,set_intersection2(X0,X1))
| in(apply(sK5,sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_944])]) ).
fof(f15690,plain,
( ! [X0,X1] :
( ~ sP0(sK5,set_intersection2(X0,X1))
| in(apply(sK5,sK4),X0) )
| ~ spl22_129
| ~ spl22_718 ),
inference(resolution,[],[f15681,f1156]) ).
fof(f23617,plain,
( spl22_943
| ~ spl22_149
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2597,f2559,f1401,f23615]) ).
fof(f23615,plain,
( spl22_943
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_943])]) ).
fof(f2597,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| ~ empty(X2) )
| ~ spl22_149
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1402]) ).
fof(f23613,plain,
( spl22_942
| ~ spl22_142
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2582,f2559,f1341,f23611]) ).
fof(f23611,plain,
( spl22_942
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X1,relation_dom(X0))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_942])]) ).
fof(f2582,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X1,relation_dom(X0))
| ~ empty(relation_dom(X1)) )
| ~ spl22_142
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1342]) ).
fof(f23609,plain,
( spl22_941
| ~ spl22_126
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2410,f2367,f1143,f23607]) ).
fof(f23607,plain,
( spl22_941
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK10(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_941])]) ).
fof(f1143,plain,
( spl22_126
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_126])]) ).
fof(f2410,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK10(powerset(X0))) = X1 )
| ~ spl22_126
| ~ spl22_218 ),
inference(resolution,[],[f2368,f1144]) ).
fof(f1144,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl22_126 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f23605,plain,
( spl22_940
| ~ spl22_125
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2409,f2367,f1139,f23603]) ).
fof(f23603,plain,
( spl22_940
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK10(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_940])]) ).
fof(f1139,plain,
( spl22_125
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_125])]) ).
fof(f2409,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK10(powerset(X0))) = X1 )
| ~ spl22_125
| ~ spl22_218 ),
inference(resolution,[],[f2368,f1140]) ).
fof(f1140,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl22_125 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f23554,plain,
( spl22_939
| ~ spl22_173
| ~ spl22_215 ),
inference(avatar_split_clause,[],[f2320,f2316,f1739,f23552]) ).
fof(f23552,plain,
( spl22_939
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2)
| apply(relation_dom_restriction(X2,X3),apply(X0,sK8(X0,X1))) = apply(X2,apply(X0,sK8(X0,X1)))
| ~ sP0(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_939])]) ).
fof(f2320,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2)
| apply(relation_dom_restriction(X2,X3),apply(X0,sK8(X0,X1))) = apply(X2,apply(X0,sK8(X0,X1)))
| ~ sP0(X0,X3) )
| ~ spl22_173
| ~ spl22_215 ),
inference(resolution,[],[f2317,f1740]) ).
fof(f23396,plain,
( spl22_938
| ~ spl22_130
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15689,f15680,f1159,f23394]) ).
fof(f23394,plain,
( spl22_938
<=> ! [X0,X1] :
( ~ sP0(sK5,set_intersection2(X0,X1))
| in(apply(sK5,sK4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_938])]) ).
fof(f15689,plain,
( ! [X0,X1] :
( ~ sP0(sK5,set_intersection2(X0,X1))
| in(apply(sK5,sK4),X1) )
| ~ spl22_130
| ~ spl22_718 ),
inference(resolution,[],[f15681,f1160]) ).
fof(f23368,plain,
( spl22_937
| ~ spl22_209
| ~ spl22_526 ),
inference(avatar_split_clause,[],[f10195,f10141,f2241,f23366]) ).
fof(f23366,plain,
( spl22_937
<=> ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK15,X0),sK7(sK5,X0)) = apply(sK15,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_937])]) ).
fof(f10141,plain,
( spl22_526
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_526])]) ).
fof(f10195,plain,
( ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK15,X0),sK7(sK5,X0)) = apply(sK15,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) )
| ~ spl22_209
| ~ spl22_526 ),
inference(resolution,[],[f10142,f2242]) ).
fof(f10142,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1)) )
| ~ spl22_526 ),
inference(avatar_component_clause,[],[f10141]) ).
fof(f23364,plain,
( spl22_936
| ~ spl22_209
| ~ spl22_525 ),
inference(avatar_split_clause,[],[f10135,f10080,f2241,f23362]) ).
fof(f23362,plain,
( spl22_936
<=> ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK20,X0),sK7(sK5,X0)) = apply(sK20,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_936])]) ).
fof(f10080,plain,
( spl22_525
<=> ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK20,X1),sK7(X0,X1)) = apply(sK20,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_525])]) ).
fof(f10135,plain,
( ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK20,X0),sK7(sK5,X0)) = apply(sK20,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) )
| ~ spl22_209
| ~ spl22_525 ),
inference(resolution,[],[f10081,f2242]) ).
fof(f10081,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK20,X1),sK7(X0,X1)) = apply(sK20,sK7(X0,X1)) )
| ~ spl22_525 ),
inference(avatar_component_clause,[],[f10080]) ).
fof(f23360,plain,
( spl22_935
| ~ spl22_209
| ~ spl22_524 ),
inference(avatar_split_clause,[],[f10074,f10020,f2241,f23358]) ).
fof(f23358,plain,
( spl22_935
<=> ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK19,X0),sK7(sK5,X0)) = apply(sK19,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_935])]) ).
fof(f10020,plain,
( spl22_524
<=> ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK19,X1),sK7(X0,X1)) = apply(sK19,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_524])]) ).
fof(f10074,plain,
( ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK19,X0),sK7(sK5,X0)) = apply(sK19,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) )
| ~ spl22_209
| ~ spl22_524 ),
inference(resolution,[],[f10021,f2242]) ).
fof(f10021,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK19,X1),sK7(X0,X1)) = apply(sK19,sK7(X0,X1)) )
| ~ spl22_524 ),
inference(avatar_component_clause,[],[f10020]) ).
fof(f23356,plain,
( spl22_934
| ~ spl22_216
| ~ spl22_397 ),
inference(avatar_split_clause,[],[f5171,f5130,f2344,f23354]) ).
fof(f23354,plain,
( spl22_934
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_934])]) ).
fof(f5171,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X2,sK7(X0,powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,sK7(X0,powerset(X1)))) = apply(sK5,sK8(X2,sK7(X0,powerset(X1)))) )
| ~ spl22_216
| ~ spl22_397 ),
inference(resolution,[],[f5131,f2345]) ).
fof(f23352,plain,
( spl22_933
| ~ spl22_209
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2539,f2531,f2241,f23350]) ).
fof(f23350,plain,
( spl22_933
<=> ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK5,X0),sK7(sK5,X0)) = apply(sK5,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_933])]) ).
fof(f2539,plain,
( ! [X0,X1] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| apply(relation_dom_restriction(sK5,X0),sK7(sK5,X0)) = apply(sK5,sK7(sK5,X0))
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X0),apply(sK5,sK4)) = apply(X1,apply(sK5,sK4))
| ~ function(X1) )
| ~ spl22_209
| ~ spl22_232 ),
inference(resolution,[],[f2532,f2242]) ).
fof(f23348,plain,
( spl22_932
| ~ spl22_153
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2520,f2510,f1508,f23346]) ).
fof(f23346,plain,
( spl22_932
<=> ! [X2,X0,X1] :
( sP2(X0,X1,relation_rng(X2))
| apply(sK5,sK13(X0,X1,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_rng(X2)))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_932])]) ).
fof(f1508,plain,
( spl22_153
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,sK9(X1,X0)) = X0
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_153])]) ).
fof(f2520,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,relation_rng(X2))
| apply(sK5,sK13(X0,X1,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_rng(X2)))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) )
| ~ spl22_153
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1509]) ).
fof(f1509,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,sK9(X1,X0)) = X0
| ~ sP1(X1) )
| ~ spl22_153 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f23179,plain,
( spl22_931
| ~ spl22_153
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2499,f2489,f1508,f23177]) ).
fof(f23177,plain,
( spl22_931
<=> ! [X2,X0,X1] :
( sP2(relation_rng(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_rng(X0),X1,X2)) = apply(sK5,sK13(relation_rng(X0),X1,X2))
| sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_931])]) ).
fof(f2499,plain,
( ! [X2,X0,X1] :
( sP2(relation_rng(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_rng(X0),X1,X2)) = apply(sK5,sK13(relation_rng(X0),X1,X2))
| sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0) )
| ~ spl22_153
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1509]) ).
fof(f23175,plain,
( spl22_930
| ~ spl22_153
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2478,f2468,f1508,f23173]) ).
fof(f23173,plain,
( spl22_930
<=> ! [X2,X0,X1] :
( sP2(X0,X1,relation_rng(X2))
| apply(sK5,sK13(X0,X1,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_rng(X2)))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_930])]) ).
fof(f2478,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,relation_rng(X2))
| apply(sK5,sK13(X0,X1,relation_rng(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_rng(X2)))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) )
| ~ spl22_153
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1509]) ).
fof(f23171,plain,
( spl22_929
| ~ spl22_153
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2457,f2447,f1508,f23169]) ).
fof(f23169,plain,
( spl22_929
<=> ! [X2,X0,X1] :
( sP2(X0,relation_rng(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,relation_rng(X1),X2)) = apply(sK5,sK13(X0,relation_rng(X1),X2))
| sK13(X0,relation_rng(X1),X2) = apply(X1,sK9(X1,sK13(X0,relation_rng(X1),X2)))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_929])]) ).
fof(f2457,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_rng(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,relation_rng(X1),X2)) = apply(sK5,sK13(X0,relation_rng(X1),X2))
| sK13(X0,relation_rng(X1),X2) = apply(X1,sK9(X1,sK13(X0,relation_rng(X1),X2)))
| ~ sP1(X1) )
| ~ spl22_153
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1509]) ).
fof(f23063,plain,
( spl22_928
| ~ spl22_216
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f4285,f3929,f2344,f23061]) ).
fof(f23061,plain,
( spl22_928
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK7(X2,apply(X1,X0)),X3)
| ~ sP0(X1,powerset(X3))
| sP0(X2,apply(X1,X0))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,apply(X1,X0))) = apply(sK5,sK8(X2,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_928])]) ).
fof(f4285,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| element(sK7(X2,apply(X1,X0)),X3)
| ~ sP0(X1,powerset(X3))
| sP0(X2,apply(X1,X0))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,apply(X1,X0))) = apply(sK5,sK8(X2,apply(X1,X0))) )
| ~ spl22_216
| ~ spl22_339 ),
inference(resolution,[],[f3930,f2345]) ).
fof(f23059,plain,
( spl22_927
| ~ spl22_74
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2515,f2510,f662,f23057]) ).
fof(f23057,plain,
( spl22_927
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_927])]) ).
fof(f662,plain,
( spl22_74
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_74])]) ).
fof(f2515,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_231 ),
inference(resolution,[],[f2511,f663]) ).
fof(f663,plain,
( ! [X2,X0,X1] :
( ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f23055,plain,
( spl22_926
| ~ spl22_635
| ~ spl22_905 ),
inference(avatar_split_clause,[],[f22396,f22330,f13056,f23053]) ).
fof(f23053,plain,
( spl22_926
<=> ! [X0] :
( ~ sP0(X0,sK15)
| ~ sP1(X0)
| sP0(sK15,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_926])]) ).
fof(f22330,plain,
( spl22_905
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| ~ in(X1,relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_905])]) ).
fof(f22396,plain,
( ! [X0] :
( ~ sP0(X0,sK15)
| ~ sP1(X0)
| sP0(sK15,relation_rng(X0)) )
| ~ spl22_635
| ~ spl22_905 ),
inference(resolution,[],[f22331,f13057]) ).
fof(f22331,plain,
( ! [X0,X1] :
( ~ in(X1,relation_rng(X0))
| ~ sP0(X0,sK15)
| ~ sP1(X0) )
| ~ spl22_905 ),
inference(avatar_component_clause,[],[f22330]) ).
fof(f23051,plain,
( spl22_925
| ~ spl22_74
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2494,f2489,f662,f23049]) ).
fof(f23049,plain,
( spl22_925
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_925])]) ).
fof(f2494,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_230 ),
inference(resolution,[],[f2490,f663]) ).
fof(f23047,plain,
( spl22_924
| ~ spl22_74
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2473,f2468,f662,f23045]) ).
fof(f23045,plain,
( spl22_924
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_924])]) ).
fof(f2473,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_229 ),
inference(resolution,[],[f2469,f663]) ).
fof(f23043,plain,
( spl22_923
| ~ spl22_74
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2452,f2447,f662,f23041]) ).
fof(f23041,plain,
( spl22_923
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_923])]) ).
fof(f2452,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_228 ),
inference(resolution,[],[f2448,f663]) ).
fof(f22873,plain,
( spl22_922
| spl22_921
| spl22_89
| ~ spl22_524 ),
inference(avatar_split_clause,[],[f10076,f10020,f783,f22778,f22870]) ).
fof(f22870,plain,
( spl22_922
<=> apply(relation_dom_restriction(sK19,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK19,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_922])]) ).
fof(f22778,plain,
( spl22_921
<=> sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) = apply(sK5,sK8(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_921])]) ).
fof(f783,plain,
( spl22_89
<=> sP0(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_89])]) ).
fof(f10076,plain,
( sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) = apply(sK5,sK8(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| apply(relation_dom_restriction(sK19,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK19,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| spl22_89
| ~ spl22_524 ),
inference(resolution,[],[f10021,f785]) ).
fof(f785,plain,
( ~ sP0(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))
| spl22_89 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f22781,plain,
( spl22_920
| spl22_921
| spl22_89
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2538,f2531,f783,f22778,f22774]) ).
fof(f22774,plain,
( spl22_920
<=> apply(relation_dom_restriction(sK5,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK5,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_920])]) ).
fof(f2538,plain,
( sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) = apply(sK5,sK8(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| apply(relation_dom_restriction(sK5,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK5,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| spl22_89
| ~ spl22_232 ),
inference(resolution,[],[f2532,f785]) ).
fof(f22772,plain,
( spl22_919
| ~ spl22_147
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2524,f2510,f1393,f22770]) ).
fof(f22770,plain,
( spl22_919
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| apply(sK5,sK13(X0,X1,apply(X2,X3))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,apply(X2,X3)))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_919])]) ).
fof(f2524,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| apply(sK5,sK13(X0,X1,apply(X2,X3))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,apply(X2,X3)))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1394]) ).
fof(f22768,plain,
( spl22_918
| ~ spl22_147
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2503,f2489,f1393,f22766]) ).
fof(f22766,plain,
( spl22_918
<=> ! [X0,X3,X2,X1] :
( sP2(apply(X0,X1),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(apply(X0,X1),X2,X3)) = apply(sK5,sK13(apply(X0,X1),X2,X3))
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_918])]) ).
fof(f2503,plain,
( ! [X2,X3,X0,X1] :
( sP2(apply(X0,X1),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(apply(X0,X1),X2,X3)) = apply(sK5,sK13(apply(X0,X1),X2,X3))
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_147
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1394]) ).
fof(f22764,plain,
( spl22_917
| ~ spl22_147
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2482,f2468,f1393,f22762]) ).
fof(f22762,plain,
( spl22_917
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| apply(sK5,sK13(X0,X1,apply(X2,X3))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,apply(X2,X3)))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_917])]) ).
fof(f2482,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| apply(sK5,sK13(X0,X1,apply(X2,X3))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,apply(X2,X3)))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1394]) ).
fof(f22760,plain,
( spl22_916
| ~ spl22_147
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2461,f2447,f1393,f22758]) ).
fof(f22758,plain,
( spl22_916
<=> ! [X0,X3,X2,X1] :
( sP2(X0,apply(X1,X2),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,apply(X1,X2),X3)) = apply(sK5,sK13(X0,apply(X1,X2),X3))
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_916])]) ).
fof(f2461,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,apply(X1,X2),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,apply(X1,X2),X3)) = apply(sK5,sK13(X0,apply(X1,X2),X3))
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1394]) ).
fof(f22657,plain,
( spl22_915
| ~ spl22_718
| ~ spl22_905 ),
inference(avatar_split_clause,[],[f22395,f22330,f15680,f22655]) ).
fof(f22655,plain,
( spl22_915
<=> ! [X0] :
( ~ sP0(X0,sK15)
| ~ sP1(X0)
| ~ sP0(sK5,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_915])]) ).
fof(f22395,plain,
( ! [X0] :
( ~ sP0(X0,sK15)
| ~ sP1(X0)
| ~ sP0(sK5,relation_rng(X0)) )
| ~ spl22_718
| ~ spl22_905 ),
inference(resolution,[],[f22331,f15681]) ).
fof(f22368,plain,
( spl22_914
| ~ spl22_62
| ~ spl22_243 ),
inference(avatar_split_clause,[],[f2723,f2706,f582,f22366]) ).
fof(f22366,plain,
( spl22_914
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(X2,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_914])]) ).
fof(f2706,plain,
( spl22_243
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_243])]) ).
fof(f2723,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(X2,X1) = X0 )
| ~ spl22_62
| ~ spl22_243 ),
inference(resolution,[],[f2707,f583]) ).
fof(f2707,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl22_243 ),
inference(avatar_component_clause,[],[f2706]) ).
fof(f22364,plain,
( spl22_913
| ~ spl22_62
| ~ spl22_242 ),
inference(avatar_split_clause,[],[f2719,f2702,f582,f22362]) ).
fof(f22362,plain,
( spl22_913
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_913])]) ).
fof(f2702,plain,
( spl22_242
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_242])]) ).
fof(f2719,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_intersection2(X1,X2) = X0 )
| ~ spl22_62
| ~ spl22_242 ),
inference(resolution,[],[f2703,f583]) ).
fof(f2703,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl22_242 ),
inference(avatar_component_clause,[],[f2702]) ).
fof(f22360,plain,
( spl22_912
| ~ spl22_218
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2670,f2575,f2367,f22358]) ).
fof(f22358,plain,
( spl22_912
<=> ! [X0] :
( sK15 = relation_dom(relation_dom(sK10(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_912])]) ).
fof(f2670,plain,
( ! [X0] :
( sK15 = relation_dom(relation_dom(sK10(powerset(X0))))
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_237 ),
inference(resolution,[],[f2576,f2368]) ).
fof(f22356,plain,
( spl22_911
| ~ spl22_24
| ~ spl22_697 ),
inference(avatar_split_clause,[],[f15271,f15268,f339,f22354]) ).
fof(f22354,plain,
( spl22_911
<=> ! [X0] : apply(relation_dom_restriction(sK5,powerset(X0)),sK15) = apply(sK5,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_911])]) ).
fof(f339,plain,
( spl22_24
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_24])]) ).
fof(f15268,plain,
( spl22_697
<=> ! [X0] :
( apply(relation_dom_restriction(sK5,powerset(X0)),sK15) = apply(sK5,sK15)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_697])]) ).
fof(f15271,plain,
( ! [X0] : apply(relation_dom_restriction(sK5,powerset(X0)),sK15) = apply(sK5,sK15)
| ~ spl22_24
| ~ spl22_697 ),
inference(resolution,[],[f15269,f340]) ).
fof(f340,plain,
( ! [X0] : ~ empty(powerset(X0))
| ~ spl22_24 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f15269,plain,
( ! [X0] :
( empty(powerset(X0))
| apply(relation_dom_restriction(sK5,powerset(X0)),sK15) = apply(sK5,sK15) )
| ~ spl22_697 ),
inference(avatar_component_clause,[],[f15268]) ).
fof(f22352,plain,
( spl22_910
| ~ spl22_218
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2653,f2571,f2367,f22350]) ).
fof(f22350,plain,
( spl22_910
<=> ! [X0] :
( sK15 = relation_dom(relation_rng(sK10(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_910])]) ).
fof(f2653,plain,
( ! [X0] :
( sK15 = relation_dom(relation_rng(sK10(powerset(X0))))
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_236 ),
inference(resolution,[],[f2572,f2368]) ).
fof(f22348,plain,
( spl22_909
| ~ spl22_218
| ~ spl22_235 ),
inference(avatar_split_clause,[],[f2636,f2567,f2367,f22346]) ).
fof(f22346,plain,
( spl22_909
<=> ! [X0] :
( sK15 = relation_rng(relation_dom(sK10(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_909])]) ).
fof(f2636,plain,
( ! [X0] :
( sK15 = relation_rng(relation_dom(sK10(powerset(X0))))
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_235 ),
inference(resolution,[],[f2568,f2368]) ).
fof(f22344,plain,
( spl22_908
| ~ spl22_218
| ~ spl22_234 ),
inference(avatar_split_clause,[],[f2619,f2563,f2367,f22342]) ).
fof(f22342,plain,
( spl22_908
<=> ! [X0] :
( sK15 = relation_rng(relation_rng(sK10(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_908])]) ).
fof(f2619,plain,
( ! [X0] :
( sK15 = relation_rng(relation_rng(sK10(powerset(X0))))
| ~ empty(X0) )
| ~ spl22_218
| ~ spl22_234 ),
inference(resolution,[],[f2564,f2368]) ).
fof(f22340,plain,
( spl22_907
| ~ spl22_138
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2594,f2559,f1286,f22338]) ).
fof(f22338,plain,
( spl22_907
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,relation_dom(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_907])]) ).
fof(f2594,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,relation_dom(X0),relation_dom(X0)) )
| ~ spl22_138
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1287]) ).
fof(f22336,plain,
( spl22_906
| ~ spl22_139
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2593,f2559,f1290,f22334]) ).
fof(f22334,plain,
( spl22_906
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP2(relation_dom(X0),X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_906])]) ).
fof(f2593,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP2(relation_dom(X0),X1,relation_dom(X0)) )
| ~ spl22_139
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1291]) ).
fof(f22332,plain,
( spl22_905
| ~ spl22_145
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2591,f2559,f1384,f22330]) ).
fof(f1384,plain,
( spl22_145
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| in(sK9(X1,X0),relation_dom(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_145])]) ).
fof(f2591,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| ~ in(X1,relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_145
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1385]) ).
fof(f1385,plain,
( ! [X0,X1] :
( in(sK9(X1,X0),relation_dom(X1))
| ~ in(X0,relation_rng(X1))
| ~ sP1(X1) )
| ~ spl22_145 ),
inference(avatar_component_clause,[],[f1384]) ).
fof(f22328,plain,
( spl22_904
| ~ spl22_55
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2405,f2367,f519,f22326]) ).
fof(f22326,plain,
( spl22_904
<=> ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_904])]) ).
fof(f2405,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = X1
| ~ empty(X1) )
| ~ spl22_55
| ~ spl22_218 ),
inference(resolution,[],[f2368,f520]) ).
fof(f22225,plain,
( ~ spl22_88
| ~ spl22_39
| spl22_903
| ~ spl22_112
| ~ spl22_167
| ~ spl22_203 ),
inference(avatar_split_clause,[],[f2207,f2166,f1616,f948,f22223,f410,f777]) ).
fof(f22223,plain,
( spl22_903
<=> ! [X0] : sK15 = relation_dom_restriction(sK15,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_903])]) ).
fof(f1616,plain,
( spl22_167
<=> ! [X0,X1] :
( relation_dom_restriction(X0,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_167])]) ).
fof(f2207,plain,
( ! [X0] :
( sK15 = relation_dom_restriction(sK15,X0)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_112
| ~ spl22_167
| ~ spl22_203 ),
inference(trivial_inequality_removal,[],[f2206]) ).
fof(f2206,plain,
( ! [X0] :
( sK15 != sK15
| sK15 = relation_dom_restriction(sK15,X0)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_112
| ~ spl22_167
| ~ spl22_203 ),
inference(forward_demodulation,[],[f2195,f949]) ).
fof(f2195,plain,
( ! [X0] :
( sK15 != set_intersection2(sK15,X0)
| sK15 = relation_dom_restriction(sK15,X0)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_167
| ~ spl22_203 ),
inference(superposition,[],[f1617,f2168]) ).
fof(f1617,plain,
( ! [X0,X1] :
( relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| relation_dom_restriction(X0,X1) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_167 ),
inference(avatar_component_clause,[],[f1616]) ).
fof(f21898,plain,
( spl22_902
| ~ spl22_232
| ~ spl22_309 ),
inference(avatar_split_clause,[],[f3555,f3534,f2531,f21896]) ).
fof(f21896,plain,
( spl22_902
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X3,X0)
| sK7(X2,relation_dom(X3)) = apply(X2,sK8(X2,relation_dom(X3)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK7(X2,relation_dom(X3))) = apply(sK5,sK7(X2,relation_dom(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_902])]) ).
fof(f3534,plain,
( spl22_309
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_309])]) ).
fof(f3555,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X3,X0)
| sK7(X2,relation_dom(X3)) = apply(X2,sK8(X2,relation_dom(X3)))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK7(X2,relation_dom(X3))) = apply(sK5,sK7(X2,relation_dom(X3))) )
| ~ spl22_232
| ~ spl22_309 ),
inference(resolution,[],[f3535,f2532]) ).
fof(f3535,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X3,relation_dom(X0))
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP0(X0,X1) )
| ~ spl22_309 ),
inference(avatar_component_clause,[],[f3534]) ).
fof(f21773,plain,
( spl22_901
| ~ spl22_230
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3829,f3697,f2489,f21771]) ).
fof(f21771,plain,
( spl22_901
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(apply(X1,X0),X3,X4)) = apply(sK5,sK13(apply(X1,X0),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_901])]) ).
fof(f3829,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(apply(X1,X0),X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(apply(X1,X0),X3,X4)) = apply(sK5,sK13(apply(X1,X0),X3,X4)) )
| ~ spl22_230
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2490]) ).
fof(f21769,plain,
( spl22_900
| ~ spl22_228
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3825,f3697,f2447,f21767]) ).
fof(f21767,plain,
( spl22_900
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,apply(X1,X0),X4)) = apply(sK5,sK13(X3,apply(X1,X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_900])]) ).
fof(f3825,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,apply(X1,X0),X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X3,apply(X1,X0),X4)) = apply(sK5,sK13(X3,apply(X1,X0),X4)) )
| ~ spl22_228
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2448]) ).
fof(f21765,plain,
( spl22_899
| ~ spl22_231
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3824,f3697,f2510,f21763]) ).
fof(f21763,plain,
( spl22_899
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| apply(sK5,sK13(X3,X4,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_899])]) ).
fof(f3824,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| apply(sK5,sK13(X3,X4,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,apply(X1,X0))) )
| ~ spl22_231
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2511]) ).
fof(f21761,plain,
( spl22_898
| ~ spl22_229
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3823,f3697,f2468,f21759]) ).
fof(f21759,plain,
( spl22_898
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| apply(sK5,sK13(X3,X4,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_898])]) ).
fof(f3823,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP2(X3,X4,apply(X1,X0))
| apply(sK5,sK13(X3,X4,apply(X1,X0))) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,apply(X1,X0))) )
| ~ spl22_229
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2469]) ).
fof(f21601,plain,
( spl22_897
| ~ spl22_153
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2353,f2344,f1508,f21599]) ).
fof(f21599,plain,
( spl22_897
<=> ! [X0,X1] :
( sP0(X0,relation_rng(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_rng(X1))) = apply(sK5,sK8(X0,relation_rng(X1)))
| sK7(X0,relation_rng(X1)) = apply(X1,sK9(X1,sK7(X0,relation_rng(X1))))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_897])]) ).
fof(f2353,plain,
( ! [X0,X1] :
( sP0(X0,relation_rng(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_rng(X1))) = apply(sK5,sK8(X0,relation_rng(X1)))
| sK7(X0,relation_rng(X1)) = apply(X1,sK9(X1,sK7(X0,relation_rng(X1))))
| ~ sP1(X1) )
| ~ spl22_153
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1509]) ).
fof(f21517,plain,
( spl22_896
| ~ spl22_147
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2357,f2344,f1393,f21515]) ).
fof(f21515,plain,
( spl22_896
<=> ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,apply(X1,X2))) = apply(sK5,sK8(X0,apply(X1,X2)))
| ~ sP0(X1,sK7(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_896])]) ).
fof(f2357,plain,
( ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,apply(X1,X2))) = apply(sK5,sK8(X0,apply(X1,X2)))
| ~ sP0(X1,sK7(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1394]) ).
fof(f21513,plain,
( spl22_895
| ~ spl22_74
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2348,f2344,f662,f21511]) ).
fof(f21511,plain,
( spl22_895
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_895])]) ).
fof(f2348,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_216 ),
inference(resolution,[],[f2345,f663]) ).
fof(f21509,plain,
( spl22_894
| ~ spl22_74
| ~ spl22_215 ),
inference(avatar_split_clause,[],[f2323,f2316,f662,f21507]) ).
fof(f21507,plain,
( spl22_894
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| apply(relation_dom_restriction(X2,relation_dom(X0)),sK8(X0,X1)) = apply(X2,sK8(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_894])]) ).
fof(f2323,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| apply(relation_dom_restriction(X2,relation_dom(X0)),sK8(X0,X1)) = apply(X2,sK8(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_215 ),
inference(resolution,[],[f2317,f663]) ).
fof(f20847,plain,
( spl22_893
| ~ spl22_495
| ~ spl22_870 ),
inference(avatar_split_clause,[],[f20632,f19532,f9032,f20845]) ).
fof(f19532,plain,
( spl22_870
<=> ! [X0,X1] :
( empty(set_intersection2(sK10(powerset(X0)),X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_870])]) ).
fof(f20632,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,sK10(powerset(X0))),sK15) )
| ~ spl22_495
| ~ spl22_870 ),
inference(resolution,[],[f19533,f9033]) ).
fof(f19533,plain,
( ! [X0,X1] :
( empty(set_intersection2(sK10(powerset(X0)),X1))
| ~ empty(X0) )
| ~ spl22_870 ),
inference(avatar_component_clause,[],[f19532]) ).
fof(f20832,plain,
( spl22_892
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_528 ),
inference(avatar_split_clause,[],[f10343,f10230,f4126,f935,f511,f15306,f20830]) ).
fof(f20830,plain,
( spl22_892
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_892])]) ).
fof(f10343,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_528 ),
inference(forward_demodulation,[],[f10342,f512]) ).
fof(f10342,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_528 ),
inference(forward_demodulation,[],[f10330,f4127]) ).
fof(f10330,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_528 ),
inference(superposition,[],[f10231,f937]) ).
fof(f20828,plain,
( spl22_891
| ~ spl22_216
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3804,f3697,f2344,f20826]) ).
fof(f20826,plain,
( spl22_891
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP0(X3,apply(X1,X0))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,apply(X1,X0))) = apply(sK5,sK8(X3,apply(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_891])]) ).
fof(f3804,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X2)
| ~ sP0(X1,powerset(X2))
| sP0(X3,apply(X1,X0))
| apply(relation_dom_restriction(sK5,relation_dom(X3)),sK8(X3,apply(X1,X0))) = apply(sK5,sK8(X3,apply(X1,X0))) )
| ~ spl22_216
| ~ spl22_328 ),
inference(resolution,[],[f3698,f2345]) ).
fof(f20824,plain,
( spl22_890
| ~ spl22_128
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2526,f2510,f1151,f20822]) ).
fof(f20822,plain,
( spl22_890
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK10(powerset(X2))))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_890])]) ).
fof(f2526,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK10(powerset(X2))))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) )
| ~ spl22_128
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1152]) ).
fof(f20820,plain,
( spl22_889
| ~ spl22_129
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2519,f2510,f1155,f20818]) ).
fof(f20818,plain,
( spl22_889
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_889])]) ).
fof(f2519,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) )
| ~ spl22_129
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1156]) ).
fof(f20816,plain,
( spl22_888
| ~ spl22_130
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2518,f2510,f1159,f20814]) ).
fof(f20814,plain,
( spl22_888
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_888])]) ).
fof(f2518,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) )
| ~ spl22_130
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1160]) ).
fof(f20812,plain,
( spl22_887
| ~ spl22_128
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2505,f2489,f1151,f20810]) ).
fof(f20810,plain,
( spl22_887
<=> ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(sK10(powerset(X0)),X1,X2)) = apply(sK5,sK13(sK10(powerset(X0)),X1,X2))
| element(sK13(sK10(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_887])]) ).
fof(f2505,plain,
( ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(sK10(powerset(X0)),X1,X2)) = apply(sK5,sK13(sK10(powerset(X0)),X1,X2))
| element(sK13(sK10(powerset(X0)),X1,X2),X0) )
| ~ spl22_128
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1152]) ).
fof(f20808,plain,
( spl22_886
| ~ spl22_129
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2498,f2489,f1155,f20806]) ).
fof(f20806,plain,
( spl22_886
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(set_intersection2(X0,X1),X2,X3)) = apply(sK5,sK13(set_intersection2(X0,X1),X2,X3))
| in(sK13(set_intersection2(X0,X1),X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_886])]) ).
fof(f2498,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(set_intersection2(X0,X1),X2,X3)) = apply(sK5,sK13(set_intersection2(X0,X1),X2,X3))
| in(sK13(set_intersection2(X0,X1),X2,X3),X0) )
| ~ spl22_129
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1156]) ).
fof(f20804,plain,
( spl22_885
| ~ spl22_130
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2497,f2489,f1159,f20802]) ).
fof(f20802,plain,
( spl22_885
<=> ! [X0,X3,X2,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(set_intersection2(X0,X1),X2,X3)) = apply(sK5,sK13(set_intersection2(X0,X1),X2,X3))
| in(sK13(set_intersection2(X0,X1),X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_885])]) ).
fof(f2497,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(set_intersection2(X0,X1),X2,X3)) = apply(sK5,sK13(set_intersection2(X0,X1),X2,X3))
| in(sK13(set_intersection2(X0,X1),X2,X3),X1) )
| ~ spl22_130
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1160]) ).
fof(f20800,plain,
( spl22_884
| ~ spl22_128
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2484,f2468,f1151,f20798]) ).
fof(f20798,plain,
( spl22_884
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK10(powerset(X2))))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_884])]) ).
fof(f2484,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK10(powerset(X2))))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) )
| ~ spl22_128
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1152]) ).
fof(f20796,plain,
( spl22_883
| ~ spl22_495
| ~ spl22_869 ),
inference(avatar_split_clause,[],[f20582,f19528,f9032,f20794]) ).
fof(f19528,plain,
( spl22_869
<=> ! [X0,X1] :
( empty(set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_869])]) ).
fof(f20582,plain,
( ! [X0] :
( ~ sP0(X0,sK15)
| sP0(relation_dom_restriction(sK5,relation_dom(X0)),sK15) )
| ~ spl22_495
| ~ spl22_869 ),
inference(resolution,[],[f19529,f9033]) ).
fof(f19529,plain,
( ! [X0,X1] :
( empty(set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,sK15) )
| ~ spl22_869 ),
inference(avatar_component_clause,[],[f19528]) ).
fof(f20792,plain,
( spl22_882
| ~ spl22_129
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2477,f2468,f1155,f20790]) ).
fof(f20790,plain,
( spl22_882
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_882])]) ).
fof(f2477,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) )
| ~ spl22_129
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1156]) ).
fof(f20788,plain,
( spl22_881
| ~ spl22_130
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2476,f2468,f1159,f20786]) ).
fof(f20786,plain,
( spl22_881
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_881])]) ).
fof(f2476,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| apply(sK5,sK13(X0,X1,set_intersection2(X2,X3))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,set_intersection2(X2,X3)))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) )
| ~ spl22_130
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1160]) ).
fof(f20784,plain,
( spl22_880
| ~ spl22_128
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2463,f2447,f1151,f20782]) ).
fof(f20782,plain,
( spl22_880
<=> ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,sK10(powerset(X1)),X2)) = apply(sK5,sK13(X0,sK10(powerset(X1)),X2))
| element(sK13(X0,sK10(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_880])]) ).
fof(f2463,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,sK10(powerset(X1)),X2)) = apply(sK5,sK13(X0,sK10(powerset(X1)),X2))
| element(sK13(X0,sK10(powerset(X1)),X2),X1) )
| ~ spl22_128
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1152]) ).
fof(f20780,plain,
( spl22_879
| ~ spl22_129
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2456,f2447,f1155,f20778]) ).
fof(f20778,plain,
( spl22_879
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,set_intersection2(X1,X2),X3)) = apply(sK5,sK13(X0,set_intersection2(X1,X2),X3))
| in(sK13(X0,set_intersection2(X1,X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_879])]) ).
fof(f2456,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,set_intersection2(X1,X2),X3)) = apply(sK5,sK13(X0,set_intersection2(X1,X2),X3))
| in(sK13(X0,set_intersection2(X1,X2),X3),X1) )
| ~ spl22_129
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1156]) ).
fof(f20776,plain,
( spl22_878
| ~ spl22_130
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2455,f2447,f1159,f20774]) ).
fof(f20774,plain,
( spl22_878
<=> ! [X0,X3,X2,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,set_intersection2(X1,X2),X3)) = apply(sK5,sK13(X0,set_intersection2(X1,X2),X3))
| in(sK13(X0,set_intersection2(X1,X2),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_878])]) ).
fof(f2455,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X0,set_intersection2(X1,X2),X3)) = apply(sK5,sK13(X0,set_intersection2(X1,X2),X3))
| in(sK13(X0,set_intersection2(X1,X2),X3),X2) )
| ~ spl22_130
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1160]) ).
fof(f20198,plain,
( spl22_877
| ~ spl22_801
| ~ spl22_849 ),
inference(avatar_split_clause,[],[f19960,f19428,f17032,f20196]) ).
fof(f17032,plain,
( spl22_801
<=> ! [X0] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_801])]) ).
fof(f19960,plain,
( ! [X0,X1] :
( sP0(relation_dom_restriction(sK5,X0),X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_801
| ~ spl22_849 ),
inference(resolution,[],[f19429,f17033]) ).
fof(f17033,plain,
( ! [X0] :
( sP0(relation_dom_restriction(sK5,X0),sK15)
| ~ empty(X0) )
| ~ spl22_801 ),
inference(avatar_component_clause,[],[f17032]) ).
fof(f19893,plain,
( spl22_876
| ~ spl22_47
| ~ spl22_684 ),
inference(avatar_split_clause,[],[f15147,f14820,f462,f19891]) ).
fof(f15147,plain,
( ! [X0] :
( sP0(sK15,relation_dom(X0))
| ~ empty(relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_684 ),
inference(resolution,[],[f14821,f463]) ).
fof(f19744,plain,
( ~ spl22_39
| spl22_875
| ~ spl22_7
| ~ spl22_92
| ~ spl22_112
| ~ spl22_203
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3590,f3551,f2166,f948,f798,f254,f19742,f410]) ).
fof(f19742,plain,
( spl22_875
<=> ! [X0] : sK15 = relation_dom(relation_dom_restriction(sK15,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_875])]) ).
fof(f3590,plain,
( ! [X0] :
( sK15 = relation_dom(relation_dom_restriction(sK15,X0))
| ~ function(sK15) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_112
| ~ spl22_203
| ~ spl22_313 ),
inference(forward_demodulation,[],[f3589,f949]) ).
fof(f3589,plain,
( ! [X0] :
( set_intersection2(sK15,X0) = relation_dom(relation_dom_restriction(sK15,X0))
| ~ function(sK15) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_203
| ~ spl22_313 ),
inference(forward_demodulation,[],[f3588,f2168]) ).
fof(f3588,plain,
( ! [X0] :
( set_intersection2(relation_dom(sK15),X0) = relation_dom(relation_dom_restriction(sK15,X0))
| ~ function(sK15) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_313 ),
inference(forward_demodulation,[],[f3587,f800]) ).
fof(f3587,plain,
( ! [X0] :
( ~ function(sK15)
| set_intersection2(relation_dom(empty_set),X0) = relation_dom(relation_dom_restriction(empty_set,X0)) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_313 ),
inference(forward_demodulation,[],[f3578,f800]) ).
fof(f3578,plain,
( ! [X0] :
( ~ function(empty_set)
| set_intersection2(relation_dom(empty_set),X0) = relation_dom(relation_dom_restriction(empty_set,X0)) )
| ~ spl22_7
| ~ spl22_313 ),
inference(resolution,[],[f3552,f256]) ).
fof(f19646,plain,
( spl22_874
| ~ spl22_20
| ~ spl22_19
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f3251,f2999,f314,f319,f19643]) ).
fof(f19643,plain,
( spl22_874
<=> sK20 = relation_dom_restriction(sK20,relation_dom(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_874])]) ).
fof(f3251,plain,
( ~ function(sK20)
| sK20 = relation_dom_restriction(sK20,relation_dom(sK20))
| ~ spl22_19
| ~ spl22_278 ),
inference(resolution,[],[f3000,f316]) ).
fof(f19547,plain,
( spl22_873
| ~ spl22_18
| ~ spl22_17
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f3250,f2999,f304,f309,f19544]) ).
fof(f19544,plain,
( spl22_873
<=> sK19 = relation_dom_restriction(sK19,relation_dom(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_873])]) ).
fof(f3250,plain,
( ~ function(sK19)
| sK19 = relation_dom_restriction(sK19,relation_dom(sK19))
| ~ spl22_17
| ~ spl22_278 ),
inference(resolution,[],[f3000,f306]) ).
fof(f19542,plain,
( spl22_872
| ~ spl22_121
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3137,f2907,f1110,f19540]) ).
fof(f19540,plain,
( spl22_872
<=> ! [X0,X1] :
( empty(set_intersection2(X0,sK10(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_872])]) ).
fof(f3137,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,sK10(powerset(X1))))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_255 ),
inference(resolution,[],[f2908,f1111]) ).
fof(f19538,plain,
( spl22_871
| ~ spl22_233
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3131,f2907,f2559,f19536]) ).
fof(f19536,plain,
( spl22_871
<=> ! [X0,X1] :
( empty(set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_871])]) ).
fof(f3131,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,relation_dom(X1)))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_255 ),
inference(resolution,[],[f2908,f2560]) ).
fof(f19534,plain,
( spl22_870
| ~ spl22_121
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3113,f2903,f1110,f19532]) ).
fof(f3113,plain,
( ! [X0,X1] :
( empty(set_intersection2(sK10(powerset(X0)),X1))
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_254 ),
inference(resolution,[],[f2904,f1111]) ).
fof(f19530,plain,
( spl22_869
| ~ spl22_233
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3107,f2903,f2559,f19528]) ).
fof(f3107,plain,
( ! [X0,X1] :
( empty(set_intersection2(relation_dom(X0),X1))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_254 ),
inference(resolution,[],[f2904,f2560]) ).
fof(f19506,plain,
( spl22_868
| ~ spl22_121
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3092,f2895,f1110,f19504]) ).
fof(f19504,plain,
( spl22_868
<=> ! [X0,X1] :
( sP2(sK15,X0,sK10(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_868])]) ).
fof(f3092,plain,
( ! [X0,X1] :
( sP2(sK15,X0,sK10(powerset(X1)))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_252 ),
inference(resolution,[],[f2896,f1111]) ).
fof(f19502,plain,
( spl22_867
| ~ spl22_233
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f3086,f2895,f2559,f19500]) ).
fof(f19500,plain,
( spl22_867
<=> ! [X0,X1] :
( sP2(sK15,X0,relation_dom(X1))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_867])]) ).
fof(f3086,plain,
( ! [X0,X1] :
( sP2(sK15,X0,relation_dom(X1))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_252 ),
inference(resolution,[],[f2896,f2560]) ).
fof(f19498,plain,
( spl22_866
| ~ spl22_121
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3073,f2891,f1110,f19496]) ).
fof(f19496,plain,
( spl22_866
<=> ! [X0,X1] :
( sP2(X0,sK15,sK10(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_866])]) ).
fof(f3073,plain,
( ! [X0,X1] :
( sP2(X0,sK15,sK10(powerset(X1)))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_251 ),
inference(resolution,[],[f2892,f1111]) ).
fof(f19494,plain,
( spl22_865
| ~ spl22_233
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f3067,f2891,f2559,f19492]) ).
fof(f19492,plain,
( spl22_865
<=> ! [X0,X1] :
( sP2(X0,sK15,relation_dom(X1))
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_865])]) ).
fof(f3067,plain,
( ! [X0,X1] :
( sP2(X0,sK15,relation_dom(X1))
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_251 ),
inference(resolution,[],[f2892,f2560]) ).
fof(f19490,plain,
( spl22_864
| ~ spl22_121
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3037,f2887,f1110,f19488]) ).
fof(f19488,plain,
( spl22_864
<=> ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK15)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_864])]) ).
fof(f3037,plain,
( ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK15)
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_250 ),
inference(resolution,[],[f2888,f1111]) ).
fof(f19486,plain,
( spl22_863
| ~ spl22_233
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f3031,f2887,f2559,f19484]) ).
fof(f19484,plain,
( spl22_863
<=> ! [X0,X1] :
( sP2(X0,relation_dom(X1),sK15)
| ~ sP0(X1,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_863])]) ).
fof(f3031,plain,
( ! [X0,X1] :
( sP2(X0,relation_dom(X1),sK15)
| ~ sP0(X1,sK15) )
| ~ spl22_233
| ~ spl22_250 ),
inference(resolution,[],[f2888,f2560]) ).
fof(f19482,plain,
( spl22_862
| ~ spl22_121
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3018,f2883,f1110,f19480]) ).
fof(f19480,plain,
( spl22_862
<=> ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK15)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_862])]) ).
fof(f3018,plain,
( ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK15)
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_249 ),
inference(resolution,[],[f2884,f1111]) ).
fof(f19478,plain,
( spl22_861
| ~ spl22_233
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f3012,f2883,f2559,f19476]) ).
fof(f19476,plain,
( spl22_861
<=> ! [X0,X1] :
( sP2(relation_dom(X0),X1,sK15)
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_861])]) ).
fof(f3012,plain,
( ! [X0,X1] :
( sP2(relation_dom(X0),X1,sK15)
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_249 ),
inference(resolution,[],[f2884,f2560]) ).
fof(f19474,plain,
( spl22_860
| ~ spl22_119
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2841,f2743,f1064,f19472]) ).
fof(f19472,plain,
( spl22_860
<=> ! [X0] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_860])]) ).
fof(f2841,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| empty(relation_rng(X0)) )
| ~ spl22_119
| ~ spl22_248 ),
inference(resolution,[],[f2744,f1065]) ).
fof(f19470,plain,
( spl22_859
| ~ spl22_47
| ~ spl22_239 ),
inference(avatar_split_clause,[],[f2709,f2690,f462,f19468]) ).
fof(f19468,plain,
( spl22_859
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| empty(relation_dom(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_859])]) ).
fof(f2709,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| empty(relation_dom(X0))
| ~ sP1(X0) )
| ~ spl22_47
| ~ spl22_239 ),
inference(resolution,[],[f2691,f463]) ).
fof(f19466,plain,
( ~ spl22_105
| spl22_858
| ~ spl22_61
| ~ spl22_202
| ~ spl22_646 ),
inference(avatar_split_clause,[],[f13553,f13295,f2161,f578,f19464,f907]) ).
fof(f19464,plain,
( spl22_858
<=> ! [X0] :
( relation_dom(X0) = sK15
| ~ sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_858])]) ).
fof(f13553,plain,
( ! [X0] :
( relation_dom(X0) = sK15
| ~ sP0(X0,sK15)
| ~ sP1(sK15) )
| ~ spl22_61
| ~ spl22_202
| ~ spl22_646 ),
inference(forward_demodulation,[],[f13501,f2163]) ).
fof(f13501,plain,
( ! [X0] :
( ~ sP0(X0,sK15)
| relation_dom(X0) = relation_rng(sK15)
| ~ sP1(sK15) )
| ~ spl22_61
| ~ spl22_646 ),
inference(resolution,[],[f13296,f579]) ).
fof(f19462,plain,
( spl22_857
| ~ spl22_36
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2668,f2575,f398,f19460]) ).
fof(f19460,plain,
( spl22_857
<=> ! [X0] :
( sK15 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_857])]) ).
fof(f2668,plain,
( ! [X0] :
( sK15 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_237 ),
inference(resolution,[],[f2576,f399]) ).
fof(f19458,plain,
( spl22_856
| ~ spl22_34
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2667,f2575,f390,f19456]) ).
fof(f19456,plain,
( spl22_856
<=> ! [X0] :
( sK15 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_856])]) ).
fof(f2667,plain,
( ! [X0] :
( sK15 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_237 ),
inference(resolution,[],[f2576,f391]) ).
fof(f19454,plain,
( spl22_855
| ~ spl22_36
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2651,f2571,f398,f19452]) ).
fof(f19452,plain,
( spl22_855
<=> ! [X0] :
( sK15 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_855])]) ).
fof(f2651,plain,
( ! [X0] :
( sK15 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_236 ),
inference(resolution,[],[f2572,f399]) ).
fof(f19450,plain,
( spl22_854
| ~ spl22_34
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2650,f2571,f390,f19448]) ).
fof(f19448,plain,
( spl22_854
<=> ! [X0] :
( sK15 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_854])]) ).
fof(f2650,plain,
( ! [X0] :
( sK15 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_236 ),
inference(resolution,[],[f2572,f391]) ).
fof(f19446,plain,
( spl22_853
| ~ spl22_36
| ~ spl22_235 ),
inference(avatar_split_clause,[],[f2634,f2567,f398,f19444]) ).
fof(f19444,plain,
( spl22_853
<=> ! [X0] :
( sK15 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_853])]) ).
fof(f2634,plain,
( ! [X0] :
( sK15 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_235 ),
inference(resolution,[],[f2568,f399]) ).
fof(f19442,plain,
( spl22_852
| ~ spl22_34
| ~ spl22_235 ),
inference(avatar_split_clause,[],[f2633,f2567,f390,f19440]) ).
fof(f19440,plain,
( spl22_852
<=> ! [X0] :
( sK15 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_852])]) ).
fof(f2633,plain,
( ! [X0] :
( sK15 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_235 ),
inference(resolution,[],[f2568,f391]) ).
fof(f19438,plain,
( spl22_851
| ~ spl22_36
| ~ spl22_234 ),
inference(avatar_split_clause,[],[f2617,f2563,f398,f19436]) ).
fof(f19436,plain,
( spl22_851
<=> ! [X0] :
( sK15 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_851])]) ).
fof(f2617,plain,
( ! [X0] :
( sK15 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_234 ),
inference(resolution,[],[f2564,f399]) ).
fof(f19434,plain,
( spl22_850
| ~ spl22_34
| ~ spl22_234 ),
inference(avatar_split_clause,[],[f2616,f2563,f390,f19432]) ).
fof(f19432,plain,
( spl22_850
<=> ! [X0] :
( sK15 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_850])]) ).
fof(f2616,plain,
( ! [X0] :
( sK15 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_234 ),
inference(resolution,[],[f2564,f391]) ).
fof(f19430,plain,
( spl22_849
| ~ spl22_143
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2588,f2559,f1345,f19428]) ).
fof(f1345,plain,
( spl22_143
<=> ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_143])]) ).
fof(f2588,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_143
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1346]) ).
fof(f1346,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_143 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f19426,plain,
( spl22_848
| ~ spl22_117
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2408,f2367,f1053,f19424]) ).
fof(f19424,plain,
( spl22_848
<=> ! [X0] :
( ~ empty(X0)
| sK15 = relation_dom(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_848])]) ).
fof(f2408,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_dom(sK10(powerset(X0))) )
| ~ spl22_117
| ~ spl22_218 ),
inference(resolution,[],[f2368,f1054]) ).
fof(f19410,plain,
( spl22_847
| ~ spl22_116
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2407,f2367,f1049,f19408]) ).
fof(f19408,plain,
( spl22_847
<=> ! [X0] :
( ~ empty(X0)
| sK15 = relation_rng(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_847])]) ).
fof(f2407,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_rng(sK10(powerset(X0))) )
| ~ spl22_116
| ~ spl22_218 ),
inference(resolution,[],[f2368,f1050]) ).
fof(f19258,plain,
( spl22_846
| ~ spl22_71
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2534,f2531,f642,f19256]) ).
fof(f19256,plain,
( spl22_846
<=> ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(X2,X1)
| apply(X0,sK9(X0,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_846])]) ).
fof(f642,plain,
( spl22_71
<=> ! [X5,X0,X1] :
( apply(X0,sK9(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_71])]) ).
fof(f2534,plain,
( ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(X2,X1)
| apply(X0,sK9(X0,X2)) = X2 )
| ~ spl22_71
| ~ spl22_232 ),
inference(resolution,[],[f2532,f643]) ).
fof(f643,plain,
( ! [X0,X1,X5] :
( ~ sP0(X0,X1)
| ~ in(X5,X1)
| apply(X0,sK9(X0,X5)) = X5 )
| ~ spl22_71 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f18723,plain,
( spl22_845
| ~ spl22_68
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2535,f2531,f624,f18721]) ).
fof(f18721,plain,
( spl22_845
<=> ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(X2,X1)
| in(sK9(X0,X2),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_845])]) ).
fof(f2535,plain,
( ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(X2,X1)
| in(sK9(X0,X2),relation_dom(X0)) )
| ~ spl22_68
| ~ spl22_232 ),
inference(resolution,[],[f2532,f625]) ).
fof(f18719,plain,
( spl22_844
| ~ spl22_80
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2529,f2510,f716,f18717]) ).
fof(f18717,plain,
( spl22_844
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_844])]) ).
fof(f716,plain,
( spl22_80
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_80])]) ).
fof(f2529,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) )
| ~ spl22_80
| ~ spl22_231 ),
inference(duplicate_literal_removal,[],[f2513]) ).
fof(f2513,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_80
| ~ spl22_231 ),
inference(resolution,[],[f2511,f717]) ).
fof(f717,plain,
( ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,X2),X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_80 ),
inference(avatar_component_clause,[],[f716]) ).
fof(f18715,plain,
( spl22_843
| ~ spl22_132
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2525,f2510,f1242,f18713]) ).
fof(f18713,plain,
( spl22_843
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| apply(sK5,sK13(X0,X1,sK6(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK6(X2)))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_843])]) ).
fof(f2525,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| apply(sK5,sK13(X0,X1,sK6(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK6(X2)))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1243]) ).
fof(f18711,plain,
( spl22_842
| ~ spl22_132
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2504,f2489,f1242,f18709]) ).
fof(f18709,plain,
( spl22_842
<=> ! [X2,X0,X1] :
( sP2(sK6(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(sK6(X0),X1,X2)) = apply(sK5,sK13(sK6(X0),X1,X2))
| element(sK13(sK6(X0),X1,X2),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_842])]) ).
fof(f2504,plain,
( ! [X2,X0,X1] :
( sP2(sK6(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(sK6(X0),X1,X2)) = apply(sK5,sK13(sK6(X0),X1,X2))
| element(sK13(sK6(X0),X1,X2),X0)
| empty(X0) )
| ~ spl22_132
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1243]) ).
fof(f18707,plain,
( spl22_841
| ~ spl22_80
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2487,f2468,f716,f18705]) ).
fof(f18705,plain,
( spl22_841
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_841])]) ).
fof(f2487,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) )
| ~ spl22_80
| ~ spl22_229 ),
inference(duplicate_literal_removal,[],[f2471]) ).
fof(f2471,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_80
| ~ spl22_229 ),
inference(resolution,[],[f2469,f717]) ).
fof(f18703,plain,
( spl22_840
| ~ spl22_132
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2483,f2468,f1242,f18701]) ).
fof(f18701,plain,
( spl22_840
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| apply(sK5,sK13(X0,X1,sK6(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK6(X2)))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_840])]) ).
fof(f2483,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| apply(sK5,sK13(X0,X1,sK6(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK6(X2)))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1243]) ).
fof(f18699,plain,
( spl22_839
| ~ spl22_132
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2462,f2447,f1242,f18697]) ).
fof(f18697,plain,
( spl22_839
<=> ! [X2,X0,X1] :
( sP2(X0,sK6(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,sK6(X1),X2)) = apply(sK5,sK13(X0,sK6(X1),X2))
| element(sK13(X0,sK6(X1),X2),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_839])]) ).
fof(f2462,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK6(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,sK6(X1),X2)) = apply(sK5,sK13(X0,sK6(X1),X2))
| element(sK13(X0,sK6(X1),X2),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1243]) ).
fof(f18592,plain,
( spl22_838
| ~ spl22_133
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15702,f15680,f1246,f18590]) ).
fof(f18590,plain,
( spl22_838
<=> ! [X0,X1] :
( ~ sP0(sK5,relation_dom(X0))
| ~ sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_838])]) ).
fof(f15702,plain,
( ! [X0,X1] :
( ~ sP0(sK5,relation_dom(X0))
| ~ sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_133
| ~ spl22_718 ),
inference(resolution,[],[f15681,f1247]) ).
fof(f18578,plain,
( spl22_837
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_507 ),
inference(avatar_split_clause,[],[f9485,f9264,f4126,f935,f511,f15306,f18576]) ).
fof(f18576,plain,
( spl22_837
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| element(sK13(X0,X1,apply(sK5,sK4)),X0)
| sP2(X0,X1,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_837])]) ).
fof(f9485,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| element(sK13(X0,X1,apply(sK5,sK4)),X0) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_507 ),
inference(forward_demodulation,[],[f9484,f512]) ).
fof(f9484,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| element(sK13(X0,X1,apply(sK5,sK4)),X0) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_507 ),
inference(forward_demodulation,[],[f9472,f4127]) ).
fof(f9472,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| element(sK13(X0,X1,apply(sK5,sK4)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_507 ),
inference(superposition,[],[f9265,f937]) ).
fof(f18564,plain,
( spl22_836
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_506 ),
inference(avatar_split_clause,[],[f9465,f9260,f4126,f935,f511,f15306,f18562]) ).
fof(f18562,plain,
( spl22_836
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| element(sK13(apply(sK5,sK4),X0,X1),X1)
| sP2(apply(sK5,sK4),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_836])]) ).
fof(f9465,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| sP2(apply(sK5,sK4),X0,X1)
| element(sK13(apply(sK5,sK4),X0,X1),X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_506 ),
inference(forward_demodulation,[],[f9464,f512]) ).
fof(f9464,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| sP2(apply(sK5,sK4),X0,X1)
| element(sK13(apply(sK5,sK4),X0,X1),X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_506 ),
inference(forward_demodulation,[],[f9452,f4127]) ).
fof(f9452,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| sP2(apply(sK5,sK4),X0,X1)
| element(sK13(apply(sK5,sK4),X0,X1),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_506 ),
inference(superposition,[],[f9261,f937]) ).
fof(f18550,plain,
( spl22_835
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_505 ),
inference(avatar_split_clause,[],[f9441,f9256,f4126,f935,f511,f15306,f18548]) ).
fof(f18548,plain,
( spl22_835
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| element(sK13(X0,X1,apply(sK5,sK4)),X1)
| sP2(X0,X1,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_835])]) ).
fof(f9441,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| element(sK13(X0,X1,apply(sK5,sK4)),X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_505 ),
inference(forward_demodulation,[],[f9440,f512]) ).
fof(f9440,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| element(sK13(X0,X1,apply(sK5,sK4)),X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_505 ),
inference(forward_demodulation,[],[f9428,f4127]) ).
fof(f9428,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| element(sK13(X0,X1,apply(sK5,sK4)),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_505 ),
inference(superposition,[],[f9257,f937]) ).
fof(f18536,plain,
( spl22_834
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_504 ),
inference(avatar_split_clause,[],[f9421,f9252,f4126,f935,f511,f15306,f18534]) ).
fof(f18534,plain,
( spl22_834
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| element(sK13(X0,apply(sK5,sK4),X1),X1)
| sP2(X0,apply(sK5,sK4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_834])]) ).
fof(f9421,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| sP2(X0,apply(sK5,sK4),X1)
| element(sK13(X0,apply(sK5,sK4),X1),X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_504 ),
inference(forward_demodulation,[],[f9420,f512]) ).
fof(f9420,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| sP2(X0,apply(sK5,sK4),X1)
| element(sK13(X0,apply(sK5,sK4),X1),X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_504 ),
inference(forward_demodulation,[],[f9408,f4127]) ).
fof(f9408,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| sP2(X0,apply(sK5,sK4),X1)
| element(sK13(X0,apply(sK5,sK4),X1),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_504 ),
inference(superposition,[],[f9253,f937]) ).
fof(f18522,plain,
( spl22_833
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_499 ),
inference(avatar_split_clause,[],[f9349,f9232,f4126,f935,f511,f15306,f18520]) ).
fof(f18520,plain,
( spl22_833
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| sP2(apply(sK5,sK4),X0,X1)
| in(sK13(apply(sK5,sK4),X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_833])]) ).
fof(f9349,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| in(sK13(apply(sK5,sK4),X0,X1),X1)
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_499 ),
inference(forward_demodulation,[],[f9348,f512]) ).
fof(f9348,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| in(sK13(apply(sK5,sK4),X0,X1),X1)
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_499 ),
inference(forward_demodulation,[],[f9336,f4127]) ).
fof(f9336,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| in(sK13(apply(sK5,sK4),X0,X1),X1)
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_109
| ~ spl22_499 ),
inference(superposition,[],[f9233,f937]) ).
fof(f18518,plain,
( spl22_832
| ~ spl22_248
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15694,f15680,f2743,f18516]) ).
fof(f18516,plain,
( spl22_832
<=> ! [X0] :
( ~ sP0(sK5,relation_rng(X0))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_832])]) ).
fof(f15694,plain,
( ! [X0] :
( ~ sP0(sK5,relation_rng(X0))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl22_248
| ~ spl22_718 ),
inference(resolution,[],[f15681,f2744]) ).
fof(f18504,plain,
( spl22_831
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_498 ),
inference(avatar_split_clause,[],[f9329,f9228,f4126,f935,f511,f15306,f18502]) ).
fof(f18502,plain,
( spl22_831
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| sP2(X0,apply(sK5,sK4),X1)
| in(sK13(X0,apply(sK5,sK4),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_831])]) ).
fof(f9329,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| in(sK13(X0,apply(sK5,sK4),X1),X1)
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_498 ),
inference(forward_demodulation,[],[f9328,f512]) ).
fof(f9328,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| in(sK13(X0,apply(sK5,sK4),X1),X1)
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_498 ),
inference(forward_demodulation,[],[f9316,f4127]) ).
fof(f9316,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| in(sK13(X0,apply(sK5,sK4),X1),X1)
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_109
| ~ spl22_498 ),
inference(superposition,[],[f9229,f937]) ).
fof(f18490,plain,
( spl22_830
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_497 ),
inference(avatar_split_clause,[],[f9309,f9223,f4126,f935,f511,f15306,f18488]) ).
fof(f18488,plain,
( spl22_830
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| in(sK13(X0,X1,apply(sK5,sK4)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_830])]) ).
fof(f9309,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X1)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_497 ),
inference(forward_demodulation,[],[f9308,f512]) ).
fof(f9308,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X1)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_497 ),
inference(forward_demodulation,[],[f9296,f4127]) ).
fof(f9296,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| in(sK13(X0,X1,apply(sK5,sK4)),X1)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_497 ),
inference(superposition,[],[f9224,f937]) ).
fof(f18476,plain,
( spl22_829
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_496 ),
inference(avatar_split_clause,[],[f9289,f9219,f4126,f935,f511,f15306,f18474]) ).
fof(f18474,plain,
( spl22_829
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| in(sK13(X0,X1,apply(sK5,sK4)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_829])]) ).
fof(f9289,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X0)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_496 ),
inference(forward_demodulation,[],[f9288,f512]) ).
fof(f9288,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X0)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_496 ),
inference(forward_demodulation,[],[f9276,f4127]) ).
fof(f9276,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| in(sK13(X0,X1,apply(sK5,sK4)),X0)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_496 ),
inference(superposition,[],[f9220,f937]) ).
fof(f18472,plain,
( spl22_828
| ~ spl22_128
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2359,f2344,f1151,f18470]) ).
fof(f18470,plain,
( spl22_828
<=> ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK10(powerset(X1)))) = apply(sK5,sK8(X0,sK10(powerset(X1))))
| element(sK7(X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_828])]) ).
fof(f2359,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK10(powerset(X1)))) = apply(sK5,sK8(X0,sK10(powerset(X1))))
| element(sK7(X0,sK10(powerset(X1))),X1) )
| ~ spl22_128
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1152]) ).
fof(f18468,plain,
( spl22_827
| ~ spl22_129
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2352,f2344,f1155,f18466]) ).
fof(f18466,plain,
( spl22_827
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,set_intersection2(X1,X2))) = apply(sK5,sK8(X0,set_intersection2(X1,X2)))
| in(sK7(X0,set_intersection2(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_827])]) ).
fof(f2352,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,set_intersection2(X1,X2))) = apply(sK5,sK8(X0,set_intersection2(X1,X2)))
| in(sK7(X0,set_intersection2(X1,X2)),X1) )
| ~ spl22_129
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1156]) ).
fof(f18464,plain,
( spl22_826
| ~ spl22_130
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2351,f2344,f1159,f18462]) ).
fof(f18462,plain,
( spl22_826
<=> ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,set_intersection2(X1,X2))) = apply(sK5,sK8(X0,set_intersection2(X1,X2)))
| in(sK7(X0,set_intersection2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_826])]) ).
fof(f2351,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,set_intersection2(X1,X2))) = apply(sK5,sK8(X0,set_intersection2(X1,X2)))
| in(sK7(X0,set_intersection2(X1,X2)),X2) )
| ~ spl22_130
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1160]) ).
fof(f18150,plain,
( spl22_825
| ~ spl22_230
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3372,f3304,f2489,f18148]) ).
fof(f18148,plain,
( spl22_825
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_rng(X0),X2,X3)) = apply(sK5,sK13(relation_rng(X0),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_825])]) ).
fof(f3372,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(relation_rng(X0),X2,X3)
| apply(relation_dom_restriction(sK5,X3),sK13(relation_rng(X0),X2,X3)) = apply(sK5,sK13(relation_rng(X0),X2,X3)) )
| ~ spl22_230
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2490]) ).
fof(f18146,plain,
( spl22_824
| ~ spl22_228
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3368,f3304,f2447,f18144]) ).
fof(f18144,plain,
( spl22_824
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,relation_rng(X0),X3)) = apply(sK5,sK13(X2,relation_rng(X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_824])]) ).
fof(f3368,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,relation_rng(X0),X3)
| apply(relation_dom_restriction(sK5,X3),sK13(X2,relation_rng(X0),X3)) = apply(sK5,sK13(X2,relation_rng(X0),X3)) )
| ~ spl22_228
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2448]) ).
fof(f18142,plain,
( spl22_823
| ~ spl22_231
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3367,f3304,f2510,f18140]) ).
fof(f18140,plain,
( spl22_823
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_823])]) ).
fof(f3367,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X2,X3,relation_rng(X0))) )
| ~ spl22_231
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2511]) ).
fof(f18138,plain,
( spl22_822
| ~ spl22_229
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3366,f3304,f2468,f18136]) ).
fof(f18136,plain,
( spl22_822
<=> ! [X0,X3,X2,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_822])]) ).
fof(f3366,plain,
( ! [X2,X3,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP2(X2,X3,relation_rng(X0))
| apply(sK5,sK13(X2,X3,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X3),sK13(X2,X3,relation_rng(X0))) )
| ~ spl22_229
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2469]) ).
fof(f17945,plain,
( spl22_821
| ~ spl22_546
| ~ spl22_583
| ~ spl22_814 ),
inference(avatar_split_clause,[],[f17895,f17600,f11535,f10626,f17942]) ).
fof(f17942,plain,
( spl22_821
<=> sK15 = sK10(powerset(sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_821])]) ).
fof(f10626,plain,
( spl22_546
<=> empty(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_546])]) ).
fof(f11535,plain,
( spl22_583
<=> sK15 = relation_dom_restriction(sK5,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_583])]) ).
fof(f17600,plain,
( spl22_814
<=> ! [X0] :
( ~ empty(X0)
| sK15 = sK10(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_814])]) ).
fof(f17895,plain,
( sK15 = sK10(powerset(sK15))
| ~ spl22_546
| ~ spl22_583
| ~ spl22_814 ),
inference(forward_demodulation,[],[f17888,f11537]) ).
fof(f11537,plain,
( sK15 = relation_dom_restriction(sK5,sK15)
| ~ spl22_583 ),
inference(avatar_component_clause,[],[f11535]) ).
fof(f17888,plain,
( sK15 = sK10(powerset(relation_dom_restriction(sK5,sK15)))
| ~ spl22_546
| ~ spl22_814 ),
inference(resolution,[],[f17601,f10628]) ).
fof(f10628,plain,
( empty(relation_dom_restriction(sK5,sK15))
| ~ spl22_546 ),
inference(avatar_component_clause,[],[f10626]) ).
fof(f17601,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = sK10(powerset(X0)) )
| ~ spl22_814 ),
inference(avatar_component_clause,[],[f17600]) ).
fof(f17784,plain,
( ~ spl22_39
| spl22_820
| ~ spl22_7
| ~ spl22_92
| ~ spl22_203
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f3255,f2999,f2166,f798,f254,f17781,f410]) ).
fof(f17781,plain,
( spl22_820
<=> sK15 = relation_dom_restriction(sK15,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_820])]) ).
fof(f3255,plain,
( sK15 = relation_dom_restriction(sK15,sK15)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_92
| ~ spl22_203
| ~ spl22_278 ),
inference(forward_demodulation,[],[f3254,f2168]) ).
fof(f3254,plain,
( sK15 = relation_dom_restriction(sK15,relation_dom(sK15))
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_92
| ~ spl22_278 ),
inference(forward_demodulation,[],[f3253,f800]) ).
fof(f3253,plain,
( ~ function(sK15)
| empty_set = relation_dom_restriction(empty_set,relation_dom(empty_set))
| ~ spl22_7
| ~ spl22_92
| ~ spl22_278 ),
inference(forward_demodulation,[],[f3244,f800]) ).
fof(f3244,plain,
( ~ function(empty_set)
| empty_set = relation_dom_restriction(empty_set,relation_dom(empty_set))
| ~ spl22_7
| ~ spl22_278 ),
inference(resolution,[],[f3000,f256]) ).
fof(f17779,plain,
( spl22_819
| ~ spl22_36
| ~ spl22_241 ),
inference(avatar_split_clause,[],[f2714,f2698,f398,f17777]) ).
fof(f2714,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_241 ),
inference(resolution,[],[f2699,f399]) ).
fof(f17775,plain,
( spl22_818
| ~ spl22_62
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2441,f2399,f582,f17773]) ).
fof(f17773,plain,
( spl22_818
<=> ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X1,X0) = sK15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_818])]) ).
fof(f2399,plain,
( spl22_226
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_226])]) ).
fof(f2441,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X1,X0) = sK15 )
| ~ spl22_62
| ~ spl22_226 ),
inference(resolution,[],[f2400,f583]) ).
fof(f2400,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ empty(X0) )
| ~ spl22_226 ),
inference(avatar_component_clause,[],[f2399]) ).
fof(f17771,plain,
( spl22_817
| ~ spl22_62
| ~ spl22_223 ),
inference(avatar_split_clause,[],[f2432,f2387,f582,f17769]) ).
fof(f17769,plain,
( spl22_817
<=> ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X0,X1) = sK15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_817])]) ).
fof(f2387,plain,
( spl22_223
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_223])]) ).
fof(f2432,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X0,X1) = sK15 )
| ~ spl22_62
| ~ spl22_223 ),
inference(resolution,[],[f2388,f583]) ).
fof(f2388,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ empty(X1) )
| ~ spl22_223 ),
inference(avatar_component_clause,[],[f2387]) ).
fof(f17767,plain,
( spl22_816
| ~ spl22_62
| ~ spl22_220 ),
inference(avatar_split_clause,[],[f2421,f2375,f582,f17765]) ).
fof(f17765,plain,
( spl22_816
<=> ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_816])]) ).
fof(f2375,plain,
( spl22_220
<=> ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_220])]) ).
fof(f2421,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X1,X0) = X0 )
| ~ spl22_62
| ~ spl22_220 ),
inference(resolution,[],[f2376,f583]) ).
fof(f2376,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ empty(X0) )
| ~ spl22_220 ),
inference(avatar_component_clause,[],[f2375]) ).
fof(f17763,plain,
( spl22_815
| ~ spl22_62
| ~ spl22_219 ),
inference(avatar_split_clause,[],[f2417,f2371,f582,f17761]) ).
fof(f17761,plain,
( spl22_815
<=> ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_815])]) ).
fof(f2371,plain,
( spl22_219
<=> ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_219])]) ).
fof(f2417,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_intersection2(X0,X1) = X0 )
| ~ spl22_62
| ~ spl22_219 ),
inference(resolution,[],[f2372,f583]) ).
fof(f2372,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ empty(X1) )
| ~ spl22_219 ),
inference(avatar_component_clause,[],[f2371]) ).
fof(f17602,plain,
( spl22_814
| ~ spl22_113
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2406,f2367,f952,f17600]) ).
fof(f2406,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = sK10(powerset(X0)) )
| ~ spl22_113
| ~ spl22_218 ),
inference(resolution,[],[f2368,f953]) ).
fof(f17571,plain,
( spl22_813
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_476 ),
inference(avatar_split_clause,[],[f8891,f8373,f4126,f935,f511,f15306,f17569]) ).
fof(f17569,plain,
( spl22_813
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| element(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| sP0(X0,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_813])]) ).
fof(f8891,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| element(sK8(X0,apply(sK5,sK4)),relation_dom(X0)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_476 ),
inference(forward_demodulation,[],[f8890,f512]) ).
fof(f8890,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| element(sK8(X0,apply(sK5,sK4)),relation_dom(X0)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_476 ),
inference(forward_demodulation,[],[f8878,f4127]) ).
fof(f8878,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| element(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_476 ),
inference(superposition,[],[f8374,f937]) ).
fof(f17558,plain,
( spl22_812
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_471 ),
inference(avatar_split_clause,[],[f8851,f8353,f4126,f935,f511,f15306,f17556]) ).
fof(f17556,plain,
( spl22_812
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_812])]) ).
fof(f8851,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_471 ),
inference(forward_demodulation,[],[f8850,f512]) ).
fof(f8850,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_471 ),
inference(forward_demodulation,[],[f8838,f4127]) ).
fof(f8838,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_471 ),
inference(superposition,[],[f8354,f937]) ).
fof(f17554,plain,
( spl22_811
| ~ spl22_61
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2536,f2531,f578,f17552]) ).
fof(f17552,plain,
( spl22_811
<=> ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| relation_rng(X0) = X1
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_811])]) ).
fof(f2536,plain,
( ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| relation_rng(X0) = X1
| ~ sP1(X0) )
| ~ spl22_61
| ~ spl22_232 ),
inference(resolution,[],[f2532,f579]) ).
fof(f17550,plain,
( spl22_810
| ~ spl22_132
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2358,f2344,f1242,f17548]) ).
fof(f17548,plain,
( spl22_810
<=> ! [X0,X1] :
( sP0(X0,sK6(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK6(X1))) = apply(sK5,sK8(X0,sK6(X1)))
| element(sK7(X0,sK6(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_810])]) ).
fof(f2358,plain,
( ! [X0,X1] :
( sP0(X0,sK6(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK6(X1))) = apply(sK5,sK8(X0,sK6(X1)))
| element(sK7(X0,sK6(X1)),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1243]) ).
fof(f17546,plain,
( ~ spl22_10
| spl22_809
| ~ spl22_684
| ~ spl22_747 ),
inference(avatar_split_clause,[],[f16209,f16158,f14820,f17544,f269]) ).
fof(f269,plain,
( spl22_10
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_10])]) ).
fof(f16158,plain,
( spl22_747
<=> ! [X0] :
( sP0(X0,sK15)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_747])]) ).
fof(f16209,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(sK15,relation_dom(X0))
| ~ empty(sK15) )
| ~ spl22_684
| ~ spl22_747 ),
inference(resolution,[],[f16159,f14821]) ).
fof(f16159,plain,
( ! [X0] :
( sP0(X0,sK15)
| ~ empty(X0) )
| ~ spl22_747 ),
inference(avatar_component_clause,[],[f16158]) ).
fof(f17542,plain,
( spl22_808
| ~ spl22_321
| ~ spl22_807 ),
inference(avatar_split_clause,[],[f17538,f17534,f3666,f17540]) ).
fof(f17540,plain,
( spl22_808
<=> ! [X0] :
( sP0(sK5,X0)
| apply(sK5,sK4) != sK7(sK5,X0)
| ~ in(apply(sK5,sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_808])]) ).
fof(f3666,plain,
( spl22_321
<=> sK5 = relation_dom_restriction(sK5,relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_321])]) ).
fof(f17534,plain,
( spl22_807
<=> ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| ~ in(apply(sK5,sK4),X0)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_807])]) ).
fof(f17538,plain,
( ! [X0] :
( sP0(sK5,X0)
| apply(sK5,sK4) != sK7(sK5,X0)
| ~ in(apply(sK5,sK4),X0) )
| ~ spl22_321
| ~ spl22_807 ),
inference(forward_demodulation,[],[f17537,f3668]) ).
fof(f3668,plain,
( sK5 = relation_dom_restriction(sK5,relation_dom(sK5))
| ~ spl22_321 ),
inference(avatar_component_clause,[],[f3666]) ).
fof(f17537,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(sK5,X0)
| ~ in(apply(sK5,sK4),X0)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_321
| ~ spl22_807 ),
inference(forward_demodulation,[],[f17535,f3668]) ).
fof(f17535,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| ~ in(apply(sK5,sK4),X0)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_807 ),
inference(avatar_component_clause,[],[f17534]) ).
fof(f17536,plain,
( ~ spl22_711
| spl22_807
| ~ spl22_78
| ~ spl22_193 ),
inference(avatar_split_clause,[],[f2101,f2093,f706,f17534,f15518]) ).
fof(f15518,plain,
( spl22_711
<=> in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_711])]) ).
fof(f706,plain,
( spl22_78
<=> ! [X0,X1,X3] :
( sP0(X0,X1)
| apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_78])]) ).
fof(f2093,plain,
( spl22_193
<=> apply(sK5,sK4) = apply(relation_dom_restriction(sK5,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_193])]) ).
fof(f2101,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| ~ in(apply(sK5,sK4),X0) )
| ~ spl22_78
| ~ spl22_193 ),
inference(inner_rewriting,[],[f2099]) ).
fof(f2099,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| ~ in(sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X0),X0) )
| ~ spl22_78
| ~ spl22_193 ),
inference(superposition,[],[f707,f2095]) ).
fof(f2095,plain,
( apply(sK5,sK4) = apply(relation_dom_restriction(sK5,relation_dom(sK5)),sK4)
| ~ spl22_193 ),
inference(avatar_component_clause,[],[f2093]) ).
fof(f707,plain,
( ! [X3,X0,X1] :
( apply(X0,X3) != sK7(X0,X1)
| sP0(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK7(X0,X1),X1) )
| ~ spl22_78 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f17054,plain,
( spl22_806
| ~ spl22_216
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f3349,f3304,f2344,f17052]) ).
fof(f17052,plain,
( spl22_806
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP0(X2,relation_rng(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,relation_rng(X0))) = apply(sK5,sK8(X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_806])]) ).
fof(f3349,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ sP0(X0,X1)
| ~ empty(X1)
| sP0(X2,relation_rng(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,relation_rng(X0))) = apply(sK5,sK8(X2,relation_rng(X0))) )
| ~ spl22_216
| ~ spl22_290 ),
inference(resolution,[],[f3305,f2345]) ).
fof(f17050,plain,
( spl22_805
| ~ spl22_230
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2856,f2743,f2489,f17048]) ).
fof(f17048,plain,
( spl22_805
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(relation_rng(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_rng(X0),X1,X2)) = apply(sK5,sK13(relation_rng(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_805])]) ).
fof(f2856,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(relation_rng(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_rng(X0),X1,X2)) = apply(sK5,sK13(relation_rng(X0),X1,X2)) )
| ~ spl22_230
| ~ spl22_248 ),
inference(resolution,[],[f2744,f2490]) ).
fof(f17046,plain,
( spl22_804
| ~ spl22_228
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2852,f2743,f2447,f17044]) ).
fof(f17044,plain,
( spl22_804
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X1,relation_rng(X0),X2)) = apply(sK5,sK13(X1,relation_rng(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_804])]) ).
fof(f2852,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X1,relation_rng(X0),X2)) = apply(sK5,sK13(X1,relation_rng(X0),X2)) )
| ~ spl22_228
| ~ spl22_248 ),
inference(resolution,[],[f2744,f2448]) ).
fof(f17042,plain,
( spl22_803
| ~ spl22_231
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2851,f2743,f2510,f17040]) ).
fof(f17040,plain,
( spl22_803
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| apply(sK5,sK13(X1,X2,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X1),sK13(X1,X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_803])]) ).
fof(f2851,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| apply(sK5,sK13(X1,X2,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X1),sK13(X1,X2,relation_rng(X0))) )
| ~ spl22_231
| ~ spl22_248 ),
inference(resolution,[],[f2744,f2511]) ).
fof(f17038,plain,
( spl22_802
| ~ spl22_229
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2850,f2743,f2468,f17036]) ).
fof(f17036,plain,
( spl22_802
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| apply(sK5,sK13(X1,X2,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X1,X2,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_802])]) ).
fof(f2850,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,X2,relation_rng(X0))
| apply(sK5,sK13(X1,X2,relation_rng(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X1,X2,relation_rng(X0))) )
| ~ spl22_229
| ~ spl22_248 ),
inference(resolution,[],[f2744,f2469]) ).
fof(f17034,plain,
( spl22_801
| ~ spl22_495
| ~ spl22_771 ),
inference(avatar_split_clause,[],[f16580,f16521,f9032,f17032]) ).
fof(f16521,plain,
( spl22_771
<=> ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_771])]) ).
fof(f16580,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_495
| ~ spl22_771 ),
inference(resolution,[],[f16522,f9033]) ).
fof(f16522,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ empty(X0) )
| ~ spl22_771 ),
inference(avatar_component_clause,[],[f16521]) ).
fof(f17030,plain,
( spl22_800
| ~ spl22_121
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2527,f2510,f1110,f17028]) ).
fof(f17028,plain,
( spl22_800
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_800])]) ).
fof(f2527,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1111]) ).
fof(f17026,plain,
( spl22_799
| ~ spl22_133
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2523,f2510,f1246,f17024]) ).
fof(f17024,plain,
( spl22_799
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_799])]) ).
fof(f2523,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_231 ),
inference(resolution,[],[f2511,f1247]) ).
fof(f17022,plain,
( spl22_798
| ~ spl22_121
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2506,f2489,f1110,f17020]) ).
fof(f17020,plain,
( spl22_798
<=> ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(sK10(powerset(X0)),X1,X2)) = apply(sK5,sK13(sK10(powerset(X0)),X1,X2))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_798])]) ).
fof(f2506,plain,
( ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(sK10(powerset(X0)),X1,X2)) = apply(sK5,sK13(sK10(powerset(X0)),X1,X2))
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1111]) ).
fof(f17018,plain,
( spl22_797
| ~ spl22_133
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2502,f2489,f1246,f17016]) ).
fof(f17016,plain,
( spl22_797
<=> ! [X0,X3,X2,X1] :
( sP2(relation_dom(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_dom(X0),X1,X2)) = apply(sK5,sK13(relation_dom(X0),X1,X2))
| ~ sP0(X0,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_797])]) ).
fof(f2502,plain,
( ! [X2,X3,X0,X1] :
( sP2(relation_dom(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_dom(X0),X1,X2)) = apply(sK5,sK13(relation_dom(X0),X1,X2))
| ~ sP0(X0,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_230 ),
inference(resolution,[],[f2490,f1247]) ).
fof(f17014,plain,
( spl22_796
| ~ spl22_121
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2485,f2468,f1110,f17012]) ).
fof(f17012,plain,
( spl22_796
<=> ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_796])]) ).
fof(f2485,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| apply(sK5,sK13(X0,X1,sK10(powerset(X2)))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1111]) ).
fof(f17010,plain,
( spl22_795
| ~ spl22_133
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2481,f2468,f1246,f17008]) ).
fof(f17008,plain,
( spl22_795
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_795])]) ).
fof(f2481,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| apply(sK5,sK13(X0,X1,relation_dom(X2))) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,relation_dom(X2)))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_229 ),
inference(resolution,[],[f2469,f1247]) ).
fof(f17006,plain,
( spl22_794
| ~ spl22_121
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2464,f2447,f1110,f17004]) ).
fof(f17004,plain,
( spl22_794
<=> ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,sK10(powerset(X1)),X2)) = apply(sK5,sK13(X0,sK10(powerset(X1)),X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_794])]) ).
fof(f2464,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,sK10(powerset(X1)),X2)) = apply(sK5,sK13(X0,sK10(powerset(X1)),X2))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1111]) ).
fof(f17002,plain,
( spl22_793
| ~ spl22_133
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2460,f2447,f1246,f17000]) ).
fof(f17000,plain,
( spl22_793
<=> ! [X0,X3,X2,X1] :
( sP2(X0,relation_dom(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,relation_dom(X1),X2)) = apply(sK5,sK13(X0,relation_dom(X1),X2))
| ~ sP0(X1,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_793])]) ).
fof(f2460,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,relation_dom(X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,relation_dom(X1),X2)) = apply(sK5,sK13(X0,relation_dom(X1),X2))
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_228 ),
inference(resolution,[],[f2448,f1247]) ).
fof(f16989,plain,
( spl22_792
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_444 ),
inference(avatar_split_clause,[],[f7228,f6337,f4126,f935,f511,f15306,f16987]) ).
fof(f16987,plain,
( spl22_792
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,apply(sK5,sK4)))
| sP2(apply(sK5,sK4),X0,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_792])]) ).
fof(f7228,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,apply(sK5,sK4)))
| sP2(apply(sK5,sK4),X0,apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_444 ),
inference(forward_demodulation,[],[f7227,f512]) ).
fof(f7227,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,apply(sK5,sK4)))
| sP2(apply(sK5,sK4),X0,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_444 ),
inference(forward_demodulation,[],[f7218,f4127]) ).
fof(f7218,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP2(apply(sK5,sK4),X0,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_444 ),
inference(superposition,[],[f6338,f937]) ).
fof(f16964,plain,
( spl22_791
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_443 ),
inference(avatar_split_clause,[],[f7212,f6333,f4126,f935,f511,f15306,f16962]) ).
fof(f16962,plain,
( spl22_791
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),apply(sK5,sK4)))
| sP2(X0,apply(sK5,sK4),apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_791])]) ).
fof(f7212,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),apply(sK5,sK4)))
| sP2(X0,apply(sK5,sK4),apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_443 ),
inference(forward_demodulation,[],[f7211,f512]) ).
fof(f7211,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),apply(sK5,sK4)))
| sP2(X0,apply(sK5,sK4),apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_443 ),
inference(forward_demodulation,[],[f7202,f4127]) ).
fof(f7202,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP2(X0,apply(sK5,sK4),apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_443 ),
inference(superposition,[],[f6334,f937]) ).
fof(f16716,plain,
( spl22_790
| ~ spl22_216
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2835,f2743,f2344,f16714]) ).
fof(f16714,plain,
( spl22_790
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP0(X1,relation_rng(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X1)),sK8(X1,relation_rng(X0))) = apply(sK5,sK8(X1,relation_rng(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_790])]) ).
fof(f2835,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ empty(relation_dom(X0))
| sP0(X1,relation_rng(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X1)),sK8(X1,relation_rng(X0))) = apply(sK5,sK8(X1,relation_rng(X0))) )
| ~ spl22_216
| ~ spl22_248 ),
inference(resolution,[],[f2744,f2345]) ).
fof(f16712,plain,
( spl22_789
| ~ spl22_230
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2607,f2559,f2489,f16710]) ).
fof(f16710,plain,
( spl22_789
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(relation_dom(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_dom(X0),X1,X2)) = apply(sK5,sK13(relation_dom(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_789])]) ).
fof(f2607,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(relation_dom(X0),X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(relation_dom(X0),X1,X2)) = apply(sK5,sK13(relation_dom(X0),X1,X2)) )
| ~ spl22_230
| ~ spl22_233 ),
inference(resolution,[],[f2560,f2490]) ).
fof(f16708,plain,
( spl22_788
| ~ spl22_228
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2603,f2559,f2447,f16706]) ).
fof(f16706,plain,
( spl22_788
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,relation_dom(X0),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X1,relation_dom(X0),X2)) = apply(sK5,sK13(X1,relation_dom(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_788])]) ).
fof(f2603,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,relation_dom(X0),X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X1,relation_dom(X0),X2)) = apply(sK5,sK13(X1,relation_dom(X0),X2)) )
| ~ spl22_228
| ~ spl22_233 ),
inference(resolution,[],[f2560,f2448]) ).
fof(f16704,plain,
( spl22_787
| ~ spl22_121
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15720,f15680,f1110,f16702]) ).
fof(f16702,plain,
( spl22_787
<=> ! [X0] :
( ~ sP0(sK5,sK10(powerset(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_787])]) ).
fof(f15720,plain,
( ! [X0] :
( ~ sP0(sK5,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_718 ),
inference(resolution,[],[f15681,f1111]) ).
fof(f16700,plain,
( spl22_786
| ~ spl22_231
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2602,f2559,f2510,f16698]) ).
fof(f16698,plain,
( spl22_786
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| apply(sK5,sK13(X1,X2,relation_dom(X0))) = apply(relation_dom_restriction(sK5,X1),sK13(X1,X2,relation_dom(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_786])]) ).
fof(f2602,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| apply(sK5,sK13(X1,X2,relation_dom(X0))) = apply(relation_dom_restriction(sK5,X1),sK13(X1,X2,relation_dom(X0))) )
| ~ spl22_231
| ~ spl22_233 ),
inference(resolution,[],[f2560,f2511]) ).
fof(f16696,plain,
( spl22_785
| ~ spl22_229
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2601,f2559,f2468,f16694]) ).
fof(f16694,plain,
( spl22_785
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| apply(sK5,sK13(X1,X2,relation_dom(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X1,X2,relation_dom(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_785])]) ).
fof(f2601,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| sP2(X1,X2,relation_dom(X0))
| apply(sK5,sK13(X1,X2,relation_dom(X0))) = apply(relation_dom_restriction(sK5,X2),sK13(X1,X2,relation_dom(X0))) )
| ~ spl22_229
| ~ spl22_233 ),
inference(resolution,[],[f2560,f2469]) ).
fof(f16692,plain,
( spl22_784
| ~ spl22_45
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2517,f2510,f454,f16690]) ).
fof(f16690,plain,
( spl22_784
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_784])]) ).
fof(f2517,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_231 ),
inference(resolution,[],[f2511,f455]) ).
fof(f16688,plain,
( spl22_783
| ~ spl22_46
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2516,f2510,f458,f16686]) ).
fof(f16686,plain,
( spl22_783
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_783])]) ).
fof(f2516,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X2) )
| ~ spl22_46
| ~ spl22_231 ),
inference(resolution,[],[f2511,f459]) ).
fof(f16684,plain,
( spl22_782
| ~ spl22_45
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2496,f2489,f454,f16682]) ).
fof(f16682,plain,
( spl22_782
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ in(X0,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_782])]) ).
fof(f2496,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ in(X0,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_230 ),
inference(resolution,[],[f2490,f455]) ).
fof(f16680,plain,
( spl22_781
| ~ spl22_46
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2495,f2489,f458,f16678]) ).
fof(f16678,plain,
( spl22_781
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_781])]) ).
fof(f2495,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X0) )
| ~ spl22_46
| ~ spl22_230 ),
inference(resolution,[],[f2490,f459]) ).
fof(f16676,plain,
( spl22_780
| ~ spl22_45
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2475,f2468,f454,f16674]) ).
fof(f16674,plain,
( spl22_780
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_780])]) ).
fof(f2475,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_229 ),
inference(resolution,[],[f2469,f455]) ).
fof(f16672,plain,
( spl22_779
| ~ spl22_46
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2474,f2468,f458,f16670]) ).
fof(f16670,plain,
( spl22_779
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_779])]) ).
fof(f2474,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X2) )
| ~ spl22_46
| ~ spl22_229 ),
inference(resolution,[],[f2469,f459]) ).
fof(f16668,plain,
( spl22_778
| ~ spl22_45
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2454,f2447,f454,f16666]) ).
fof(f16666,plain,
( spl22_778
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ in(X1,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_778])]) ).
fof(f2454,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ in(X1,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_228 ),
inference(resolution,[],[f2448,f455]) ).
fof(f16664,plain,
( spl22_777
| ~ spl22_46
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2453,f2447,f458,f16662]) ).
fof(f16662,plain,
( spl22_777
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_777])]) ).
fof(f2453,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| element(sK13(X0,X1,X2),X1) )
| ~ spl22_46
| ~ spl22_228 ),
inference(resolution,[],[f2448,f459]) ).
fof(f16660,plain,
( spl22_776
| ~ spl22_233
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15700,f15680,f2559,f16658]) ).
fof(f15700,plain,
( ! [X0] :
( ~ sP0(sK5,relation_dom(X0))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_718 ),
inference(resolution,[],[f15681,f2560]) ).
fof(f16656,plain,
( spl22_775
| ~ spl22_121
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2360,f2344,f1110,f16654]) ).
fof(f16654,plain,
( spl22_775
<=> ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK10(powerset(X1)))) = apply(sK5,sK8(X0,sK10(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_775])]) ).
fof(f2360,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK10(powerset(X1)))) = apply(sK5,sK8(X0,sK10(powerset(X1))))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1111]) ).
fof(f16652,plain,
( spl22_774
| ~ spl22_133
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2356,f2344,f1246,f16650]) ).
fof(f16650,plain,
( spl22_774
<=> ! [X2,X0,X1] :
( sP0(X0,relation_dom(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_dom(X1))) = apply(sK5,sK8(X0,relation_dom(X1)))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_774])]) ).
fof(f2356,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_dom(X1))
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,relation_dom(X1))) = apply(sK5,sK8(X0,relation_dom(X1)))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_216 ),
inference(resolution,[],[f2345,f1247]) ).
fof(f16648,plain,
( ~ spl22_698
| spl22_773
| ~ spl22_78
| ~ spl22_109 ),
inference(avatar_split_clause,[],[f1058,f935,f706,f16646,f15296]) ).
fof(f15296,plain,
( spl22_698
<=> in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_698])]) ).
fof(f16646,plain,
( spl22_773
<=> ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| ~ in(apply(sK5,sK4),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_773])]) ).
fof(f1058,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ in(apply(sK5,sK4),X0) )
| ~ spl22_78
| ~ spl22_109 ),
inference(inner_rewriting,[],[f1056]) ).
fof(f1056,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ in(sK7(relation_dom_restriction(sK5,sK3),X0),X0) )
| ~ spl22_78
| ~ spl22_109 ),
inference(superposition,[],[f707,f937]) ).
fof(f16527,plain,
( spl22_772
| ~ spl22_41
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f3122,f2907,f419,f16525]) ).
fof(f16525,plain,
( spl22_772
<=> ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_772])]) ).
fof(f3122,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_255 ),
inference(resolution,[],[f2908,f420]) ).
fof(f16523,plain,
( spl22_771
| ~ spl22_41
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f3098,f2903,f419,f16521]) ).
fof(f3098,plain,
( ! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_254 ),
inference(resolution,[],[f2904,f420]) ).
fof(f16519,plain,
( spl22_770
| ~ spl22_119
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2592,f2559,f1064,f16517]) ).
fof(f16517,plain,
( spl22_770
<=> ! [X0] :
( ~ sP0(X0,sK15)
| empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_770])]) ).
fof(f2592,plain,
( ! [X0] :
( ~ sP0(X0,sK15)
| empty(relation_dom(X0)) )
| ~ spl22_119
| ~ spl22_233 ),
inference(resolution,[],[f2560,f1065]) ).
fof(f16515,plain,
( spl22_769
| ~ spl22_28
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2404,f2367,f355,f16513]) ).
fof(f16513,plain,
( spl22_769
<=> ! [X0] :
( ~ empty(X0)
| relation(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_769])]) ).
fof(f2404,plain,
( ! [X0] :
( ~ empty(X0)
| relation(sK10(powerset(X0))) )
| ~ spl22_28
| ~ spl22_218 ),
inference(resolution,[],[f2368,f356]) ).
fof(f16511,plain,
( spl22_768
| ~ spl22_27
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2403,f2367,f351,f16509]) ).
fof(f16509,plain,
( spl22_768
<=> ! [X0] :
( ~ empty(X0)
| function(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_768])]) ).
fof(f2403,plain,
( ! [X0] :
( ~ empty(X0)
| function(sK10(powerset(X0))) )
| ~ spl22_27
| ~ spl22_218 ),
inference(resolution,[],[f2368,f352]) ).
fof(f16498,plain,
( spl22_767
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_407 ),
inference(avatar_split_clause,[],[f5506,f5270,f4126,f935,f511,f15306,f16496]) ).
fof(f16496,plain,
( spl22_767
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_767])]) ).
fof(f5506,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ empty(X0)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_407 ),
inference(forward_demodulation,[],[f5505,f512]) ).
fof(f5505,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ empty(X0)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_407 ),
inference(forward_demodulation,[],[f5496,f4127]) ).
fof(f5496,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ empty(X0)
| sP2(X0,X1,apply(sK5,sK4))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_407 ),
inference(superposition,[],[f5271,f937]) ).
fof(f16485,plain,
( spl22_766
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_406 ),
inference(avatar_split_clause,[],[f5490,f5266,f4126,f935,f511,f15306,f16483]) ).
fof(f16483,plain,
( spl22_766
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| sP2(apply(sK5,sK4),X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_766])]) ).
fof(f5490,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| ~ empty(X1)
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_406 ),
inference(forward_demodulation,[],[f5489,f512]) ).
fof(f5489,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| ~ empty(X1)
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_406 ),
inference(forward_demodulation,[],[f5480,f4127]) ).
fof(f5480,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| ~ empty(X1)
| sP2(apply(sK5,sK4),X0,X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_406 ),
inference(superposition,[],[f5267,f937]) ).
fof(f16472,plain,
( spl22_765
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5474,f5262,f4126,f935,f511,f15306,f16470]) ).
fof(f16470,plain,
( spl22_765
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_765])]) ).
fof(f5474,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ empty(X1)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_405 ),
inference(forward_demodulation,[],[f5473,f512]) ).
fof(f5473,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ empty(X1)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_405 ),
inference(forward_demodulation,[],[f5464,f4127]) ).
fof(f5464,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| ~ empty(X1)
| sP2(X0,X1,apply(sK5,sK4))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_405 ),
inference(superposition,[],[f5263,f937]) ).
fof(f16458,plain,
( spl22_764
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_404 ),
inference(avatar_split_clause,[],[f5458,f5258,f4126,f935,f511,f15306,f16456]) ).
fof(f16456,plain,
( spl22_764
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| sP2(X0,apply(sK5,sK4),X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_764])]) ).
fof(f5458,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| ~ empty(X1)
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_404 ),
inference(forward_demodulation,[],[f5457,f512]) ).
fof(f5457,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| ~ empty(X1)
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_404 ),
inference(forward_demodulation,[],[f5448,f4127]) ).
fof(f5448,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| ~ empty(X1)
| sP2(X0,apply(sK5,sK4),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_404 ),
inference(superposition,[],[f5259,f937]) ).
fof(f16380,plain,
( spl22_763
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5159,f5122,f4126,f935,f511,f15306,f16378]) ).
fof(f16378,plain,
( spl22_763
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| ~ empty(relation_dom(X0))
| sP0(X0,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_763])]) ).
fof(f5159,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| ~ empty(relation_dom(X0)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_395 ),
inference(forward_demodulation,[],[f5158,f512]) ).
fof(f5158,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| ~ empty(relation_dom(X0)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_395 ),
inference(forward_demodulation,[],[f5149,f4127]) ).
fof(f5149,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP0(X0,apply(sK5,sK4))
| ~ empty(relation_dom(X0)) )
| ~ spl22_109
| ~ spl22_395 ),
inference(superposition,[],[f5123,f937]) ).
fof(f16376,plain,
( spl22_762
| ~ spl22_216
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2580,f2559,f2344,f16374]) ).
fof(f16374,plain,
( spl22_762
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X1,relation_dom(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X1)),sK8(X1,relation_dom(X0))) = apply(sK5,sK8(X1,relation_dom(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_762])]) ).
fof(f2580,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X1,relation_dom(X0))
| apply(relation_dom_restriction(sK5,relation_dom(X1)),sK8(X1,relation_dom(X0))) = apply(sK5,sK8(X1,relation_dom(X0))) )
| ~ spl22_216
| ~ spl22_233 ),
inference(resolution,[],[f2560,f2345]) ).
fof(f16362,plain,
( ~ spl22_761
| ~ spl22_45
| ~ spl22_700 ),
inference(avatar_split_clause,[],[f15360,f15306,f454,f16359]) ).
fof(f16359,plain,
( spl22_761
<=> in(set_intersection2(sK3,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_761])]) ).
fof(f15360,plain,
( ~ in(set_intersection2(sK3,relation_dom(sK5)),sK4)
| ~ spl22_45
| ~ spl22_700 ),
inference(resolution,[],[f15307,f455]) ).
fof(f16335,plain,
( spl22_760
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_393 ),
inference(avatar_split_clause,[],[f5113,f4952,f4126,f935,f511,f15306,f16333]) ).
fof(f16333,plain,
( spl22_760
<=> ! [X0,X1] :
( ~ sP0(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),apply(X0,X1))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_760])]) ).
fof(f5113,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(X0,apply(sK5,sK4))
| ~ in(X1,relation_dom(X0))
| ~ sP0(relation_dom_restriction(sK5,sK3),apply(X0,X1)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_371
| ~ spl22_393 ),
inference(forward_demodulation,[],[f5112,f512]) ).
fof(f5112,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(X0,apply(sK5,sK4))
| ~ in(X1,relation_dom(X0))
| ~ sP0(relation_dom_restriction(sK5,sK3),apply(X0,X1)) )
| ~ spl22_109
| ~ spl22_371
| ~ spl22_393 ),
inference(forward_demodulation,[],[f5103,f4127]) ).
fof(f5103,plain,
( ! [X0,X1] :
( ~ sP0(X0,apply(sK5,sK4))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ in(X1,relation_dom(X0))
| ~ sP0(relation_dom_restriction(sK5,sK3),apply(X0,X1)) )
| ~ spl22_109
| ~ spl22_393 ),
inference(superposition,[],[f4953,f937]) ).
fof(f16331,plain,
( spl22_759
| ~ spl22_45
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2350,f2344,f454,f16329]) ).
fof(f16329,plain,
( spl22_759
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| ~ in(X1,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_759])]) ).
fof(f2350,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| ~ in(X1,sK7(X0,X1)) )
| ~ spl22_45
| ~ spl22_216 ),
inference(resolution,[],[f2345,f455]) ).
fof(f16327,plain,
( spl22_758
| ~ spl22_46
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2349,f2344,f458,f16325]) ).
fof(f16325,plain,
( spl22_758
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| element(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_758])]) ).
fof(f2349,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| element(sK7(X0,X1),X1) )
| ~ spl22_46
| ~ spl22_216 ),
inference(resolution,[],[f2345,f459]) ).
fof(f16323,plain,
( spl22_757
| ~ spl22_45
| ~ spl22_215 ),
inference(avatar_split_clause,[],[f2325,f2316,f454,f16321]) ).
fof(f16321,plain,
( spl22_757
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(relation_dom(X0),sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_757])]) ).
fof(f2325,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(relation_dom(X0),sK8(X0,X1)) )
| ~ spl22_45
| ~ spl22_215 ),
inference(resolution,[],[f2317,f455]) ).
fof(f16319,plain,
( spl22_756
| ~ spl22_46
| ~ spl22_215 ),
inference(avatar_split_clause,[],[f2324,f2316,f458,f16317]) ).
fof(f16317,plain,
( spl22_756
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| element(sK8(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_756])]) ).
fof(f2324,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| element(sK8(X0,X1),relation_dom(X0)) )
| ~ spl22_46
| ~ spl22_215 ),
inference(resolution,[],[f2317,f459]) ).
fof(f16299,plain,
( spl22_755
| ~ spl22_46
| ~ spl22_700 ),
inference(avatar_split_clause,[],[f15359,f15306,f458,f16296]) ).
fof(f16296,plain,
( spl22_755
<=> element(sK4,set_intersection2(sK3,relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_755])]) ).
fof(f15359,plain,
( element(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_46
| ~ spl22_700 ),
inference(resolution,[],[f15307,f459]) ).
fof(f16253,plain,
( ~ spl22_2
| spl22_754
| ~ spl22_1
| ~ spl22_466 ),
inference(avatar_split_clause,[],[f8121,f8074,f224,f16251,f229]) ).
fof(f16251,plain,
( spl22_754
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X0)) = apply(sK5,sK13(X0,X1,X0))
| sP2(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_754])]) ).
fof(f8074,plain,
( spl22_466
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X0)
| apply(relation_dom_restriction(X2,X0),sK13(X0,X1,X0)) = apply(X2,sK13(X0,X1,X0))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_466])]) ).
fof(f8121,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X0)) = apply(sK5,sK13(X0,X1,X0))
| ~ function(sK5)
| sP2(X0,X1,X0) )
| ~ spl22_1
| ~ spl22_466 ),
inference(resolution,[],[f8075,f226]) ).
fof(f226,plain,
( relation(sK5)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f8075,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| apply(relation_dom_restriction(X2,X0),sK13(X0,X1,X0)) = apply(X2,sK13(X0,X1,X0))
| ~ function(X2)
| sP2(X0,X1,X0) )
| ~ spl22_466 ),
inference(avatar_component_clause,[],[f8074]) ).
fof(f16245,plain,
( ~ spl22_2
| spl22_753
| ~ spl22_1
| ~ spl22_465 ),
inference(avatar_split_clause,[],[f8100,f8070,f224,f16243,f229]) ).
fof(f16243,plain,
( spl22_753
<=> ! [X0,X1] :
( apply(relation_dom_restriction(sK5,X0),sK13(X1,X0,X0)) = apply(sK5,sK13(X1,X0,X0))
| sP2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_753])]) ).
fof(f8070,plain,
( spl22_465
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X1)
| apply(relation_dom_restriction(X2,X1),sK13(X0,X1,X1)) = apply(X2,sK13(X0,X1,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_465])]) ).
fof(f8100,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(sK5,X0),sK13(X1,X0,X0)) = apply(sK5,sK13(X1,X0,X0))
| ~ function(sK5)
| sP2(X1,X0,X0) )
| ~ spl22_1
| ~ spl22_465 ),
inference(resolution,[],[f8071,f226]) ).
fof(f8071,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| apply(relation_dom_restriction(X2,X1),sK13(X0,X1,X1)) = apply(X2,sK13(X0,X1,X1))
| ~ function(X2)
| sP2(X0,X1,X1) )
| ~ spl22_465 ),
inference(avatar_component_clause,[],[f8070]) ).
fof(f16241,plain,
( spl22_752
| ~ spl22_41
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2514,f2510,f419,f16239]) ).
fof(f16239,plain,
( spl22_752
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_752])]) ).
fof(f2514,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_231 ),
inference(resolution,[],[f2511,f420]) ).
fof(f16237,plain,
( spl22_751
| ~ spl22_41
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2493,f2489,f419,f16235]) ).
fof(f16235,plain,
( spl22_751
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_751])]) ).
fof(f2493,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_230 ),
inference(resolution,[],[f2490,f420]) ).
fof(f16233,plain,
( spl22_750
| ~ spl22_41
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2472,f2468,f419,f16231]) ).
fof(f16231,plain,
( spl22_750
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_750])]) ).
fof(f2472,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_229 ),
inference(resolution,[],[f2469,f420]) ).
fof(f16229,plain,
( spl22_749
| ~ spl22_41
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2451,f2447,f419,f16227]) ).
fof(f16227,plain,
( spl22_749
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_749])]) ).
fof(f2451,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_228 ),
inference(resolution,[],[f2448,f420]) ).
fof(f16225,plain,
( spl22_748
| ~ spl22_133
| ~ spl22_215 ),
inference(avatar_split_clause,[],[f2321,f2316,f1246,f16223]) ).
fof(f16223,plain,
( spl22_748
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ sP0(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_748])]) ).
fof(f2321,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_215 ),
inference(resolution,[],[f2317,f1247]) ).
fof(f16160,plain,
( spl22_747
| ~ spl22_36
| ~ spl22_221 ),
inference(avatar_split_clause,[],[f2422,f2379,f398,f16158]) ).
fof(f2379,plain,
( spl22_221
<=> ! [X0] :
( sP0(X0,sK15)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_221])]) ).
fof(f2422,plain,
( ! [X0] :
( sP0(X0,sK15)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_221 ),
inference(resolution,[],[f2380,f399]) ).
fof(f2380,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK15) )
| ~ spl22_221 ),
inference(avatar_component_clause,[],[f2379]) ).
fof(f16149,plain,
( spl22_746
| ~ spl22_700
| ~ spl22_53
| ~ spl22_109
| ~ spl22_339
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4336,f4126,f3929,f935,f511,f15306,f16147]) ).
fof(f16147,plain,
( spl22_746
<=> ! [X0,X1] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),powerset(X1))
| element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_746])]) ).
fof(f4336,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ in(X0,apply(sK5,sK4))
| element(X0,X1)
| ~ sP0(relation_dom_restriction(sK5,sK3),powerset(X1)) )
| ~ spl22_53
| ~ spl22_109
| ~ spl22_339
| ~ spl22_371 ),
inference(forward_demodulation,[],[f4335,f512]) ).
fof(f4335,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ in(X0,apply(sK5,sK4))
| element(X0,X1)
| ~ sP0(relation_dom_restriction(sK5,sK3),powerset(X1)) )
| ~ spl22_109
| ~ spl22_339
| ~ spl22_371 ),
inference(forward_demodulation,[],[f4326,f4127]) ).
fof(f4326,plain,
( ! [X0,X1] :
( ~ in(X0,apply(sK5,sK4))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| element(X0,X1)
| ~ sP0(relation_dom_restriction(sK5,sK3),powerset(X1)) )
| ~ spl22_109
| ~ spl22_339 ),
inference(superposition,[],[f3930,f937]) ).
fof(f16139,plain,
( ~ spl22_745
| ~ spl22_321
| spl22_744 ),
inference(avatar_split_clause,[],[f16134,f16130,f3666,f16136]) ).
fof(f16136,plain,
( spl22_745
<=> sP0(sK5,sK10(apply(sK5,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_745])]) ).
fof(f16130,plain,
( spl22_744
<=> sP0(relation_dom_restriction(sK5,relation_dom(sK5)),sK10(apply(sK5,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_744])]) ).
fof(f16134,plain,
( ~ sP0(sK5,sK10(apply(sK5,sK4)))
| ~ spl22_321
| spl22_744 ),
inference(forward_demodulation,[],[f16132,f3668]) ).
fof(f16132,plain,
( ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),sK10(apply(sK5,sK4)))
| spl22_744 ),
inference(avatar_component_clause,[],[f16130]) ).
fof(f16133,plain,
( spl22_726
| ~ spl22_711
| ~ spl22_744
| ~ spl22_193
| ~ spl22_317 ),
inference(avatar_split_clause,[],[f3655,f3614,f2093,f16130,f15518,f15781]) ).
fof(f3655,plain,
( ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),sK10(apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| empty(apply(sK5,sK4))
| ~ spl22_193
| ~ spl22_317 ),
inference(superposition,[],[f3615,f2095]) ).
fof(f16104,plain,
( ~ spl22_85
| spl22_743
| ~ spl22_47
| ~ spl22_209 ),
inference(avatar_split_clause,[],[f2246,f2241,f462,f16102,f761]) ).
fof(f761,plain,
( spl22_85
<=> sP1(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_85])]) ).
fof(f16102,plain,
( spl22_743
<=> ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| apply(X0,apply(sK5,sK4)) = apply(relation_dom_restriction(X0,relation_rng(sK5)),apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_743])]) ).
fof(f2246,plain,
( ! [X0] :
( ~ relation(X0)
| apply(X0,apply(sK5,sK4)) = apply(relation_dom_restriction(X0,relation_rng(sK5)),apply(sK5,sK4))
| ~ function(X0)
| ~ sP1(sK5) )
| ~ spl22_47
| ~ spl22_209 ),
inference(resolution,[],[f2242,f463]) ).
fof(f16092,plain,
( ~ spl22_742
| ~ spl22_713
| ~ spl22_718 ),
inference(avatar_split_clause,[],[f15749,f15680,f15532,f16089]) ).
fof(f16089,plain,
( spl22_742
<=> sP0(sK5,apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_742])]) ).
fof(f15532,plain,
( spl22_713
<=> ! [X0] :
( ~ sP0(sK5,X0)
| ~ in(X0,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_713])]) ).
fof(f15749,plain,
( ~ sP0(sK5,apply(sK5,sK4))
| ~ spl22_713
| ~ spl22_718 ),
inference(duplicate_literal_removal,[],[f15706]) ).
fof(f15706,plain,
( ~ sP0(sK5,apply(sK5,sK4))
| ~ sP0(sK5,apply(sK5,sK4))
| ~ spl22_713
| ~ spl22_718 ),
inference(resolution,[],[f15681,f15533]) ).
fof(f15533,plain,
( ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(sK5,X0) )
| ~ spl22_713 ),
inference(avatar_component_clause,[],[f15532]) ).
fof(f15922,plain,
( spl22_741
| ~ spl22_4
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5870,f5679,f239,f15920]) ).
fof(f15920,plain,
( spl22_741
<=> ! [X0,X1] :
( ~ in(sK4,X0)
| apply(X1,sK4) = apply(relation_dom_restriction(X1,set_intersection2(X0,relation_dom(sK5))),sK4)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_741])]) ).
fof(f239,plain,
( spl22_4
<=> in(sK4,relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_4])]) ).
fof(f5870,plain,
( ! [X0,X1] :
( ~ in(sK4,X0)
| apply(X1,sK4) = apply(relation_dom_restriction(X1,set_intersection2(X0,relation_dom(sK5))),sK4)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_4
| ~ spl22_419 ),
inference(resolution,[],[f5680,f241]) ).
fof(f241,plain,
( in(sK4,relation_dom(sK5))
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f15894,plain,
( ~ spl22_2
| spl22_740
| ~ spl22_1
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5852,f5675,f224,f15892,f229]) ).
fof(f15892,plain,
( spl22_740
<=> ! [X0] :
( empty(X0)
| empty(powerset(X0))
| apply(relation_dom_restriction(sK5,powerset(X0)),sK6(X0)) = apply(sK5,sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_740])]) ).
fof(f5852,plain,
( ! [X0] :
( empty(X0)
| apply(relation_dom_restriction(sK5,powerset(X0)),sK6(X0)) = apply(sK5,sK6(X0))
| ~ function(sK5)
| empty(powerset(X0)) )
| ~ spl22_1
| ~ spl22_418 ),
inference(resolution,[],[f5676,f226]) ).
fof(f15883,plain,
( spl22_738
| ~ spl22_698
| spl22_739
| ~ spl22_109
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3841,f3697,f935,f15881,f15296,f15878]) ).
fof(f15878,plain,
( spl22_738
<=> ! [X1] :
( ~ empty(X1)
| ~ sP0(relation_dom_restriction(sK5,sK3),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_738])]) ).
fof(f3841,plain,
( ! [X0,X1] :
( ~ in(X0,apply(sK5,sK4))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ empty(X1)
| ~ sP0(relation_dom_restriction(sK5,sK3),powerset(X1)) )
| ~ spl22_109
| ~ spl22_328 ),
inference(superposition,[],[f3698,f937]) ).
fof(f15870,plain,
( ~ spl22_698
| spl22_737
| ~ spl22_109
| ~ spl22_323 ),
inference(avatar_split_clause,[],[f3732,f3677,f935,f15868,f15296]) ).
fof(f15868,plain,
( spl22_737
<=> ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_737])]) ).
fof(f3732,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| empty(X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK6(X0)) )
| ~ spl22_109
| ~ spl22_323 ),
inference(superposition,[],[f3678,f937]) ).
fof(f15866,plain,
( spl22_736
| ~ spl22_215
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2586,f2559,f2316,f15864]) ).
fof(f15864,plain,
( spl22_736
<=> ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_736])]) ).
fof(f2586,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK15)
| sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1)) )
| ~ spl22_215
| ~ spl22_233 ),
inference(resolution,[],[f2560,f2317]) ).
fof(f15862,plain,
( spl22_735
| ~ spl22_115
| ~ spl22_231 ),
inference(avatar_split_clause,[],[f2528,f2510,f959,f15860]) ).
fof(f15860,plain,
( spl22_735
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK5,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_735])]) ).
fof(f2528,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK5,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,sK15)) )
| ~ spl22_115
| ~ spl22_231 ),
inference(resolution,[],[f2511,f960]) ).
fof(f15858,plain,
( spl22_734
| ~ spl22_115
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2507,f2489,f959,f15856]) ).
fof(f15856,plain,
( spl22_734
<=> ! [X0,X1] :
( sP2(sK15,X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK13(sK15,X0,X1)) = apply(sK5,sK13(sK15,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_734])]) ).
fof(f2507,plain,
( ! [X0,X1] :
( sP2(sK15,X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK13(sK15,X0,X1)) = apply(sK5,sK13(sK15,X0,X1)) )
| ~ spl22_115
| ~ spl22_230 ),
inference(resolution,[],[f2490,f960]) ).
fof(f15854,plain,
( spl22_733
| ~ spl22_115
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2486,f2468,f959,f15852]) ).
fof(f15852,plain,
( spl22_733
<=> ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK5,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_733])]) ).
fof(f2486,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| apply(sK5,sK13(X0,X1,sK15)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,sK15)) )
| ~ spl22_115
| ~ spl22_229 ),
inference(resolution,[],[f2469,f960]) ).
fof(f15850,plain,
( spl22_732
| ~ spl22_115
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2465,f2447,f959,f15848]) ).
fof(f15848,plain,
( spl22_732
<=> ! [X0,X1] :
( sP2(X0,sK15,X1)
| apply(relation_dom_restriction(sK5,X1),sK13(X0,sK15,X1)) = apply(sK5,sK13(X0,sK15,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_732])]) ).
fof(f2465,plain,
( ! [X0,X1] :
( sP2(X0,sK15,X1)
| apply(relation_dom_restriction(sK5,X1),sK13(X0,sK15,X1)) = apply(sK5,sK13(X0,sK15,X1)) )
| ~ spl22_115
| ~ spl22_228 ),
inference(resolution,[],[f2448,f960]) ).
fof(f15846,plain,
( spl22_731
| ~ spl22_41
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2347,f2344,f419,f15844]) ).
fof(f15844,plain,
( spl22_731
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_731])]) ).
fof(f2347,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_216 ),
inference(resolution,[],[f2345,f420]) ).
fof(f15842,plain,
( ~ spl22_730
| ~ spl22_412
| spl22_714 ),
inference(avatar_split_clause,[],[f15766,f15658,f5443,f15839]) ).
fof(f15839,plain,
( spl22_730
<=> empty(relation_dom_restriction(sK5,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_730])]) ).
fof(f15658,plain,
( spl22_714
<=> empty(set_intersection2(sK3,relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_714])]) ).
fof(f15766,plain,
( ~ empty(relation_dom_restriction(sK5,sK3))
| ~ spl22_412
| spl22_714 ),
inference(resolution,[],[f15660,f5444]) ).
fof(f15660,plain,
( ~ empty(set_intersection2(sK3,relation_dom(sK5)))
| spl22_714 ),
inference(avatar_component_clause,[],[f15658]) ).
fof(f15837,plain,
( spl22_729
| ~ spl22_41
| ~ spl22_215 ),
inference(avatar_split_clause,[],[f2322,f2316,f419,f15835]) ).
fof(f15835,plain,
( spl22_729
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_729])]) ).
fof(f2322,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ empty(relation_dom(X0)) )
| ~ spl22_41
| ~ spl22_215 ),
inference(resolution,[],[f2317,f420]) ).
fof(f15799,plain,
( spl22_728
| ~ spl22_3
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5869,f5679,f234,f15797]) ).
fof(f15797,plain,
( spl22_728
<=> ! [X0,X1] :
( ~ in(sK4,X0)
| apply(relation_dom_restriction(X1,set_intersection2(X0,sK3)),sK4) = apply(X1,sK4)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_728])]) ).
fof(f5869,plain,
( ! [X0,X1] :
( ~ in(sK4,X0)
| apply(relation_dom_restriction(X1,set_intersection2(X0,sK3)),sK4) = apply(X1,sK4)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_3
| ~ spl22_419 ),
inference(resolution,[],[f5680,f236]) ).
fof(f236,plain,
( in(sK4,sK3)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f15788,plain,
( spl22_726
| ~ spl22_698
| ~ spl22_727
| ~ spl22_109
| ~ spl22_317 ),
inference(avatar_split_clause,[],[f3651,f3614,f935,f15785,f15296,f15781]) ).
fof(f15785,plain,
( spl22_727
<=> sP0(relation_dom_restriction(sK5,sK3),sK10(apply(sK5,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_727])]) ).
fof(f3651,plain,
( ~ sP0(relation_dom_restriction(sK5,sK3),sK10(apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| empty(apply(sK5,sK4))
| ~ spl22_109
| ~ spl22_317 ),
inference(superposition,[],[f3615,f937]) ).
fof(f15779,plain,
( spl22_725
| ~ spl22_58
| ~ spl22_208 ),
inference(avatar_split_clause,[],[f2245,f2237,f553,f15777]) ).
fof(f15777,plain,
( spl22_725
<=> ! [X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_725])]) ).
fof(f553,plain,
( spl22_58
<=> ! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_58])]) ).
fof(f2237,plain,
( spl22_208
<=> ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_208])]) ).
fof(f2245,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_58
| ~ spl22_208 ),
inference(duplicate_literal_removal,[],[f2244]) ).
fof(f2244,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_208 ),
inference(resolution,[],[f2238,f554]) ).
fof(f554,plain,
( ! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f2238,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0) )
| ~ spl22_208 ),
inference(avatar_component_clause,[],[f2237]) ).
fof(f15775,plain,
( ~ spl22_723
| spl22_724
| ~ spl22_147
| ~ spl22_196 ),
inference(avatar_split_clause,[],[f2131,f2127,f1393,f15773,f15769]) ).
fof(f15769,plain,
( spl22_723
<=> in(sK4,relation_dom(relation_dom_restriction(sK15,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_723])]) ).
fof(f15773,plain,
( spl22_724
<=> ! [X0] :
( ~ in(X0,apply(sK15,sK4))
| ~ sP0(relation_dom_restriction(sK15,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_724])]) ).
fof(f2127,plain,
( spl22_196
<=> apply(sK15,sK4) = apply(relation_dom_restriction(sK15,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_196])]) ).
fof(f2131,plain,
( ! [X0] :
( ~ in(X0,apply(sK15,sK4))
| ~ sP0(relation_dom_restriction(sK15,relation_dom(sK5)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK15,relation_dom(sK5)))) )
| ~ spl22_147
| ~ spl22_196 ),
inference(superposition,[],[f1394,f2129]) ).
fof(f2129,plain,
( apply(sK15,sK4) = apply(relation_dom_restriction(sK15,relation_dom(sK5)),sK4)
| ~ spl22_196 ),
inference(avatar_component_clause,[],[f2127]) ).
fof(f15765,plain,
( ~ spl22_721
| spl22_722
| ~ spl22_147
| ~ spl22_195 ),
inference(avatar_split_clause,[],[f2121,f2117,f1393,f15763,f15759]) ).
fof(f15763,plain,
( spl22_722
<=> ! [X0] :
( ~ in(X0,apply(sK20,sK4))
| ~ sP0(relation_dom_restriction(sK20,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_722])]) ).
fof(f2117,plain,
( spl22_195
<=> apply(sK20,sK4) = apply(relation_dom_restriction(sK20,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_195])]) ).
fof(f2121,plain,
( ! [X0] :
( ~ in(X0,apply(sK20,sK4))
| ~ sP0(relation_dom_restriction(sK20,relation_dom(sK5)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK20,relation_dom(sK5)))) )
| ~ spl22_147
| ~ spl22_195 ),
inference(superposition,[],[f1394,f2119]) ).
fof(f2119,plain,
( apply(sK20,sK4) = apply(relation_dom_restriction(sK20,relation_dom(sK5)),sK4)
| ~ spl22_195 ),
inference(avatar_component_clause,[],[f2117]) ).
fof(f15757,plain,
( ~ spl22_719
| spl22_720
| ~ spl22_147
| ~ spl22_194 ),
inference(avatar_split_clause,[],[f2111,f2107,f1393,f15755,f15751]) ).
fof(f15755,plain,
( spl22_720
<=> ! [X0] :
( ~ in(X0,apply(sK19,sK4))
| ~ sP0(relation_dom_restriction(sK19,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_720])]) ).
fof(f2107,plain,
( spl22_194
<=> apply(sK19,sK4) = apply(relation_dom_restriction(sK19,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_194])]) ).
fof(f2111,plain,
( ! [X0] :
( ~ in(X0,apply(sK19,sK4))
| ~ sP0(relation_dom_restriction(sK19,relation_dom(sK5)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK19,relation_dom(sK5)))) )
| ~ spl22_147
| ~ spl22_194 ),
inference(superposition,[],[f1394,f2109]) ).
fof(f2109,plain,
( apply(sK19,sK4) = apply(relation_dom_restriction(sK19,relation_dom(sK5)),sK4)
| ~ spl22_194 ),
inference(avatar_component_clause,[],[f2107]) ).
fof(f15682,plain,
( spl22_718
| ~ spl22_321
| ~ spl22_717 ),
inference(avatar_split_clause,[],[f15678,f15675,f3666,f15680]) ).
fof(f15675,plain,
( spl22_717
<=> ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_717])]) ).
fof(f15678,plain,
( ! [X0] :
( ~ sP0(sK5,X0)
| in(apply(sK5,sK4),X0) )
| ~ spl22_321
| ~ spl22_717 ),
inference(forward_demodulation,[],[f15676,f3668]) ).
fof(f15676,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_717 ),
inference(avatar_component_clause,[],[f15675]) ).
fof(f15677,plain,
( ~ spl22_711
| spl22_717
| ~ spl22_69
| ~ spl22_193 ),
inference(avatar_split_clause,[],[f2100,f2093,f628,f15675,f15518]) ).
fof(f2100,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_69
| ~ spl22_193 ),
inference(superposition,[],[f629,f2095]) ).
fof(f15670,plain,
( spl22_716
| ~ spl22_321
| ~ spl22_715 ),
inference(avatar_split_clause,[],[f15666,f15663,f3666,f15668]) ).
fof(f15663,plain,
( spl22_715
<=> ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_715])]) ).
fof(f15666,plain,
( ! [X0] :
( ~ sP0(sK5,X0)
| element(apply(sK5,sK4),X0) )
| ~ spl22_321
| ~ spl22_715 ),
inference(forward_demodulation,[],[f15664,f3668]) ).
fof(f15664,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_715 ),
inference(avatar_component_clause,[],[f15663]) ).
fof(f15665,plain,
( ~ spl22_711
| spl22_715
| ~ spl22_146
| ~ spl22_193 ),
inference(avatar_split_clause,[],[f2098,f2093,f1389,f15663,f15518]) ).
fof(f1389,plain,
( spl22_146
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| element(apply(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_146])]) ).
fof(f2098,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5)))) )
| ~ spl22_146
| ~ spl22_193 ),
inference(superposition,[],[f1390,f2095]) ).
fof(f1390,plain,
( ! [X2,X0,X1] :
( element(apply(X1,X0),X2)
| ~ sP0(X1,X2)
| ~ in(X0,relation_dom(X1)) )
| ~ spl22_146 ),
inference(avatar_component_clause,[],[f1389]) ).
fof(f15661,plain,
( ~ spl22_714
| ~ spl22_41
| ~ spl22_700 ),
inference(avatar_split_clause,[],[f15357,f15306,f419,f15658]) ).
fof(f15357,plain,
( ~ empty(set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_41
| ~ spl22_700 ),
inference(resolution,[],[f15307,f420]) ).
fof(f15534,plain,
( spl22_713
| ~ spl22_321
| ~ spl22_712 ),
inference(avatar_split_clause,[],[f15528,f15522,f3666,f15532]) ).
fof(f15522,plain,
( spl22_712
<=> ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_712])]) ).
fof(f15528,plain,
( ! [X0] :
( ~ sP0(sK5,X0)
| ~ in(X0,apply(sK5,sK4)) )
| ~ spl22_321
| ~ spl22_712 ),
inference(forward_demodulation,[],[f15523,f3668]) ).
fof(f15523,plain,
( ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_712 ),
inference(avatar_component_clause,[],[f15522]) ).
fof(f15527,plain,
( ~ spl22_4
| ~ spl22_40
| ~ spl22_371
| spl22_711 ),
inference(avatar_split_clause,[],[f15526,f15518,f4126,f415,f239]) ).
fof(f415,plain,
( spl22_40
<=> ! [X0] : set_intersection2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_40])]) ).
fof(f15526,plain,
( ~ in(sK4,relation_dom(sK5))
| ~ spl22_40
| ~ spl22_371
| spl22_711 ),
inference(forward_demodulation,[],[f15525,f416]) ).
fof(f416,plain,
( ! [X0] : set_intersection2(X0,X0) = X0
| ~ spl22_40 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f15525,plain,
( ~ in(sK4,set_intersection2(relation_dom(sK5),relation_dom(sK5)))
| ~ spl22_371
| spl22_711 ),
inference(forward_demodulation,[],[f15520,f4127]) ).
fof(f15520,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| spl22_711 ),
inference(avatar_component_clause,[],[f15518]) ).
fof(f15524,plain,
( ~ spl22_711
| spl22_712
| ~ spl22_147
| ~ spl22_193 ),
inference(avatar_split_clause,[],[f2097,f2093,f1393,f15522,f15518]) ).
fof(f2097,plain,
( ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5)))) )
| ~ spl22_147
| ~ spl22_193 ),
inference(superposition,[],[f1394,f2095]) ).
fof(f15351,plain,
( ~ spl22_4
| ~ spl22_3
| ~ spl22_141
| spl22_700 ),
inference(avatar_split_clause,[],[f15310,f15306,f1337,f234,f239]) ).
fof(f15310,plain,
( ~ in(sK4,sK3)
| ~ in(sK4,relation_dom(sK5))
| ~ spl22_141
| spl22_700 ),
inference(resolution,[],[f15308,f1338]) ).
fof(f15308,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| spl22_700 ),
inference(avatar_component_clause,[],[f15306]) ).
fof(f15350,plain,
( spl22_710
| ~ spl22_115
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2361,f2344,f959,f15348]) ).
fof(f15348,plain,
( spl22_710
<=> ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK15)) = apply(sK5,sK8(X0,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_710])]) ).
fof(f2361,plain,
( ! [X0] :
( sP0(X0,sK15)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,sK15)) = apply(sK5,sK8(X0,sK15)) )
| ~ spl22_115
| ~ spl22_216 ),
inference(resolution,[],[f2345,f960]) ).
fof(f15346,plain,
( spl22_709
| ~ spl22_58
| ~ spl22_207 ),
inference(avatar_split_clause,[],[f2235,f2231,f553,f15344]) ).
fof(f15344,plain,
( spl22_709
<=> ! [X0,X1] :
( apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_709])]) ).
fof(f2231,plain,
( spl22_207
<=> ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_207])]) ).
fof(f2235,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_58
| ~ spl22_207 ),
inference(duplicate_literal_removal,[],[f2234]) ).
fof(f2234,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_207 ),
inference(resolution,[],[f2232,f554]) ).
fof(f2232,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0) )
| ~ spl22_207 ),
inference(avatar_component_clause,[],[f2231]) ).
fof(f15342,plain,
( ~ spl22_707
| spl22_708
| ~ spl22_147
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1729,f1679,f1393,f15340,f15336]) ).
fof(f15336,plain,
( spl22_707
<=> in(sK4,relation_dom(relation_dom_restriction(sK15,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_707])]) ).
fof(f15340,plain,
( spl22_708
<=> ! [X0] :
( ~ in(X0,apply(sK15,sK4))
| ~ sP0(relation_dom_restriction(sK15,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_708])]) ).
fof(f1679,plain,
( spl22_168
<=> apply(relation_dom_restriction(sK15,sK3),sK4) = apply(sK15,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_168])]) ).
fof(f1729,plain,
( ! [X0] :
( ~ in(X0,apply(sK15,sK4))
| ~ sP0(relation_dom_restriction(sK15,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK15,sK3))) )
| ~ spl22_147
| ~ spl22_168 ),
inference(superposition,[],[f1394,f1681]) ).
fof(f1681,plain,
( apply(relation_dom_restriction(sK15,sK3),sK4) = apply(sK15,sK4)
| ~ spl22_168 ),
inference(avatar_component_clause,[],[f1679]) ).
fof(f15334,plain,
( ~ spl22_705
| spl22_706
| ~ spl22_134
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1594,f1393,f1251,f15332,f15328]) ).
fof(f15332,plain,
( spl22_706
<=> ! [X0] :
( ~ in(X0,apply(sK20,sK4))
| ~ sP0(relation_dom_restriction(sK20,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_706])]) ).
fof(f1251,plain,
( spl22_134
<=> apply(relation_dom_restriction(sK20,sK3),sK4) = apply(sK20,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_134])]) ).
fof(f1594,plain,
( ! [X0] :
( ~ in(X0,apply(sK20,sK4))
| ~ sP0(relation_dom_restriction(sK20,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK20,sK3))) )
| ~ spl22_134
| ~ spl22_147 ),
inference(superposition,[],[f1394,f1253]) ).
fof(f1253,plain,
( apply(relation_dom_restriction(sK20,sK3),sK4) = apply(sK20,sK4)
| ~ spl22_134 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f15326,plain,
( ~ spl22_698
| spl22_704
| ~ spl22_109
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1440,f1393,f935,f15324,f15296]) ).
fof(f15324,plain,
( spl22_704
<=> ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_704])]) ).
fof(f1440,plain,
( ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_147 ),
inference(superposition,[],[f1394,f937]) ).
fof(f15322,plain,
( ~ spl22_698
| spl22_703
| ~ spl22_109
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1427,f1389,f935,f15320,f15296]) ).
fof(f15320,plain,
( spl22_703
<=> ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_703])]) ).
fof(f1427,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_109
| ~ spl22_146 ),
inference(superposition,[],[f1390,f937]) ).
fof(f15318,plain,
( ~ spl22_701
| spl22_702
| ~ spl22_69
| ~ spl22_122 ),
inference(avatar_split_clause,[],[f1167,f1126,f628,f15316,f15312]) ).
fof(f15316,plain,
( spl22_702
<=> ! [X0] :
( in(apply(sK19,sK4),X0)
| ~ sP0(relation_dom_restriction(sK19,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_702])]) ).
fof(f1126,plain,
( spl22_122
<=> apply(relation_dom_restriction(sK19,sK3),sK4) = apply(sK19,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_122])]) ).
fof(f1167,plain,
( ! [X0] :
( in(apply(sK19,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK19,sK3)))
| ~ sP0(relation_dom_restriction(sK19,sK3),X0) )
| ~ spl22_69
| ~ spl22_122 ),
inference(superposition,[],[f629,f1128]) ).
fof(f1128,plain,
( apply(relation_dom_restriction(sK19,sK3),sK4) = apply(sK19,sK4)
| ~ spl22_122 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f15309,plain,
( ~ spl22_700
| ~ spl22_53
| ~ spl22_371
| spl22_698 ),
inference(avatar_split_clause,[],[f15304,f15296,f4126,f511,f15306]) ).
fof(f15304,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_53
| ~ spl22_371
| spl22_698 ),
inference(forward_demodulation,[],[f15303,f512]) ).
fof(f15303,plain,
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ spl22_371
| spl22_698 ),
inference(forward_demodulation,[],[f15298,f4127]) ).
fof(f15298,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| spl22_698 ),
inference(avatar_component_clause,[],[f15296]) ).
fof(f15302,plain,
( ~ spl22_698
| spl22_699
| ~ spl22_69
| ~ spl22_109 ),
inference(avatar_split_clause,[],[f1057,f935,f628,f15300,f15296]) ).
fof(f1057,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) )
| ~ spl22_69
| ~ spl22_109 ),
inference(superposition,[],[f629,f937]) ).
fof(f15270,plain,
( ~ spl22_2
| spl22_697
| ~ spl22_1
| ~ spl22_375 ),
inference(avatar_split_clause,[],[f4815,f4748,f224,f15268,f229]) ).
fof(f4815,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK5,powerset(X0)),sK15) = apply(sK5,sK15)
| ~ function(sK5)
| empty(powerset(X0)) )
| ~ spl22_1
| ~ spl22_375 ),
inference(resolution,[],[f4749,f226]) ).
fof(f15223,plain,
( ~ spl22_2
| spl22_696
| ~ spl22_1
| ~ spl22_374 ),
inference(avatar_split_clause,[],[f4796,f4744,f224,f15221,f229]) ).
fof(f4796,plain,
( ! [X0] :
( apply(relation_dom_restriction(sK5,X0),sK10(X0)) = apply(sK5,sK10(X0))
| ~ function(sK5)
| empty(X0) )
| ~ spl22_1
| ~ spl22_374 ),
inference(resolution,[],[f4745,f226]) ).
fof(f15189,plain,
( spl22_695
| ~ spl22_83
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2039,f1998,f742,f15187]) ).
fof(f15187,plain,
( spl22_695
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1)))
| apply(X3,sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X3,X4),sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_dom_restriction(X3,X4))
| ~ relation(relation_dom_restriction(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_695])]) ).
fof(f1998,plain,
( spl22_188
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3)))) = apply(relation_dom_restriction(X0,X3),sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| in(sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))),X2)
| sP2(X1,X2,relation_dom(relation_dom_restriction(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_188])]) ).
fof(f2039,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1)))
| apply(X3,sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X3,X4),sK13(X2,relation_dom(relation_dom_restriction(X3,X4)),relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_dom_restriction(X3,X4))
| ~ relation(relation_dom_restriction(X3,X4)) )
| ~ spl22_83
| ~ spl22_188 ),
inference(resolution,[],[f1999,f743]) ).
fof(f1999,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| apply(X0,sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3)))) = apply(relation_dom_restriction(X0,X3),sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))))
| sP2(X1,X2,relation_dom(relation_dom_restriction(X0,X3))) )
| ~ spl22_188 ),
inference(avatar_component_clause,[],[f1998]) ).
fof(f15185,plain,
( spl22_694
| ~ spl22_83
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2022,f1994,f742,f15183]) ).
fof(f15183,plain,
( spl22_694
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X2,sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X2,X3),sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_694])]) ).
fof(f1994,plain,
( spl22_187
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3)))) = apply(relation_dom_restriction(X0,X3),sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| in(sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))),X1)
| sP2(X1,X2,relation_dom(relation_dom_restriction(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_187])]) ).
fof(f2022,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X2,sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X2,X3),sK13(relation_dom(relation_dom_restriction(X2,X3)),X4,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_187 ),
inference(resolution,[],[f1995,f743]) ).
fof(f1995,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| apply(X0,sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3)))) = apply(relation_dom_restriction(X0,X3),sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))))
| sP2(X1,X2,relation_dom(relation_dom_restriction(X0,X3))) )
| ~ spl22_187 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f15083,plain,
( spl22_693
| ~ spl22_83
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1974,f1964,f742,f15081]) ).
fof(f15081,plain,
( spl22_693
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3))))
| sP0(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3)))
| apply(X2,sK7(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK7(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_693])]) ).
fof(f1964,plain,
( spl22_185
<=> ! [X2,X0,X1] :
( apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| in(sK7(relation_dom_restriction(X0,X1),X2),X2)
| sP0(relation_dom_restriction(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_185])]) ).
fof(f1974,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3))))
| sP0(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3)))
| apply(X2,sK7(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK7(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_185 ),
inference(resolution,[],[f1965,f743]) ).
fof(f1965,plain,
( ! [X2,X0,X1] :
( in(sK7(relation_dom_restriction(X0,X1),X2),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| sP0(relation_dom_restriction(X0,X1),X2) )
| ~ spl22_185 ),
inference(avatar_component_clause,[],[f1964]) ).
fof(f15047,plain,
( spl22_692
| ~ spl22_173
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2074,f2011,f1739,f15045]) ).
fof(f15045,plain,
( spl22_692
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3)))) = apply(X4,apply(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))))
| ~ sP0(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_692])]) ).
fof(f2011,plain,
( spl22_191
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| in(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3),X3)
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_191])]) ).
fof(f2074,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3)))) = apply(X4,apply(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))))
| ~ sP0(X3,X5) )
| ~ spl22_173
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1740]) ).
fof(f2012,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3),X3)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3) )
| ~ spl22_191 ),
inference(avatar_component_clause,[],[f2011]) ).
fof(f15043,plain,
( spl22_691
| ~ spl22_173
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2057,f2007,f1739,f15041]) ).
fof(f15041,plain,
( spl22_691
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3)))) = apply(X4,apply(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))))
| ~ sP0(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_691])]) ).
fof(f2007,plain,
( spl22_190
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3)) = apply(relation_dom_restriction(X0,X2),sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| in(sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3),X3)
| sP2(X1,relation_dom(relation_dom_restriction(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_190])]) ).
fof(f2057,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3)))) = apply(X4,apply(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))))
| ~ sP0(X3,X5) )
| ~ spl22_173
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1740]) ).
fof(f2008,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3),X3)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| apply(X0,sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3)) = apply(relation_dom_restriction(X0,X2),sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3))
| sP2(X1,relation_dom(relation_dom_restriction(X0,X2)),X3) )
| ~ spl22_190 ),
inference(avatar_component_clause,[],[f2007]) ).
fof(f15039,plain,
( spl22_690
| ~ spl22_173
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2040,f1998,f1739,f15037]) ).
fof(f15037,plain,
( spl22_690
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X3,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1))))) = apply(X4,apply(X3,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP0(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_690])]) ).
fof(f2040,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X3,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1))))) = apply(X4,apply(X3,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP0(X3,X5) )
| ~ spl22_173
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1740]) ).
fof(f15035,plain,
( spl22_689
| ~ spl22_173
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2023,f1994,f1739,f15033]) ).
fof(f15033,plain,
( spl22_689
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X2,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))) = apply(X4,apply(X2,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP0(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_689])]) ).
fof(f2023,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X4)
| ~ relation(X4)
| apply(relation_dom_restriction(X4,X5),apply(X2,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))) = apply(X4,apply(X2,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP0(X2,X5) )
| ~ spl22_173
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1740]) ).
fof(f14886,plain,
( spl22_688
| ~ spl22_173
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1987,f1983,f1739,f14884]) ).
fof(f14884,plain,
( spl22_688
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))) = apply(X3,apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP0(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_688])]) ).
fof(f1983,plain,
( spl22_186
<=> ! [X2,X0,X1] :
( apply(X0,sK7(X1,relation_dom(relation_dom_restriction(X0,X2)))) = apply(relation_dom_restriction(X0,X2),sK7(X1,relation_dom(relation_dom_restriction(X0,X2))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| in(sK8(X1,relation_dom(relation_dom_restriction(X0,X2))),relation_dom(X1))
| sP0(X1,relation_dom(relation_dom_restriction(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_186])]) ).
fof(f1987,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))) = apply(X3,apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP0(X2,X4) )
| ~ spl22_173
| ~ spl22_186 ),
inference(resolution,[],[f1984,f1740]) ).
fof(f1984,plain,
( ! [X2,X0,X1] :
( in(sK8(X1,relation_dom(relation_dom_restriction(X0,X2))),relation_dom(X1))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| apply(X0,sK7(X1,relation_dom(relation_dom_restriction(X0,X2)))) = apply(relation_dom_restriction(X0,X2),sK7(X1,relation_dom(relation_dom_restriction(X0,X2))))
| sP0(X1,relation_dom(relation_dom_restriction(X0,X2))) )
| ~ spl22_186 ),
inference(avatar_component_clause,[],[f1983]) ).
fof(f14882,plain,
( spl22_687
| ~ spl22_173
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1975,f1964,f1739,f14880]) ).
fof(f14880,plain,
( spl22_687
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_dom(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_dom(X2)))
| sP0(relation_dom_restriction(X0,X1),relation_dom(X2))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK7(relation_dom_restriction(X0,X1),relation_dom(X2)))) = apply(X3,apply(X2,sK7(relation_dom_restriction(X0,X1),relation_dom(X2))))
| ~ sP0(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_687])]) ).
fof(f1975,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_dom(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_dom(X2)))
| sP0(relation_dom_restriction(X0,X1),relation_dom(X2))
| ~ function(X3)
| ~ relation(X3)
| apply(relation_dom_restriction(X3,X4),apply(X2,sK7(relation_dom_restriction(X0,X1),relation_dom(X2)))) = apply(X3,apply(X2,sK7(relation_dom_restriction(X0,X1),relation_dom(X2))))
| ~ sP0(X2,X4) )
| ~ spl22_173
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1740]) ).
fof(f14830,plain,
( spl22_686
| ~ spl22_153
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2072,f2011,f1508,f14828]) ).
fof(f14828,plain,
( spl22_686
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3))
| sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3)) = apply(X3,sK9(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3))))
| ~ sP1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_686])]) ).
fof(f2072,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3))
| sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3)) = apply(X3,sK9(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_rng(X3))))
| ~ sP1(X3) )
| ~ spl22_153
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1509]) ).
fof(f14826,plain,
( spl22_685
| ~ spl22_153
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2055,f2007,f1508,f14824]) ).
fof(f14824,plain,
( spl22_685
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3))
| sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3)) = apply(X3,sK9(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3))))
| ~ sP1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_685])]) ).
fof(f2055,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3))
| sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3)) = apply(X3,sK9(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_rng(X3))))
| ~ sP1(X3) )
| ~ spl22_153
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1509]) ).
fof(f14822,plain,
( spl22_684
| ~ spl22_133
| ~ spl22_635 ),
inference(avatar_split_clause,[],[f13115,f13056,f1246,f14820]) ).
fof(f13115,plain,
( ! [X0,X1] :
( sP0(sK15,relation_dom(X0))
| ~ sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_133
| ~ spl22_635 ),
inference(resolution,[],[f13057,f1247]) ).
fof(f14818,plain,
( spl22_683
| ~ spl22_153
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2038,f1998,f1508,f14816]) ).
fof(f14816,plain,
( spl22_683
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1)))
| sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1))) = apply(X3,sK9(X3,sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_683])]) ).
fof(f2038,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1)))
| sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1))) = apply(X3,sK9(X3,sK13(X2,relation_rng(X3),relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP1(X3) )
| ~ spl22_153
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1509]) ).
fof(f14814,plain,
( spl22_682
| ~ spl22_153
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2021,f1994,f1508,f14812]) ).
fof(f14812,plain,
( spl22_682
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK9(X2,sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_682])]) ).
fof(f2021,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK9(X2,sK13(relation_rng(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))))
| ~ sP1(X2) )
| ~ spl22_153
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1509]) ).
fof(f14778,plain,
( spl22_681
| ~ spl22_74
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2067,f2011,f662,f14776]) ).
fof(f14776,plain,
( spl22_681
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| apply(relation_dom_restriction(X4,X3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(X4,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_681])]) ).
fof(f2067,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| apply(relation_dom_restriction(X4,X3),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(X4,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_74
| ~ spl22_191 ),
inference(resolution,[],[f2012,f663]) ).
fof(f14774,plain,
( spl22_680
| ~ spl22_74
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2050,f2007,f662,f14772]) ).
fof(f14772,plain,
( spl22_680
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)
| apply(relation_dom_restriction(X4,X3),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) = apply(X4,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_680])]) ).
fof(f2050,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)
| apply(relation_dom_restriction(X4,X3),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) = apply(X4,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_74
| ~ spl22_190 ),
inference(resolution,[],[f2008,f663]) ).
fof(f14770,plain,
( spl22_679
| ~ spl22_74
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2033,f1998,f662,f14768]) ).
fof(f14768,plain,
( spl22_679
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X4,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X4,X3),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_679])]) ).
fof(f2033,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X4,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X4,X3),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_74
| ~ spl22_188 ),
inference(resolution,[],[f1999,f663]) ).
fof(f14766,plain,
( spl22_678
| ~ spl22_74
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2016,f1994,f662,f14764]) ).
fof(f14764,plain,
( spl22_678
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(X4,X2),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(X4,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_678])]) ).
fof(f2016,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(X4,X2),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(X4,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_74
| ~ spl22_187 ),
inference(resolution,[],[f1995,f663]) ).
fof(f14762,plain,
( spl22_677
| ~ spl22_248
| ~ spl22_635 ),
inference(avatar_split_clause,[],[f13109,f13056,f2743,f14760]) ).
fof(f14760,plain,
( spl22_677
<=> ! [X0] :
( sP0(sK15,relation_rng(X0))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_677])]) ).
fof(f13109,plain,
( ! [X0] :
( sP0(sK15,relation_rng(X0))
| ~ sP1(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl22_248
| ~ spl22_635 ),
inference(resolution,[],[f13057,f2744]) ).
fof(f14751,plain,
( spl22_676
| ~ spl22_184
| ~ spl22_192 ),
inference(avatar_split_clause,[],[f2091,f2083,f1959,f14749]) ).
fof(f14749,plain,
( spl22_676
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(X2))
| apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_676])]) ).
fof(f2091,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(X2))
| apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3)) )
| ~ spl22_184
| ~ spl22_192 ),
inference(duplicate_literal_removal,[],[f2086]) ).
fof(f2086,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(X3,relation_dom(X2))
| apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3)) )
| ~ spl22_184
| ~ spl22_192 ),
inference(resolution,[],[f2084,f1960]) ).
fof(f14603,plain,
( spl22_675
| ~ spl22_147
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2076,f2011,f1393,f14601]) ).
fof(f2076,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4))
| ~ sP0(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,apply(X3,X4)))
| ~ in(X4,relation_dom(X3)) )
| ~ spl22_147
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1394]) ).
fof(f14599,plain,
( spl22_674
| ~ spl22_147
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2059,f2007,f1393,f14597]) ).
fof(f2059,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4))
| ~ sP0(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),apply(X3,X4)))
| ~ in(X4,relation_dom(X3)) )
| ~ spl22_147
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1394]) ).
fof(f14595,plain,
( spl22_673
| ~ spl22_147
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2042,f1998,f1393,f14593]) ).
fof(f2042,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X3,sK13(X2,apply(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X4,relation_dom(X3)) )
| ~ spl22_147
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1394]) ).
fof(f14590,plain,
( spl22_672
| ~ spl22_147
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2025,f1994,f1393,f14588]) ).
fof(f2025,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X2,sK13(apply(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1394]) ).
fof(f14586,plain,
( spl22_671
| ~ spl22_74
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1990,f1983,f662,f14584]) ).
fof(f14584,plain,
( spl22_671
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(X3,relation_dom(X2)),sK8(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(X3,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_671])]) ).
fof(f1990,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(X3,relation_dom(X2)),sK8(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(X3,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_186 ),
inference(resolution,[],[f1984,f663]) ).
fof(f14441,plain,
( spl22_670
| ~ spl22_71
| ~ spl22_192 ),
inference(avatar_split_clause,[],[f2087,f2083,f642,f14439]) ).
fof(f14439,plain,
( spl22_670
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X2,sK9(X2,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_670])]) ).
fof(f2087,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X2,sK9(X2,X3)) = X3 )
| ~ spl22_71
| ~ spl22_192 ),
inference(resolution,[],[f2084,f643]) ).
fof(f14296,plain,
( spl22_669
| ~ spl22_68
| ~ spl22_192 ),
inference(avatar_split_clause,[],[f2088,f2083,f624,f14294]) ).
fof(f14294,plain,
( spl22_669
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(relation_dom_restriction(X0,X1)))
| in(sK9(X2,X3),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_669])]) ).
fof(f2088,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ in(X3,relation_dom(relation_dom_restriction(X0,X1)))
| in(sK9(X2,X3),relation_dom(X2)) )
| ~ spl22_68
| ~ spl22_192 ),
inference(resolution,[],[f2084,f625]) ).
fof(f14165,plain,
( spl22_668
| ~ spl22_45
| ~ spl22_635 ),
inference(avatar_split_clause,[],[f13103,f13056,f454,f14163]) ).
fof(f14163,plain,
( spl22_668
<=> ! [X0] :
( sP0(sK15,X0)
| ~ in(X0,sK7(sK15,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_668])]) ).
fof(f13103,plain,
( ! [X0] :
( sP0(sK15,X0)
| ~ in(X0,sK7(sK15,X0)) )
| ~ spl22_45
| ~ spl22_635 ),
inference(resolution,[],[f13057,f455]) ).
fof(f13812,plain,
( spl22_667
| ~ spl22_128
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2078,f2011,f1151,f13810]) ).
fof(f13810,plain,
( spl22_667
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3))))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))
| element(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_667])]) ).
fof(f2078,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3))))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))
| element(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3))),X3) )
| ~ spl22_128
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1152]) ).
fof(f13808,plain,
( spl22_666
| ~ spl22_129
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2071,f2011,f1155,f13806]) ).
fof(f13806,plain,
( spl22_666
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))
| in(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_666])]) ).
fof(f2071,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))
| in(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)),X3) )
| ~ spl22_129
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1156]) ).
fof(f13672,plain,
( spl22_665
| ~ spl22_130
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2070,f2011,f1159,f13670]) ).
fof(f13670,plain,
( spl22_665
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))
| in(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_665])]) ).
fof(f2070,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4))
| in(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,set_intersection2(X3,X4)),X4) )
| ~ spl22_130
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1160]) ).
fof(f13668,plain,
( spl22_664
| ~ spl22_128
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2061,f2007,f1151,f13666]) ).
fof(f13666,plain,
( spl22_664
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3))))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))
| element(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_664])]) ).
fof(f2061,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3))))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))
| element(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3))),X3) )
| ~ spl22_128
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1152]) ).
fof(f13664,plain,
( spl22_663
| ~ spl22_129
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2054,f2007,f1155,f13662]) ).
fof(f13662,plain,
( spl22_663
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))
| in(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_663])]) ).
fof(f2054,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))
| in(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)),X3) )
| ~ spl22_129
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1156]) ).
fof(f13660,plain,
( spl22_662
| ~ spl22_130
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2053,f2007,f1159,f13658]) ).
fof(f13658,plain,
( spl22_662
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))
| in(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_662])]) ).
fof(f2053,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4))
| in(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),set_intersection2(X3,X4)),X4) )
| ~ spl22_130
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1160]) ).
fof(f13656,plain,
( spl22_661
| ~ spl22_128
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2044,f1998,f1151,f13654]) ).
fof(f13654,plain,
( spl22_661
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_661])]) ).
fof(f2044,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1))),X3) )
| ~ spl22_128
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1152]) ).
fof(f13652,plain,
( spl22_660
| ~ spl22_129
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2037,f1998,f1155,f13650]) ).
fof(f13650,plain,
( spl22_660
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_660])]) ).
fof(f2037,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))),X3) )
| ~ spl22_129
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1156]) ).
fof(f13648,plain,
( spl22_659
| ~ spl22_130
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2036,f1998,f1159,f13646]) ).
fof(f13646,plain,
( spl22_659
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_659])]) ).
fof(f2036,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(X2,set_intersection2(X3,X4),relation_dom(relation_dom_restriction(X0,X1))),X4) )
| ~ spl22_130
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1160]) ).
fof(f13644,plain,
( spl22_658
| ~ spl22_128
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2027,f1994,f1151,f13642]) ).
fof(f13642,plain,
( spl22_658
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_658])]) ).
fof(f2027,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1))),X2) )
| ~ spl22_128
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1152]) ).
fof(f13640,plain,
( spl22_657
| ~ spl22_129
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2020,f1994,f1155,f13638]) ).
fof(f13638,plain,
( spl22_657
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_657])]) ).
fof(f2020,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))),X2) )
| ~ spl22_129
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1156]) ).
fof(f13636,plain,
( spl22_656
| ~ spl22_130
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2019,f1994,f1159,f13634]) ).
fof(f13634,plain,
( spl22_656
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_656])]) ).
fof(f2019,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1)))
| in(sK13(set_intersection2(X2,X3),X4,relation_dom(relation_dom_restriction(X0,X1))),X3) )
| ~ spl22_130
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1160]) ).
fof(f13444,plain,
( spl22_655
| ~ spl22_153
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1973,f1964,f1508,f13442]) ).
fof(f13442,plain,
( spl22_655
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_rng(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_rng(X2)))
| sP0(relation_dom_restriction(X0,X1),relation_rng(X2))
| sK7(relation_dom_restriction(X0,X1),relation_rng(X2)) = apply(X2,sK9(X2,sK7(relation_dom_restriction(X0,X1),relation_rng(X2))))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_655])]) ).
fof(f1973,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_rng(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_rng(X2)))
| sP0(relation_dom_restriction(X0,X1),relation_rng(X2))
| sK7(relation_dom_restriction(X0,X1),relation_rng(X2)) = apply(X2,sK9(X2,sK7(relation_dom_restriction(X0,X1),relation_rng(X2))))
| ~ sP1(X2) )
| ~ spl22_153
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1509]) ).
fof(f13387,plain,
( spl22_654
| ~ spl22_61
| ~ spl22_192 ),
inference(avatar_split_clause,[],[f2089,f2083,f578,f13385]) ).
fof(f13385,plain,
( spl22_654
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| relation_dom(relation_dom_restriction(X0,X1)) = relation_rng(X2)
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_654])]) ).
fof(f2089,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| sK7(X2,relation_dom(relation_dom_restriction(X0,X1))) = apply(X2,sK8(X2,relation_dom(relation_dom_restriction(X0,X1))))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| relation_dom(relation_dom_restriction(X0,X1)) = relation_rng(X2)
| ~ sP1(X2) )
| ~ spl22_61
| ~ spl22_192 ),
inference(resolution,[],[f2084,f579]) ).
fof(f13383,plain,
( spl22_653
| ~ spl22_132
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2077,f2011,f1242,f13381]) ).
fof(f13381,plain,
( spl22_653
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3))
| element(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3)),X3)
| empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_653])]) ).
fof(f2077,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3))
| element(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK6(X3)),X3)
| empty(X3) )
| ~ spl22_132
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1243]) ).
fof(f13379,plain,
( spl22_652
| ~ spl22_121
| ~ spl22_635 ),
inference(avatar_split_clause,[],[f13126,f13056,f1110,f13377]) ).
fof(f13377,plain,
( spl22_652
<=> ! [X0] :
( sP0(sK15,sK10(powerset(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_652])]) ).
fof(f13126,plain,
( ! [X0] :
( sP0(sK15,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_635 ),
inference(resolution,[],[f13057,f1111]) ).
fof(f13375,plain,
( spl22_651
| ~ spl22_132
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2060,f2007,f1242,f13373]) ).
fof(f13373,plain,
( spl22_651
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3))
| element(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3)),X3)
| empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_651])]) ).
fof(f2060,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3))
| element(sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK6(X3)),X3)
| empty(X3) )
| ~ spl22_132
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1243]) ).
fof(f13371,plain,
( spl22_650
| ~ spl22_132
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2043,f1998,f1242,f13369]) ).
fof(f13369,plain,
( spl22_650
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1))),X3)
| empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_650])]) ).
fof(f2043,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(X2,sK6(X3),relation_dom(relation_dom_restriction(X0,X1))),X3)
| empty(X3) )
| ~ spl22_132
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1243]) ).
fof(f13367,plain,
( spl22_649
| ~ spl22_132
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2026,f1994,f1242,f13365]) ).
fof(f13365,plain,
( spl22_649
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1))),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_649])]) ).
fof(f2026,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| element(sK13(sK6(X2),X3,relation_dom(relation_dom_restriction(X0,X1))),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1243]) ).
fof(f13363,plain,
( spl22_648
| ~ spl22_74
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1968,f1964,f662,f13361]) ).
fof(f13361,plain,
( spl22_648
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| sP0(relation_dom_restriction(X0,X1),X2)
| apply(relation_dom_restriction(X3,X2),sK7(relation_dom_restriction(X0,X1),X2)) = apply(X3,sK7(relation_dom_restriction(X0,X1),X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_648])]) ).
fof(f1968,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| sP0(relation_dom_restriction(X0,X1),X2)
| apply(relation_dom_restriction(X3,X2),sK7(relation_dom_restriction(X0,X1),X2)) = apply(X3,sK7(relation_dom_restriction(X0,X1),X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_185 ),
inference(resolution,[],[f1965,f663]) ).
fof(f13329,plain,
( spl22_647
| ~ spl22_147
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1977,f1964,f1393,f13327]) ).
fof(f1977,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),apply(X2,X3))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),apply(X2,X3)))
| sP0(relation_dom_restriction(X0,X1),apply(X2,X3))
| ~ sP0(X2,sK7(relation_dom_restriction(X0,X1),apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1394]) ).
fof(f13297,plain,
( spl22_646
| ~ spl22_233
| ~ spl22_635 ),
inference(avatar_split_clause,[],[f13113,f13056,f2559,f13295]) ).
fof(f13113,plain,
( ! [X0] :
( sP0(sK15,relation_dom(X0))
| ~ sP0(X0,sK15) )
| ~ spl22_233
| ~ spl22_635 ),
inference(resolution,[],[f13057,f2560]) ).
fof(f13098,plain,
( spl22_645
| ~ spl22_45
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2069,f2011,f454,f13096]) ).
fof(f13096,plain,
( spl22_645
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| ~ in(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_645])]) ).
fof(f2069,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| ~ in(X3,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) )
| ~ spl22_45
| ~ spl22_191 ),
inference(resolution,[],[f2012,f455]) ).
fof(f13094,plain,
( spl22_644
| ~ spl22_45
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2052,f2007,f454,f13092]) ).
fof(f13092,plain,
( spl22_644
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)
| ~ in(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_644])]) ).
fof(f2052,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)
| ~ in(X3,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),X3)) )
| ~ spl22_45
| ~ spl22_190 ),
inference(resolution,[],[f2008,f455]) ).
fof(f13090,plain,
( spl22_643
| ~ spl22_45
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2035,f1998,f454,f13088]) ).
fof(f13088,plain,
( spl22_643
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ in(X3,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_643])]) ).
fof(f2035,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ in(X3,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) )
| ~ spl22_45
| ~ spl22_188 ),
inference(resolution,[],[f1999,f455]) ).
fof(f13086,plain,
( spl22_642
| ~ spl22_45
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2018,f1994,f454,f13084]) ).
fof(f13084,plain,
( spl22_642
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ in(X2,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_642])]) ).
fof(f2018,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ in(X2,sK13(X2,X3,relation_dom(relation_dom_restriction(X0,X1)))) )
| ~ spl22_45
| ~ spl22_187 ),
inference(resolution,[],[f1995,f455]) ).
fof(f13082,plain,
( spl22_641
| ~ spl22_128
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1979,f1964,f1151,f13080]) ).
fof(f13080,plain,
( spl22_641
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2)))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2))))
| sP0(relation_dom_restriction(X0,X1),sK10(powerset(X2)))
| element(sK7(relation_dom_restriction(X0,X1),sK10(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_641])]) ).
fof(f1979,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2)))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2))))
| sP0(relation_dom_restriction(X0,X1),sK10(powerset(X2)))
| element(sK7(relation_dom_restriction(X0,X1),sK10(powerset(X2))),X2) )
| ~ spl22_128
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1152]) ).
fof(f13078,plain,
( spl22_640
| ~ spl22_129
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1972,f1964,f1155,f13076]) ).
fof(f13076,plain,
( spl22_640
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)))
| sP0(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))
| in(sK7(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_640])]) ).
fof(f1972,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)))
| sP0(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))
| in(sK7(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)),X2) )
| ~ spl22_129
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1156]) ).
fof(f13074,plain,
( spl22_639
| ~ spl22_130
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1971,f1964,f1159,f13072]) ).
fof(f13072,plain,
( spl22_639
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)))
| sP0(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))
| in(sK7(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_639])]) ).
fof(f1971,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)))
| sP0(relation_dom_restriction(X0,X1),set_intersection2(X2,X3))
| in(sK7(relation_dom_restriction(X0,X1),set_intersection2(X2,X3)),X3) )
| ~ spl22_130
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1160]) ).
fof(f13070,plain,
( spl22_638
| ~ spl22_158
| ~ spl22_184 ),
inference(avatar_split_clause,[],[f1962,f1959,f1544,f13068]) ).
fof(f13068,plain,
( spl22_638
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(X2,relation_dom(X3))
| apply(X0,apply(X3,X2)) = apply(relation_dom_restriction(X0,X1),apply(X3,X2))
| sK7(X3,relation_dom(relation_dom_restriction(X0,X1))) = apply(X3,sK8(X3,relation_dom(relation_dom_restriction(X0,X1))))
| ~ empty(relation_dom(relation_dom_restriction(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_638])]) ).
fof(f1962,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(X2,relation_dom(X3))
| apply(X0,apply(X3,X2)) = apply(relation_dom_restriction(X0,X1),apply(X3,X2))
| sK7(X3,relation_dom(relation_dom_restriction(X0,X1))) = apply(X3,sK8(X3,relation_dom(relation_dom_restriction(X0,X1))))
| ~ empty(relation_dom(relation_dom_restriction(X0,X1))) )
| ~ spl22_158
| ~ spl22_184 ),
inference(resolution,[],[f1960,f1545]) ).
fof(f13066,plain,
( spl22_637
| ~ spl22_83
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1695,f1608,f742,f13064]) ).
fof(f13064,plain,
( spl22_637
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))),X0)
| sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_637])]) ).
fof(f1695,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))),X0)
| sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_165 ),
inference(resolution,[],[f1609,f743]) ).
fof(f13062,plain,
( spl22_636
| ~ spl22_83
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1670,f1600,f742,f13060]) ).
fof(f13060,plain,
( spl22_636
<=> ! [X0,X3,X2,X1] :
( element(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3),X3)
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_636])]) ).
fof(f1670,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3),X3)
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_163 ),
inference(resolution,[],[f1601,f743]) ).
fof(f13058,plain,
( spl22_635
| spl22_114
| ~ spl22_310
| ~ spl22_607 ),
inference(avatar_split_clause,[],[f12658,f12473,f3538,f956,f13056]) ).
fof(f12473,plain,
( spl22_607
<=> ! [X0] :
( sP0(sK15,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_607])]) ).
fof(f12658,plain,
( ! [X0,X1] :
( ~ empty(X0)
| in(sK7(sK15,X1),X1)
| sP0(sK15,X1) )
| ~ spl22_310
| ~ spl22_607 ),
inference(duplicate_literal_removal,[],[f12583]) ).
fof(f12583,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X0)
| in(sK7(sK15,X1),X1)
| sP0(sK15,X1) )
| ~ spl22_310
| ~ spl22_607 ),
inference(resolution,[],[f12474,f3539]) ).
fof(f12474,plain,
( ! [X0] :
( sP0(sK15,X0)
| ~ empty(X0) )
| ~ spl22_607 ),
inference(avatar_component_clause,[],[f12473]) ).
fof(f13054,plain,
( spl22_634
| ~ spl22_83
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1650,f1587,f742,f13052]) ).
fof(f13052,plain,
( spl22_634
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))),X1)
| sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_634])]) ).
fof(f1650,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))),X1)
| sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_161 ),
inference(resolution,[],[f1588,f743]) ).
fof(f13050,plain,
( spl22_633
| ~ spl22_83
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1630,f1579,f742,f13048]) ).
fof(f13048,plain,
( spl22_633
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3),X3)
| sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_633])]) ).
fof(f1630,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3),X3)
| sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_159 ),
inference(resolution,[],[f1580,f743]) ).
fof(f13046,plain,
( spl22_632
| ~ spl22_83
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1329,f1290,f742,f13044]) ).
fof(f13044,plain,
( spl22_632
<=> ! [X2,X0,X1] :
( sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_632])]) ).
fof(f1329,plain,
( ! [X2,X0,X1] :
( sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(relation_dom_restriction(X0,X1)))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_139 ),
inference(resolution,[],[f1291,f743]) ).
fof(f13042,plain,
( spl22_631
| ~ spl22_83
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1315,f1286,f742,f13040]) ).
fof(f13040,plain,
( spl22_631
<=> ! [X2,X0,X1] :
( sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),relation_dom(relation_dom_restriction(X1,X2)))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_631])]) ).
fof(f1315,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),relation_dom(relation_dom_restriction(X1,X2)))
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_138 ),
inference(resolution,[],[f1287,f743]) ).
fof(f12975,plain,
( spl22_630
| ~ spl22_121
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2079,f2011,f1110,f12973]) ).
fof(f12973,plain,
( spl22_630
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3))))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_630])]) ).
fof(f2079,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3))))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK10(powerset(X3)))
| ~ empty(X3) )
| ~ spl22_121
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1111]) ).
fof(f12971,plain,
( spl22_629
| ~ spl22_133
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2075,f2011,f1246,f12969]) ).
fof(f12969,plain,
( spl22_629
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_629])]) ).
fof(f2075,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3)))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,relation_dom(X3))
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_191 ),
inference(resolution,[],[f2012,f1247]) ).
fof(f12967,plain,
( spl22_628
| ~ spl22_121
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2062,f2007,f1110,f12965]) ).
fof(f12965,plain,
( spl22_628
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3))))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_628])]) ).
fof(f2062,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3))))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK10(powerset(X3)))
| ~ empty(X3) )
| ~ spl22_121
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1111]) ).
fof(f12963,plain,
( spl22_627
| ~ spl22_133
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2058,f2007,f1246,f12961]) ).
fof(f12961,plain,
( spl22_627
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_627])]) ).
fof(f2058,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3)))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X3))
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_190 ),
inference(resolution,[],[f2008,f1247]) ).
fof(f12959,plain,
( spl22_626
| ~ spl22_121
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2045,f1998,f1110,f12957]) ).
fof(f12957,plain,
( spl22_626
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_626])]) ).
fof(f2045,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK10(powerset(X3)),relation_dom(relation_dom_restriction(X0,X1)))
| ~ empty(X3) )
| ~ spl22_121
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1111]) ).
fof(f12955,plain,
( spl22_625
| ~ spl22_133
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2041,f1998,f1246,f12953]) ).
fof(f12953,plain,
( spl22_625
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X3,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_625])]) ).
fof(f2041,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,relation_dom(X3),relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X3,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_188 ),
inference(resolution,[],[f1999,f1247]) ).
fof(f12951,plain,
( spl22_624
| ~ spl22_121
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2028,f1994,f1110,f12949]) ).
fof(f12949,plain,
( spl22_624
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_624])]) ).
fof(f2028,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK10(powerset(X2)),X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1111]) ).
fof(f12947,plain,
( spl22_623
| ~ spl22_133
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2024,f1994,f1246,f12945]) ).
fof(f12945,plain,
( spl22_623
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X2,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_623])]) ).
fof(f2024,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(relation_dom(X2),X3,relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X2,X4)
| ~ empty(X4) )
| ~ spl22_133
| ~ spl22_187 ),
inference(resolution,[],[f1995,f1247]) ).
fof(f12943,plain,
( spl22_622
| spl22_114
| ~ spl22_311
| ~ spl22_607 ),
inference(avatar_split_clause,[],[f12657,f12473,f3543,f956,f12941]) ).
fof(f12941,plain,
( spl22_622
<=> ! [X1] :
( sP0(sK15,X1)
| element(sK7(sK15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_622])]) ).
fof(f12657,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(sK15,X1)
| element(sK7(sK15,X1),X1) )
| ~ spl22_311
| ~ spl22_607 ),
inference(duplicate_literal_removal,[],[f12584]) ).
fof(f12584,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(sK15,X1)
| element(sK7(sK15,X1),X1)
| ~ empty(X0) )
| ~ spl22_311
| ~ spl22_607 ),
inference(resolution,[],[f12474,f3544]) ).
fof(f12933,plain,
( spl22_621
| ~ spl22_132
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1978,f1964,f1242,f12931]) ).
fof(f12931,plain,
( spl22_621
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK6(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK6(X2)))
| sP0(relation_dom_restriction(X0,X1),sK6(X2))
| element(sK7(relation_dom_restriction(X0,X1),sK6(X2)),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_621])]) ).
fof(f1978,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK6(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK6(X2)))
| sP0(relation_dom_restriction(X0,X1),sK6(X2))
| element(sK7(relation_dom_restriction(X0,X1),sK6(X2)),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1243]) ).
fof(f12912,plain,
( spl22_620
| ~ spl22_45
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1992,f1983,f454,f12910]) ).
fof(f12910,plain,
( spl22_620
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ in(relation_dom(X2),sK8(X2,relation_dom(relation_dom_restriction(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_620])]) ).
fof(f1992,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ in(relation_dom(X2),sK8(X2,relation_dom(relation_dom_restriction(X0,X1)))) )
| ~ spl22_45
| ~ spl22_186 ),
inference(resolution,[],[f1984,f455]) ).
fof(f12908,plain,
( spl22_619
| ~ spl22_83
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1555,f1527,f742,f12906]) ).
fof(f12906,plain,
( spl22_619
<=> ! [X2,X0,X1] :
( element(sK8(X0,relation_dom(relation_dom_restriction(X1,X2))),relation_dom(X0))
| sP0(X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(X1,sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_619])]) ).
fof(f1555,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,relation_dom(relation_dom_restriction(X1,X2))),relation_dom(X0))
| sP0(X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(X1,sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_154 ),
inference(resolution,[],[f1528,f743]) ).
fof(f12831,plain,
( spl22_618
| ~ spl22_55
| ~ spl22_546 ),
inference(avatar_split_clause,[],[f10987,f10626,f519,f12829]) ).
fof(f12829,plain,
( spl22_618
<=> ! [X0] :
( relation_dom_restriction(sK5,sK15) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_618])]) ).
fof(f10987,plain,
( ! [X0] :
( relation_dom_restriction(sK5,sK15) = X0
| ~ empty(X0) )
| ~ spl22_55
| ~ spl22_546 ),
inference(resolution,[],[f10628,f520]) ).
fof(f12803,plain,
( spl22_617
| ~ spl22_133
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1988,f1983,f1246,f12801]) ).
fof(f12801,plain,
( spl22_617
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_617])]) ).
fof(f1988,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK7(X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK7(X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_186 ),
inference(resolution,[],[f1984,f1247]) ).
fof(f12799,plain,
( spl22_616
| ~ spl22_121
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1980,f1964,f1110,f12797]) ).
fof(f12797,plain,
( spl22_616
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2)))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2))))
| sP0(relation_dom_restriction(X0,X1),sK10(powerset(X2)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_616])]) ).
fof(f1980,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2)))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK10(powerset(X2))))
| sP0(relation_dom_restriction(X0,X1),sK10(powerset(X2)))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1111]) ).
fof(f12795,plain,
( spl22_615
| ~ spl22_133
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1976,f1964,f1246,f12793]) ).
fof(f12793,plain,
( spl22_615
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_dom(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_dom(X2)))
| sP0(relation_dom_restriction(X0,X1),relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_615])]) ).
fof(f1976,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),relation_dom(X2))) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),relation_dom(X2)))
| sP0(relation_dom_restriction(X0,X1),relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_185 ),
inference(resolution,[],[f1965,f1247]) ).
fof(f12791,plain,
( spl22_614
| ~ spl22_83
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1499,f1409,f742,f12789]) ).
fof(f12789,plain,
( spl22_614
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ empty(X0)
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_614])]) ).
fof(f1499,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ empty(X0)
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_151 ),
inference(resolution,[],[f1410,f743]) ).
fof(f12787,plain,
( spl22_613
| ~ spl22_83
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1484,f1405,f742,f12785]) ).
fof(f12785,plain,
( spl22_613
<=> ! [X0,X3,X2,X1] :
( sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| ~ empty(X3)
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_613])]) ).
fof(f1484,plain,
( ! [X2,X3,X0,X1] :
( sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)
| ~ empty(X3)
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_150 ),
inference(resolution,[],[f1406,f743]) ).
fof(f12783,plain,
( spl22_612
| ~ spl22_83
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1469,f1401,f742,f12781]) ).
fof(f12781,plain,
( spl22_612
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ empty(X1)
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_612])]) ).
fof(f1469,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ empty(X1)
| apply(X2,sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3)))) = apply(relation_dom_restriction(X2,X3),sK13(X0,X1,relation_dom(relation_dom_restriction(X2,X3))))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3)) )
| ~ spl22_83
| ~ spl22_149 ),
inference(resolution,[],[f1402,f743]) ).
fof(f12779,plain,
( spl22_611
| ~ spl22_83
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1454,f1397,f742,f12777]) ).
fof(f12777,plain,
( spl22_611
<=> ! [X0,X3,X2,X1] :
( sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)
| ~ empty(X3)
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_611])]) ).
fof(f1454,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)
| ~ empty(X3)
| apply(X1,sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3)) = apply(relation_dom_restriction(X1,X2),sK13(X0,relation_dom(relation_dom_restriction(X1,X2)),X3))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_148 ),
inference(resolution,[],[f1398,f743]) ).
fof(f12521,plain,
( spl22_610
| ~ spl22_45
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1970,f1964,f454,f12519]) ).
fof(f12519,plain,
( spl22_610
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| sP0(relation_dom_restriction(X0,X1),X2)
| ~ in(X2,sK7(relation_dom_restriction(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_610])]) ).
fof(f1970,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| sP0(relation_dom_restriction(X0,X1),X2)
| ~ in(X2,sK7(relation_dom_restriction(X0,X1),X2)) )
| ~ spl22_45
| ~ spl22_185 ),
inference(resolution,[],[f1965,f455]) ).
fof(f12517,plain,
( spl22_609
| ~ spl22_77
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1746,f1739,f698,f12515]) ).
fof(f1746,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| sK7(X3,relation_dom(X2)) = apply(X3,sK8(X3,relation_dom(X2)))
| sP0(X3,relation_dom(X2)) )
| ~ spl22_77
| ~ spl22_173 ),
inference(resolution,[],[f1740,f699]) ).
fof(f12513,plain,
( spl22_608
| ~ spl22_83
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1562,f1535,f742,f12511]) ).
fof(f12511,plain,
( spl22_608
<=> ! [X2,X0,X1] :
( element(sK7(relation_dom_restriction(X0,X1),X2),X2)
| sP0(relation_dom_restriction(X0,X1),X2)
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_608])]) ).
fof(f1562,plain,
( ! [X2,X0,X1] :
( element(sK7(relation_dom_restriction(X0,X1),X2),X2)
| sP0(relation_dom_restriction(X0,X1),X2)
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_156 ),
inference(resolution,[],[f1536,f743]) ).
fof(f12475,plain,
( spl22_607
| ~ spl22_478
| ~ spl22_583 ),
inference(avatar_split_clause,[],[f11649,f11535,f8381,f12473]) ).
fof(f11649,plain,
( ! [X0] :
( sP0(sK15,X0)
| ~ empty(X0) )
| ~ spl22_478
| ~ spl22_583 ),
inference(superposition,[],[f8382,f11537]) ).
fof(f12095,plain,
( spl22_606
| ~ spl22_115
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f2080,f2011,f959,f12093]) ).
fof(f12093,plain,
( spl22_606
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK15)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK15))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_606])]) ).
fof(f2080,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK15)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,sK15))
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,sK15) )
| ~ spl22_115
| ~ spl22_191 ),
inference(resolution,[],[f2012,f960]) ).
fof(f12002,plain,
( spl22_605
| ~ spl22_115
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f2063,f2007,f959,f12000]) ).
fof(f12000,plain,
( spl22_605
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK15)) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK15))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_605])]) ).
fof(f2063,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK15)) = apply(relation_dom_restriction(X0,X1),sK13(X2,relation_dom(relation_dom_restriction(X0,X1)),sK15))
| sP2(X2,relation_dom(relation_dom_restriction(X0,X1)),sK15) )
| ~ spl22_115
| ~ spl22_190 ),
inference(resolution,[],[f2008,f960]) ).
fof(f11998,plain,
( spl22_604
| ~ spl22_115
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f2046,f1998,f959,f11996]) ).
fof(f11996,plain,
( spl22_604
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK15,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK15,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK15,relation_dom(relation_dom_restriction(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_604])]) ).
fof(f2046,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(X2,sK15,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(X2,sK15,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(X2,sK15,relation_dom(relation_dom_restriction(X0,X1))) )
| ~ spl22_115
| ~ spl22_188 ),
inference(resolution,[],[f1999,f960]) ).
fof(f11994,plain,
( spl22_603
| ~ spl22_115
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f2029,f1994,f959,f11992]) ).
fof(f11992,plain,
( spl22_603
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK15,X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK15,X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK15,X2,relation_dom(relation_dom_restriction(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_603])]) ).
fof(f2029,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK13(sK15,X2,relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK13(sK15,X2,relation_dom(relation_dom_restriction(X0,X1))))
| sP2(sK15,X2,relation_dom(relation_dom_restriction(X0,X1))) )
| ~ spl22_115
| ~ spl22_187 ),
inference(resolution,[],[f1995,f960]) ).
fof(f11990,plain,
( spl22_602
| ~ spl22_76
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1764,f1739,f670,f11988]) ).
fof(f1764,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ sP0(X2,X1)
| in(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4) )
| ~ spl22_76
| ~ spl22_173 ),
inference(resolution,[],[f1740,f671]) ).
fof(f11986,plain,
( spl22_601
| ~ spl22_163
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1762,f1739,f1600,f11984]) ).
fof(f1762,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ sP0(X2,X1)
| element(sK13(relation_dom(X2),X3,X4),X4)
| sP2(relation_dom(X2),X3,X4) )
| ~ spl22_163
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1601]) ).
fof(f11982,plain,
( spl22_600
| ~ spl22_75
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1761,f1739,f666,f11980]) ).
fof(f1761,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ sP0(X2,X1)
| in(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4) )
| ~ spl22_75
| ~ spl22_173 ),
inference(resolution,[],[f1740,f667]) ).
fof(f11978,plain,
( spl22_599
| ~ spl22_159
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1759,f1739,f1579,f11976]) ).
fof(f1759,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ sP0(X2,X1)
| element(sK13(X3,relation_dom(X2),X4),X4)
| sP2(X3,relation_dom(X2),X4) )
| ~ spl22_159
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1580]) ).
fof(f11974,plain,
( spl22_598
| ~ spl22_75
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1758,f1739,f666,f11972]) ).
fof(f1758,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| in(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_75
| ~ spl22_173 ),
inference(resolution,[],[f1740,f667]) ).
fof(f11970,plain,
( spl22_597
| ~ spl22_76
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1757,f1739,f670,f11968]) ).
fof(f1757,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| in(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_76
| ~ spl22_173 ),
inference(resolution,[],[f1740,f671]) ).
fof(f11966,plain,
( spl22_596
| ~ spl22_161
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1754,f1739,f1587,f11964]) ).
fof(f1754,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| element(sK13(X3,X4,relation_dom(X2)),X4)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_161
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1588]) ).
fof(f11962,plain,
( spl22_595
| ~ spl22_463
| ~ spl22_583 ),
inference(avatar_split_clause,[],[f11648,f11535,f8061,f11959]) ).
fof(f11959,plain,
( spl22_595
<=> sP0(sK15,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_595])]) ).
fof(f8061,plain,
( spl22_463
<=> sP0(relation_dom_restriction(sK5,sK15),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_463])]) ).
fof(f11648,plain,
( sP0(sK15,sK15)
| ~ spl22_463
| ~ spl22_583 ),
inference(superposition,[],[f8063,f11537]) ).
fof(f8063,plain,
( sP0(relation_dom_restriction(sK5,sK15),sK15)
| ~ spl22_463 ),
inference(avatar_component_clause,[],[f8061]) ).
fof(f11957,plain,
( spl22_594
| ~ spl22_165
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1753,f1739,f1608,f11955]) ).
fof(f1753,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| element(sK13(X3,X4,relation_dom(X2)),X3)
| sP2(X3,X4,relation_dom(X2)) )
| ~ spl22_165
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1609]) ).
fof(f11953,plain,
( spl22_593
| ~ spl22_83
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1367,f1341,f742,f11951]) ).
fof(f11951,plain,
( spl22_593
<=> ! [X2,X0,X1] :
( sP0(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ empty(relation_dom(X0))
| apply(X1,sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_593])]) ).
fof(f1367,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ empty(relation_dom(X0))
| apply(X1,sK7(X0,relation_dom(relation_dom_restriction(X1,X2)))) = apply(relation_dom_restriction(X1,X2),sK7(X0,relation_dom(relation_dom_restriction(X1,X2))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_142 ),
inference(resolution,[],[f1342,f743]) ).
fof(f11834,plain,
( spl22_592
| ~ spl22_83
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1418,f1384,f742,f11832]) ).
fof(f1418,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_dom_restriction(X1,X2)))
| ~ sP1(relation_dom_restriction(X1,X2))
| apply(X1,sK9(relation_dom_restriction(X1,X2),X0)) = apply(relation_dom_restriction(X1,X2),sK9(relation_dom_restriction(X1,X2),X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_83
| ~ spl22_145 ),
inference(resolution,[],[f1385,f743]) ).
fof(f11743,plain,
( spl22_591
| ~ spl22_80
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1354,f1337,f716,f11741]) ).
fof(f1354,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| ~ in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_80
| ~ spl22_141 ),
inference(resolution,[],[f1338,f717]) ).
fof(f11566,plain,
( spl22_590
| ~ spl22_59
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1939,f1849,f557,f11564]) ).
fof(f11564,plain,
( spl22_590
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(set_intersection2(X2,X3),X1),sK7(X0,X1)) = apply(set_intersection2(X2,X3),sK7(X0,X1))
| ~ function(set_intersection2(X2,X3))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ relation(X3)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_590])]) ).
fof(f557,plain,
( spl22_59
<=> ! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_59])]) ).
fof(f1849,plain,
( spl22_183
<=> ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_183])]) ).
fof(f1939,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(set_intersection2(X2,X3),X1),sK7(X0,X1)) = apply(set_intersection2(X2,X3),sK7(X0,X1))
| ~ function(set_intersection2(X2,X3))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ relation(X3)
| ~ relation(X2) )
| ~ spl22_59
| ~ spl22_183 ),
inference(resolution,[],[f1850,f558]) ).
fof(f558,plain,
( ! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f1850,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_183 ),
inference(avatar_component_clause,[],[f1849]) ).
fof(f11562,plain,
( spl22_589
| ~ spl22_59
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1920,f1845,f557,f11560]) ).
fof(f11560,plain,
( spl22_589
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X0),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_589])]) ).
fof(f1845,plain,
( spl22_182
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_182])]) ).
fof(f1920,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X0),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_182 ),
inference(resolution,[],[f1846,f558]) ).
fof(f1846,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_182 ),
inference(avatar_component_clause,[],[f1845]) ).
fof(f11558,plain,
( spl22_588
| ~ spl22_59
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1890,f1841,f557,f11556]) ).
fof(f11556,plain,
( spl22_588
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X0)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_588])]) ).
fof(f1841,plain,
( spl22_181
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_181])]) ).
fof(f1890,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X0)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_181 ),
inference(resolution,[],[f1842,f558]) ).
fof(f1842,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_181 ),
inference(avatar_component_clause,[],[f1841]) ).
fof(f11554,plain,
( spl22_587
| ~ spl22_59
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1871,f1837,f557,f11552]) ).
fof(f11552,plain,
( spl22_587
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X1),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_587])]) ).
fof(f1837,plain,
( spl22_180
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_180])]) ).
fof(f1871,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X1),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_180 ),
inference(resolution,[],[f1838,f558]) ).
fof(f1838,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_180 ),
inference(avatar_component_clause,[],[f1837]) ).
fof(f11550,plain,
( spl22_586
| ~ spl22_59
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1852,f1833,f557,f11548]) ).
fof(f11548,plain,
( spl22_586
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X1)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_586])]) ).
fof(f1833,plain,
( spl22_179
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_179])]) ).
fof(f1852,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X1)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_179 ),
inference(resolution,[],[f1834,f558]) ).
fof(f1834,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_179 ),
inference(avatar_component_clause,[],[f1833]) ).
fof(f11546,plain,
( spl22_585
| ~ spl22_73
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1747,f1739,f652,f11544]) ).
fof(f1747,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| in(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2)) )
| ~ spl22_73
| ~ spl22_173 ),
inference(resolution,[],[f1740,f653]) ).
fof(f11542,plain,
( spl22_584
| ~ spl22_154
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1744,f1739,f1527,f11540]) ).
fof(f1744,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| element(sK8(X3,relation_dom(X2)),relation_dom(X3))
| sP0(X3,relation_dom(X2)) )
| ~ spl22_154
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1528]) ).
fof(f11538,plain,
( spl22_583
| ~ spl22_113
| ~ spl22_546 ),
inference(avatar_split_clause,[],[f10988,f10626,f952,f11535]) ).
fof(f10988,plain,
( sK15 = relation_dom_restriction(sK5,sK15)
| ~ spl22_113
| ~ spl22_546 ),
inference(resolution,[],[f10628,f953]) ).
fof(f11388,plain,
( spl22_582
| ~ spl22_139
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1766,f1739,f1290,f11386]) ).
fof(f1766,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2)))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(relation_dom(X2),X3,relation_dom(X2)) )
| ~ spl22_139
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1291]) ).
fof(f11384,plain,
( spl22_581
| ~ spl22_138
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1765,f1739,f1286,f11382]) ).
fof(f1765,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(X3,relation_dom(X2),relation_dom(X2)) )
| ~ spl22_138
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1287]) ).
fof(f11380,plain,
( spl22_580
| ~ spl22_83
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1373,f1345,f742,f11378]) ).
fof(f11378,plain,
( spl22_580
<=> ! [X2,X0,X1] :
( sP0(relation_dom_restriction(X0,X1),X2)
| ~ empty(X2)
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_580])]) ).
fof(f1373,plain,
( ! [X2,X0,X1] :
( sP0(relation_dom_restriction(X0,X1),X2)
| ~ empty(X2)
| apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_143 ),
inference(resolution,[],[f1346,f743]) ).
fof(f11363,plain,
( spl22_579
| ~ spl22_27
| ~ spl22_546 ),
inference(avatar_split_clause,[],[f10985,f10626,f351,f11360]) ).
fof(f11360,plain,
( spl22_579
<=> function(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_579])]) ).
fof(f10985,plain,
( function(relation_dom_restriction(sK5,sK15))
| ~ spl22_27
| ~ spl22_546 ),
inference(resolution,[],[f10628,f352]) ).
fof(f11239,plain,
( spl22_578
| ~ spl22_44
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1942,f1849,f450,f11237]) ).
fof(f11237,plain,
( spl22_578
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(relation_dom_restriction(X2,X3),X1),sK7(X0,X1)) = apply(relation_dom_restriction(X2,X3),sK7(X0,X1))
| ~ function(relation_dom_restriction(X2,X3))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_578])]) ).
fof(f1942,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(relation_dom_restriction(X2,X3),X1),sK7(X0,X1)) = apply(relation_dom_restriction(X2,X3),sK7(X0,X1))
| ~ function(relation_dom_restriction(X2,X3))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ relation(X2) )
| ~ spl22_44
| ~ spl22_183 ),
inference(resolution,[],[f1850,f451]) ).
fof(f11235,plain,
( spl22_577
| ~ spl22_44
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1923,f1845,f450,f11233]) ).
fof(f11233,plain,
( spl22_577
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X0),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_577])]) ).
fof(f1923,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X0),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X3) )
| ~ spl22_44
| ~ spl22_182 ),
inference(resolution,[],[f1846,f451]) ).
fof(f11231,plain,
( spl22_576
| ~ spl22_44
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1893,f1841,f450,f11229]) ).
fof(f11229,plain,
( spl22_576
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X2),sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X0)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_576])]) ).
fof(f1893,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X2),sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X0)
| ~ relation(X3) )
| ~ spl22_44
| ~ spl22_181 ),
inference(resolution,[],[f1842,f451]) ).
fof(f11227,plain,
( spl22_575
| ~ spl22_44
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1874,f1837,f450,f11225]) ).
fof(f11225,plain,
( spl22_575
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X1),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_575])]) ).
fof(f1874,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X1),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X3) )
| ~ spl22_44
| ~ spl22_180 ),
inference(resolution,[],[f1838,f451]) ).
fof(f11223,plain,
( spl22_574
| ~ spl22_44
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1855,f1833,f450,f11221]) ).
fof(f11221,plain,
( spl22_574
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X2),sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X1)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_574])]) ).
fof(f1855,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom_restriction(X3,X4),X2),sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X4),sK13(X0,X1,X2))
| ~ function(relation_dom_restriction(X3,X4))
| in(sK13(X0,X1,X2),X1)
| ~ relation(X3) )
| ~ spl22_44
| ~ spl22_179 ),
inference(resolution,[],[f1834,f451]) ).
fof(f11148,plain,
( spl22_573
| ~ spl22_150
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1763,f1739,f1405,f11146]) ).
fof(f1763,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(relation_dom(X2),X3,X4))) = apply(X0,apply(X2,sK13(relation_dom(X2),X3,X4)))
| ~ sP0(X2,X1)
| sP2(relation_dom(X2),X3,X4)
| ~ empty(X4) )
| ~ spl22_150
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1406]) ).
fof(f11144,plain,
( spl22_572
| ~ spl22_148
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1760,f1739,f1397,f11142]) ).
fof(f1760,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,relation_dom(X2),X4))) = apply(X0,apply(X2,sK13(X3,relation_dom(X2),X4)))
| ~ sP0(X2,X1)
| sP2(X3,relation_dom(X2),X4)
| ~ empty(X4) )
| ~ spl22_148
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1398]) ).
fof(f11140,plain,
( spl22_571
| ~ spl22_149
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1756,f1739,f1401,f11138]) ).
fof(f1756,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X4) )
| ~ spl22_149
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1402]) ).
fof(f11136,plain,
( spl22_570
| ~ spl22_151
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1755,f1739,f1409,f11134]) ).
fof(f1755,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK13(X3,X4,relation_dom(X2)))) = apply(X0,apply(X2,sK13(X3,X4,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP2(X3,X4,relation_dom(X2))
| ~ empty(X3) )
| ~ spl22_151
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1410]) ).
fof(f11053,plain,
( spl22_569
| ~ spl22_115
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1981,f1964,f959,f11051]) ).
fof(f11051,plain,
( spl22_569
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK15)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK15))
| sP0(relation_dom_restriction(X0,X1),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_569])]) ).
fof(f1981,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| apply(X0,sK8(relation_dom_restriction(X0,X1),sK15)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),sK15))
| sP0(relation_dom_restriction(X0,X1),sK15) )
| ~ spl22_115
| ~ spl22_185 ),
inference(resolution,[],[f1965,f960]) ).
fof(f11049,plain,
( spl22_568
| ~ spl22_59
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1808,f1778,f557,f11047]) ).
fof(f11047,plain,
( spl22_568
<=> ! [X0,X3,X2,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(X2)),sK8(X2,X3)) = apply(set_intersection2(X0,X1),sK8(X2,X3))
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_568])]) ).
fof(f1778,plain,
( spl22_176
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(X0,relation_dom(X1)),sK8(X1,X2)) = apply(X0,sK8(X1,X2))
| ~ function(X0)
| ~ relation(X0)
| in(sK7(X1,X2),X2)
| sP0(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_176])]) ).
fof(f1808,plain,
( ! [X2,X3,X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(X2)),sK8(X2,X3)) = apply(set_intersection2(X0,X1),sK8(X2,X3))
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_176 ),
inference(resolution,[],[f1779,f558]) ).
fof(f1779,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| apply(relation_dom_restriction(X0,relation_dom(X1)),sK8(X1,X2)) = apply(X0,sK8(X1,X2))
| in(sK7(X1,X2),X2)
| sP0(X1,X2) )
| ~ spl22_176 ),
inference(avatar_component_clause,[],[f1778]) ).
fof(f10982,plain,
( spl22_567
| ~ spl22_59
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1785,f1774,f557,f10980]) ).
fof(f10980,plain,
( spl22_567
<=> ! [X0,X3,X2,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),X2),sK7(X3,X2)) = apply(set_intersection2(X0,X1),sK7(X3,X2))
| in(sK8(X3,X2),relation_dom(X3))
| sP0(X3,X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_567])]) ).
fof(f1774,plain,
( spl22_175
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK7(X2,X1)) = apply(X0,sK7(X2,X1))
| ~ function(X0)
| ~ relation(X0)
| in(sK8(X2,X1),relation_dom(X2))
| sP0(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_175])]) ).
fof(f1785,plain,
( ! [X2,X3,X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),X2),sK7(X3,X2)) = apply(set_intersection2(X0,X1),sK7(X3,X2))
| in(sK8(X3,X2),relation_dom(X3))
| sP0(X3,X2)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_175 ),
inference(resolution,[],[f1775,f558]) ).
fof(f1775,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| apply(relation_dom_restriction(X0,X1),sK7(X2,X1)) = apply(X0,sK7(X2,X1))
| in(sK8(X2,X1),relation_dom(X2))
| sP0(X2,X1) )
| ~ spl22_175 ),
inference(avatar_component_clause,[],[f1774]) ).
fof(f10978,plain,
( spl22_566
| ~ spl22_83
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f1103,f1064,f742,f10976]) ).
fof(f10976,plain,
( spl22_566
<=> ! [X0,X1] :
( empty(relation_dom(relation_dom_restriction(X0,X1)))
| apply(X0,sK10(relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK10(relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_566])]) ).
fof(f1103,plain,
( ! [X0,X1] :
( empty(relation_dom(relation_dom_restriction(X0,X1)))
| apply(X0,sK10(relation_dom(relation_dom_restriction(X0,X1)))) = apply(relation_dom_restriction(X0,X1),sK10(relation_dom(relation_dom_restriction(X0,X1))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_83
| ~ spl22_119 ),
inference(resolution,[],[f1065,f743]) ).
fof(f10948,plain,
( spl22_565
| ~ spl22_142
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1745,f1739,f1341,f10946]) ).
fof(f1745,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK7(X3,relation_dom(X2)))) = apply(X0,apply(X2,sK7(X3,relation_dom(X2))))
| ~ sP0(X2,X1)
| sP0(X3,relation_dom(X2))
| ~ empty(relation_dom(X3)) )
| ~ spl22_142
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1342]) ).
fof(f10920,plain,
( ~ spl22_1
| ~ spl22_44
| spl22_547 ),
inference(avatar_split_clause,[],[f10853,f10630,f450,f224]) ).
fof(f10630,plain,
( spl22_547
<=> relation(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_547])]) ).
fof(f10853,plain,
( ~ relation(sK5)
| ~ spl22_44
| spl22_547 ),
inference(resolution,[],[f10632,f451]) ).
fof(f10632,plain,
( ~ relation(relation_dom_restriction(sK5,sK15))
| spl22_547 ),
inference(avatar_component_clause,[],[f10630]) ).
fof(f10857,plain,
( spl22_564
| ~ spl22_37
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1941,f1849,f402,f10855]) ).
fof(f10855,plain,
( spl22_564
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(relation_dom(X2),X1),sK7(X0,X1)) = apply(relation_dom(X2),sK7(X0,X1))
| ~ function(relation_dom(X2))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_564])]) ).
fof(f1941,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(relation_dom(X2),X1),sK7(X0,X1)) = apply(relation_dom(X2),sK7(X0,X1))
| ~ function(relation_dom(X2))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ empty(X2) )
| ~ spl22_37
| ~ spl22_183 ),
inference(resolution,[],[f1850,f403]) ).
fof(f10852,plain,
( spl22_563
| ~ spl22_35
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1940,f1849,f394,f10850]) ).
fof(f10850,plain,
( spl22_563
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(relation_rng(X2),X1),sK7(X0,X1)) = apply(relation_rng(X2),sK7(X0,X1))
| ~ function(relation_rng(X2))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_563])]) ).
fof(f1940,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(relation_rng(X2),X1),sK7(X0,X1)) = apply(relation_rng(X2),sK7(X0,X1))
| ~ function(relation_rng(X2))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ empty(X2) )
| ~ spl22_35
| ~ spl22_183 ),
inference(resolution,[],[f1850,f395]) ).
fof(f10848,plain,
( spl22_562
| ~ spl22_37
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1922,f1845,f402,f10846]) ).
fof(f10846,plain,
( spl22_562
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom(X3),X0),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_562])]) ).
fof(f1922,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom(X3),X0),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) )
| ~ spl22_37
| ~ spl22_182 ),
inference(resolution,[],[f1846,f403]) ).
fof(f10844,plain,
( spl22_561
| ~ spl22_35
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1921,f1845,f394,f10842]) ).
fof(f10842,plain,
( spl22_561
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_rng(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_rng(X3),X0),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_561])]) ).
fof(f1921,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_rng(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_rng(X3),X0),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) )
| ~ spl22_35
| ~ spl22_182 ),
inference(resolution,[],[f1846,f395]) ).
fof(f10840,plain,
( spl22_560
| ~ spl22_37
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1892,f1841,f402,f10838]) ).
fof(f10838,plain,
( spl22_560
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom(X3),X2),sK13(X0,X1,X2)) = apply(relation_dom(X3),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X0)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_560])]) ).
fof(f1892,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom(X3),X2),sK13(X0,X1,X2)) = apply(relation_dom(X3),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X0)
| ~ empty(X3) )
| ~ spl22_37
| ~ spl22_181 ),
inference(resolution,[],[f1842,f403]) ).
fof(f10836,plain,
( spl22_559
| ~ spl22_35
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1891,f1841,f394,f10834]) ).
fof(f10834,plain,
( spl22_559
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_rng(X3),X2),sK13(X0,X1,X2)) = apply(relation_rng(X3),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X0)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_559])]) ).
fof(f1891,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_rng(X3),X2),sK13(X0,X1,X2)) = apply(relation_rng(X3),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X0)
| ~ empty(X3) )
| ~ spl22_35
| ~ spl22_181 ),
inference(resolution,[],[f1842,f395]) ).
fof(f10832,plain,
( spl22_558
| ~ spl22_37
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1873,f1837,f402,f10830]) ).
fof(f10830,plain,
( spl22_558
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom(X3),X1),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_558])]) ).
fof(f1873,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_dom(X3),X1),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) )
| ~ spl22_37
| ~ spl22_180 ),
inference(resolution,[],[f1838,f403]) ).
fof(f10828,plain,
( spl22_557
| ~ spl22_35
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1872,f1837,f394,f10826]) ).
fof(f10826,plain,
( spl22_557
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_rng(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_rng(X3),X1),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_557])]) ).
fof(f1872,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_rng(X3),sK13(X0,X1,X2)) = apply(relation_dom_restriction(relation_rng(X3),X1),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X2)
| ~ empty(X3) )
| ~ spl22_35
| ~ spl22_180 ),
inference(resolution,[],[f1838,f395]) ).
fof(f10824,plain,
( spl22_556
| ~ spl22_37
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1854,f1833,f402,f10822]) ).
fof(f10822,plain,
( spl22_556
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom(X3),X2),sK13(X0,X1,X2)) = apply(relation_dom(X3),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X1)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_556])]) ).
fof(f1854,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_dom(X3),X2),sK13(X0,X1,X2)) = apply(relation_dom(X3),sK13(X0,X1,X2))
| ~ function(relation_dom(X3))
| in(sK13(X0,X1,X2),X1)
| ~ empty(X3) )
| ~ spl22_37
| ~ spl22_179 ),
inference(resolution,[],[f1834,f403]) ).
fof(f10820,plain,
( spl22_555
| ~ spl22_35
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1853,f1833,f394,f10818]) ).
fof(f10818,plain,
( spl22_555
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_rng(X3),X2),sK13(X0,X1,X2)) = apply(relation_rng(X3),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X1)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_555])]) ).
fof(f1853,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(relation_rng(X3),X2),sK13(X0,X1,X2)) = apply(relation_rng(X3),sK13(X0,X1,X2))
| ~ function(relation_rng(X3))
| in(sK13(X0,X1,X2),X1)
| ~ empty(X3) )
| ~ spl22_35
| ~ spl22_179 ),
inference(resolution,[],[f1834,f395]) ).
fof(f10816,plain,
( spl22_554
| ~ spl22_44
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1811,f1778,f450,f10814]) ).
fof(f10814,plain,
( spl22_554
<=> ! [X0,X3,X2,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(X2)),sK8(X2,X3)) = apply(relation_dom_restriction(X0,X1),sK8(X2,X3))
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_554])]) ).
fof(f1811,plain,
( ! [X2,X3,X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(X2)),sK8(X2,X3)) = apply(relation_dom_restriction(X0,X1),sK8(X2,X3))
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_176 ),
inference(resolution,[],[f1779,f451]) ).
fof(f10812,plain,
( spl22_553
| ~ spl22_44
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1788,f1774,f450,f10810]) ).
fof(f10810,plain,
( spl22_553
<=> ! [X0,X3,X2,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(relation_dom_restriction(X0,X1),X2),sK7(X3,X2)) = apply(relation_dom_restriction(X0,X1),sK7(X3,X2))
| in(sK8(X3,X2),relation_dom(X3))
| sP0(X3,X2)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_553])]) ).
fof(f1788,plain,
( ! [X2,X3,X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(relation_dom_restriction(X0,X1),X2),sK7(X3,X2)) = apply(relation_dom_restriction(X0,X1),sK7(X3,X2))
| in(sK8(X3,X2),relation_dom(X3))
| sP0(X3,X2)
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_175 ),
inference(resolution,[],[f1775,f451]) ).
fof(f10808,plain,
( spl22_552
| ~ spl22_73
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1750,f1739,f652,f10806]) ).
fof(f1750,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ sP0(X2,X1)
| in(sK7(X2,X3),X3)
| sP0(X2,X3) )
| ~ spl22_73
| ~ spl22_173 ),
inference(resolution,[],[f1740,f653]) ).
fof(f10804,plain,
( spl22_551
| ~ spl22_156
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1748,f1739,f1535,f10802]) ).
fof(f1748,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ sP0(X2,X1)
| element(sK7(X2,X3),X3)
| sP0(X2,X3) )
| ~ spl22_156
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1536]) ).
fof(f10800,plain,
( spl22_550
| ~ spl22_69
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1742,f1739,f628,f10798]) ).
fof(f1742,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,apply(X3,X4))) = apply(X0,apply(X2,apply(X3,X4)))
| ~ sP0(X2,X1)
| ~ in(X4,relation_dom(X3))
| ~ sP0(X3,relation_dom(X2)) )
| ~ spl22_69
| ~ spl22_173 ),
inference(resolution,[],[f1740,f629]) ).
fof(f10649,plain,
( spl22_549
| ~ spl22_145
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1751,f1739,f1384,f10647]) ).
fof(f1751,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK9(X2,X3))) = apply(X0,apply(X2,sK9(X2,X3)))
| ~ sP0(X2,X1)
| ~ in(X3,relation_rng(X2))
| ~ sP1(X2) )
| ~ spl22_145
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1385]) ).
fof(f10645,plain,
( spl22_548
| ~ spl22_77
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1513,f1508,f698,f10643]) ).
fof(f1513,plain,
( ! [X0,X1] :
( sK7(X1,relation_rng(X0)) = apply(X0,sK9(X0,sK7(X1,relation_rng(X0))))
| ~ sP1(X0)
| sK7(X1,relation_rng(X0)) = apply(X1,sK8(X1,relation_rng(X0)))
| sP0(X1,relation_rng(X0)) )
| ~ spl22_77
| ~ spl22_153 ),
inference(resolution,[],[f1509,f699]) ).
fof(f10633,plain,
( spl22_546
| ~ spl22_547
| ~ spl22_10
| ~ spl22_51
| ~ spl22_515 ),
inference(avatar_split_clause,[],[f10294,f9631,f503,f269,f10630,f10626]) ).
fof(f9631,plain,
( spl22_515
<=> sK15 = relation_rng(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_515])]) ).
fof(f10294,plain,
( ~ empty(sK15)
| ~ relation(relation_dom_restriction(sK5,sK15))
| empty(relation_dom_restriction(sK5,sK15))
| ~ spl22_51
| ~ spl22_515 ),
inference(superposition,[],[f504,f9633]) ).
fof(f9633,plain,
( sK15 = relation_rng(relation_dom_restriction(sK5,sK15))
| ~ spl22_515 ),
inference(avatar_component_clause,[],[f9631]) ).
fof(f10323,plain,
( spl22_545
| ~ spl22_37
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1810,f1778,f402,f10321]) ).
fof(f10321,plain,
( spl22_545
<=> ! [X2,X0,X1] :
( ~ function(relation_dom(X0))
| apply(relation_dom_restriction(relation_dom(X0),relation_dom(X1)),sK8(X1,X2)) = apply(relation_dom(X0),sK8(X1,X2))
| in(sK7(X1,X2),X2)
| sP0(X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_545])]) ).
fof(f1810,plain,
( ! [X2,X0,X1] :
( ~ function(relation_dom(X0))
| apply(relation_dom_restriction(relation_dom(X0),relation_dom(X1)),sK8(X1,X2)) = apply(relation_dom(X0),sK8(X1,X2))
| in(sK7(X1,X2),X2)
| sP0(X1,X2)
| ~ empty(X0) )
| ~ spl22_37
| ~ spl22_176 ),
inference(resolution,[],[f1779,f403]) ).
fof(f10319,plain,
( spl22_544
| ~ spl22_35
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1809,f1778,f394,f10317]) ).
fof(f10317,plain,
( spl22_544
<=> ! [X2,X0,X1] :
( ~ function(relation_rng(X0))
| apply(relation_dom_restriction(relation_rng(X0),relation_dom(X1)),sK8(X1,X2)) = apply(relation_rng(X0),sK8(X1,X2))
| in(sK7(X1,X2),X2)
| sP0(X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_544])]) ).
fof(f1809,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng(X0))
| apply(relation_dom_restriction(relation_rng(X0),relation_dom(X1)),sK8(X1,X2)) = apply(relation_rng(X0),sK8(X1,X2))
| in(sK7(X1,X2),X2)
| sP0(X1,X2)
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_176 ),
inference(resolution,[],[f1779,f395]) ).
fof(f10315,plain,
( spl22_543
| ~ spl22_37
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1787,f1774,f402,f10313]) ).
fof(f10313,plain,
( spl22_543
<=> ! [X2,X0,X1] :
( ~ function(relation_dom(X0))
| apply(relation_dom_restriction(relation_dom(X0),X1),sK7(X2,X1)) = apply(relation_dom(X0),sK7(X2,X1))
| in(sK8(X2,X1),relation_dom(X2))
| sP0(X2,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_543])]) ).
fof(f1787,plain,
( ! [X2,X0,X1] :
( ~ function(relation_dom(X0))
| apply(relation_dom_restriction(relation_dom(X0),X1),sK7(X2,X1)) = apply(relation_dom(X0),sK7(X2,X1))
| in(sK8(X2,X1),relation_dom(X2))
| sP0(X2,X1)
| ~ empty(X0) )
| ~ spl22_37
| ~ spl22_175 ),
inference(resolution,[],[f1775,f403]) ).
fof(f10290,plain,
( spl22_542
| ~ spl22_35
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1786,f1774,f394,f10288]) ).
fof(f10288,plain,
( spl22_542
<=> ! [X2,X0,X1] :
( ~ function(relation_rng(X0))
| apply(relation_dom_restriction(relation_rng(X0),X1),sK7(X2,X1)) = apply(relation_rng(X0),sK7(X2,X1))
| in(sK8(X2,X1),relation_dom(X2))
| sP0(X2,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_542])]) ).
fof(f1786,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng(X0))
| apply(relation_dom_restriction(relation_rng(X0),X1),sK7(X2,X1)) = apply(relation_rng(X0),sK7(X2,X1))
| in(sK8(X2,X1),relation_dom(X2))
| sP0(X2,X1)
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_175 ),
inference(resolution,[],[f1775,f395]) ).
fof(f10286,plain,
( spl22_541
| ~ spl22_143
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1749,f1739,f1345,f10284]) ).
fof(f1749,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK8(X2,X3))) = apply(X0,apply(X2,sK8(X2,X3)))
| ~ sP0(X2,X1)
| sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_143
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1346]) ).
fof(f10282,plain,
( spl22_540
| ~ spl22_153
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1694,f1608,f1508,f10280]) ).
fof(f10280,plain,
( spl22_540
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,relation_rng(X2)),X0)
| sP2(X0,X1,relation_rng(X2))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_540])]) ).
fof(f1694,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,relation_rng(X2)),X0)
| sP2(X0,X1,relation_rng(X2))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) )
| ~ spl22_153
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1509]) ).
fof(f10278,plain,
( spl22_539
| ~ spl22_74
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1689,f1608,f662,f10276]) ).
fof(f10276,plain,
( spl22_539
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_539])]) ).
fof(f1689,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_165 ),
inference(resolution,[],[f1609,f663]) ).
fof(f10274,plain,
( spl22_538
| ~ spl22_153
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1669,f1600,f1508,f10272]) ).
fof(f10272,plain,
( spl22_538
<=> ! [X2,X0,X1] :
( element(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2)
| sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_538])]) ).
fof(f1669,plain,
( ! [X2,X0,X1] :
( element(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2)
| sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0) )
| ~ spl22_153
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1509]) ).
fof(f10270,plain,
( spl22_537
| ~ spl22_74
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1664,f1600,f662,f10268]) ).
fof(f10268,plain,
( spl22_537
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_537])]) ).
fof(f1664,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_163 ),
inference(resolution,[],[f1601,f663]) ).
fof(f10266,plain,
( spl22_536
| ~ spl22_153
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1649,f1587,f1508,f10264]) ).
fof(f10264,plain,
( spl22_536
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,relation_rng(X2)),X1)
| sP2(X0,X1,relation_rng(X2))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_536])]) ).
fof(f1649,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,relation_rng(X2)),X1)
| sP2(X0,X1,relation_rng(X2))
| sK13(X0,X1,relation_rng(X2)) = apply(X2,sK9(X2,sK13(X0,X1,relation_rng(X2))))
| ~ sP1(X2) )
| ~ spl22_153
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1509]) ).
fof(f10262,plain,
( spl22_535
| ~ spl22_74
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1644,f1587,f662,f10260]) ).
fof(f10260,plain,
( spl22_535
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_535])]) ).
fof(f1644,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_161 ),
inference(resolution,[],[f1588,f663]) ).
fof(f10258,plain,
( spl22_534
| ~ spl22_153
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1629,f1579,f1508,f10256]) ).
fof(f10256,plain,
( spl22_534
<=> ! [X2,X0,X1] :
( element(sK13(X0,relation_rng(X1),X2),X2)
| sP2(X0,relation_rng(X1),X2)
| sK13(X0,relation_rng(X1),X2) = apply(X1,sK9(X1,sK13(X0,relation_rng(X1),X2)))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_534])]) ).
fof(f1629,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,relation_rng(X1),X2),X2)
| sP2(X0,relation_rng(X1),X2)
| sK13(X0,relation_rng(X1),X2) = apply(X1,sK9(X1,sK13(X0,relation_rng(X1),X2)))
| ~ sP1(X1) )
| ~ spl22_153
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1509]) ).
fof(f10254,plain,
( spl22_533
| ~ spl22_74
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1624,f1579,f662,f10252]) ).
fof(f10252,plain,
( spl22_533
<=> ! [X0,X3,X2,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_533])]) ).
fof(f1624,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_159 ),
inference(resolution,[],[f1580,f663]) ).
fof(f10248,plain,
( spl22_532
| ~ spl22_76
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1523,f1508,f670,f10246]) ).
fof(f10246,plain,
( spl22_532
<=> ! [X2,X0,X1] :
( sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0)
| in(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_532])]) ).
fof(f1523,plain,
( ! [X2,X0,X1] :
( sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0)
| in(sK13(relation_rng(X0),X1,X2),X2)
| sP2(relation_rng(X0),X1,X2) )
| ~ spl22_76
| ~ spl22_153 ),
inference(resolution,[],[f1509,f671]) ).
fof(f10244,plain,
( spl22_531
| ~ spl22_75
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1521,f1508,f666,f10242]) ).
fof(f10242,plain,
( spl22_531
<=> ! [X2,X0,X1] :
( sK13(X1,relation_rng(X0),X2) = apply(X0,sK9(X0,sK13(X1,relation_rng(X0),X2)))
| ~ sP1(X0)
| in(sK13(X1,relation_rng(X0),X2),X2)
| sP2(X1,relation_rng(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_531])]) ).
fof(f1521,plain,
( ! [X2,X0,X1] :
( sK13(X1,relation_rng(X0),X2) = apply(X0,sK9(X0,sK13(X1,relation_rng(X0),X2)))
| ~ sP1(X0)
| in(sK13(X1,relation_rng(X0),X2),X2)
| sP2(X1,relation_rng(X0),X2) )
| ~ spl22_75
| ~ spl22_153 ),
inference(resolution,[],[f1509,f667]) ).
fof(f10240,plain,
( spl22_530
| ~ spl22_75
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1519,f1508,f666,f10238]) ).
fof(f10238,plain,
( spl22_530
<=> ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| in(sK13(X1,X2,relation_rng(X0)),X2)
| sP2(X1,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_530])]) ).
fof(f1519,plain,
( ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| in(sK13(X1,X2,relation_rng(X0)),X2)
| sP2(X1,X2,relation_rng(X0)) )
| ~ spl22_75
| ~ spl22_153 ),
inference(resolution,[],[f1509,f667]) ).
fof(f10236,plain,
( spl22_529
| ~ spl22_76
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1518,f1508,f670,f10234]) ).
fof(f10234,plain,
( spl22_529
<=> ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| in(sK13(X1,X2,relation_rng(X0)),X1)
| sP2(X1,X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_529])]) ).
fof(f1518,plain,
( ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| in(sK13(X1,X2,relation_rng(X0)),X1)
| sP2(X1,X2,relation_rng(X0)) )
| ~ spl22_76
| ~ spl22_153 ),
inference(resolution,[],[f1509,f671]) ).
fof(f10232,plain,
( spl22_528
| ~ spl22_77
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1431,f1393,f698,f10230]) ).
fof(f1431,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sK7(X1,apply(X0,X2)) = apply(X1,sK8(X1,apply(X0,X2)))
| sP0(X1,apply(X0,X2)) )
| ~ spl22_77
| ~ spl22_147 ),
inference(resolution,[],[f1394,f699]) ).
fof(f10228,plain,
( spl22_527
| ~ spl22_80
| ~ spl22_136 ),
inference(avatar_split_clause,[],[f1299,f1278,f716,f10226]) ).
fof(f10226,plain,
( spl22_527
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(sK13(X1,X2,powerset(X0)),X0)
| ~ in(sK13(X1,X2,powerset(X0)),X1)
| ~ in(sK13(X1,X2,powerset(X0)),X2)
| sP2(X1,X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_527])]) ).
fof(f1299,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(sK13(X1,X2,powerset(X0)),X0)
| ~ in(sK13(X1,X2,powerset(X0)),X1)
| ~ in(sK13(X1,X2,powerset(X0)),X2)
| sP2(X1,X2,powerset(X0)) )
| ~ spl22_80
| ~ spl22_136 ),
inference(resolution,[],[f1279,f717]) ).
fof(f10143,plain,
( spl22_526
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1953,f1849,f798,f254,f410,f10141]) ).
fof(f1953,plain,
( ! [X0,X1] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1))
| sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_183 ),
inference(forward_demodulation,[],[f1952,f800]) ).
fof(f1952,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X1),sK7(X0,X1)) = apply(sK15,sK7(X0,X1))
| sP0(X0,X1)
| ~ function(empty_set)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_183 ),
inference(forward_demodulation,[],[f1943,f800]) ).
fof(f1943,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(empty_set,X1),sK7(X0,X1)) = apply(empty_set,sK7(X0,X1))
| ~ function(empty_set)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_7
| ~ spl22_183 ),
inference(resolution,[],[f1850,f256]) ).
fof(f10083,plain,
( ~ spl22_2
| ~ spl22_1
| ~ spl22_240
| spl22_514 ),
inference(avatar_split_clause,[],[f9850,f9627,f2694,f224,f229]) ).
fof(f9627,plain,
( spl22_514
<=> sP1(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_514])]) ).
fof(f9850,plain,
( ~ relation(sK5)
| ~ function(sK5)
| ~ spl22_240
| spl22_514 ),
inference(resolution,[],[f9629,f2695]) ).
fof(f9629,plain,
( ~ sP1(relation_dom_restriction(sK5,sK15))
| spl22_514 ),
inference(avatar_component_clause,[],[f9627]) ).
fof(f10082,plain,
( ~ spl22_20
| spl22_525
| ~ spl22_19
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1950,f1849,f314,f10080,f319]) ).
fof(f1950,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,X1),sK7(X0,X1)) = apply(sK20,sK7(X0,X1))
| ~ function(sK20)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_19
| ~ spl22_183 ),
inference(resolution,[],[f1850,f316]) ).
fof(f10022,plain,
( ~ spl22_18
| spl22_524
| ~ spl22_17
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1949,f1849,f304,f10020,f309]) ).
fof(f1949,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,X1),sK7(X0,X1)) = apply(sK19,sK7(X0,X1))
| ~ function(sK19)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_17
| ~ spl22_183 ),
inference(resolution,[],[f1850,f306]) ).
fof(f9979,plain,
( spl22_523
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1934,f1845,f798,f254,f410,f9977]) ).
fof(f1934,plain,
( ! [X2,X0,X1] :
( ~ function(sK15)
| apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X0),sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_182 ),
inference(forward_demodulation,[],[f1933,f800]) ).
fof(f1933,plain,
( ! [X2,X0,X1] :
( apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X0),sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_182 ),
inference(forward_demodulation,[],[f1924,f800]) ).
fof(f1924,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(empty_set,sK13(X0,X1,X2)) = apply(relation_dom_restriction(empty_set,X0),sK13(X0,X1,X2))
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_7
| ~ spl22_182 ),
inference(resolution,[],[f1846,f256]) ).
fof(f9936,plain,
( ~ spl22_20
| spl22_522
| ~ spl22_19
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1931,f1845,f314,f9934,f319]) ).
fof(f1931,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK20,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK20,X0),sK13(X0,X1,X2))
| ~ function(sK20)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_19
| ~ spl22_182 ),
inference(resolution,[],[f1846,f316]) ).
fof(f9893,plain,
( ~ spl22_18
| spl22_521
| ~ spl22_17
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1930,f1845,f304,f9891,f309]) ).
fof(f1930,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK19,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK19,X0),sK13(X0,X1,X2))
| ~ function(sK19)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_17
| ~ spl22_182 ),
inference(resolution,[],[f1846,f306]) ).
fof(f9849,plain,
( spl22_520
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1904,f1841,f798,f254,f410,f9847]) ).
fof(f1904,plain,
( ! [X2,X0,X1] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_181 ),
inference(forward_demodulation,[],[f1903,f800]) ).
fof(f1903,plain,
( ! [X2,X0,X1] :
( apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_181 ),
inference(forward_demodulation,[],[f1894,f800]) ).
fof(f1894,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(empty_set,X2),sK13(X0,X1,X2)) = apply(empty_set,sK13(X0,X1,X2))
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_7
| ~ spl22_181 ),
inference(resolution,[],[f1842,f256]) ).
fof(f9806,plain,
( ~ spl22_20
| spl22_519
| ~ spl22_19
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1901,f1841,f314,f9804,f319]) ).
fof(f1901,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK20,X2),sK13(X0,X1,X2)) = apply(sK20,sK13(X0,X1,X2))
| ~ function(sK20)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_19
| ~ spl22_181 ),
inference(resolution,[],[f1842,f316]) ).
fof(f9763,plain,
( ~ spl22_18
| spl22_518
| ~ spl22_17
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1900,f1841,f304,f9761,f309]) ).
fof(f1900,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK19,X2),sK13(X0,X1,X2)) = apply(sK19,sK13(X0,X1,X2))
| ~ function(sK19)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_17
| ~ spl22_181 ),
inference(resolution,[],[f1842,f306]) ).
fof(f9720,plain,
( spl22_517
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1885,f1837,f798,f254,f410,f9718]) ).
fof(f1885,plain,
( ! [X2,X0,X1] :
( ~ function(sK15)
| apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X1),sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_180 ),
inference(forward_demodulation,[],[f1884,f800]) ).
fof(f1884,plain,
( ! [X2,X0,X1] :
( apply(sK15,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK15,X1),sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_180 ),
inference(forward_demodulation,[],[f1875,f800]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(empty_set,sK13(X0,X1,X2)) = apply(relation_dom_restriction(empty_set,X1),sK13(X0,X1,X2))
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_7
| ~ spl22_180 ),
inference(resolution,[],[f1838,f256]) ).
fof(f9677,plain,
( ~ spl22_20
| spl22_516
| ~ spl22_19
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1882,f1837,f314,f9675,f319]) ).
fof(f1882,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK20,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK20,X1),sK13(X0,X1,X2))
| ~ function(sK20)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_19
| ~ spl22_180 ),
inference(resolution,[],[f1838,f316]) ).
fof(f9634,plain,
( ~ spl22_514
| spl22_515
| ~ spl22_61
| ~ spl22_463 ),
inference(avatar_split_clause,[],[f8138,f8061,f578,f9631,f9627]) ).
fof(f8138,plain,
( sK15 = relation_rng(relation_dom_restriction(sK5,sK15))
| ~ sP1(relation_dom_restriction(sK5,sK15))
| ~ spl22_61
| ~ spl22_463 ),
inference(resolution,[],[f8063,f579]) ).
fof(f9625,plain,
( ~ spl22_18
| spl22_513
| ~ spl22_17
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1881,f1837,f304,f9623,f309]) ).
fof(f1881,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK19,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK19,X1),sK13(X0,X1,X2))
| ~ function(sK19)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_17
| ~ spl22_180 ),
inference(resolution,[],[f1838,f306]) ).
fof(f9582,plain,
( spl22_512
| ~ spl22_39
| ~ spl22_7
| ~ spl22_92
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1866,f1833,f798,f254,f410,f9580]) ).
fof(f1866,plain,
( ! [X2,X0,X1] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_179 ),
inference(forward_demodulation,[],[f1865,f800]) ).
fof(f1865,plain,
( ! [X2,X0,X1] :
( apply(relation_dom_restriction(sK15,X2),sK13(X0,X1,X2)) = apply(sK15,sK13(X0,X1,X2))
| sP2(X0,X1,X2)
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_179 ),
inference(forward_demodulation,[],[f1856,f800]) ).
fof(f1856,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(empty_set,X2),sK13(X0,X1,X2)) = apply(empty_set,sK13(X0,X1,X2))
| ~ function(empty_set)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_7
| ~ spl22_179 ),
inference(resolution,[],[f1834,f256]) ).
fof(f9539,plain,
( ~ spl22_20
| spl22_511
| ~ spl22_19
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1863,f1833,f314,f9537,f319]) ).
fof(f1863,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK20,X2),sK13(X0,X1,X2)) = apply(sK20,sK13(X0,X1,X2))
| ~ function(sK20)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_19
| ~ spl22_179 ),
inference(resolution,[],[f1834,f316]) ).
fof(f9496,plain,
( ~ spl22_18
| spl22_510
| ~ spl22_17
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1862,f1833,f304,f9494,f309]) ).
fof(f1862,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK19,X2),sK13(X0,X1,X2)) = apply(sK19,sK13(X0,X1,X2))
| ~ function(sK19)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_17
| ~ spl22_179 ),
inference(resolution,[],[f1834,f306]) ).
fof(f9492,plain,
( spl22_509
| ~ spl22_119
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1752,f1739,f1064,f9490]) ).
fof(f1752,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(X2,sK10(relation_dom(X2)))) = apply(X0,apply(X2,sK10(relation_dom(X2))))
| ~ sP0(X2,X1)
| empty(relation_dom(X2)) )
| ~ spl22_119
| ~ spl22_173 ),
inference(resolution,[],[f1740,f1065]) ).
fof(f9448,plain,
( spl22_508
| ~ spl22_113
| ~ spl22_412 ),
inference(avatar_split_clause,[],[f6247,f5443,f952,f9446]) ).
fof(f9446,plain,
( spl22_508
<=> ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = set_intersection2(X0,relation_dom(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_508])]) ).
fof(f6247,plain,
( ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = set_intersection2(X0,relation_dom(sK5)) )
| ~ spl22_113
| ~ spl22_412 ),
inference(resolution,[],[f5444,f953]) ).
fof(f9266,plain,
( spl22_507
| ~ spl22_147
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1697,f1608,f1393,f9264]) ).
fof(f1697,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,apply(X2,X3)),X0)
| sP2(X0,X1,apply(X2,X3))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1394]) ).
fof(f9262,plain,
( spl22_506
| ~ spl22_147
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1672,f1600,f1393,f9260]) ).
fof(f1672,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(apply(X0,X1),X2,X3),X3)
| sP2(apply(X0,X1),X2,X3)
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_147
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1394]) ).
fof(f9258,plain,
( spl22_505
| ~ spl22_147
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1652,f1587,f1393,f9256]) ).
fof(f1652,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,apply(X2,X3)),X1)
| sP2(X0,X1,apply(X2,X3))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1394]) ).
fof(f9254,plain,
( spl22_504
| ~ spl22_147
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1632,f1579,f1393,f9252]) ).
fof(f1632,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,apply(X1,X2),X3),X3)
| sP2(X0,apply(X1,X2),X3)
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1394]) ).
fof(f9250,plain,
( spl22_503
| ~ spl22_74
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1565,f1535,f662,f9248]) ).
fof(f9248,plain,
( spl22_503
<=> ! [X2,X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,relation_dom(X0)),sK8(X0,X1)) = apply(X2,sK8(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_503])]) ).
fof(f1565,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,relation_dom(X0)),sK8(X0,X1)) = apply(X2,sK8(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_156 ),
inference(resolution,[],[f1536,f663]) ).
fof(f9246,plain,
( spl22_502
| ~ spl22_153
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1554,f1527,f1508,f9244]) ).
fof(f9244,plain,
( spl22_502
<=> ! [X0,X1] :
( element(sK8(X0,relation_rng(X1)),relation_dom(X0))
| sP0(X0,relation_rng(X1))
| sK7(X0,relation_rng(X1)) = apply(X1,sK9(X1,sK7(X0,relation_rng(X1))))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_502])]) ).
fof(f1554,plain,
( ! [X0,X1] :
( element(sK8(X0,relation_rng(X1)),relation_dom(X0))
| sP0(X0,relation_rng(X1))
| sK7(X0,relation_rng(X1)) = apply(X1,sK9(X1,sK7(X0,relation_rng(X1))))
| ~ sP1(X1) )
| ~ spl22_153
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1509]) ).
fof(f9242,plain,
( spl22_501
| ~ spl22_74
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1549,f1527,f662,f9240]) ).
fof(f9240,plain,
( spl22_501
<=> ! [X2,X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_501])]) ).
fof(f1549,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_154 ),
inference(resolution,[],[f1528,f663]) ).
fof(f9238,plain,
( spl22_500
| ~ spl22_73
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1514,f1508,f652,f9236]) ).
fof(f9236,plain,
( spl22_500
<=> ! [X0,X1] :
( sK7(X1,relation_rng(X0)) = apply(X0,sK9(X0,sK7(X1,relation_rng(X0))))
| ~ sP1(X0)
| in(sK8(X1,relation_rng(X0)),relation_dom(X1))
| sP0(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_500])]) ).
fof(f1514,plain,
( ! [X0,X1] :
( sK7(X1,relation_rng(X0)) = apply(X0,sK9(X0,sK7(X1,relation_rng(X0))))
| ~ sP1(X0)
| in(sK8(X1,relation_rng(X0)),relation_dom(X1))
| sP0(X1,relation_rng(X0)) )
| ~ spl22_73
| ~ spl22_153 ),
inference(resolution,[],[f1509,f653]) ).
fof(f9234,plain,
( spl22_499
| ~ spl22_76
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1437,f1393,f670,f9232]) ).
fof(f1437,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0))
| in(sK13(apply(X0,X1),X2,X3),X3)
| sP2(apply(X0,X1),X2,X3) )
| ~ spl22_76
| ~ spl22_147 ),
inference(resolution,[],[f1394,f671]) ).
fof(f9230,plain,
( spl22_498
| ~ spl22_75
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1436,f1393,f666,f9228]) ).
fof(f1436,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(X1,apply(X0,X2),X3))
| ~ in(X2,relation_dom(X0))
| in(sK13(X1,apply(X0,X2),X3),X3)
| sP2(X1,apply(X0,X2),X3) )
| ~ spl22_75
| ~ spl22_147 ),
inference(resolution,[],[f1394,f667]) ).
fof(f9225,plain,
( spl22_497
| ~ spl22_75
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1435,f1393,f666,f9223]) ).
fof(f1435,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(X1,X2,apply(X0,X3)))
| ~ in(X3,relation_dom(X0))
| in(sK13(X1,X2,apply(X0,X3)),X2)
| sP2(X1,X2,apply(X0,X3)) )
| ~ spl22_75
| ~ spl22_147 ),
inference(resolution,[],[f1394,f667]) ).
fof(f9221,plain,
( spl22_496
| ~ spl22_76
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1434,f1393,f670,f9219]) ).
fof(f1434,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(X1,X2,apply(X0,X3)))
| ~ in(X3,relation_dom(X0))
| in(sK13(X1,X2,apply(X0,X3)),X1)
| sP2(X1,X2,apply(X0,X3)) )
| ~ spl22_76
| ~ spl22_147 ),
inference(resolution,[],[f1394,f671]) ).
fof(f9034,plain,
( spl22_495
| ~ spl22_53
| ~ spl22_462 ),
inference(avatar_split_clause,[],[f7590,f7120,f511,f9032]) ).
fof(f7120,plain,
( spl22_462
<=> ! [X0] :
( ~ empty(set_intersection2(relation_dom(sK5),X0))
| sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_462])]) ).
fof(f7590,plain,
( ! [X0] :
( ~ empty(set_intersection2(X0,relation_dom(sK5)))
| sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_53
| ~ spl22_462 ),
inference(superposition,[],[f7121,f512]) ).
fof(f7121,plain,
( ! [X0] :
( ~ empty(set_intersection2(relation_dom(sK5),X0))
| sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_462 ),
inference(avatar_component_clause,[],[f7120]) ).
fof(f9027,plain,
( spl22_494
| ~ spl22_139
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1525,f1508,f1290,f9025]) ).
fof(f9025,plain,
( spl22_494
<=> ! [X0,X1] :
( sK13(relation_rng(X0),X1,relation_rng(X0)) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,relation_rng(X0))))
| ~ sP1(X0)
| sP2(relation_rng(X0),X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_494])]) ).
fof(f1525,plain,
( ! [X0,X1] :
( sK13(relation_rng(X0),X1,relation_rng(X0)) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,relation_rng(X0))))
| ~ sP1(X0)
| sP2(relation_rng(X0),X1,relation_rng(X0)) )
| ~ spl22_139
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1291]) ).
fof(f9023,plain,
( spl22_493
| ~ spl22_138
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1524,f1508,f1286,f9021]) ).
fof(f9021,plain,
( spl22_493
<=> ! [X0,X1] :
( sK13(X1,relation_rng(X0),relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,relation_rng(X0),relation_rng(X0))))
| ~ sP1(X0)
| sP2(X1,relation_rng(X0),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_493])]) ).
fof(f1524,plain,
( ! [X0,X1] :
( sK13(X1,relation_rng(X0),relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,relation_rng(X0),relation_rng(X0))))
| ~ sP1(X0)
| sP2(X1,relation_rng(X0),relation_rng(X0)) )
| ~ spl22_138
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1287]) ).
fof(f9019,plain,
( spl22_492
| ~ spl22_74
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1494,f1409,f662,f9017]) ).
fof(f9017,plain,
( spl22_492
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_492])]) ).
fof(f1494,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_151 ),
inference(resolution,[],[f1410,f663]) ).
fof(f9015,plain,
( spl22_491
| ~ spl22_74
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1479,f1405,f662,f9013]) ).
fof(f9013,plain,
( spl22_491
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_491])]) ).
fof(f1479,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_150 ),
inference(resolution,[],[f1406,f663]) ).
fof(f9011,plain,
( spl22_490
| ~ spl22_74
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1464,f1401,f662,f9009]) ).
fof(f9009,plain,
( spl22_490
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_490])]) ).
fof(f1464,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_149 ),
inference(resolution,[],[f1402,f663]) ).
fof(f9007,plain,
( spl22_489
| ~ spl22_74
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1449,f1397,f662,f9005]) ).
fof(f9005,plain,
( spl22_489
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_489])]) ).
fof(f1449,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_148 ),
inference(resolution,[],[f1398,f663]) ).
fof(f9003,plain,
( spl22_488
| ~ spl22_77
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1225,f1159,f698,f9001]) ).
fof(f9001,plain,
( spl22_488
<=> ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| sK7(X0,set_intersection2(X1,X2)) = apply(X0,sK8(X0,set_intersection2(X1,X2)))
| sP0(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_488])]) ).
fof(f1225,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| sK7(X0,set_intersection2(X1,X2)) = apply(X0,sK8(X0,set_intersection2(X1,X2)))
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_77
| ~ spl22_130 ),
inference(resolution,[],[f1160,f699]) ).
fof(f8999,plain,
( spl22_487
| ~ spl22_77
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1211,f1155,f698,f8997]) ).
fof(f8997,plain,
( spl22_487
<=> ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| sK7(X0,set_intersection2(X1,X2)) = apply(X0,sK8(X0,set_intersection2(X1,X2)))
| sP0(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_487])]) ).
fof(f1211,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| sK7(X0,set_intersection2(X1,X2)) = apply(X0,sK8(X0,set_intersection2(X1,X2)))
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_77
| ~ spl22_129 ),
inference(resolution,[],[f1156,f699]) ).
fof(f8995,plain,
( spl22_486
| ~ spl22_77
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1203,f1151,f698,f8993]) ).
fof(f8993,plain,
( spl22_486
<=> ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sK7(X0,sK10(powerset(X1))) = apply(X0,sK8(X0,sK10(powerset(X1))))
| sP0(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_486])]) ).
fof(f1203,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sK7(X0,sK10(powerset(X1))) = apply(X0,sK8(X0,sK10(powerset(X1))))
| sP0(X0,sK10(powerset(X1))) )
| ~ spl22_77
| ~ spl22_128 ),
inference(resolution,[],[f1152,f699]) ).
fof(f8991,plain,
( spl22_485
| ~ spl22_113
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4909,f4627,f952,f8989]) ).
fof(f8989,plain,
( spl22_485
<=> ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = set_intersection2(relation_dom(sK5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_485])]) ).
fof(f4909,plain,
( ! [X0] :
( ~ empty(relation_dom_restriction(sK5,X0))
| sK15 = set_intersection2(relation_dom(sK5),X0) )
| ~ spl22_113
| ~ spl22_372 ),
inference(resolution,[],[f4628,f953]) ).
fof(f8707,plain,
( ~ spl22_39
| spl22_484
| ~ spl22_7
| ~ spl22_92
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1822,f1778,f798,f254,f8705,f410]) ).
fof(f1822,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,X1)) = apply(sK15,sK8(X0,X1))
| ~ function(sK15)
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_176 ),
inference(forward_demodulation,[],[f1821,f800]) ).
fof(f1821,plain,
( ! [X0,X1] :
( ~ function(sK15)
| apply(relation_dom_restriction(empty_set,relation_dom(X0)),sK8(X0,X1)) = apply(empty_set,sK8(X0,X1))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_176 ),
inference(forward_demodulation,[],[f1812,f800]) ).
fof(f1812,plain,
( ! [X0,X1] :
( ~ function(empty_set)
| apply(relation_dom_restriction(empty_set,relation_dom(X0)),sK8(X0,X1)) = apply(empty_set,sK8(X0,X1))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_7
| ~ spl22_176 ),
inference(resolution,[],[f1779,f256]) ).
fof(f8469,plain,
( spl22_483
| ~ spl22_20
| ~ spl22_19
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1819,f1778,f314,f319,f8467]) ).
fof(f1819,plain,
( ! [X0,X1] :
( ~ function(sK20)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,X1)) = apply(sK20,sK8(X0,X1))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_19
| ~ spl22_176 ),
inference(resolution,[],[f1779,f316]) ).
fof(f8432,plain,
( spl22_482
| ~ spl22_18
| ~ spl22_17
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1818,f1778,f304,f309,f8430]) ).
fof(f1818,plain,
( ! [X0,X1] :
( ~ function(sK19)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,X1)) = apply(sK19,sK8(X0,X1))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_17
| ~ spl22_176 ),
inference(resolution,[],[f1779,f306]) ).
fof(f8417,plain,
( ~ spl22_39
| spl22_481
| ~ spl22_7
| ~ spl22_92
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1799,f1774,f798,f254,f8415,f410]) ).
fof(f1799,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(sK15,X0),sK7(X1,X0)) = apply(sK15,sK7(X1,X0))
| ~ function(sK15)
| in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_175 ),
inference(forward_demodulation,[],[f1798,f800]) ).
fof(f1798,plain,
( ! [X0,X1] :
( ~ function(sK15)
| apply(relation_dom_restriction(empty_set,X0),sK7(X1,X0)) = apply(empty_set,sK7(X1,X0))
| in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0) )
| ~ spl22_7
| ~ spl22_92
| ~ spl22_175 ),
inference(forward_demodulation,[],[f1789,f800]) ).
fof(f1789,plain,
( ! [X0,X1] :
( ~ function(empty_set)
| apply(relation_dom_restriction(empty_set,X0),sK7(X1,X0)) = apply(empty_set,sK7(X1,X0))
| in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0) )
| ~ spl22_7
| ~ spl22_175 ),
inference(resolution,[],[f1775,f256]) ).
fof(f8402,plain,
( spl22_480
| ~ spl22_20
| ~ spl22_19
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1796,f1774,f314,f319,f8400]) ).
fof(f1796,plain,
( ! [X0,X1] :
( ~ function(sK20)
| apply(relation_dom_restriction(sK20,X0),sK7(X1,X0)) = apply(sK20,sK7(X1,X0))
| in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0) )
| ~ spl22_19
| ~ spl22_175 ),
inference(resolution,[],[f1775,f316]) ).
fof(f8387,plain,
( spl22_479
| ~ spl22_18
| ~ spl22_17
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1795,f1774,f304,f309,f8385]) ).
fof(f1795,plain,
( ! [X0,X1] :
( ~ function(sK19)
| apply(relation_dom_restriction(sK19,X0),sK7(X1,X0)) = apply(sK19,sK7(X1,X0))
| in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0) )
| ~ spl22_17
| ~ spl22_175 ),
inference(resolution,[],[f1775,f306]) ).
fof(f8383,plain,
( ~ spl22_10
| spl22_478
| ~ spl22_268
| ~ spl22_463 ),
inference(avatar_split_clause,[],[f8142,f8061,f2959,f8381,f269]) ).
fof(f8142,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(relation_dom_restriction(sK5,sK15),X0)
| ~ empty(sK15) )
| ~ spl22_268
| ~ spl22_463 ),
inference(resolution,[],[f8063,f2960]) ).
fof(f8379,plain,
( spl22_477
| ~ spl22_65
| ~ spl22_169 ),
inference(avatar_split_clause,[],[f1725,f1712,f604,f8377]) ).
fof(f1712,plain,
( spl22_169
<=> ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_169])]) ).
fof(f1725,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_169 ),
inference(resolution,[],[f1713,f605]) ).
fof(f1713,plain,
( ! [X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_169 ),
inference(avatar_component_clause,[],[f1712]) ).
fof(f8375,plain,
( spl22_476
| ~ spl22_147
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1557,f1527,f1393,f8373]) ).
fof(f1557,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,apply(X1,X2)),relation_dom(X0))
| sP0(X0,apply(X1,X2))
| ~ sP0(X1,sK7(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1394]) ).
fof(f8371,plain,
( spl22_475
| ~ spl22_150
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1522,f1508,f1405,f8369]) ).
fof(f8369,plain,
( spl22_475
<=> ! [X2,X0,X1] :
( sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0)
| sP2(relation_rng(X0),X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_475])]) ).
fof(f1522,plain,
( ! [X2,X0,X1] :
( sK13(relation_rng(X0),X1,X2) = apply(X0,sK9(X0,sK13(relation_rng(X0),X1,X2)))
| ~ sP1(X0)
| sP2(relation_rng(X0),X1,X2)
| ~ empty(X2) )
| ~ spl22_150
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1406]) ).
fof(f8367,plain,
( spl22_474
| ~ spl22_148
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1520,f1508,f1397,f8365]) ).
fof(f8365,plain,
( spl22_474
<=> ! [X2,X0,X1] :
( sK13(X1,relation_rng(X0),X2) = apply(X0,sK9(X0,sK13(X1,relation_rng(X0),X2)))
| ~ sP1(X0)
| sP2(X1,relation_rng(X0),X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_474])]) ).
fof(f1520,plain,
( ! [X2,X0,X1] :
( sK13(X1,relation_rng(X0),X2) = apply(X0,sK9(X0,sK13(X1,relation_rng(X0),X2)))
| ~ sP1(X0)
| sP2(X1,relation_rng(X0),X2)
| ~ empty(X2) )
| ~ spl22_148
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1398]) ).
fof(f8363,plain,
( spl22_473
| ~ spl22_149
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1517,f1508,f1401,f8361]) ).
fof(f8361,plain,
( spl22_473
<=> ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_473])]) ).
fof(f1517,plain,
( ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X2) )
| ~ spl22_149
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1402]) ).
fof(f8359,plain,
( spl22_472
| ~ spl22_151
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1516,f1508,f1409,f8357]) ).
fof(f8357,plain,
( spl22_472
<=> ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_472])]) ).
fof(f1516,plain,
( ! [X2,X0,X1] :
( sK13(X1,X2,relation_rng(X0)) = apply(X0,sK9(X0,sK13(X1,X2,relation_rng(X0))))
| ~ sP1(X0)
| sP2(X1,X2,relation_rng(X0))
| ~ empty(X1) )
| ~ spl22_151
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1410]) ).
fof(f8355,plain,
( spl22_471
| ~ spl22_73
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1432,f1393,f652,f8353]) ).
fof(f1432,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| in(sK8(X1,apply(X0,X2)),relation_dom(X1))
| sP0(X1,apply(X0,X2)) )
| ~ spl22_73
| ~ spl22_147 ),
inference(resolution,[],[f1394,f653]) ).
fof(f8351,plain,
( spl22_470
| ~ spl22_74
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1421,f1384,f662,f8349]) ).
fof(f1421,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| apply(relation_dom_restriction(X2,relation_dom(X1)),sK9(X1,X0)) = apply(X2,sK9(X1,X0))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_145 ),
inference(resolution,[],[f1385,f663]) ).
fof(f8088,plain,
( spl22_469
| ~ spl22_63
| ~ spl22_169 ),
inference(avatar_split_clause,[],[f1724,f1712,f586,f8086]) ).
fof(f1724,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_63
| ~ spl22_169 ),
inference(resolution,[],[f1713,f587]) ).
fof(f8084,plain,
( spl22_468
| ~ spl22_74
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1376,f1345,f662,f8082]) ).
fof(f8082,plain,
( spl22_468
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| apply(relation_dom_restriction(X2,relation_dom(X0)),sK8(X0,X1)) = apply(X2,sK8(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_468])]) ).
fof(f1376,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| apply(relation_dom_restriction(X2,relation_dom(X0)),sK8(X0,X1)) = apply(X2,sK8(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_143 ),
inference(resolution,[],[f1346,f663]) ).
fof(f8080,plain,
( spl22_467
| ~ spl22_74
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1362,f1341,f662,f8078]) ).
fof(f8078,plain,
( spl22_467
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_467])]) ).
fof(f1362,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_142 ),
inference(resolution,[],[f1342,f663]) ).
fof(f8076,plain,
( spl22_466
| ~ spl22_74
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1324,f1290,f662,f8074]) ).
fof(f1324,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X0)
| apply(relation_dom_restriction(X2,X0),sK13(X0,X1,X0)) = apply(X2,sK13(X0,X1,X0))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_139 ),
inference(resolution,[],[f1291,f663]) ).
fof(f8072,plain,
( spl22_465
| ~ spl22_74
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1310,f1286,f662,f8070]) ).
fof(f1310,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X1)
| apply(relation_dom_restriction(X2,X1),sK13(X0,X1,X1)) = apply(X2,sK13(X0,X1,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_138 ),
inference(resolution,[],[f1287,f663]) ).
fof(f8068,plain,
( spl22_464
| ~ spl22_77
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1256,f1242,f698,f8066]) ).
fof(f8066,plain,
( spl22_464
<=> ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sK7(X0,sK6(X1)) = apply(X0,sK8(X0,sK6(X1)))
| sP0(X0,sK6(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_464])]) ).
fof(f1256,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sK7(X0,sK6(X1)) = apply(X0,sK8(X0,sK6(X1)))
| sP0(X0,sK6(X1)) )
| ~ spl22_77
| ~ spl22_132 ),
inference(resolution,[],[f1243,f699]) ).
fof(f8064,plain,
( ~ spl22_10
| spl22_463
| ~ spl22_31
| ~ spl22_92
| ~ spl22_462 ),
inference(avatar_split_clause,[],[f7595,f7120,f798,f378,f8061,f269]) ).
fof(f7595,plain,
( sP0(relation_dom_restriction(sK5,sK15),sK15)
| ~ empty(sK15)
| ~ spl22_31
| ~ spl22_92
| ~ spl22_462 ),
inference(forward_demodulation,[],[f7594,f800]) ).
fof(f7594,plain,
( ~ empty(sK15)
| sP0(relation_dom_restriction(sK5,empty_set),sK15)
| ~ spl22_31
| ~ spl22_92
| ~ spl22_462 ),
inference(forward_demodulation,[],[f7592,f800]) ).
fof(f7592,plain,
( ~ empty(empty_set)
| sP0(relation_dom_restriction(sK5,empty_set),sK15)
| ~ spl22_31
| ~ spl22_462 ),
inference(superposition,[],[f7121,f379]) ).
fof(f7122,plain,
( spl22_462
| ~ spl22_221
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4438,f4126,f2379,f7120]) ).
fof(f4438,plain,
( ! [X0] :
( ~ empty(set_intersection2(relation_dom(sK5),X0))
| sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_221
| ~ spl22_371 ),
inference(superposition,[],[f2380,f4127]) ).
fof(f6415,plain,
( spl22_461
| ~ spl22_128
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1699,f1608,f1151,f6413]) ).
fof(f1699,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2)))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) )
| ~ spl22_128
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1152]) ).
fof(f6411,plain,
( spl22_460
| ~ spl22_129
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1693,f1608,f1155,f6409]) ).
fof(f1693,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) )
| ~ spl22_129
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1156]) ).
fof(f6407,plain,
( spl22_459
| ~ spl22_130
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1692,f1608,f1159,f6405]) ).
fof(f1692,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) )
| ~ spl22_130
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1160]) ).
fof(f6403,plain,
( spl22_458
| ~ spl22_65
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1686,f1608,f604,f6401]) ).
fof(f1686,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) )
| ~ spl22_65
| ~ spl22_165 ),
inference(resolution,[],[f1609,f605]) ).
fof(f6399,plain,
( spl22_457
| ~ spl22_128
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1674,f1600,f1151,f6397]) ).
fof(f1674,plain,
( ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2)
| element(sK13(sK10(powerset(X0)),X1,X2),X0) )
| ~ spl22_128
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1152]) ).
fof(f6395,plain,
( spl22_456
| ~ spl22_129
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1668,f1600,f1155,f6393]) ).
fof(f1668,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X0) )
| ~ spl22_129
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1156]) ).
fof(f6391,plain,
( spl22_455
| ~ spl22_130
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1667,f1600,f1159,f6389]) ).
fof(f1667,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X1) )
| ~ spl22_130
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1160]) ).
fof(f6387,plain,
( spl22_454
| ~ spl22_65
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1661,f1600,f604,f6385]) ).
fof(f1661,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_163 ),
inference(resolution,[],[f1601,f605]) ).
fof(f6383,plain,
( spl22_453
| ~ spl22_128
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1654,f1587,f1151,f6381]) ).
fof(f1654,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2)))
| element(sK13(X0,X1,sK10(powerset(X2))),X2) )
| ~ spl22_128
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1152]) ).
fof(f6371,plain,
( spl22_452
| ~ spl22_129
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1648,f1587,f1155,f6369]) ).
fof(f1648,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) )
| ~ spl22_129
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1156]) ).
fof(f6367,plain,
( spl22_451
| ~ spl22_130
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1647,f1587,f1159,f6365]) ).
fof(f1647,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3))
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) )
| ~ spl22_130
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1160]) ).
fof(f6363,plain,
( spl22_450
| ~ spl22_65
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1641,f1587,f604,f6361]) ).
fof(f1641,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) )
| ~ spl22_65
| ~ spl22_161 ),
inference(resolution,[],[f1588,f605]) ).
fof(f6359,plain,
( spl22_449
| ~ spl22_128
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1634,f1579,f1151,f6357]) ).
fof(f1634,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X2)
| sP2(X0,sK10(powerset(X1)),X2)
| element(sK13(X0,sK10(powerset(X1)),X2),X1) )
| ~ spl22_128
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1152]) ).
fof(f6355,plain,
( spl22_448
| ~ spl22_129
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1628,f1579,f1155,f6353]) ).
fof(f1628,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X1) )
| ~ spl22_129
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1156]) ).
fof(f6351,plain,
( spl22_447
| ~ spl22_130
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1627,f1579,f1159,f6349]) ).
fof(f1627,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X2) )
| ~ spl22_130
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1160]) ).
fof(f6347,plain,
( spl22_446
| ~ spl22_65
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1621,f1579,f604,f6345]) ).
fof(f1621,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_159 ),
inference(resolution,[],[f1580,f605]) ).
fof(f6343,plain,
( spl22_445
| ~ spl22_142
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1512,f1508,f1341,f6341]) ).
fof(f6341,plain,
( spl22_445
<=> ! [X0,X1] :
( sK7(X1,relation_rng(X0)) = apply(X0,sK9(X0,sK7(X1,relation_rng(X0))))
| ~ sP1(X0)
| sP0(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_445])]) ).
fof(f1512,plain,
( ! [X0,X1] :
( sK7(X1,relation_rng(X0)) = apply(X0,sK9(X0,sK7(X1,relation_rng(X0))))
| ~ sP1(X0)
| sP0(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) )
| ~ spl22_142
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1342]) ).
fof(f6339,plain,
( spl22_444
| ~ spl22_139
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1439,f1393,f1290,f6337]) ).
fof(f1439,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| sP2(apply(X0,X1),X2,apply(X0,X1)) )
| ~ spl22_139
| ~ spl22_147 ),
inference(resolution,[],[f1394,f1291]) ).
fof(f6335,plain,
( spl22_443
| ~ spl22_138
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1438,f1393,f1286,f6333]) ).
fof(f1438,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK13(X1,apply(X0,X2),apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP2(X1,apply(X0,X2),apply(X0,X2)) )
| ~ spl22_138
| ~ spl22_147 ),
inference(resolution,[],[f1394,f1287]) ).
fof(f6311,plain,
( spl22_442
| ~ spl22_76
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1231,f1159,f670,f6309]) ).
fof(f1231,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X1)
| in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_76
| ~ spl22_130 ),
inference(resolution,[],[f1160,f671]) ).
fof(f6307,plain,
( spl22_441
| ~ spl22_75
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1230,f1159,f666,f6305]) ).
fof(f1230,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X2)
| in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_75
| ~ spl22_130 ),
inference(resolution,[],[f1160,f667]) ).
fof(f6303,plain,
( spl22_440
| ~ spl22_75
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1229,f1159,f666,f6301]) ).
fof(f1229,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_75
| ~ spl22_130 ),
inference(resolution,[],[f1160,f667]) ).
fof(f6299,plain,
( spl22_439
| ~ spl22_76
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1228,f1159,f670,f6297]) ).
fof(f1228,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_76
| ~ spl22_130 ),
inference(resolution,[],[f1160,f671]) ).
fof(f6295,plain,
( spl22_438
| ~ spl22_76
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1217,f1155,f670,f6293]) ).
fof(f1217,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(set_intersection2(X0,X1),X2,X3),X0)
| in(sK13(set_intersection2(X0,X1),X2,X3),X3)
| sP2(set_intersection2(X0,X1),X2,X3) )
| ~ spl22_76
| ~ spl22_129 ),
inference(resolution,[],[f1156,f671]) ).
fof(f6291,plain,
( spl22_437
| ~ spl22_75
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1216,f1155,f666,f6289]) ).
fof(f1216,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,set_intersection2(X1,X2),X3),X1)
| in(sK13(X0,set_intersection2(X1,X2),X3),X3)
| sP2(X0,set_intersection2(X1,X2),X3) )
| ~ spl22_75
| ~ spl22_129 ),
inference(resolution,[],[f1156,f667]) ).
fof(f6287,plain,
( spl22_436
| ~ spl22_75
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1215,f1155,f666,f6285]) ).
fof(f1215,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X1)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_75
| ~ spl22_129 ),
inference(resolution,[],[f1156,f667]) ).
fof(f6283,plain,
( spl22_435
| ~ spl22_76
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1214,f1155,f670,f6281]) ).
fof(f1214,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X0)
| sP2(X0,X1,set_intersection2(X2,X3)) )
| ~ spl22_76
| ~ spl22_129 ),
inference(resolution,[],[f1156,f671]) ).
fof(f6279,plain,
( spl22_434
| ~ spl22_76
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1209,f1151,f670,f6277]) ).
fof(f1209,plain,
( ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X0)
| in(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2) )
| ~ spl22_76
| ~ spl22_128 ),
inference(resolution,[],[f1152,f671]) ).
fof(f6275,plain,
( spl22_433
| ~ spl22_75
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1208,f1151,f666,f6273]) ).
fof(f1208,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X1)
| in(sK13(X0,sK10(powerset(X1)),X2),X2)
| sP2(X0,sK10(powerset(X1)),X2) )
| ~ spl22_75
| ~ spl22_128 ),
inference(resolution,[],[f1152,f667]) ).
fof(f6242,plain,
( spl22_432
| ~ spl22_75
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1207,f1151,f666,f6240]) ).
fof(f1207,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_75
| ~ spl22_128 ),
inference(resolution,[],[f1152,f667]) ).
fof(f6238,plain,
( spl22_431
| ~ spl22_76
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1206,f1151,f670,f6236]) ).
fof(f1206,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X2)
| in(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2))) )
| ~ spl22_76
| ~ spl22_128 ),
inference(resolution,[],[f1152,f671]) ).
fof(f5954,plain,
( spl22_430
| ~ spl22_53
| ~ spl22_386 ),
inference(avatar_split_clause,[],[f5275,f4837,f511,f5952]) ).
fof(f5952,plain,
( spl22_430
<=> ! [X0] :
( sP1(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_430])]) ).
fof(f4837,plain,
( spl22_386
<=> ! [X0] :
( sP1(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_386])]) ).
fof(f5275,plain,
( ! [X0] :
( sP1(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_53
| ~ spl22_386 ),
inference(superposition,[],[f4838,f512]) ).
fof(f4838,plain,
( ! [X0] :
( sP1(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_386 ),
inference(avatar_component_clause,[],[f4837]) ).
fof(f5721,plain,
( spl22_429
| ~ spl22_132
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1698,f1608,f1242,f5719]) ).
fof(f1698,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X0)
| sP2(X0,X1,sK6(X2))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1243]) ).
fof(f5717,plain,
( spl22_428
| ~ spl22_63
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1685,f1608,f586,f5715]) ).
fof(f1685,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) )
| ~ spl22_63
| ~ spl22_165 ),
inference(resolution,[],[f1609,f587]) ).
fof(f5713,plain,
( spl22_427
| ~ spl22_132
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1673,f1600,f1242,f5711]) ).
fof(f1673,plain,
( ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,X2),X2)
| sP2(sK6(X0),X1,X2)
| element(sK13(sK6(X0),X1,X2),X0)
| empty(X0) )
| ~ spl22_132
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1243]) ).
fof(f5709,plain,
( spl22_426
| ~ spl22_53
| ~ spl22_378 ),
inference(avatar_split_clause,[],[f5228,f4760,f511,f5707]) ).
fof(f5707,plain,
( spl22_426
<=> ! [X0] :
( function(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_426])]) ).
fof(f4760,plain,
( spl22_378
<=> ! [X0] :
( function(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_378])]) ).
fof(f5228,plain,
( ! [X0] :
( function(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_53
| ~ spl22_378 ),
inference(superposition,[],[f4761,f512]) ).
fof(f4761,plain,
( ! [X0] :
( function(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_378 ),
inference(avatar_component_clause,[],[f4760]) ).
fof(f5705,plain,
( spl22_425
| ~ spl22_63
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1660,f1600,f586,f5703]) ).
fof(f1660,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_63
| ~ spl22_163 ),
inference(resolution,[],[f1601,f587]) ).
fof(f5701,plain,
( spl22_424
| ~ spl22_132
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1653,f1587,f1242,f5699]) ).
fof(f1653,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X1)
| sP2(X0,X1,sK6(X2))
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1243]) ).
fof(f5697,plain,
( spl22_423
| ~ spl22_63
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1640,f1587,f586,f5695]) ).
fof(f1640,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) )
| ~ spl22_63
| ~ spl22_161 ),
inference(resolution,[],[f1588,f587]) ).
fof(f5693,plain,
( spl22_422
| ~ spl22_132
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1633,f1579,f1242,f5691]) ).
fof(f1633,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),X2),X2)
| sP2(X0,sK6(X1),X2)
| element(sK13(X0,sK6(X1),X2),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1243]) ).
fof(f5689,plain,
( spl22_421
| ~ spl22_63
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1620,f1579,f586,f5687]) ).
fof(f1620,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_63
| ~ spl22_159 ),
inference(resolution,[],[f1580,f587]) ).
fof(f5685,plain,
( spl22_420
| ~ spl22_69
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1511,f1508,f628,f5683]) ).
fof(f1511,plain,
( ! [X2,X0,X1] :
( apply(X1,X2) = apply(X0,sK9(X0,apply(X1,X2)))
| ~ sP1(X0)
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,relation_rng(X0)) )
| ~ spl22_69
| ~ spl22_153 ),
inference(resolution,[],[f1509,f629]) ).
fof(f5681,plain,
( spl22_419
| ~ spl22_74
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1351,f1337,f662,f5679]) ).
fof(f1351,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| apply(relation_dom_restriction(X3,set_intersection2(X1,X2)),X0) = apply(X3,X0)
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_141 ),
inference(resolution,[],[f1338,f663]) ).
fof(f5677,plain,
( spl22_418
| ~ spl22_74
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1301,f1282,f662,f5675]) ).
fof(f1282,plain,
( spl22_137
<=> ! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_137])]) ).
fof(f1301,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(X0)
| apply(relation_dom_restriction(X1,powerset(X0)),sK6(X0)) = apply(X1,sK6(X0))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_74
| ~ spl22_137 ),
inference(resolution,[],[f1283,f663]) ).
fof(f1283,plain,
( ! [X0] :
( in(sK6(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl22_137 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f5673,plain,
( spl22_417
| ~ spl22_76
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1262,f1242,f670,f5671]) ).
fof(f1262,plain,
( ! [X2,X0,X1] :
( element(sK13(sK6(X0),X1,X2),X0)
| empty(X0)
| in(sK13(sK6(X0),X1,X2),X2)
| sP2(sK6(X0),X1,X2) )
| ~ spl22_76
| ~ spl22_132 ),
inference(resolution,[],[f1243,f671]) ).
fof(f5669,plain,
( spl22_416
| ~ spl22_75
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1261,f1242,f666,f5667]) ).
fof(f1261,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK6(X1),X2),X1)
| empty(X1)
| in(sK13(X0,sK6(X1),X2),X2)
| sP2(X0,sK6(X1),X2) )
| ~ spl22_75
| ~ spl22_132 ),
inference(resolution,[],[f1243,f667]) ).
fof(f5665,plain,
( spl22_415
| ~ spl22_53
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f5093,f4718,f511,f5663]) ).
fof(f5663,plain,
( spl22_415
<=> ! [X0] :
( relation(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_415])]) ).
fof(f4718,plain,
( spl22_373
<=> ! [X0] :
( relation(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_373])]) ).
fof(f5093,plain,
( ! [X0] :
( relation(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_53
| ~ spl22_373 ),
inference(superposition,[],[f4719,f512]) ).
fof(f4719,plain,
( ! [X0] :
( relation(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_373 ),
inference(avatar_component_clause,[],[f4718]) ).
fof(f5661,plain,
( spl22_414
| ~ spl22_75
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1260,f1242,f666,f5659]) ).
fof(f1260,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2)
| in(sK13(X0,X1,sK6(X2)),X1)
| sP2(X0,X1,sK6(X2)) )
| ~ spl22_75
| ~ spl22_132 ),
inference(resolution,[],[f1243,f667]) ).
fof(f5657,plain,
( spl22_413
| ~ spl22_76
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1259,f1242,f670,f5655]) ).
fof(f1259,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2)
| in(sK13(X0,X1,sK6(X2)),X0)
| sP2(X0,X1,sK6(X2)) )
| ~ spl22_76
| ~ spl22_132 ),
inference(resolution,[],[f1243,f671]) ).
fof(f5445,plain,
( spl22_412
| ~ spl22_53
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4930,f4627,f511,f5443]) ).
fof(f4930,plain,
( ! [X0] :
( empty(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_53
| ~ spl22_372 ),
inference(superposition,[],[f4628,f512]) ).
fof(f5296,plain,
( spl22_411
| ~ spl22_65
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1570,f1535,f604,f5294]) ).
fof(f1570,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_156 ),
inference(resolution,[],[f1536,f605]) ).
fof(f5292,plain,
( spl22_410
| ~ spl22_128
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1559,f1527,f1151,f5290]) ).
fof(f5290,plain,
( spl22_410
<=> ! [X0,X1] :
( element(sK8(X0,sK10(powerset(X1))),relation_dom(X0))
| sP0(X0,sK10(powerset(X1)))
| element(sK7(X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_410])]) ).
fof(f1559,plain,
( ! [X0,X1] :
( element(sK8(X0,sK10(powerset(X1))),relation_dom(X0))
| sP0(X0,sK10(powerset(X1)))
| element(sK7(X0,sK10(powerset(X1))),X1) )
| ~ spl22_128
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1152]) ).
fof(f5288,plain,
( spl22_409
| ~ spl22_129
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1553,f1527,f1155,f5286]) ).
fof(f1553,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| in(sK7(X0,set_intersection2(X1,X2)),X1) )
| ~ spl22_129
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1156]) ).
fof(f5284,plain,
( spl22_408
| ~ spl22_130
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1552,f1527,f1159,f5282]) ).
fof(f1552,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2))
| in(sK7(X0,set_intersection2(X1,X2)),X2) )
| ~ spl22_130
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1160]) ).
fof(f5272,plain,
( spl22_407
| ~ spl22_147
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1501,f1409,f1393,f5270]) ).
fof(f1501,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| ~ empty(X0)
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_151 ),
inference(resolution,[],[f1410,f1394]) ).
fof(f5268,plain,
( spl22_406
| ~ spl22_147
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1486,f1405,f1393,f5266]) ).
fof(f1486,plain,
( ! [X2,X3,X0,X1] :
( sP2(apply(X0,X1),X2,X3)
| ~ empty(X3)
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| ~ in(X1,relation_dom(X0)) )
| ~ spl22_147
| ~ spl22_150 ),
inference(resolution,[],[f1406,f1394]) ).
fof(f5264,plain,
( spl22_405
| ~ spl22_147
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1471,f1401,f1393,f5262]) ).
fof(f1471,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| ~ empty(X1)
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| ~ in(X3,relation_dom(X2)) )
| ~ spl22_147
| ~ spl22_149 ),
inference(resolution,[],[f1402,f1394]) ).
fof(f5260,plain,
( spl22_404
| ~ spl22_147
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1456,f1397,f1393,f5258]) ).
fof(f1456,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,apply(X1,X2),X3)
| ~ empty(X3)
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| ~ in(X2,relation_dom(X1)) )
| ~ spl22_147
| ~ spl22_148 ),
inference(resolution,[],[f1398,f1394]) ).
fof(f5256,plain,
( spl22_403
| ~ spl22_74
| ~ spl22_136 ),
inference(avatar_split_clause,[],[f1296,f1278,f662,f5254]) ).
fof(f1296,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| apply(X2,X1) = apply(relation_dom_restriction(X2,powerset(X0)),X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_136 ),
inference(resolution,[],[f1279,f663]) ).
fof(f5252,plain,
( spl22_402
| ~ spl22_77
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1265,f1246,f698,f5250]) ).
fof(f5250,plain,
( spl22_402
<=> ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| sK7(X2,relation_dom(X0)) = apply(X2,sK8(X2,relation_dom(X0)))
| sP0(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_402])]) ).
fof(f1265,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| sK7(X2,relation_dom(X0)) = apply(X2,sK8(X2,relation_dom(X0)))
| sP0(X2,relation_dom(X0)) )
| ~ spl22_77
| ~ spl22_133 ),
inference(resolution,[],[f1247,f699]) ).
fof(f5248,plain,
( spl22_401
| ~ spl22_73
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1226,f1159,f652,f5246]) ).
fof(f1226,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X2)
| in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_73
| ~ spl22_130 ),
inference(resolution,[],[f1160,f653]) ).
fof(f5244,plain,
( spl22_400
| ~ spl22_73
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1212,f1155,f652,f5242]) ).
fof(f1212,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2)),X1)
| in(sK8(X0,set_intersection2(X1,X2)),relation_dom(X0))
| sP0(X0,set_intersection2(X1,X2)) )
| ~ spl22_73
| ~ spl22_129 ),
inference(resolution,[],[f1156,f653]) ).
fof(f5240,plain,
( spl22_399
| ~ spl22_73
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1204,f1151,f652,f5238]) ).
fof(f1204,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| in(sK8(X0,sK10(powerset(X1))),relation_dom(X0))
| sP0(X0,sK10(powerset(X1))) )
| ~ spl22_73
| ~ spl22_128 ),
inference(resolution,[],[f1152,f653]) ).
fof(f5236,plain,
( spl22_398
| ~ spl22_77
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1118,f1110,f698,f5234]) ).
fof(f1118,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK7(X1,sK10(powerset(X0))) = apply(X1,sK8(X1,sK10(powerset(X0))))
| sP0(X1,sK10(powerset(X0))) )
| ~ spl22_77
| ~ spl22_121 ),
inference(resolution,[],[f1111,f699]) ).
fof(f5132,plain,
( spl22_397
| ~ spl22_63
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1569,f1535,f586,f5130]) ).
fof(f1569,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_63
| ~ spl22_156 ),
inference(resolution,[],[f1536,f587]) ).
fof(f5128,plain,
( spl22_396
| ~ spl22_132
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1558,f1527,f1242,f5126]) ).
fof(f1558,plain,
( ! [X0,X1] :
( element(sK8(X0,sK6(X1)),relation_dom(X0))
| sP0(X0,sK6(X1))
| element(sK7(X0,sK6(X1)),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1243]) ).
fof(f5124,plain,
( spl22_395
| ~ spl22_142
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1430,f1393,f1341,f5122]) ).
fof(f1430,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK7(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP0(X1,apply(X0,X2))
| ~ empty(relation_dom(X1)) )
| ~ spl22_142
| ~ spl22_147 ),
inference(resolution,[],[f1394,f1342]) ).
fof(f5120,plain,
( spl22_394
| ~ spl22_73
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1257,f1242,f652,f5118]) ).
fof(f1257,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| in(sK8(X0,sK6(X1)),relation_dom(X0))
| sP0(X0,sK6(X1)) )
| ~ spl22_73
| ~ spl22_132 ),
inference(resolution,[],[f1243,f653]) ).
fof(f4954,plain,
( spl22_393
| ~ spl22_69
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1429,f1393,f628,f4952]) ).
fof(f1429,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,apply(X1,X2))
| ~ in(X3,relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,apply(X0,X3)) )
| ~ spl22_69
| ~ spl22_147 ),
inference(resolution,[],[f1394,f629]) ).
fof(f4950,plain,
( spl22_392
| ~ spl22_128
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1332,f1290,f1151,f4948]) ).
fof(f4948,plain,
( spl22_392
<=> ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK10(powerset(X0)))
| element(sK13(sK10(powerset(X0)),X1,sK10(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_392])]) ).
fof(f1332,plain,
( ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK10(powerset(X0)))
| element(sK13(sK10(powerset(X0)),X1,sK10(powerset(X0))),X0) )
| ~ spl22_128
| ~ spl22_139 ),
inference(resolution,[],[f1291,f1152]) ).
fof(f4946,plain,
( spl22_391
| ~ spl22_129
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1328,f1290,f1155,f4944]) ).
fof(f1328,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| in(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0) )
| ~ spl22_129
| ~ spl22_139 ),
inference(resolution,[],[f1291,f1156]) ).
fof(f4942,plain,
( spl22_390
| ~ spl22_130
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1327,f1290,f1159,f4940]) ).
fof(f1327,plain,
( ! [X2,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| in(sK13(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) )
| ~ spl22_130
| ~ spl22_139 ),
inference(resolution,[],[f1291,f1160]) ).
fof(f4938,plain,
( spl22_389
| ~ spl22_128
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1318,f1286,f1151,f4936]) ).
fof(f4936,plain,
( spl22_389
<=> ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK10(powerset(X1)))
| element(sK13(X0,sK10(powerset(X1)),sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_389])]) ).
fof(f1318,plain,
( ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK10(powerset(X1)))
| element(sK13(X0,sK10(powerset(X1)),sK10(powerset(X1))),X1) )
| ~ spl22_128
| ~ spl22_138 ),
inference(resolution,[],[f1287,f1152]) ).
fof(f4904,plain,
( spl22_388
| ~ spl22_129
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1314,f1286,f1155,f4902]) ).
fof(f1314,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| in(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1) )
| ~ spl22_129
| ~ spl22_138 ),
inference(resolution,[],[f1287,f1156]) ).
fof(f4900,plain,
( spl22_387
| ~ spl22_130
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1313,f1286,f1159,f4898]) ).
fof(f1313,plain,
( ! [X2,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| in(sK13(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2) )
| ~ spl22_130
| ~ spl22_138 ),
inference(resolution,[],[f1287,f1160]) ).
fof(f4839,plain,
( spl22_386
| ~ spl22_212
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4436,f4126,f2274,f4837]) ).
fof(f2274,plain,
( spl22_212
<=> ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_212])]) ).
fof(f4436,plain,
( ! [X0] :
( sP1(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_212
| ~ spl22_371 ),
inference(superposition,[],[f2275,f4127]) ).
fof(f2275,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_212 ),
inference(avatar_component_clause,[],[f2274]) ).
fof(f4790,plain,
( spl22_385
| ~ spl22_133
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1696,f1608,f1246,f4788]) ).
fof(f1696,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,relation_dom(X2)),X0)
| sP2(X0,X1,relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1247]) ).
fof(f4786,plain,
( spl22_384
| ~ spl22_133
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1671,f1600,f1246,f4784]) ).
fof(f1671,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(relation_dom(X0),X1,X2),X2)
| sP2(relation_dom(X0),X1,X2)
| ~ sP0(X0,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1247]) ).
fof(f4782,plain,
( spl22_383
| ~ spl22_133
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1651,f1587,f1246,f4780]) ).
fof(f1651,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,relation_dom(X2)),X1)
| sP2(X0,X1,relation_dom(X2))
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1247]) ).
fof(f4778,plain,
( spl22_382
| ~ spl22_133
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1631,f1579,f1246,f4776]) ).
fof(f1631,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,relation_dom(X1),X2),X2)
| sP2(X0,relation_dom(X1),X2)
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1247]) ).
fof(f4774,plain,
( spl22_381
| ~ spl22_61
| ~ spl22_158 ),
inference(avatar_split_clause,[],[f1574,f1544,f578,f4772]) ).
fof(f1574,plain,
( ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ empty(X1)
| relation_rng(X0) = X1
| ~ sP1(X0) )
| ~ spl22_61
| ~ spl22_158 ),
inference(resolution,[],[f1545,f579]) ).
fof(f4770,plain,
( spl22_380
| ~ spl22_76
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1272,f1246,f670,f4768]) ).
fof(f1272,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(relation_dom(X0),X2,X3),X3)
| sP2(relation_dom(X0),X2,X3) )
| ~ spl22_76
| ~ spl22_133 ),
inference(resolution,[],[f1247,f671]) ).
fof(f4766,plain,
( spl22_379
| ~ spl22_75
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1271,f1246,f666,f4764]) ).
fof(f1271,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,relation_dom(X0),X3),X3)
| sP2(X2,relation_dom(X0),X3) )
| ~ spl22_75
| ~ spl22_133 ),
inference(resolution,[],[f1247,f667]) ).
fof(f4762,plain,
( spl22_378
| ~ spl22_111
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4421,f4126,f944,f4760]) ).
fof(f944,plain,
( spl22_111
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_111])]) ).
fof(f4421,plain,
( ! [X0] :
( function(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_111
| ~ spl22_371 ),
inference(superposition,[],[f945,f4127]) ).
fof(f945,plain,
( ! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_111 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f4758,plain,
( spl22_377
| ~ spl22_75
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1270,f1246,f666,f4756]) ).
fof(f1270,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_dom(X0)),X3)
| sP2(X2,X3,relation_dom(X0)) )
| ~ spl22_75
| ~ spl22_133 ),
inference(resolution,[],[f1247,f667]) ).
fof(f4754,plain,
( spl22_376
| ~ spl22_76
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1269,f1246,f670,f4752]) ).
fof(f1269,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK13(X2,X3,relation_dom(X0)),X2)
| sP2(X2,X3,relation_dom(X0)) )
| ~ spl22_76
| ~ spl22_133 ),
inference(resolution,[],[f1247,f671]) ).
fof(f4750,plain,
( spl22_375
| ~ spl22_74
| ~ spl22_120 ),
inference(avatar_split_clause,[],[f1114,f1106,f662,f4748]) ).
fof(f1106,plain,
( spl22_120
<=> ! [X0] :
( in(sK15,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_120])]) ).
fof(f1114,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| apply(relation_dom_restriction(X1,powerset(X0)),sK15) = apply(X1,sK15)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_74
| ~ spl22_120 ),
inference(resolution,[],[f1107,f663]) ).
fof(f1107,plain,
( ! [X0] :
( in(sK15,powerset(X0))
| empty(powerset(X0)) )
| ~ spl22_120 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f4746,plain,
( spl22_374
| ~ spl22_74
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f1100,f1064,f662,f4744]) ).
fof(f1100,plain,
( ! [X0,X1] :
( empty(X0)
| apply(relation_dom_restriction(X1,X0),sK10(X0)) = apply(X1,sK10(X0))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_74
| ~ spl22_119 ),
inference(resolution,[],[f1065,f663]) ).
fof(f4720,plain,
( spl22_373
| ~ spl22_37
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4416,f4126,f402,f4718]) ).
fof(f4416,plain,
( ! [X0] :
( relation(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_37
| ~ spl22_371 ),
inference(superposition,[],[f403,f4127]) ).
fof(f4629,plain,
( spl22_372
| ~ spl22_36
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4415,f4126,f398,f4627]) ).
fof(f4415,plain,
( ! [X0] :
( empty(set_intersection2(relation_dom(sK5),X0))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_36
| ~ spl22_371 ),
inference(superposition,[],[f399,f4127]) ).
fof(f4128,plain,
( spl22_371
| ~ spl22_2
| ~ spl22_1
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3579,f3551,f224,f229,f4126]) ).
fof(f3579,plain,
( ! [X0] :
( ~ function(sK5)
| set_intersection2(relation_dom(sK5),X0) = relation_dom(relation_dom_restriction(sK5,X0)) )
| ~ spl22_1
| ~ spl22_313 ),
inference(resolution,[],[f3552,f226]) ).
fof(f4058,plain,
( spl22_370
| ~ spl22_53
| ~ spl22_167 ),
inference(avatar_split_clause,[],[f1706,f1616,f511,f4056]) ).
fof(f4056,plain,
( spl22_370
<=> ! [X0,X1] :
( relation_dom(X0) != set_intersection2(X1,relation_dom(X0))
| relation_dom_restriction(X0,X1) = X0
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_370])]) ).
fof(f1706,plain,
( ! [X0,X1] :
( relation_dom(X0) != set_intersection2(X1,relation_dom(X0))
| relation_dom_restriction(X0,X1) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_53
| ~ spl22_167 ),
inference(superposition,[],[f1617,f512]) ).
fof(f4054,plain,
( spl22_369
| ~ spl22_121
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1700,f1608,f1110,f4052]) ).
fof(f4052,plain,
( spl22_369
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_369])]) ).
fof(f1700,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X0)
| sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_165 ),
inference(resolution,[],[f1609,f1111]) ).
fof(f4050,plain,
( spl22_368
| ~ spl22_45
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1691,f1608,f454,f4048]) ).
fof(f4048,plain,
( spl22_368
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_368])]) ).
fof(f1691,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_165 ),
inference(resolution,[],[f1609,f455]) ).
fof(f4046,plain,
( spl22_367
| ~ spl22_121
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1675,f1600,f1110,f4044]) ).
fof(f4044,plain,
( spl22_367
<=> ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_367])]) ).
fof(f1675,plain,
( ! [X2,X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2)
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_163 ),
inference(resolution,[],[f1601,f1111]) ).
fof(f4042,plain,
( spl22_366
| ~ spl22_45
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1666,f1600,f454,f4040]) ).
fof(f4040,plain,
( spl22_366
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X0,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_366])]) ).
fof(f1666,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X0,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_163 ),
inference(resolution,[],[f1601,f455]) ).
fof(f4038,plain,
( spl22_365
| ~ spl22_46
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1665,f1600,f458,f4036]) ).
fof(f4036,plain,
( spl22_365
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_365])]) ).
fof(f1665,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X0) )
| ~ spl22_46
| ~ spl22_163 ),
inference(resolution,[],[f1601,f459]) ).
fof(f4034,plain,
( spl22_364
| ~ spl22_121
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1655,f1587,f1110,f4032]) ).
fof(f4032,plain,
( spl22_364
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_364])]) ).
fof(f1655,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X2))),X1)
| sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_161 ),
inference(resolution,[],[f1588,f1111]) ).
fof(f4028,plain,
( spl22_363
| ~ spl22_45
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1646,f1587,f454,f4026]) ).
fof(f4026,plain,
( spl22_363
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_363])]) ).
fof(f1646,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_161 ),
inference(resolution,[],[f1588,f455]) ).
fof(f4024,plain,
( spl22_362
| ~ spl22_121
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1635,f1579,f1110,f4022]) ).
fof(f4022,plain,
( spl22_362
<=> ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X2)
| sP2(X0,sK10(powerset(X1)),X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_362])]) ).
fof(f1635,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X2),X2)
| sP2(X0,sK10(powerset(X1)),X2)
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_159 ),
inference(resolution,[],[f1580,f1111]) ).
fof(f4020,plain,
( spl22_361
| ~ spl22_45
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1626,f1579,f454,f4018]) ).
fof(f4018,plain,
( spl22_361
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X1,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_361])]) ).
fof(f1626,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X1,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_159 ),
inference(resolution,[],[f1580,f455]) ).
fof(f4016,plain,
( spl22_360
| ~ spl22_46
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1625,f1579,f458,f4014]) ).
fof(f4014,plain,
( spl22_360
<=> ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_360])]) ).
fof(f1625,plain,
( ! [X2,X0,X1] :
( element(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X1) )
| ~ spl22_46
| ~ spl22_159 ),
inference(resolution,[],[f1580,f459]) ).
fof(f4012,plain,
( spl22_359
| ~ spl22_133
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1556,f1527,f1246,f4010]) ).
fof(f1556,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,relation_dom(X1)),relation_dom(X0))
| sP0(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1247]) ).
fof(f4008,plain,
( spl22_358
| ~ spl22_119
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1515,f1508,f1064,f4006]) ).
fof(f1515,plain,
( ! [X0] :
( sK10(relation_rng(X0)) = apply(X0,sK9(X0,sK10(relation_rng(X0))))
| ~ sP1(X0)
| empty(relation_rng(X0)) )
| ~ spl22_119
| ~ spl22_153 ),
inference(resolution,[],[f1509,f1065]) ).
fof(f4004,plain,
( spl22_357
| ~ spl22_128
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1503,f1409,f1151,f4002]) ).
fof(f1503,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X0)
| element(sK13(X0,X1,sK10(powerset(X2))),X2) )
| ~ spl22_128
| ~ spl22_151 ),
inference(resolution,[],[f1410,f1152]) ).
fof(f4000,plain,
( spl22_356
| ~ spl22_132
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1502,f1409,f1242,f3998]) ).
fof(f1502,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| ~ empty(X0)
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_151 ),
inference(resolution,[],[f1410,f1243]) ).
fof(f3996,plain,
( spl22_355
| ~ spl22_129
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1498,f1409,f1155,f3994]) ).
fof(f1498,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) )
| ~ spl22_129
| ~ spl22_151 ),
inference(resolution,[],[f1410,f1156]) ).
fof(f3992,plain,
( spl22_354
| ~ spl22_130
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1497,f1409,f1159,f3990]) ).
fof(f1497,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X0)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) )
| ~ spl22_130
| ~ spl22_151 ),
inference(resolution,[],[f1410,f1160]) ).
fof(f3988,plain,
( spl22_353
| ~ spl22_128
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1488,f1405,f1151,f3986]) ).
fof(f1488,plain,
( ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| ~ empty(X2)
| element(sK13(sK10(powerset(X0)),X1,X2),X0) )
| ~ spl22_128
| ~ spl22_150 ),
inference(resolution,[],[f1406,f1152]) ).
fof(f3984,plain,
( spl22_352
| ~ spl22_132
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1487,f1405,f1242,f3982]) ).
fof(f1487,plain,
( ! [X2,X0,X1] :
( sP2(sK6(X0),X1,X2)
| ~ empty(X2)
| element(sK13(sK6(X0),X1,X2),X0)
| empty(X0) )
| ~ spl22_132
| ~ spl22_150 ),
inference(resolution,[],[f1406,f1243]) ).
fof(f3980,plain,
( spl22_351
| ~ spl22_129
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1483,f1405,f1155,f3978]) ).
fof(f1483,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X0) )
| ~ spl22_129
| ~ spl22_150 ),
inference(resolution,[],[f1406,f1156]) ).
fof(f3976,plain,
( spl22_350
| ~ spl22_130
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1482,f1405,f1159,f3974]) ).
fof(f1482,plain,
( ! [X2,X3,X0,X1] :
( sP2(set_intersection2(X0,X1),X2,X3)
| ~ empty(X3)
| in(sK13(set_intersection2(X0,X1),X2,X3),X1) )
| ~ spl22_130
| ~ spl22_150 ),
inference(resolution,[],[f1406,f1160]) ).
fof(f3972,plain,
( spl22_349
| ~ spl22_128
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1473,f1401,f1151,f3970]) ).
fof(f1473,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X1)
| element(sK13(X0,X1,sK10(powerset(X2))),X2) )
| ~ spl22_128
| ~ spl22_149 ),
inference(resolution,[],[f1402,f1152]) ).
fof(f3968,plain,
( spl22_348
| ~ spl22_132
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1472,f1401,f1242,f3966]) ).
fof(f1472,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK6(X2))
| ~ empty(X1)
| element(sK13(X0,X1,sK6(X2)),X2)
| empty(X2) )
| ~ spl22_132
| ~ spl22_149 ),
inference(resolution,[],[f1402,f1243]) ).
fof(f3964,plain,
( spl22_347
| ~ spl22_129
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1468,f1401,f1155,f3962]) ).
fof(f1468,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X2) )
| ~ spl22_129
| ~ spl22_149 ),
inference(resolution,[],[f1402,f1156]) ).
fof(f3960,plain,
( spl22_346
| ~ spl22_130
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1467,f1401,f1159,f3958]) ).
fof(f1467,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,set_intersection2(X2,X3))
| ~ empty(X1)
| in(sK13(X0,X1,set_intersection2(X2,X3)),X3) )
| ~ spl22_130
| ~ spl22_149 ),
inference(resolution,[],[f1402,f1160]) ).
fof(f3956,plain,
( spl22_345
| ~ spl22_128
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1458,f1397,f1151,f3954]) ).
fof(f1458,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| ~ empty(X2)
| element(sK13(X0,sK10(powerset(X1)),X2),X1) )
| ~ spl22_128
| ~ spl22_148 ),
inference(resolution,[],[f1398,f1152]) ).
fof(f3952,plain,
( spl22_344
| ~ spl22_132
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1457,f1397,f1242,f3950]) ).
fof(f1457,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK6(X1),X2)
| ~ empty(X2)
| element(sK13(X0,sK6(X1),X2),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_148 ),
inference(resolution,[],[f1398,f1243]) ).
fof(f3948,plain,
( spl22_342
| ~ spl22_343
| ~ spl22_119
| ~ spl22_280 ),
inference(avatar_split_clause,[],[f3871,f3221,f1064,f3945,f3941]) ).
fof(f3941,plain,
( spl22_342
<=> empty(sK7(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_342])]) ).
fof(f3945,plain,
( spl22_343
<=> sP0(sK5,sK10(sK7(sK5,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_343])]) ).
fof(f3221,plain,
( spl22_280
<=> ! [X0] :
( ~ in(X0,sK7(sK5,sK15))
| ~ sP0(sK5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_280])]) ).
fof(f3871,plain,
( ~ sP0(sK5,sK10(sK7(sK5,sK15)))
| empty(sK7(sK5,sK15))
| ~ spl22_119
| ~ spl22_280 ),
inference(resolution,[],[f3222,f1065]) ).
fof(f3222,plain,
( ! [X0] :
( ~ in(X0,sK7(sK5,sK15))
| ~ sP0(sK5,X0) )
| ~ spl22_280 ),
inference(avatar_component_clause,[],[f3221]) ).
fof(f3939,plain,
( spl22_341
| ~ spl22_129
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1453,f1397,f1155,f3937]) ).
fof(f1453,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X1) )
| ~ spl22_129
| ~ spl22_148 ),
inference(resolution,[],[f1398,f1156]) ).
fof(f3935,plain,
( spl22_340
| ~ spl22_130
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1452,f1397,f1159,f3933]) ).
fof(f1452,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,set_intersection2(X1,X2),X3)
| ~ empty(X3)
| in(sK13(X0,set_intersection2(X1,X2),X3),X2) )
| ~ spl22_130
| ~ spl22_148 ),
inference(resolution,[],[f1398,f1160]) ).
fof(f3931,plain,
( spl22_339
| ~ spl22_65
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1426,f1389,f604,f3929]) ).
fof(f1426,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| element(X3,X1)
| ~ in(X3,apply(X0,X2)) )
| ~ spl22_65
| ~ spl22_146 ),
inference(resolution,[],[f1390,f605]) ).
fof(f3927,plain,
( spl22_338
| ~ spl22_80
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1335,f1290,f716,f3925]) ).
fof(f3925,plain,
( spl22_338
<=> ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(sK13(X0,X1,X0),X0)
| ~ in(sK13(X0,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_338])]) ).
fof(f1335,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(sK13(X0,X1,X0),X0)
| ~ in(sK13(X0,X1,X0),X1) )
| ~ spl22_80
| ~ spl22_139 ),
inference(duplicate_literal_removal,[],[f1322]) ).
fof(f1322,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(sK13(X0,X1,X0),X0)
| ~ in(sK13(X0,X1,X0),X1)
| sP2(X0,X1,X0) )
| ~ spl22_80
| ~ spl22_139 ),
inference(resolution,[],[f1291,f717]) ).
fof(f3923,plain,
( spl22_337
| ~ spl22_132
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1331,f1290,f1242,f3921]) ).
fof(f1331,plain,
( ! [X0,X1] :
( sP2(sK6(X0),X1,sK6(X0))
| element(sK13(sK6(X0),X1,sK6(X0)),X0)
| empty(X0) )
| ~ spl22_132
| ~ spl22_139 ),
inference(resolution,[],[f1291,f1243]) ).
fof(f3919,plain,
( spl22_336
| ~ spl22_80
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1321,f1286,f716,f3917]) ).
fof(f1321,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(sK13(X0,X1,X1),X0)
| ~ in(sK13(X0,X1,X1),X1) )
| ~ spl22_80
| ~ spl22_138 ),
inference(duplicate_literal_removal,[],[f1308]) ).
fof(f1308,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(sK13(X0,X1,X1),X0)
| ~ in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl22_80
| ~ spl22_138 ),
inference(resolution,[],[f1287,f717]) ).
fof(f3915,plain,
( spl22_335
| ~ spl22_132
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1317,f1286,f1242,f3913]) ).
fof(f1317,plain,
( ! [X0,X1] :
( sP2(X0,sK6(X1),sK6(X1))
| element(sK13(X0,sK6(X1),sK6(X1)),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_138 ),
inference(resolution,[],[f1287,f1243]) ).
fof(f3911,plain,
( spl22_334
| ~ spl22_73
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1266,f1246,f652,f3909]) ).
fof(f1266,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK8(X2,relation_dom(X0)),relation_dom(X2))
| sP0(X2,relation_dom(X0)) )
| ~ spl22_73
| ~ spl22_133 ),
inference(resolution,[],[f1247,f653]) ).
fof(f3907,plain,
( spl22_333
| ~ spl22_76
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1124,f1110,f670,f3905]) ).
fof(f1124,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(sK10(powerset(X0)),X1,X2),X2)
| sP2(sK10(powerset(X0)),X1,X2) )
| ~ spl22_76
| ~ spl22_121 ),
inference(resolution,[],[f1111,f671]) ).
fof(f3903,plain,
( spl22_332
| ~ spl22_75
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1123,f1110,f666,f3901]) ).
fof(f1123,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(X1,sK10(powerset(X0)),X2),X2)
| sP2(X1,sK10(powerset(X0)),X2) )
| ~ spl22_75
| ~ spl22_121 ),
inference(resolution,[],[f1111,f667]) ).
fof(f3861,plain,
( spl22_331
| ~ spl22_75
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1122,f1110,f666,f3859]) ).
fof(f1122,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(X1,X2,sK10(powerset(X0))),X2)
| sP2(X1,X2,sK10(powerset(X0))) )
| ~ spl22_75
| ~ spl22_121 ),
inference(resolution,[],[f1111,f667]) ).
fof(f3857,plain,
( spl22_330
| ~ spl22_76
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1121,f1110,f670,f3855]) ).
fof(f1121,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK13(X1,X2,sK10(powerset(X0))),X1)
| sP2(X1,X2,sK10(powerset(X0))) )
| ~ spl22_76
| ~ spl22_121 ),
inference(resolution,[],[f1111,f671]) ).
fof(f3703,plain,
( spl22_329
| ~ spl22_121
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1560,f1527,f1110,f3701]) ).
fof(f3701,plain,
( spl22_329
<=> ! [X0,X1] :
( element(sK8(X0,sK10(powerset(X1))),relation_dom(X0))
| sP0(X0,sK10(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_329])]) ).
fof(f1560,plain,
( ! [X0,X1] :
( element(sK8(X0,sK10(powerset(X1))),relation_dom(X0))
| sP0(X0,sK10(powerset(X1)))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_154 ),
inference(resolution,[],[f1528,f1111]) ).
fof(f3699,plain,
( spl22_328
| ~ spl22_63
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1425,f1389,f586,f3697]) ).
fof(f1425,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) )
| ~ spl22_63
| ~ spl22_146 ),
inference(resolution,[],[f1390,f587]) ).
fof(f3695,plain,
( spl22_327
| ~ spl22_128
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1370,f1341,f1151,f3693]) ).
fof(f1370,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| ~ empty(relation_dom(X0))
| element(sK7(X0,sK10(powerset(X1))),X1) )
| ~ spl22_128
| ~ spl22_142 ),
inference(resolution,[],[f1342,f1152]) ).
fof(f3691,plain,
( spl22_326
| ~ spl22_132
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1369,f1341,f1242,f3689]) ).
fof(f1369,plain,
( ! [X0,X1] :
( sP0(X0,sK6(X1))
| ~ empty(relation_dom(X0))
| element(sK7(X0,sK6(X1)),X1)
| empty(X1) )
| ~ spl22_132
| ~ spl22_142 ),
inference(resolution,[],[f1342,f1243]) ).
fof(f3687,plain,
( spl22_325
| ~ spl22_129
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1366,f1341,f1155,f3685]) ).
fof(f1366,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| ~ empty(relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X1) )
| ~ spl22_129
| ~ spl22_142 ),
inference(resolution,[],[f1342,f1156]) ).
fof(f3683,plain,
( spl22_324
| ~ spl22_130
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1365,f1341,f1159,f3681]) ).
fof(f1365,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_intersection2(X1,X2))
| ~ empty(relation_dom(X0))
| in(sK7(X0,set_intersection2(X1,X2)),X2) )
| ~ spl22_130
| ~ spl22_142 ),
inference(resolution,[],[f1342,f1160]) ).
fof(f3679,plain,
( spl22_323
| ~ spl22_69
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1255,f1242,f628,f3677]) ).
fof(f1255,plain,
( ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| empty(X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK6(X2)) )
| ~ spl22_69
| ~ spl22_132 ),
inference(resolution,[],[f1243,f629]) ).
fof(f3675,plain,
( spl22_322
| ~ spl22_73
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1119,f1110,f652,f3673]) ).
fof(f1119,plain,
( ! [X0,X1] :
( ~ empty(X0)
| in(sK8(X1,sK10(powerset(X0))),relation_dom(X1))
| sP0(X1,sK10(powerset(X0))) )
| ~ spl22_73
| ~ spl22_121 ),
inference(resolution,[],[f1111,f653]) ).
fof(f3669,plain,
( spl22_321
| ~ spl22_2
| ~ spl22_1
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f3245,f2999,f224,f229,f3666]) ).
fof(f3245,plain,
( ~ function(sK5)
| sK5 = relation_dom_restriction(sK5,relation_dom(sK5))
| ~ spl22_1
| ~ spl22_278 ),
inference(resolution,[],[f3000,f226]) ).
fof(f3628,plain,
( spl22_320
| ~ spl22_45
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1567,f1535,f454,f3626]) ).
fof(f3626,plain,
( spl22_320
<=> ! [X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ in(relation_dom(X0),sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_320])]) ).
fof(f1567,plain,
( ! [X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ in(relation_dom(X0),sK8(X0,X1)) )
| ~ spl22_45
| ~ spl22_156 ),
inference(resolution,[],[f1536,f455]) ).
fof(f3624,plain,
( spl22_319
| ~ spl22_45
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1551,f1527,f454,f3622]) ).
fof(f3622,plain,
( spl22_319
<=> ! [X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_319])]) ).
fof(f1551,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) )
| ~ spl22_45
| ~ spl22_154 ),
inference(resolution,[],[f1528,f455]) ).
fof(f3620,plain,
( spl22_318
| ~ spl22_46
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1550,f1527,f458,f3618]) ).
fof(f1550,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) )
| ~ spl22_46
| ~ spl22_154 ),
inference(resolution,[],[f1528,f459]) ).
fof(f3616,plain,
( spl22_317
| ~ spl22_119
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1433,f1393,f1064,f3614]) ).
fof(f1433,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK10(apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| empty(apply(X0,X1)) )
| ~ spl22_119
| ~ spl22_147 ),
inference(resolution,[],[f1394,f1065]) ).
fof(f3612,plain,
( spl22_316
| ~ spl22_69
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1224,f1159,f628,f3610]) ).
fof(f1224,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X3,X2)) )
| ~ spl22_69
| ~ spl22_130 ),
inference(resolution,[],[f1160,f629]) ).
fof(f3608,plain,
( spl22_315
| ~ spl22_69
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1210,f1155,f628,f3606]) ).
fof(f1210,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X2,X3)) )
| ~ spl22_69
| ~ spl22_129 ),
inference(resolution,[],[f1156,f629]) ).
fof(f3604,plain,
( spl22_314
| ~ spl22_69
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1202,f1151,f628,f3602]) ).
fof(f1202,plain,
( ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK10(powerset(X2))) )
| ~ spl22_69
| ~ spl22_128 ),
inference(resolution,[],[f1152,f629]) ).
fof(f3553,plain,
( spl22_313
| ~ spl22_58
| ~ spl22_171 ),
inference(avatar_split_clause,[],[f1728,f1720,f553,f3551]) ).
fof(f1720,plain,
( spl22_171
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_171])]) ).
fof(f1728,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ spl22_58
| ~ spl22_171 ),
inference(duplicate_literal_removal,[],[f1727]) ).
fof(f1727,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_171 ),
inference(resolution,[],[f1721,f554]) ).
fof(f1721,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ spl22_171 ),
inference(avatar_component_clause,[],[f1720]) ).
fof(f3549,plain,
( spl22_312
| ~ spl22_31
| ~ spl22_92
| ~ spl22_167 ),
inference(avatar_split_clause,[],[f1710,f1616,f798,f378,f3547]) ).
fof(f3547,plain,
( spl22_312
<=> ! [X0] :
( relation_dom_restriction(X0,sK15) = X0
| relation_dom(X0) != sK15
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_312])]) ).
fof(f1710,plain,
( ! [X0] :
( relation_dom_restriction(X0,sK15) = X0
| relation_dom(X0) != sK15
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_31
| ~ spl22_92
| ~ spl22_167 ),
inference(forward_demodulation,[],[f1709,f800]) ).
fof(f1709,plain,
( ! [X0] :
( relation_dom(X0) != sK15
| relation_dom_restriction(X0,empty_set) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_31
| ~ spl22_92
| ~ spl22_167 ),
inference(forward_demodulation,[],[f1704,f800]) ).
fof(f1704,plain,
( ! [X0] :
( relation_dom(X0) != empty_set
| relation_dom_restriction(X0,empty_set) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_31
| ~ spl22_167 ),
inference(superposition,[],[f1617,f379]) ).
fof(f3545,plain,
( spl22_311
| ~ spl22_133
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1563,f1535,f1246,f3543]) ).
fof(f1563,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_156 ),
inference(resolution,[],[f1536,f1247]) ).
fof(f3540,plain,
( spl22_310
| ~ spl22_73
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1267,f1246,f652,f3538]) ).
fof(f1267,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| in(sK7(X0,X2),X2)
| sP0(X0,X2) )
| ~ spl22_73
| ~ spl22_133 ),
inference(resolution,[],[f1247,f653]) ).
fof(f3536,plain,
( spl22_309
| ~ spl22_69
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1263,f1246,f628,f3534]) ).
fof(f1263,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,relation_dom(X0)) )
| ~ spl22_69
| ~ spl22_133 ),
inference(resolution,[],[f1247,f629]) ).
fof(f3502,plain,
( ~ spl22_308
| ~ spl22_45
| ~ spl22_279 ),
inference(avatar_split_clause,[],[f3407,f3217,f454,f3499]) ).
fof(f3499,plain,
( spl22_308
<=> in(relation_dom(sK5),sK8(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_308])]) ).
fof(f3217,plain,
( spl22_279
<=> in(sK8(sK5,sK15),relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_279])]) ).
fof(f3407,plain,
( ~ in(relation_dom(sK5),sK8(sK5,sK15))
| ~ spl22_45
| ~ spl22_279 ),
inference(resolution,[],[f3218,f455]) ).
fof(f3218,plain,
( in(sK8(sK5,sK15),relation_dom(sK5))
| ~ spl22_279 ),
inference(avatar_component_clause,[],[f3217]) ).
fof(f3461,plain,
( spl22_307
| ~ spl22_133
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1500,f1409,f1246,f3459]) ).
fof(f1500,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| ~ empty(X0)
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_151 ),
inference(resolution,[],[f1410,f1247]) ).
fof(f3457,plain,
( spl22_306
| ~ spl22_45
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1496,f1409,f454,f3455]) ).
fof(f3455,plain,
( spl22_306
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_306])]) ).
fof(f1496,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_151 ),
inference(resolution,[],[f1410,f455]) ).
fof(f3453,plain,
( spl22_305
| ~ spl22_46
| ~ spl22_279 ),
inference(avatar_split_clause,[],[f3406,f3217,f458,f3450]) ).
fof(f3450,plain,
( spl22_305
<=> element(sK8(sK5,sK15),relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_305])]) ).
fof(f3406,plain,
( element(sK8(sK5,sK15),relation_dom(sK5))
| ~ spl22_46
| ~ spl22_279 ),
inference(resolution,[],[f3218,f459]) ).
fof(f3448,plain,
( spl22_304
| ~ spl22_46
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1495,f1409,f458,f3446]) ).
fof(f1495,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X0)
| element(sK13(X0,X1,X2),X2) )
| ~ spl22_46
| ~ spl22_151 ),
inference(resolution,[],[f1410,f459]) ).
fof(f3444,plain,
( spl22_303
| ~ spl22_133
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1485,f1405,f1246,f3442]) ).
fof(f1485,plain,
( ! [X2,X3,X0,X1] :
( sP2(relation_dom(X0),X1,X2)
| ~ empty(X2)
| ~ sP0(X0,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_150 ),
inference(resolution,[],[f1406,f1247]) ).
fof(f3440,plain,
( spl22_302
| ~ spl22_45
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1481,f1405,f454,f3438]) ).
fof(f3438,plain,
( spl22_302
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_302])]) ).
fof(f1481,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_150 ),
inference(resolution,[],[f1406,f455]) ).
fof(f3436,plain,
( spl22_301
| ~ spl22_46
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1480,f1405,f458,f3434]) ).
fof(f1480,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| element(sK13(X0,X1,X2),X0) )
| ~ spl22_46
| ~ spl22_150 ),
inference(resolution,[],[f1406,f459]) ).
fof(f3432,plain,
( spl22_300
| ~ spl22_133
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1470,f1401,f1246,f3430]) ).
fof(f1470,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,relation_dom(X2))
| ~ empty(X1)
| ~ sP0(X2,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_149 ),
inference(resolution,[],[f1402,f1247]) ).
fof(f3428,plain,
( spl22_299
| ~ spl22_45
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1466,f1401,f454,f3426]) ).
fof(f3426,plain,
( spl22_299
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_299])]) ).
fof(f1466,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_149 ),
inference(resolution,[],[f1402,f455]) ).
fof(f3424,plain,
( spl22_298
| ~ spl22_46
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1465,f1401,f458,f3422]) ).
fof(f1465,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X1)
| element(sK13(X0,X1,X2),X2) )
| ~ spl22_46
| ~ spl22_149 ),
inference(resolution,[],[f1402,f459]) ).
fof(f3420,plain,
( spl22_297
| ~ spl22_133
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1455,f1397,f1246,f3418]) ).
fof(f1455,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,relation_dom(X1),X2)
| ~ empty(X2)
| ~ sP0(X1,X3)
| ~ empty(X3) )
| ~ spl22_133
| ~ spl22_148 ),
inference(resolution,[],[f1398,f1247]) ).
fof(f3416,plain,
( spl22_296
| ~ spl22_45
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1451,f1397,f454,f3414]) ).
fof(f3414,plain,
( spl22_296
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_296])]) ).
fof(f1451,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_148 ),
inference(resolution,[],[f1398,f455]) ).
fof(f3412,plain,
( spl22_295
| ~ spl22_46
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1450,f1397,f458,f3410]) ).
fof(f1450,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| element(sK13(X0,X1,X2),X1) )
| ~ spl22_46
| ~ spl22_148 ),
inference(resolution,[],[f1398,f459]) ).
fof(f3400,plain,
( spl22_294
| ~ spl22_45
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1423,f1384,f454,f3398]) ).
fof(f3398,plain,
( spl22_294
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ in(relation_dom(X1),sK9(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_294])]) ).
fof(f1423,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ in(relation_dom(X1),sK9(X1,X0)) )
| ~ spl22_45
| ~ spl22_145 ),
inference(resolution,[],[f1385,f455]) ).
fof(f3396,plain,
( spl22_293
| ~ spl22_46
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1422,f1384,f458,f3394]) ).
fof(f3394,plain,
( spl22_293
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| element(sK9(X1,X0),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_293])]) ).
fof(f1422,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| element(sK9(X1,X0),relation_dom(X1)) )
| ~ spl22_46
| ~ spl22_145 ),
inference(resolution,[],[f1385,f459]) ).
fof(f3392,plain,
( spl22_292
| ~ spl22_133
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1368,f1341,f1246,f3390]) ).
fof(f1368,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_dom(X1))
| ~ empty(relation_dom(X0))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_142 ),
inference(resolution,[],[f1342,f1247]) ).
fof(f3388,plain,
( spl22_291
| ~ spl22_77
| ~ spl22_115 ),
inference(avatar_split_clause,[],[f1027,f959,f698,f3386]) ).
fof(f1027,plain,
( ! [X0] :
( sK7(X0,sK15) = apply(X0,sK8(X0,sK15))
| sP0(X0,sK15) )
| ~ spl22_77
| ~ spl22_115 ),
inference(resolution,[],[f960,f699]) ).
fof(f3331,plain,
( ~ spl22_10
| spl22_238
| ~ spl22_143
| spl22_279 ),
inference(avatar_split_clause,[],[f3281,f3217,f1345,f2685,f269]) ).
fof(f2685,plain,
( spl22_238
<=> sP0(sK5,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_238])]) ).
fof(f3281,plain,
( sP0(sK5,sK15)
| ~ empty(sK15)
| ~ spl22_143
| spl22_279 ),
inference(resolution,[],[f3219,f1346]) ).
fof(f3219,plain,
( ~ in(sK8(sK5,sK15),relation_dom(sK5))
| spl22_279 ),
inference(avatar_component_clause,[],[f3217]) ).
fof(f3306,plain,
( spl22_290
| ~ spl22_133
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1419,f1384,f1246,f3304]) ).
fof(f1419,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_145 ),
inference(resolution,[],[f1385,f1247]) ).
fof(f3302,plain,
( spl22_289
| ~ spl22_45
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1378,f1345,f454,f3300]) ).
fof(f3300,plain,
( spl22_289
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ in(relation_dom(X0),sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_289])]) ).
fof(f1378,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ in(relation_dom(X0),sK8(X0,X1)) )
| ~ spl22_45
| ~ spl22_143 ),
inference(resolution,[],[f1346,f455]) ).
fof(f3298,plain,
( spl22_288
| ~ spl22_46
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1377,f1345,f458,f3296]) ).
fof(f3296,plain,
( spl22_288
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| element(sK8(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_288])]) ).
fof(f1377,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| element(sK8(X0,X1),relation_dom(X0)) )
| ~ spl22_46
| ~ spl22_143 ),
inference(resolution,[],[f1346,f459]) ).
fof(f3294,plain,
( spl22_287
| ~ spl22_45
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1364,f1341,f454,f3292]) ).
fof(f3292,plain,
( spl22_287
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| ~ in(X1,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_287])]) ).
fof(f1364,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| ~ in(X1,sK7(X0,X1)) )
| ~ spl22_45
| ~ spl22_142 ),
inference(resolution,[],[f1342,f455]) ).
fof(f3290,plain,
( spl22_286
| ~ spl22_46
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1363,f1341,f458,f3288]) ).
fof(f1363,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| element(sK7(X0,X1),X1) )
| ~ spl22_46
| ~ spl22_142 ),
inference(resolution,[],[f1342,f459]) ).
fof(f3286,plain,
( spl22_285
| ~ spl22_45
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1353,f1337,f454,f3284]) ).
fof(f3284,plain,
( spl22_285
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ in(set_intersection2(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_285])]) ).
fof(f1353,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ in(set_intersection2(X1,X2),X0) )
| ~ spl22_45
| ~ spl22_141 ),
inference(resolution,[],[f1338,f455]) ).
fof(f3278,plain,
( spl22_284
| ~ spl22_46
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1352,f1337,f458,f3276]) ).
fof(f3276,plain,
( spl22_284
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| element(X0,set_intersection2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_284])]) ).
fof(f1352,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| element(X0,set_intersection2(X1,X2)) )
| ~ spl22_46
| ~ spl22_141 ),
inference(resolution,[],[f1338,f459]) ).
fof(f3274,plain,
( spl22_283
| ~ spl22_133
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1330,f1290,f1246,f3272]) ).
fof(f1330,plain,
( ! [X2,X0,X1] :
( sP2(relation_dom(X0),X1,relation_dom(X0))
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_139 ),
inference(resolution,[],[f1291,f1247]) ).
fof(f3270,plain,
( spl22_282
| ~ spl22_133
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1316,f1286,f1246,f3268]) ).
fof(f1316,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1),relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_138 ),
inference(resolution,[],[f1287,f1247]) ).
fof(f3266,plain,
( spl22_281
| ~ spl22_69
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1117,f1110,f628,f3264]) ).
fof(f1117,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,sK10(powerset(X0))) )
| ~ spl22_69
| ~ spl22_121 ),
inference(resolution,[],[f1111,f629]) ).
fof(f3223,plain,
( ~ spl22_279
| spl22_280
| ~ spl22_147
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f2102,f2002,f1393,f3221,f3217]) ).
fof(f2002,plain,
( spl22_189
<=> sK7(sK5,sK15) = apply(sK5,sK8(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_189])]) ).
fof(f2102,plain,
( ! [X0] :
( ~ in(X0,sK7(sK5,sK15))
| ~ sP0(sK5,X0)
| ~ in(sK8(sK5,sK15),relation_dom(sK5)) )
| ~ spl22_147
| ~ spl22_189 ),
inference(superposition,[],[f1394,f2004]) ).
fof(f2004,plain,
( sK7(sK5,sK15) = apply(sK5,sK8(sK5,sK15))
| ~ spl22_189 ),
inference(avatar_component_clause,[],[f2002]) ).
fof(f3001,plain,
( spl22_278
| ~ spl22_40
| ~ spl22_167 ),
inference(avatar_split_clause,[],[f1708,f1616,f415,f2999]) ).
fof(f1708,plain,
( ! [X0] :
( relation_dom_restriction(X0,relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_40
| ~ spl22_167 ),
inference(trivial_inequality_removal,[],[f1705]) ).
fof(f1705,plain,
( ! [X0] :
( relation_dom(X0) != relation_dom(X0)
| relation_dom_restriction(X0,relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_40
| ~ spl22_167 ),
inference(superposition,[],[f1617,f416]) ).
fof(f2997,plain,
( spl22_277
| ~ spl22_115
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1701,f1608,f959,f2995]) ).
fof(f1701,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK15),X0)
| sP2(X0,X1,sK15) )
| ~ spl22_115
| ~ spl22_165 ),
inference(resolution,[],[f1609,f960]) ).
fof(f2993,plain,
( spl22_276
| ~ spl22_115
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1676,f1600,f959,f2991]) ).
fof(f1676,plain,
( ! [X0,X1] :
( element(sK13(sK15,X0,X1),X1)
| sP2(sK15,X0,X1) )
| ~ spl22_115
| ~ spl22_163 ),
inference(resolution,[],[f1601,f960]) ).
fof(f2989,plain,
( spl22_275
| ~ spl22_115
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1656,f1587,f959,f2987]) ).
fof(f1656,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK15),X1)
| sP2(X0,X1,sK15) )
| ~ spl22_115
| ~ spl22_161 ),
inference(resolution,[],[f1588,f960]) ).
fof(f2985,plain,
( spl22_274
| ~ spl22_115
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1636,f1579,f959,f2983]) ).
fof(f1636,plain,
( ! [X0,X1] :
( element(sK13(X0,sK15,X1),X1)
| sP2(X0,sK15,X1) )
| ~ spl22_115
| ~ spl22_159 ),
inference(resolution,[],[f1580,f960]) ).
fof(f2981,plain,
( spl22_273
| ~ spl22_121
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1504,f1409,f1110,f2979]) ).
fof(f1504,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_151 ),
inference(resolution,[],[f1410,f1111]) ).
fof(f2977,plain,
( spl22_272
| ~ spl22_121
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1489,f1405,f1110,f2975]) ).
fof(f1489,plain,
( ! [X2,X0,X1] :
( sP2(sK10(powerset(X0)),X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_150 ),
inference(resolution,[],[f1406,f1111]) ).
fof(f2973,plain,
( spl22_271
| ~ spl22_121
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1474,f1401,f1110,f2971]) ).
fof(f1474,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,sK10(powerset(X2)))
| ~ empty(X1)
| ~ empty(X2) )
| ~ spl22_121
| ~ spl22_149 ),
inference(resolution,[],[f1402,f1111]) ).
fof(f2969,plain,
( spl22_270
| ~ spl22_111
| ~ spl22_205 ),
inference(avatar_split_clause,[],[f2229,f2217,f944,f2967]) ).
fof(f2967,plain,
( spl22_270
<=> ! [X0] :
( apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_270])]) ).
fof(f2217,plain,
( spl22_205
<=> ! [X0] :
( ~ function(relation_dom(X0))
| apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_205])]) ).
fof(f2229,plain,
( ! [X0] :
( apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_205 ),
inference(duplicate_literal_removal,[],[f2227]) ).
fof(f2227,plain,
( ! [X0] :
( apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_205 ),
inference(resolution,[],[f2218,f945]) ).
fof(f2218,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_205 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f2965,plain,
( spl22_269
| ~ spl22_121
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1459,f1397,f1110,f2963]) ).
fof(f1459,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(X1)),X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_148 ),
inference(resolution,[],[f1398,f1111]) ).
fof(f2961,plain,
( spl22_268
| ~ spl22_133
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1374,f1345,f1246,f2959]) ).
fof(f1374,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ sP0(X0,X2)
| ~ empty(X2) )
| ~ spl22_133
| ~ spl22_143 ),
inference(resolution,[],[f1346,f1247]) ).
fof(f2957,plain,
( spl22_267
| ~ spl22_121
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1371,f1341,f1110,f2955]) ).
fof(f1371,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| ~ empty(relation_dom(X0))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_142 ),
inference(resolution,[],[f1342,f1111]) ).
fof(f2953,plain,
( spl22_266
| ~ spl22_41
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1350,f1337,f419,f2951]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ empty(set_intersection2(X1,X2)) )
| ~ spl22_41
| ~ spl22_141 ),
inference(resolution,[],[f1338,f420]) ).
fof(f2949,plain,
( spl22_265
| ~ spl22_121
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1333,f1290,f1110,f2947]) ).
fof(f1333,plain,
( ! [X0,X1] :
( sP2(sK10(powerset(X0)),X1,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_121
| ~ spl22_139 ),
inference(resolution,[],[f1291,f1111]) ).
fof(f2945,plain,
( spl22_264
| ~ spl22_45
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1326,f1290,f454,f2943]) ).
fof(f2943,plain,
( spl22_264
<=> ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(X0,sK13(X0,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_264])]) ).
fof(f1326,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(X0,sK13(X0,X1,X0)) )
| ~ spl22_45
| ~ spl22_139 ),
inference(resolution,[],[f1291,f455]) ).
fof(f2941,plain,
( spl22_263
| ~ spl22_46
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1325,f1290,f458,f2939]) ).
fof(f1325,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| element(sK13(X0,X1,X0),X0) )
| ~ spl22_46
| ~ spl22_139 ),
inference(resolution,[],[f1291,f459]) ).
fof(f2937,plain,
( spl22_262
| ~ spl22_121
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1319,f1286,f1110,f2935]) ).
fof(f1319,plain,
( ! [X0,X1] :
( sP2(X0,sK10(powerset(X1)),sK10(powerset(X1)))
| ~ empty(X1) )
| ~ spl22_121
| ~ spl22_138 ),
inference(resolution,[],[f1287,f1111]) ).
fof(f2933,plain,
( spl22_261
| ~ spl22_45
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1312,f1286,f454,f2931]) ).
fof(f2931,plain,
( spl22_261
<=> ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(X1,sK13(X0,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_261])]) ).
fof(f1312,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(X1,sK13(X0,X1,X1)) )
| ~ spl22_45
| ~ spl22_138 ),
inference(resolution,[],[f1287,f455]) ).
fof(f2929,plain,
( spl22_260
| ~ spl22_46
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1311,f1286,f458,f2927]) ).
fof(f1311,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| element(sK13(X0,X1,X1),X1) )
| ~ spl22_46
| ~ spl22_138 ),
inference(resolution,[],[f1287,f459]) ).
fof(f2925,plain,
( spl22_259
| ~ spl22_110
| ~ spl22_204 ),
inference(avatar_split_clause,[],[f2226,f2213,f940,f2923]) ).
fof(f2923,plain,
( spl22_259
<=> ! [X0] :
( apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_259])]) ).
fof(f940,plain,
( spl22_110
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_110])]) ).
fof(f2213,plain,
( spl22_204
<=> ! [X0] :
( ~ function(relation_rng(X0))
| apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_204])]) ).
fof(f2226,plain,
( ! [X0] :
( apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_204 ),
inference(duplicate_literal_removal,[],[f2224]) ).
fof(f2224,plain,
( ! [X0] :
( apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_204 ),
inference(resolution,[],[f2214,f941]) ).
fof(f941,plain,
( ! [X0] :
( function(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_110 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f2214,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_204 ),
inference(avatar_component_clause,[],[f2213]) ).
fof(f2921,plain,
( spl22_258
| ~ spl22_45
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1303,f1282,f454,f2919]) ).
fof(f2919,plain,
( spl22_258
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_258])]) ).
fof(f1303,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK6(X0)) )
| ~ spl22_45
| ~ spl22_137 ),
inference(resolution,[],[f1283,f455]) ).
fof(f2917,plain,
( spl22_257
| ~ spl22_45
| ~ spl22_136 ),
inference(avatar_split_clause,[],[f1298,f1278,f454,f2915]) ).
fof(f1298,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl22_45
| ~ spl22_136 ),
inference(resolution,[],[f1279,f455]) ).
fof(f2913,plain,
( spl22_256
| ~ spl22_119
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1258,f1242,f1064,f2911]) ).
fof(f1258,plain,
( ! [X0] :
( element(sK10(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) )
| ~ spl22_119
| ~ spl22_132 ),
inference(resolution,[],[f1243,f1065]) ).
fof(f2909,plain,
( spl22_255
| ~ spl22_119
| ~ spl22_130 ),
inference(avatar_split_clause,[],[f1227,f1159,f1064,f2907]) ).
fof(f1227,plain,
( ! [X0,X1] :
( in(sK10(set_intersection2(X0,X1)),X1)
| empty(set_intersection2(X0,X1)) )
| ~ spl22_119
| ~ spl22_130 ),
inference(resolution,[],[f1160,f1065]) ).
fof(f2905,plain,
( spl22_254
| ~ spl22_119
| ~ spl22_129 ),
inference(avatar_split_clause,[],[f1213,f1155,f1064,f2903]) ).
fof(f1213,plain,
( ! [X0,X1] :
( in(sK10(set_intersection2(X0,X1)),X0)
| empty(set_intersection2(X0,X1)) )
| ~ spl22_119
| ~ spl22_129 ),
inference(resolution,[],[f1156,f1065]) ).
fof(f2901,plain,
( spl22_253
| ~ spl22_119
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1205,f1151,f1064,f2899]) ).
fof(f1205,plain,
( ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) )
| ~ spl22_119
| ~ spl22_128 ),
inference(resolution,[],[f1152,f1065]) ).
fof(f2897,plain,
( spl22_252
| ~ spl22_76
| ~ spl22_115 ),
inference(avatar_split_clause,[],[f1032,f959,f670,f2895]) ).
fof(f1032,plain,
( ! [X0,X1] :
( in(sK13(sK15,X0,X1),X1)
| sP2(sK15,X0,X1) )
| ~ spl22_76
| ~ spl22_115 ),
inference(resolution,[],[f960,f671]) ).
fof(f2893,plain,
( spl22_251
| ~ spl22_75
| ~ spl22_115 ),
inference(avatar_split_clause,[],[f1031,f959,f666,f2891]) ).
fof(f1031,plain,
( ! [X0,X1] :
( in(sK13(X0,sK15,X1),X1)
| sP2(X0,sK15,X1) )
| ~ spl22_75
| ~ spl22_115 ),
inference(resolution,[],[f960,f667]) ).
fof(f2889,plain,
( spl22_250
| ~ spl22_75
| ~ spl22_115 ),
inference(avatar_split_clause,[],[f1030,f959,f666,f2887]) ).
fof(f1030,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,sK15),X1)
| sP2(X0,X1,sK15) )
| ~ spl22_75
| ~ spl22_115 ),
inference(resolution,[],[f960,f667]) ).
fof(f2885,plain,
( spl22_249
| ~ spl22_76
| ~ spl22_115 ),
inference(avatar_split_clause,[],[f1029,f959,f670,f2883]) ).
fof(f1029,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,sK15),X0)
| sP2(X0,X1,sK15) )
| ~ spl22_76
| ~ spl22_115 ),
inference(resolution,[],[f960,f671]) ).
fof(f2745,plain,
( spl22_248
| ~ spl22_41
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1420,f1384,f419,f2743]) ).
fof(f1420,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl22_41
| ~ spl22_145 ),
inference(resolution,[],[f1385,f420]) ).
fof(f2741,plain,
( spl22_247
| ~ spl22_36
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1186,f1143,f398,f2739]) ).
fof(f1186,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_126 ),
inference(resolution,[],[f1144,f399]) ).
fof(f2737,plain,
( spl22_246
| ~ spl22_34
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1185,f1143,f390,f2735]) ).
fof(f1185,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl22_34
| ~ spl22_126 ),
inference(resolution,[],[f1144,f391]) ).
fof(f2733,plain,
( spl22_245
| ~ spl22_36
| ~ spl22_125 ),
inference(avatar_split_clause,[],[f1170,f1139,f398,f2731]) ).
fof(f1170,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_125 ),
inference(resolution,[],[f1140,f399]) ).
fof(f2729,plain,
( spl22_244
| ~ spl22_34
| ~ spl22_125 ),
inference(avatar_split_clause,[],[f1169,f1139,f390,f2727]) ).
fof(f1169,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl22_34
| ~ spl22_125 ),
inference(resolution,[],[f1140,f391]) ).
fof(f2708,plain,
( spl22_243
| ~ spl22_41
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1478,f1405,f419,f2706]) ).
fof(f1478,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_150 ),
inference(resolution,[],[f1406,f420]) ).
fof(f2704,plain,
( spl22_242
| ~ spl22_41
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1448,f1397,f419,f2702]) ).
fof(f1448,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_148 ),
inference(resolution,[],[f1398,f420]) ).
fof(f2700,plain,
( spl22_241
| ~ spl22_41
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1361,f1341,f419,f2698]) ).
fof(f1361,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_142 ),
inference(resolution,[],[f1342,f420]) ).
fof(f2696,plain,
( spl22_240
| ~ spl22_58
| ~ spl22_135 ),
inference(avatar_split_clause,[],[f1294,f1274,f553,f2694]) ).
fof(f1274,plain,
( spl22_135
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| sP1(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_135])]) ).
fof(f1294,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1))
| ~ function(X0) )
| ~ spl22_58
| ~ spl22_135 ),
inference(duplicate_literal_removal,[],[f1293]) ).
fof(f1293,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_135 ),
inference(resolution,[],[f1275,f554]) ).
fof(f1275,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1)) )
| ~ spl22_135 ),
inference(avatar_component_clause,[],[f1274]) ).
fof(f2692,plain,
( spl22_239
| ~ spl22_119
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1268,f1246,f1064,f2690]) ).
fof(f1268,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| empty(relation_dom(X0)) )
| ~ spl22_119
| ~ spl22_133 ),
inference(resolution,[],[f1247,f1065]) ).
fof(f2688,plain,
( ~ spl22_238
| ~ spl22_4
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2579,f2559,f239,f2685]) ).
fof(f2579,plain,
( ~ sP0(sK5,sK15)
| ~ spl22_4
| ~ spl22_233 ),
inference(resolution,[],[f2560,f241]) ).
fof(f2577,plain,
( spl22_237
| ~ spl22_36
| ~ spl22_117 ),
inference(avatar_split_clause,[],[f1079,f1053,f398,f2575]) ).
fof(f1079,plain,
( ! [X0] :
( sK15 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_117 ),
inference(resolution,[],[f1054,f399]) ).
fof(f2573,plain,
( spl22_236
| ~ spl22_34
| ~ spl22_117 ),
inference(avatar_split_clause,[],[f1078,f1053,f390,f2571]) ).
fof(f1078,plain,
( ! [X0] :
( sK15 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_117 ),
inference(resolution,[],[f1054,f391]) ).
fof(f2569,plain,
( spl22_235
| ~ spl22_36
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1068,f1049,f398,f2567]) ).
fof(f1068,plain,
( ! [X0] :
( sK15 = relation_rng(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_116 ),
inference(resolution,[],[f1050,f399]) ).
fof(f2565,plain,
( spl22_234
| ~ spl22_34
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1067,f1049,f390,f2563]) ).
fof(f1067,plain,
( ! [X0] :
( sK15 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_116 ),
inference(resolution,[],[f1050,f391]) ).
fof(f2561,plain,
( spl22_233
| ~ spl22_69
| ~ spl22_115 ),
inference(avatar_split_clause,[],[f1026,f959,f628,f2559]) ).
fof(f1026,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,sK15) )
| ~ spl22_69
| ~ spl22_115 ),
inference(resolution,[],[f960,f629]) ).
fof(f2533,plain,
( ~ spl22_2
| spl22_232
| ~ spl22_1
| ~ spl22_183 ),
inference(avatar_split_clause,[],[f1944,f1849,f224,f2531,f229]) ).
fof(f1944,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ function(sK5)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_1
| ~ spl22_183 ),
inference(resolution,[],[f1850,f226]) ).
fof(f2512,plain,
( ~ spl22_2
| spl22_231
| ~ spl22_1
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1925,f1845,f224,f2510,f229]) ).
fof(f1925,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ function(sK5)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_1
| ~ spl22_182 ),
inference(resolution,[],[f1846,f226]) ).
fof(f2491,plain,
( ~ spl22_2
| spl22_230
| ~ spl22_1
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1895,f1841,f224,f2489,f229]) ).
fof(f1895,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ function(sK5)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_1
| ~ spl22_181 ),
inference(resolution,[],[f1842,f226]) ).
fof(f2470,plain,
( ~ spl22_2
| spl22_229
| ~ spl22_1
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1876,f1837,f224,f2468,f229]) ).
fof(f1876,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ function(sK5)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_1
| ~ spl22_180 ),
inference(resolution,[],[f1838,f226]) ).
fof(f2449,plain,
( ~ spl22_2
| spl22_228
| ~ spl22_1
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1857,f1833,f224,f2447,f229]) ).
fof(f1857,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(sK5,X2),sK13(X0,X1,X2)) = apply(sK5,sK13(X0,X1,X2))
| ~ function(sK5)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_1
| ~ spl22_179 ),
inference(resolution,[],[f1834,f226]) ).
fof(f2445,plain,
( spl22_227
| ~ spl22_36
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1910,f1805,f398,f2443]) ).
fof(f2443,plain,
( spl22_227
<=> ! [X0] :
( sK7(sK5,relation_dom(X0)) = apply(sK5,sK8(sK5,relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_227])]) ).
fof(f1805,plain,
( spl22_178
<=> ! [X0] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_178])]) ).
fof(f1910,plain,
( ! [X0] :
( sK7(sK5,relation_dom(X0)) = apply(sK5,sK8(sK5,relation_dom(X0)))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_178 ),
inference(resolution,[],[f1806,f399]) ).
fof(f1806,plain,
( ! [X0] :
( ~ empty(X0)
| sK7(sK5,X0) = apply(sK5,sK8(sK5,X0)) )
| ~ spl22_178 ),
inference(avatar_component_clause,[],[f1805]) ).
fof(f2401,plain,
( spl22_226
| ~ spl22_115
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1505,f1409,f959,f2399]) ).
fof(f1505,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ empty(X0) )
| ~ spl22_115
| ~ spl22_151 ),
inference(resolution,[],[f1410,f960]) ).
fof(f2397,plain,
( spl22_225
| ~ spl22_34
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1909,f1805,f390,f2395]) ).
fof(f2395,plain,
( spl22_225
<=> ! [X0] :
( sK7(sK5,relation_rng(X0)) = apply(sK5,sK8(sK5,relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_225])]) ).
fof(f1909,plain,
( ! [X0] :
( sK7(sK5,relation_rng(X0)) = apply(sK5,sK8(sK5,relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_178 ),
inference(resolution,[],[f1806,f391]) ).
fof(f2393,plain,
( spl22_224
| ~ spl22_115
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1490,f1405,f959,f2391]) ).
fof(f2391,plain,
( spl22_224
<=> ! [X0,X1] :
( sP2(sK15,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_224])]) ).
fof(f1490,plain,
( ! [X0,X1] :
( sP2(sK15,X0,X1)
| ~ empty(X1) )
| ~ spl22_115
| ~ spl22_150 ),
inference(resolution,[],[f1406,f960]) ).
fof(f2389,plain,
( spl22_223
| ~ spl22_115
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1475,f1401,f959,f2387]) ).
fof(f1475,plain,
( ! [X0,X1] :
( sP2(X0,X1,sK15)
| ~ empty(X1) )
| ~ spl22_115
| ~ spl22_149 ),
inference(resolution,[],[f1402,f960]) ).
fof(f2385,plain,
( spl22_222
| ~ spl22_115
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1460,f1397,f959,f2383]) ).
fof(f2383,plain,
( spl22_222
<=> ! [X0,X1] :
( sP2(X0,sK15,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_222])]) ).
fof(f1460,plain,
( ! [X0,X1] :
( sP2(X0,sK15,X1)
| ~ empty(X1) )
| ~ spl22_115
| ~ spl22_148 ),
inference(resolution,[],[f1398,f960]) ).
fof(f2381,plain,
( spl22_221
| ~ spl22_115
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1372,f1341,f959,f2379]) ).
fof(f1372,plain,
( ! [X0] :
( sP0(X0,sK15)
| ~ empty(relation_dom(X0)) )
| ~ spl22_115
| ~ spl22_142 ),
inference(resolution,[],[f1342,f960]) ).
fof(f2377,plain,
( spl22_220
| ~ spl22_41
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1323,f1290,f419,f2375]) ).
fof(f1323,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_139 ),
inference(resolution,[],[f1291,f420]) ).
fof(f2373,plain,
( spl22_219
| ~ spl22_41
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1309,f1286,f419,f2371]) ).
fof(f1309,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_138 ),
inference(resolution,[],[f1287,f420]) ).
fof(f2369,plain,
( spl22_218
| ~ spl22_119
| ~ spl22_121 ),
inference(avatar_split_clause,[],[f1120,f1110,f1064,f2367]) ).
fof(f1120,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(X0))) )
| ~ spl22_119
| ~ spl22_121 ),
inference(resolution,[],[f1111,f1065]) ).
fof(f2365,plain,
( spl22_217
| ~ spl22_45
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f1102,f1064,f454,f2363]) ).
fof(f2363,plain,
( spl22_217
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK10(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_217])]) ).
fof(f1102,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK10(X0)) )
| ~ spl22_45
| ~ spl22_119 ),
inference(resolution,[],[f1065,f455]) ).
fof(f2346,plain,
( spl22_216
| ~ spl22_2
| ~ spl22_1
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1813,f1778,f224,f229,f2344]) ).
fof(f1813,plain,
( ! [X0,X1] :
( ~ function(sK5)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_1
| ~ spl22_176 ),
inference(resolution,[],[f1779,f226]) ).
fof(f2318,plain,
( spl22_215
| ~ spl22_2
| ~ spl22_1
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1790,f1774,f224,f229,f2316]) ).
fof(f1790,plain,
( ! [X0,X1] :
( ~ function(sK5)
| apply(relation_dom_restriction(sK5,X0),sK7(X1,X0)) = apply(sK5,sK7(X1,X0))
| in(sK8(X1,X0),relation_dom(X1))
| sP0(X1,X0) )
| ~ spl22_1
| ~ spl22_175 ),
inference(resolution,[],[f1775,f226]) ).
fof(f2307,plain,
( spl22_214
| ~ spl22_59
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f854,f846,f557,f2305]) ).
fof(f2305,plain,
( spl22_214
<=> ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(set_intersection2(X0,X1),sK4) = apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_214])]) ).
fof(f846,plain,
( spl22_96
<=> ! [X0] :
( apply(X0,sK4) = apply(relation_dom_restriction(X0,relation_dom(sK5)),sK4)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_96])]) ).
fof(f854,plain,
( ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(set_intersection2(X0,X1),sK4) = apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_96 ),
inference(resolution,[],[f847,f558]) ).
fof(f847,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| apply(X0,sK4) = apply(relation_dom_restriction(X0,relation_dom(sK5)),sK4) )
| ~ spl22_96 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f2296,plain,
( spl22_213
| ~ spl22_59
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f826,f823,f557,f2294]) ).
fof(f2294,plain,
( spl22_213
<=> ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),sK3),sK4) = apply(set_intersection2(X0,X1),sK4)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_213])]) ).
fof(f823,plain,
( spl22_95
<=> ! [X0] :
( apply(relation_dom_restriction(X0,sK3),sK4) = apply(X0,sK4)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_95])]) ).
fof(f826,plain,
( ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),sK3),sK4) = apply(set_intersection2(X0,X1),sK4)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_95 ),
inference(resolution,[],[f824,f558]) ).
fof(f824,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| apply(relation_dom_restriction(X0,sK3),sK4) = apply(X0,sK4) )
| ~ spl22_95 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f2276,plain,
( spl22_212
| ~ spl22_111
| ~ spl22_124 ),
inference(avatar_split_clause,[],[f1165,f1135,f944,f2274]) ).
fof(f1135,plain,
( spl22_124
<=> ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_124])]) ).
fof(f1165,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_124 ),
inference(duplicate_literal_removal,[],[f1164]) ).
fof(f1164,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_124 ),
inference(resolution,[],[f1136,f945]) ).
fof(f1136,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_124 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f2256,plain,
( spl22_211
| ~ spl22_110
| ~ spl22_123 ),
inference(avatar_split_clause,[],[f1163,f1131,f940,f2254]) ).
fof(f2254,plain,
( spl22_211
<=> ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_211])]) ).
fof(f1131,plain,
( spl22_123
<=> ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_123])]) ).
fof(f1163,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_123 ),
inference(duplicate_literal_removal,[],[f1162]) ).
fof(f1162,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_123 ),
inference(resolution,[],[f1132,f941]) ).
fof(f1132,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_123 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f2252,plain,
( spl22_210
| ~ spl22_31
| ~ spl22_92 ),
inference(avatar_split_clause,[],[f813,f798,f378,f2250]) ).
fof(f2250,plain,
( spl22_210
<=> ! [X0] : sK15 = set_intersection2(X0,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_210])]) ).
fof(f813,plain,
( ! [X0] : sK15 = set_intersection2(X0,sK15)
| ~ spl22_31
| ~ spl22_92 ),
inference(superposition,[],[f379,f800]) ).
fof(f2243,plain,
( spl22_209
| ~ spl22_4
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1743,f1739,f239,f2241]) ).
fof(f1743,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(relation_dom_restriction(X0,X1),apply(sK5,sK4)) = apply(X0,apply(sK5,sK4))
| ~ sP0(sK5,X1) )
| ~ spl22_4
| ~ spl22_173 ),
inference(resolution,[],[f1740,f241]) ).
fof(f2239,plain,
( spl22_208
| ~ spl22_44
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f857,f846,f450,f2237]) ).
fof(f857,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_96 ),
inference(resolution,[],[f847,f451]) ).
fof(f2233,plain,
( spl22_207
| ~ spl22_44
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f829,f823,f450,f2231]) ).
fof(f829,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_95 ),
inference(resolution,[],[f824,f451]) ).
fof(f2223,plain,
( spl22_206
| ~ spl22_111
| ~ spl22_198 ),
inference(avatar_split_clause,[],[f2147,f2141,f944,f2221]) ).
fof(f2221,plain,
( spl22_206
<=> ! [X0] :
( apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_206])]) ).
fof(f2141,plain,
( spl22_198
<=> ! [X0] :
( ~ function(relation_dom(X0))
| apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_198])]) ).
fof(f2147,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_198 ),
inference(duplicate_literal_removal,[],[f2146]) ).
fof(f2146,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_198 ),
inference(resolution,[],[f2142,f945]) ).
fof(f2142,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0) )
| ~ spl22_198 ),
inference(avatar_component_clause,[],[f2141]) ).
fof(f2219,plain,
( spl22_205
| ~ spl22_37
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f856,f846,f402,f2217]) ).
fof(f856,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_37
| ~ spl22_96 ),
inference(resolution,[],[f847,f403]) ).
fof(f2215,plain,
( spl22_204
| ~ spl22_35
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f855,f846,f394,f2213]) ).
fof(f855,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_96 ),
inference(resolution,[],[f847,f395]) ).
fof(f2169,plain,
( spl22_203
| ~ spl22_6
| ~ spl22_92
| ~ spl22_117 ),
inference(avatar_split_clause,[],[f1085,f1053,f798,f249,f2166]) ).
fof(f249,plain,
( spl22_6
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_6])]) ).
fof(f1085,plain,
( sK15 = relation_dom(sK15)
| ~ spl22_6
| ~ spl22_92
| ~ spl22_117 ),
inference(forward_demodulation,[],[f1080,f800]) ).
fof(f1080,plain,
( sK15 = relation_dom(empty_set)
| ~ spl22_6
| ~ spl22_117 ),
inference(resolution,[],[f1054,f251]) ).
fof(f251,plain,
( empty(empty_set)
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f2164,plain,
( spl22_202
| ~ spl22_6
| ~ spl22_92
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1074,f1049,f798,f249,f2161]) ).
fof(f1074,plain,
( sK15 = relation_rng(sK15)
| ~ spl22_6
| ~ spl22_92
| ~ spl22_116 ),
inference(forward_demodulation,[],[f1069,f800]) ).
fof(f1069,plain,
( sK15 = relation_rng(empty_set)
| ~ spl22_6
| ~ spl22_116 ),
inference(resolution,[],[f1050,f251]) ).
fof(f2159,plain,
( spl22_201
| ~ spl22_48
| ~ spl22_112 ),
inference(avatar_split_clause,[],[f1040,f948,f466,f2157]) ).
fof(f2157,plain,
( spl22_201
<=> ! [X0] : sP2(X0,sK15,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_201])]) ).
fof(f466,plain,
( spl22_48
<=> ! [X0,X1] : sP2(X1,X0,set_intersection2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_48])]) ).
fof(f1040,plain,
( ! [X0] : sP2(X0,sK15,sK15)
| ~ spl22_48
| ~ spl22_112 ),
inference(superposition,[],[f467,f949]) ).
fof(f467,plain,
( ! [X0,X1] : sP2(X1,X0,set_intersection2(X0,X1))
| ~ spl22_48 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f2155,plain,
( spl22_200
| ~ spl22_38
| ~ spl22_108 ),
inference(avatar_split_clause,[],[f932,f920,f406,f2153]) ).
fof(f2153,plain,
( spl22_200
<=> ! [X0] : element(sK15,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_200])]) ).
fof(f406,plain,
( spl22_38
<=> ! [X0] : element(sK11(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_38])]) ).
fof(f920,plain,
( spl22_108
<=> ! [X0] : sK11(X0) = sK15 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_108])]) ).
fof(f932,plain,
( ! [X0] : element(sK15,powerset(X0))
| ~ spl22_38
| ~ spl22_108 ),
inference(superposition,[],[f407,f921]) ).
fof(f921,plain,
( ! [X0] : sK11(X0) = sK15
| ~ spl22_108 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f407,plain,
( ! [X0] : element(sK11(X0),powerset(X0))
| ~ spl22_38 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f2151,plain,
( spl22_199
| ~ spl22_110
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f2145,f2137,f940,f2149]) ).
fof(f2149,plain,
( spl22_199
<=> ! [X0] :
( apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_199])]) ).
fof(f2137,plain,
( spl22_197
<=> ! [X0] :
( ~ function(relation_rng(X0))
| apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_197])]) ).
fof(f2145,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_197 ),
inference(duplicate_literal_removal,[],[f2144]) ).
fof(f2144,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_197 ),
inference(resolution,[],[f2138,f941]) ).
fof(f2138,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0) )
| ~ spl22_197 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f2143,plain,
( spl22_198
| ~ spl22_37
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f828,f823,f402,f2141]) ).
fof(f828,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0) )
| ~ spl22_37
| ~ spl22_95 ),
inference(resolution,[],[f824,f403]) ).
fof(f2139,plain,
( spl22_197
| ~ spl22_35
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f827,f823,f394,f2137]) ).
fof(f827,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_95 ),
inference(resolution,[],[f824,f395]) ).
fof(f2130,plain,
( ~ spl22_39
| spl22_196
| ~ spl22_7
| ~ spl22_92
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f868,f846,f798,f254,f2127,f410]) ).
fof(f868,plain,
( apply(sK15,sK4) = apply(relation_dom_restriction(sK15,relation_dom(sK5)),sK4)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_92
| ~ spl22_96 ),
inference(forward_demodulation,[],[f867,f800]) ).
fof(f867,plain,
( ~ function(sK15)
| apply(empty_set,sK4) = apply(relation_dom_restriction(empty_set,relation_dom(sK5)),sK4)
| ~ spl22_7
| ~ spl22_92
| ~ spl22_96 ),
inference(forward_demodulation,[],[f858,f800]) ).
fof(f858,plain,
( ~ function(empty_set)
| apply(empty_set,sK4) = apply(relation_dom_restriction(empty_set,relation_dom(sK5)),sK4)
| ~ spl22_7
| ~ spl22_96 ),
inference(resolution,[],[f847,f256]) ).
fof(f2120,plain,
( spl22_195
| ~ spl22_20
| ~ spl22_19
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f865,f846,f314,f319,f2117]) ).
fof(f865,plain,
( ~ function(sK20)
| apply(sK20,sK4) = apply(relation_dom_restriction(sK20,relation_dom(sK5)),sK4)
| ~ spl22_19
| ~ spl22_96 ),
inference(resolution,[],[f847,f316]) ).
fof(f2110,plain,
( spl22_194
| ~ spl22_18
| ~ spl22_17
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f864,f846,f304,f309,f2107]) ).
fof(f864,plain,
( ~ function(sK19)
| apply(sK19,sK4) = apply(relation_dom_restriction(sK19,relation_dom(sK5)),sK4)
| ~ spl22_17
| ~ spl22_96 ),
inference(resolution,[],[f847,f306]) ).
fof(f2096,plain,
( spl22_193
| ~ spl22_2
| ~ spl22_1
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f859,f846,f224,f229,f2093]) ).
fof(f859,plain,
( ~ function(sK5)
| apply(sK5,sK4) = apply(relation_dom_restriction(sK5,relation_dom(sK5)),sK4)
| ~ spl22_1
| ~ spl22_96 ),
inference(resolution,[],[f847,f226]) ).
fof(f2085,plain,
( spl22_192
| ~ spl22_77
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f746,f742,f698,f2083]) ).
fof(f746,plain,
( ! [X2,X0,X1] :
( apply(X0,sK7(X1,relation_dom(relation_dom_restriction(X0,X2)))) = apply(relation_dom_restriction(X0,X2),sK7(X1,relation_dom(relation_dom_restriction(X0,X2))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| sK7(X1,relation_dom(relation_dom_restriction(X0,X2))) = apply(X1,sK8(X1,relation_dom(relation_dom_restriction(X0,X2))))
| sP0(X1,relation_dom(relation_dom_restriction(X0,X2))) )
| ~ spl22_77
| ~ spl22_83 ),
inference(resolution,[],[f743,f699]) ).
fof(f2013,plain,
( spl22_191
| ~ spl22_76
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f752,f742,f670,f2011]) ).
fof(f752,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3)) = apply(relation_dom_restriction(X0,X1),sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| in(sK13(relation_dom(relation_dom_restriction(X0,X1)),X2,X3),X3)
| sP2(relation_dom(relation_dom_restriction(X0,X1)),X2,X3) )
| ~ spl22_76
| ~ spl22_83 ),
inference(resolution,[],[f743,f671]) ).
fof(f2009,plain,
( spl22_190
| ~ spl22_75
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f751,f742,f666,f2007]) ).
fof(f751,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3)) = apply(relation_dom_restriction(X0,X2),sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| in(sK13(X1,relation_dom(relation_dom_restriction(X0,X2)),X3),X3)
| sP2(X1,relation_dom(relation_dom_restriction(X0,X2)),X3) )
| ~ spl22_75
| ~ spl22_83 ),
inference(resolution,[],[f743,f667]) ).
fof(f2005,plain,
( spl22_189
| ~ spl22_6
| ~ spl22_92
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1916,f1805,f798,f249,f2002]) ).
fof(f1916,plain,
( sK7(sK5,sK15) = apply(sK5,sK8(sK5,sK15))
| ~ spl22_6
| ~ spl22_92
| ~ spl22_178 ),
inference(forward_demodulation,[],[f1911,f800]) ).
fof(f1911,plain,
( sK7(sK5,empty_set) = apply(sK5,sK8(sK5,empty_set))
| ~ spl22_6
| ~ spl22_178 ),
inference(resolution,[],[f1806,f251]) ).
fof(f2000,plain,
( spl22_188
| ~ spl22_75
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f750,f742,f666,f1998]) ).
fof(f750,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3)))) = apply(relation_dom_restriction(X0,X3),sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| in(sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))),X2)
| sP2(X1,X2,relation_dom(relation_dom_restriction(X0,X3))) )
| ~ spl22_75
| ~ spl22_83 ),
inference(resolution,[],[f743,f667]) ).
fof(f1996,plain,
( spl22_187
| ~ spl22_76
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f749,f742,f670,f1994]) ).
fof(f749,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3)))) = apply(relation_dom_restriction(X0,X3),sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| in(sK13(X1,X2,relation_dom(relation_dom_restriction(X0,X3))),X1)
| sP2(X1,X2,relation_dom(relation_dom_restriction(X0,X3))) )
| ~ spl22_76
| ~ spl22_83 ),
inference(resolution,[],[f743,f671]) ).
fof(f1985,plain,
( spl22_186
| ~ spl22_73
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f747,f742,f652,f1983]) ).
fof(f747,plain,
( ! [X2,X0,X1] :
( apply(X0,sK7(X1,relation_dom(relation_dom_restriction(X0,X2)))) = apply(relation_dom_restriction(X0,X2),sK7(X1,relation_dom(relation_dom_restriction(X0,X2))))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| in(sK8(X1,relation_dom(relation_dom_restriction(X0,X2))),relation_dom(X1))
| sP0(X1,relation_dom(relation_dom_restriction(X0,X2))) )
| ~ spl22_73
| ~ spl22_83 ),
inference(resolution,[],[f743,f653]) ).
fof(f1966,plain,
( spl22_185
| ~ spl22_73
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f748,f742,f652,f1964]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( apply(X0,sK8(relation_dom_restriction(X0,X1),X2)) = apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| in(sK7(relation_dom_restriction(X0,X1),X2),X2)
| sP0(relation_dom_restriction(X0,X1),X2) )
| ~ spl22_73
| ~ spl22_83 ),
inference(resolution,[],[f743,f653]) ).
fof(f1961,plain,
( spl22_184
| ~ spl22_69
| ~ spl22_83 ),
inference(avatar_split_clause,[],[f745,f742,f628,f1959]) ).
fof(f745,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,apply(X1,X2)) = apply(relation_dom_restriction(X0,X3),apply(X1,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X3))
| ~ relation(relation_dom_restriction(X0,X3))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,relation_dom(relation_dom_restriction(X0,X3))) )
| ~ spl22_69
| ~ spl22_83 ),
inference(resolution,[],[f743,f629]) ).
fof(f1851,plain,
( spl22_183
| ~ spl22_74
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f701,f698,f662,f1849]) ).
fof(f701,plain,
( ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_74
| ~ spl22_77 ),
inference(resolution,[],[f699,f663]) ).
fof(f1847,plain,
( spl22_182
| ~ spl22_74
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f692,f670,f662,f1845]) ).
fof(f692,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_76 ),
inference(resolution,[],[f671,f663]) ).
fof(f1843,plain,
( spl22_181
| ~ spl22_74
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f688,f670,f662,f1841]) ).
fof(f688,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_76 ),
inference(resolution,[],[f671,f663]) ).
fof(f1839,plain,
( spl22_180
| ~ spl22_74
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f683,f666,f662,f1837]) ).
fof(f683,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_75 ),
inference(resolution,[],[f667,f663]) ).
fof(f1835,plain,
( spl22_179
| ~ spl22_74
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f679,f666,f662,f1833]) ).
fof(f679,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_74
| ~ spl22_75 ),
inference(resolution,[],[f667,f663]) ).
fof(f1807,plain,
( spl22_178
| ~ spl22_140
| ~ spl22_158 ),
inference(avatar_split_clause,[],[f1577,f1544,f1305,f1805]) ).
fof(f1305,plain,
( spl22_140
<=> ! [X0] :
( ~ sP0(sK5,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_140])]) ).
fof(f1577,plain,
( ! [X0] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| ~ empty(X0) )
| ~ spl22_140
| ~ spl22_158 ),
inference(duplicate_literal_removal,[],[f1576]) ).
fof(f1576,plain,
( ! [X0] :
( sK7(sK5,X0) = apply(sK5,sK8(sK5,X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_140
| ~ spl22_158 ),
inference(resolution,[],[f1545,f1306]) ).
fof(f1306,plain,
( ! [X0] :
( ~ sP0(sK5,X0)
| ~ empty(X0) )
| ~ spl22_140 ),
inference(avatar_component_clause,[],[f1305]) ).
fof(f1784,plain,
( spl22_177
| ~ spl22_53
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f736,f731,f511,f1782]) ).
fof(f1782,plain,
( spl22_177
<=> ! [X2,X0,X1] :
( relation_dom(X2) != set_intersection2(X1,relation_dom(X0))
| in(sK12(X2,X0),relation_dom(X2))
| relation_dom_restriction(X0,X1) = X2
| ~ function(X0)
| ~ relation(X0)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_177])]) ).
fof(f731,plain,
( spl22_82
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK12(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_82])]) ).
fof(f736,plain,
( ! [X2,X0,X1] :
( relation_dom(X2) != set_intersection2(X1,relation_dom(X0))
| in(sK12(X2,X0),relation_dom(X2))
| relation_dom_restriction(X0,X1) = X2
| ~ function(X0)
| ~ relation(X0)
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_53
| ~ spl22_82 ),
inference(superposition,[],[f732,f512]) ).
fof(f732,plain,
( ! [X2,X0,X1] :
( relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| in(sK12(X1,X2),relation_dom(X1))
| relation_dom_restriction(X2,X0) = X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_82 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f1780,plain,
( spl22_176
| ~ spl22_73
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f677,f662,f652,f1778]) ).
fof(f677,plain,
( ! [X2,X0,X1] :
( apply(relation_dom_restriction(X0,relation_dom(X1)),sK8(X1,X2)) = apply(X0,sK8(X1,X2))
| ~ function(X0)
| ~ relation(X0)
| in(sK7(X1,X2),X2)
| sP0(X1,X2) )
| ~ spl22_73
| ~ spl22_74 ),
inference(resolution,[],[f663,f653]) ).
fof(f1776,plain,
( spl22_175
| ~ spl22_73
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f676,f662,f652,f1774]) ).
fof(f676,plain,
( ! [X2,X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK7(X2,X1)) = apply(X0,sK7(X2,X1))
| ~ function(X0)
| ~ relation(X0)
| in(sK8(X2,X1),relation_dom(X2))
| sP0(X2,X1) )
| ~ spl22_73
| ~ spl22_74 ),
inference(resolution,[],[f663,f653]) ).
fof(f1770,plain,
( spl22_174
| ~ spl22_40
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f735,f731,f415,f1768]) ).
fof(f1768,plain,
( spl22_174
<=> ! [X0,X1] :
( relation_dom(X0) != relation_dom(X1)
| in(sK12(X1,X0),relation_dom(X1))
| relation_dom_restriction(X0,relation_dom(X0)) = X1
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_174])]) ).
fof(f735,plain,
( ! [X0,X1] :
( relation_dom(X0) != relation_dom(X1)
| in(sK12(X1,X0),relation_dom(X1))
| relation_dom_restriction(X0,relation_dom(X0)) = X1
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_40
| ~ spl22_82 ),
inference(superposition,[],[f732,f416]) ).
fof(f1741,plain,
( spl22_173
| ~ spl22_69
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f673,f662,f628,f1739]) ).
fof(f673,plain,
( ! [X2,X3,X0,X1] :
( apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,X1) )
| ~ spl22_69
| ~ spl22_74 ),
inference(resolution,[],[f663,f629]) ).
fof(f1737,plain,
( spl22_172
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f740,f731,f386,f378,f269,f1735]) ).
fof(f386,plain,
( spl22_33
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_33])]) ).
fof(f740,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,sK15) = X1
| relation_dom(X1) != sK15
| in(sK12(X1,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_82 ),
inference(inner_rewriting,[],[f739]) ).
fof(f739,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,sK15) = X1
| relation_dom(X1) != sK15
| in(sK12(X1,X0),relation_dom(X1))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_82 ),
inference(forward_demodulation,[],[f738,f424]) ).
fof(f424,plain,
( empty_set = sK15
| ~ spl22_10
| ~ spl22_33 ),
inference(resolution,[],[f387,f271]) ).
fof(f271,plain,
( empty(sK15)
| ~ spl22_10 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f387,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl22_33 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f738,plain,
( ! [X0,X1] :
( relation_dom(X1) != sK15
| in(sK12(X1,X0),relation_dom(X1))
| relation_dom_restriction(X0,empty_set) = X1
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_82 ),
inference(forward_demodulation,[],[f734,f424]) ).
fof(f734,plain,
( ! [X0,X1] :
( empty_set != relation_dom(X1)
| in(sK12(X1,X0),relation_dom(X1))
| relation_dom_restriction(X0,empty_set) = X1
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_31
| ~ spl22_82 ),
inference(superposition,[],[f732,f379]) ).
fof(f1722,plain,
( spl22_171
| ~ spl22_44
| ~ spl22_79 ),
inference(avatar_split_clause,[],[f714,f710,f450,f1720]) ).
fof(f710,plain,
( spl22_79
<=> ! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_79])]) ).
fof(f714,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ spl22_44
| ~ spl22_79 ),
inference(duplicate_literal_removal,[],[f713]) ).
fof(f713,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1))
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_79 ),
inference(resolution,[],[f711,f451]) ).
fof(f711,plain,
( ! [X2,X0] :
( ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0)) )
| ~ spl22_79 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f1718,plain,
( spl22_170
| ~ spl22_45
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f703,f698,f454,f1716]) ).
fof(f1716,plain,
( spl22_170
<=> ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_170])]) ).
fof(f703,plain,
( ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) )
| ~ spl22_45
| ~ spl22_77 ),
inference(resolution,[],[f699,f455]) ).
fof(f1714,plain,
( spl22_169
| ~ spl22_46
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f702,f698,f458,f1712]) ).
fof(f702,plain,
( ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) )
| ~ spl22_46
| ~ spl22_77 ),
inference(resolution,[],[f699,f459]) ).
fof(f1682,plain,
( ~ spl22_39
| spl22_168
| ~ spl22_7
| ~ spl22_92
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f840,f823,f798,f254,f1679,f410]) ).
fof(f840,plain,
( apply(relation_dom_restriction(sK15,sK3),sK4) = apply(sK15,sK4)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_92
| ~ spl22_95 ),
inference(forward_demodulation,[],[f839,f800]) ).
fof(f839,plain,
( ~ function(sK15)
| apply(relation_dom_restriction(empty_set,sK3),sK4) = apply(empty_set,sK4)
| ~ spl22_7
| ~ spl22_92
| ~ spl22_95 ),
inference(forward_demodulation,[],[f830,f800]) ).
fof(f830,plain,
( ~ function(empty_set)
| apply(relation_dom_restriction(empty_set,sK3),sK4) = apply(empty_set,sK4)
| ~ spl22_7
| ~ spl22_95 ),
inference(resolution,[],[f824,f256]) ).
fof(f1618,plain,
( spl22_167
| ~ spl22_84 ),
inference(avatar_split_clause,[],[f758,f754,f1616]) ).
fof(f754,plain,
( spl22_84
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_84])]) ).
fof(f758,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_84 ),
inference(duplicate_literal_removal,[],[f757]) ).
fof(f757,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_84 ),
inference(equality_resolution,[],[f755]) ).
fof(f755,plain,
( ! [X2,X0,X1] :
( apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
| relation_dom_restriction(X2,X0) = X1
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_84 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f1614,plain,
( spl22_166
| ~ spl22_45
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f694,f670,f454,f1612]) ).
fof(f1612,plain,
( spl22_166
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X0,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_166])]) ).
fof(f694,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X0,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_76 ),
inference(resolution,[],[f671,f455]) ).
fof(f1610,plain,
( spl22_165
| ~ spl22_46
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f693,f670,f458,f1608]) ).
fof(f693,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X0) )
| ~ spl22_46
| ~ spl22_76 ),
inference(resolution,[],[f671,f459]) ).
fof(f1606,plain,
( spl22_164
| ~ spl22_45
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f690,f670,f454,f1604]) ).
fof(f1604,plain,
( spl22_164
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_164])]) ).
fof(f690,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_76 ),
inference(resolution,[],[f671,f455]) ).
fof(f1602,plain,
( spl22_163
| ~ spl22_46
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f689,f670,f458,f1600]) ).
fof(f689,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X2) )
| ~ spl22_46
| ~ spl22_76 ),
inference(resolution,[],[f671,f459]) ).
fof(f1593,plain,
( spl22_162
| ~ spl22_45
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f685,f666,f454,f1591]) ).
fof(f1591,plain,
( spl22_162
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X1,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_162])]) ).
fof(f685,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ in(X1,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_75 ),
inference(resolution,[],[f667,f455]) ).
fof(f1589,plain,
( spl22_161
| ~ spl22_46
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f684,f666,f458,f1587]) ).
fof(f684,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X1) )
| ~ spl22_46
| ~ spl22_75 ),
inference(resolution,[],[f667,f459]) ).
fof(f1585,plain,
( spl22_160
| ~ spl22_45
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f681,f666,f454,f1583]) ).
fof(f1583,plain,
( spl22_160
<=> ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_160])]) ).
fof(f681,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ in(X2,sK13(X0,X1,X2)) )
| ~ spl22_45
| ~ spl22_75 ),
inference(resolution,[],[f667,f455]) ).
fof(f1581,plain,
( spl22_159
| ~ spl22_46
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f680,f666,f458,f1579]) ).
fof(f680,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| element(sK13(X0,X1,X2),X2) )
| ~ spl22_46
| ~ spl22_75 ),
inference(resolution,[],[f667,f459]) ).
fof(f1546,plain,
( spl22_158
| ~ spl22_41
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f704,f698,f419,f1544]) ).
fof(f704,plain,
( ! [X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_77 ),
inference(resolution,[],[f699,f420]) ).
fof(f1541,plain,
( spl22_157
| ~ spl22_45
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f659,f652,f454,f1539]) ).
fof(f1539,plain,
( spl22_157
<=> ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_157])]) ).
fof(f659,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) )
| ~ spl22_45
| ~ spl22_73 ),
inference(resolution,[],[f653,f455]) ).
fof(f1537,plain,
( spl22_156
| ~ spl22_46
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f658,f652,f458,f1535]) ).
fof(f658,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) )
| ~ spl22_46
| ~ spl22_73 ),
inference(resolution,[],[f653,f459]) ).
fof(f1533,plain,
( spl22_155
| ~ spl22_45
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f656,f652,f454,f1531]) ).
fof(f1531,plain,
( spl22_155
<=> ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ in(relation_dom(X0),sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_155])]) ).
fof(f656,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ in(relation_dom(X0),sK8(X0,X1)) )
| ~ spl22_45
| ~ spl22_73 ),
inference(resolution,[],[f653,f455]) ).
fof(f1529,plain,
( spl22_154
| ~ spl22_46
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f655,f652,f458,f1527]) ).
fof(f655,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| element(sK8(X0,X1),relation_dom(X0)) )
| ~ spl22_46
| ~ spl22_73 ),
inference(resolution,[],[f653,f459]) ).
fof(f1510,plain,
( spl22_153
| ~ spl22_47
| ~ spl22_71 ),
inference(avatar_split_clause,[],[f649,f642,f462,f1508]) ).
fof(f649,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,sK9(X1,X0)) = X0
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_71 ),
inference(resolution,[],[f643,f463]) ).
fof(f1446,plain,
( ~ spl22_85
| ~ spl22_152
| ~ spl22_47
| ~ spl22_140 ),
inference(avatar_split_clause,[],[f1387,f1305,f462,f1443,f761]) ).
fof(f1443,plain,
( spl22_152
<=> empty(relation_rng(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_152])]) ).
fof(f1387,plain,
( ~ empty(relation_rng(sK5))
| ~ sP1(sK5)
| ~ spl22_47
| ~ spl22_140 ),
inference(resolution,[],[f1306,f463]) ).
fof(f1411,plain,
( spl22_151
| ~ spl22_41
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f695,f670,f419,f1409]) ).
fof(f695,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_76 ),
inference(resolution,[],[f671,f420]) ).
fof(f1407,plain,
( spl22_150
| ~ spl22_41
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f691,f670,f419,f1405]) ).
fof(f691,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_76 ),
inference(resolution,[],[f671,f420]) ).
fof(f1403,plain,
( spl22_149
| ~ spl22_41
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f686,f666,f419,f1401]) ).
fof(f686,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_75 ),
inference(resolution,[],[f667,f420]) ).
fof(f1399,plain,
( spl22_148
| ~ spl22_41
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f682,f666,f419,f1397]) ).
fof(f682,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_75 ),
inference(resolution,[],[f667,f420]) ).
fof(f1395,plain,
( spl22_147
| ~ spl22_45
| ~ spl22_69 ),
inference(avatar_split_clause,[],[f634,f628,f454,f1393]) ).
fof(f634,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ in(X2,apply(X1,X0)) )
| ~ spl22_45
| ~ spl22_69 ),
inference(resolution,[],[f629,f455]) ).
fof(f1391,plain,
( spl22_146
| ~ spl22_46
| ~ spl22_69 ),
inference(avatar_split_clause,[],[f633,f628,f458,f1389]) ).
fof(f633,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| element(apply(X1,X0),X2) )
| ~ spl22_46
| ~ spl22_69 ),
inference(resolution,[],[f629,f459]) ).
fof(f1386,plain,
( spl22_145
| ~ spl22_47
| ~ spl22_68 ),
inference(avatar_split_clause,[],[f631,f624,f462,f1384]) ).
fof(f631,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| in(sK9(X1,X0),relation_dom(X1))
| ~ sP1(X1) )
| ~ spl22_47
| ~ spl22_68 ),
inference(resolution,[],[f625,f463]) ).
fof(f1382,plain,
( spl22_144
| ~ spl22_43
| ~ spl22_59 ),
inference(avatar_split_clause,[],[f571,f557,f446,f1380]) ).
fof(f1380,plain,
( spl22_144
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(set_intersection2(X1,X0))
| sP1(set_intersection2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_144])]) ).
fof(f446,plain,
( spl22_43
<=> ! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_43])]) ).
fof(f571,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(set_intersection2(X1,X0))
| sP1(set_intersection2(X1,X0)) )
| ~ spl22_43
| ~ spl22_59 ),
inference(resolution,[],[f558,f447]) ).
fof(f447,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP1(X0) )
| ~ spl22_43 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f1347,plain,
( spl22_143
| ~ spl22_41
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f660,f652,f419,f1345]) ).
fof(f660,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_73 ),
inference(resolution,[],[f653,f420]) ).
fof(f1343,plain,
( spl22_142
| ~ spl22_41
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f657,f652,f419,f1341]) ).
fof(f657,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| ~ empty(relation_dom(X0)) )
| ~ spl22_41
| ~ spl22_73 ),
inference(resolution,[],[f653,f420]) ).
fof(f1339,plain,
( spl22_141
| ~ spl22_48
| ~ spl22_72 ),
inference(avatar_split_clause,[],[f650,f646,f466,f1337]) ).
fof(f646,plain,
( spl22_72
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_72])]) ).
fof(f650,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) )
| ~ spl22_48
| ~ spl22_72 ),
inference(resolution,[],[f647,f467]) ).
fof(f647,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl22_72 ),
inference(avatar_component_clause,[],[f646]) ).
fof(f1307,plain,
( spl22_140
| ~ spl22_4
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1264,f1246,f239,f1305]) ).
fof(f1264,plain,
( ! [X0] :
( ~ sP0(sK5,X0)
| ~ empty(X0) )
| ~ spl22_4
| ~ spl22_133 ),
inference(resolution,[],[f1247,f241]) ).
fof(f1292,plain,
( spl22_139
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f696,f670,f1290]) ).
fof(f696,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl22_76 ),
inference(factoring,[],[f671]) ).
fof(f1288,plain,
( spl22_138
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f687,f666,f1286]) ).
fof(f687,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl22_75 ),
inference(factoring,[],[f667]) ).
fof(f1284,plain,
( spl22_137
| ~ spl22_50
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f566,f545,f499,f1282]) ).
fof(f499,plain,
( spl22_50
<=> ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_50])]) ).
fof(f566,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0))
| empty(X0) )
| ~ spl22_50
| ~ spl22_56 ),
inference(resolution,[],[f546,f500]) ).
fof(f500,plain,
( ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) )
| ~ spl22_50 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f1280,plain,
( spl22_136
| ~ spl22_54
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f565,f545,f515,f1278]) ).
fof(f515,plain,
( spl22_54
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_54])]) ).
fof(f565,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl22_54
| ~ spl22_56 ),
inference(resolution,[],[f546,f516]) ).
fof(f516,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl22_54 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f1276,plain,
( spl22_135
| ~ spl22_43
| ~ spl22_44 ),
inference(avatar_split_clause,[],[f485,f450,f446,f1274]) ).
fof(f485,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| sP1(relation_dom_restriction(X0,X1)) )
| ~ spl22_43
| ~ spl22_44 ),
inference(resolution,[],[f451,f447]) ).
fof(f1254,plain,
( spl22_134
| ~ spl22_20
| ~ spl22_19
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f837,f823,f314,f319,f1251]) ).
fof(f837,plain,
( ~ function(sK20)
| apply(relation_dom_restriction(sK20,sK3),sK4) = apply(sK20,sK4)
| ~ spl22_19
| ~ spl22_95 ),
inference(resolution,[],[f824,f316]) ).
fof(f1248,plain,
( spl22_133
| ~ spl22_41
| ~ spl22_69 ),
inference(avatar_split_clause,[],[f635,f628,f419,f1246]) ).
fof(f635,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_69 ),
inference(resolution,[],[f629,f420]) ).
fof(f1244,plain,
( spl22_132
| ~ spl22_50
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f616,f604,f499,f1242]) ).
fof(f616,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(X1))
| empty(X1) )
| ~ spl22_50
| ~ spl22_65 ),
inference(resolution,[],[f605,f500]) ).
fof(f1240,plain,
( spl22_131
| ~ spl22_54
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f615,f604,f515,f1238]) ).
fof(f1238,plain,
( spl22_131
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_131])]) ).
fof(f615,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl22_54
| ~ spl22_65 ),
inference(resolution,[],[f605,f516]) ).
fof(f1161,plain,
( spl22_130
| ~ spl22_48
| ~ spl22_67 ),
inference(avatar_split_clause,[],[f622,f612,f466,f1159]) ).
fof(f612,plain,
( spl22_67
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_67])]) ).
fof(f622,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) )
| ~ spl22_48
| ~ spl22_67 ),
inference(resolution,[],[f613,f467]) ).
fof(f613,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X0) )
| ~ spl22_67 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f1157,plain,
( spl22_129
| ~ spl22_48
| ~ spl22_66 ),
inference(avatar_split_clause,[],[f621,f608,f466,f1155]) ).
fof(f608,plain,
( spl22_66
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_66])]) ).
fof(f621,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) )
| ~ spl22_48
| ~ spl22_66 ),
inference(resolution,[],[f609,f467]) ).
fof(f609,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) )
| ~ spl22_66 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f1153,plain,
( spl22_128
| ~ spl22_29
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f617,f604,f359,f1151]) ).
fof(f359,plain,
( spl22_29
<=> ! [X0] : element(sK10(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_29])]) ).
fof(f617,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(powerset(X1))) )
| ~ spl22_29
| ~ spl22_65 ),
inference(resolution,[],[f605,f360]) ).
fof(f360,plain,
( ! [X0] : element(sK10(X0),X0)
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f1149,plain,
( spl22_127
| ~ spl22_54
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f592,f586,f515,f1147]) ).
fof(f1147,plain,
( spl22_127
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_127])]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl22_54
| ~ spl22_63 ),
inference(resolution,[],[f587,f516]) ).
fof(f1145,plain,
( spl22_126
| ~ spl22_36
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f535,f519,f398,f1143]) ).
fof(f535,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_55 ),
inference(resolution,[],[f520,f399]) ).
fof(f1141,plain,
( spl22_125
| ~ spl22_34
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f534,f519,f390,f1139]) ).
fof(f534,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl22_34
| ~ spl22_55 ),
inference(resolution,[],[f520,f391]) ).
fof(f1137,plain,
( spl22_124
| ~ spl22_37
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f470,f446,f402,f1135]) ).
fof(f470,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_37
| ~ spl22_43 ),
inference(resolution,[],[f447,f403]) ).
fof(f1133,plain,
( spl22_123
| ~ spl22_35
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f469,f446,f394,f1131]) ).
fof(f469,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_43 ),
inference(resolution,[],[f447,f395]) ).
fof(f1129,plain,
( spl22_122
| ~ spl22_18
| ~ spl22_17
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f836,f823,f304,f309,f1126]) ).
fof(f836,plain,
( ~ function(sK19)
| apply(relation_dom_restriction(sK19,sK3),sK4) = apply(sK19,sK4)
| ~ spl22_17
| ~ spl22_95 ),
inference(resolution,[],[f824,f306]) ).
fof(f1112,plain,
( spl22_121
| ~ spl22_29
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f594,f586,f359,f1110]) ).
fof(f594,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK10(powerset(X0))) )
| ~ spl22_29
| ~ spl22_63 ),
inference(resolution,[],[f587,f360]) ).
fof(f1108,plain,
( spl22_120
| ~ spl22_10
| ~ spl22_25
| ~ spl22_33
| ~ spl22_38
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f570,f545,f406,f386,f343,f269,f1106]) ).
fof(f343,plain,
( spl22_25
<=> ! [X0] : empty(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_25])]) ).
fof(f570,plain,
( ! [X0] :
( in(sK15,powerset(X0))
| empty(powerset(X0)) )
| ~ spl22_10
| ~ spl22_25
| ~ spl22_33
| ~ spl22_38
| ~ spl22_56 ),
inference(forward_demodulation,[],[f569,f424]) ).
fof(f569,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl22_25
| ~ spl22_33
| ~ spl22_38
| ~ spl22_56 ),
inference(forward_demodulation,[],[f568,f423]) ).
fof(f423,plain,
( ! [X0] : empty_set = sK11(X0)
| ~ spl22_25
| ~ spl22_33 ),
inference(resolution,[],[f387,f344]) ).
fof(f344,plain,
( ! [X0] : empty(sK11(X0))
| ~ spl22_25 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f568,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK11(X0),powerset(X0)) )
| ~ spl22_38
| ~ spl22_56 ),
inference(resolution,[],[f546,f407]) ).
fof(f1066,plain,
( spl22_119
| ~ spl22_29
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f567,f545,f359,f1064]) ).
fof(f567,plain,
( ! [X0] :
( empty(X0)
| in(sK10(X0),X0) )
| ~ spl22_29
| ~ spl22_56 ),
inference(resolution,[],[f546,f360]) ).
fof(f1062,plain,
( spl22_118
| ~ spl22_48
| ~ spl22_53 ),
inference(avatar_split_clause,[],[f527,f511,f466,f1060]) ).
fof(f1060,plain,
( spl22_118
<=> ! [X0,X1] : sP2(X1,X0,set_intersection2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_118])]) ).
fof(f527,plain,
( ! [X0,X1] : sP2(X1,X0,set_intersection2(X1,X0))
| ~ spl22_48
| ~ spl22_53 ),
inference(superposition,[],[f467,f512]) ).
fof(f1055,plain,
( spl22_117
| ~ spl22_10
| ~ spl22_33
| ~ spl22_36 ),
inference(avatar_split_clause,[],[f436,f398,f386,f269,f1053]) ).
fof(f436,plain,
( ! [X0] :
( relation_dom(X0) = sK15
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_33
| ~ spl22_36 ),
inference(forward_demodulation,[],[f433,f424]) ).
fof(f433,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set )
| ~ spl22_33
| ~ spl22_36 ),
inference(resolution,[],[f399,f387]) ).
fof(f1051,plain,
( spl22_116
| ~ spl22_10
| ~ spl22_33
| ~ spl22_34 ),
inference(avatar_split_clause,[],[f432,f390,f386,f269,f1049]) ).
fof(f432,plain,
( ! [X0] :
( relation_rng(X0) = sK15
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_33
| ~ spl22_34 ),
inference(forward_demodulation,[],[f429,f424]) ).
fof(f429,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set )
| ~ spl22_33
| ~ spl22_34 ),
inference(resolution,[],[f391,f387]) ).
fof(f1006,plain,
( spl22_113
| ~ spl22_33
| ~ spl22_92 ),
inference(avatar_split_clause,[],[f972,f798,f386,f952]) ).
fof(f972,plain,
( ! [X0] :
( sK15 = X0
| ~ empty(X0) )
| ~ spl22_33
| ~ spl22_92 ),
inference(forward_demodulation,[],[f387,f800]) ).
fof(f971,plain,
( ~ spl22_6
| ~ spl22_114 ),
inference(avatar_contradiction_clause,[],[f962]) ).
fof(f962,plain,
( $false
| ~ spl22_6
| ~ spl22_114 ),
inference(resolution,[],[f957,f251]) ).
fof(f957,plain,
( ! [X0] : ~ empty(X0)
| ~ spl22_114 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f970,plain,
( ~ spl22_25
| ~ spl22_114 ),
inference(avatar_contradiction_clause,[],[f963]) ).
fof(f963,plain,
( $false
| ~ spl22_25
| ~ spl22_114 ),
inference(resolution,[],[f957,f344]) ).
fof(f969,plain,
( ~ spl22_10
| ~ spl22_114 ),
inference(avatar_contradiction_clause,[],[f964]) ).
fof(f964,plain,
( $false
| ~ spl22_10
| ~ spl22_114 ),
inference(resolution,[],[f957,f271]) ).
fof(f968,plain,
( ~ spl22_13
| ~ spl22_114 ),
inference(avatar_contradiction_clause,[],[f965]) ).
fof(f965,plain,
( $false
| ~ spl22_13
| ~ spl22_114 ),
inference(resolution,[],[f957,f286]) ).
fof(f286,plain,
( empty(sK17)
| ~ spl22_13 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f284,plain,
( spl22_13
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_13])]) ).
fof(f967,plain,
( ~ spl22_22
| ~ spl22_114 ),
inference(avatar_contradiction_clause,[],[f966]) ).
fof(f966,plain,
( $false
| ~ spl22_22
| ~ spl22_114 ),
inference(resolution,[],[f957,f331]) ).
fof(f331,plain,
( empty(sK21)
| ~ spl22_22 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f329,plain,
( spl22_22
<=> empty(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_22])]) ).
fof(f961,plain,
( spl22_114
| spl22_115
| ~ spl22_10
| ~ spl22_25
| ~ spl22_33
| ~ spl22_38
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f597,f586,f406,f386,f343,f269,f959,f956]) ).
fof(f597,plain,
( ! [X0,X1] :
( ~ in(X1,sK15)
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_25
| ~ spl22_33
| ~ spl22_38
| ~ spl22_63 ),
inference(forward_demodulation,[],[f596,f424]) ).
fof(f596,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl22_25
| ~ spl22_33
| ~ spl22_38
| ~ spl22_63 ),
inference(forward_demodulation,[],[f595,f423]) ).
fof(f595,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK11(X0)) )
| ~ spl22_38
| ~ spl22_63 ),
inference(resolution,[],[f587,f407]) ).
fof(f954,plain,
( spl22_113
| ~ spl22_10
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f538,f519,f269,f952]) ).
fof(f538,plain,
( ! [X0] :
( sK15 = X0
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_55 ),
inference(resolution,[],[f520,f271]) ).
fof(f950,plain,
( spl22_112
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_53 ),
inference(avatar_split_clause,[],[f530,f511,f386,f378,f269,f948]) ).
fof(f530,plain,
( ! [X0] : sK15 = set_intersection2(sK15,X0)
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_53 ),
inference(forward_demodulation,[],[f524,f424]) ).
fof(f524,plain,
( ! [X0] : empty_set = set_intersection2(empty_set,X0)
| ~ spl22_31
| ~ spl22_53 ),
inference(superposition,[],[f512,f379]) ).
fof(f946,plain,
( spl22_111
| ~ spl22_27
| ~ spl22_36 ),
inference(avatar_split_clause,[],[f435,f398,f351,f944]) ).
fof(f435,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl22_27
| ~ spl22_36 ),
inference(resolution,[],[f399,f352]) ).
fof(f942,plain,
( spl22_110
| ~ spl22_27
| ~ spl22_34 ),
inference(avatar_split_clause,[],[f431,f390,f351,f940]) ).
fof(f431,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl22_27
| ~ spl22_34 ),
inference(resolution,[],[f391,f352]) ).
fof(f938,plain,
( spl22_109
| ~ spl22_2
| ~ spl22_1
| ~ spl22_95 ),
inference(avatar_split_clause,[],[f831,f823,f224,f229,f935]) ).
fof(f831,plain,
( ~ function(sK5)
| apply(sK5,sK4) = apply(relation_dom_restriction(sK5,sK3),sK4)
| ~ spl22_1
| ~ spl22_95 ),
inference(resolution,[],[f824,f226]) ).
fof(f922,plain,
( spl22_108
| ~ spl22_92
| ~ spl22_98 ),
inference(avatar_split_clause,[],[f877,f874,f798,f920]) ).
fof(f874,plain,
( spl22_98
<=> ! [X0] : empty_set = sK11(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_98])]) ).
fof(f877,plain,
( ! [X0] : sK11(X0) = sK15
| ~ spl22_92
| ~ spl22_98 ),
inference(forward_demodulation,[],[f875,f800]) ).
fof(f875,plain,
( ! [X0] : empty_set = sK11(X0)
| ~ spl22_98 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f918,plain,
( spl22_107
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_48 ),
inference(avatar_split_clause,[],[f497,f466,f386,f378,f269,f916]) ).
fof(f916,plain,
( spl22_107
<=> ! [X0] : sP2(sK15,X0,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_107])]) ).
fof(f497,plain,
( ! [X0] : sP2(sK15,X0,sK15)
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_48 ),
inference(forward_demodulation,[],[f495,f424]) ).
fof(f495,plain,
( ! [X0] : sP2(empty_set,X0,empty_set)
| ~ spl22_31
| ~ spl22_48 ),
inference(superposition,[],[f467,f379]) ).
fof(f914,plain,
( spl22_106
| ~ spl22_40
| ~ spl22_48 ),
inference(avatar_split_clause,[],[f496,f466,f415,f912]) ).
fof(f912,plain,
( spl22_106
<=> ! [X0] : sP2(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_106])]) ).
fof(f496,plain,
( ! [X0] : sP2(X0,X0,X0)
| ~ spl22_40
| ~ spl22_48 ),
inference(superposition,[],[f467,f416]) ).
fof(f910,plain,
( ~ spl22_39
| spl22_105
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f480,f446,f386,f269,f254,f907,f410]) ).
fof(f480,plain,
( sP1(sK15)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_43 ),
inference(forward_demodulation,[],[f479,f424]) ).
fof(f479,plain,
( ~ function(sK15)
| sP1(empty_set)
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_43 ),
inference(forward_demodulation,[],[f471,f424]) ).
fof(f471,plain,
( ~ function(empty_set)
| sP1(empty_set)
| ~ spl22_7
| ~ spl22_43 ),
inference(resolution,[],[f447,f256]) ).
fof(f905,plain,
( spl22_104
| ~ spl22_20
| ~ spl22_19
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f477,f446,f314,f319,f902]) ).
fof(f477,plain,
( ~ function(sK20)
| sP1(sK20)
| ~ spl22_19
| ~ spl22_43 ),
inference(resolution,[],[f447,f316]) ).
fof(f900,plain,
( spl22_103
| ~ spl22_18
| ~ spl22_17
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f476,f446,f304,f309,f897]) ).
fof(f476,plain,
( ~ function(sK19)
| sP1(sK19)
| ~ spl22_17
| ~ spl22_43 ),
inference(resolution,[],[f447,f306]) ).
fof(f895,plain,
( spl22_101
| ~ spl22_102
| ~ spl22_15
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f475,f446,f294,f892,f888]) ).
fof(f888,plain,
( spl22_101
<=> sP1(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_101])]) ).
fof(f892,plain,
( spl22_102
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_102])]) ).
fof(f294,plain,
( spl22_15
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_15])]) ).
fof(f475,plain,
( ~ function(sK18)
| sP1(sK18)
| ~ spl22_15
| ~ spl22_43 ),
inference(resolution,[],[f447,f296]) ).
fof(f296,plain,
( relation(sK18)
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f886,plain,
( spl22_99
| ~ spl22_100
| ~ spl22_12
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f473,f446,f279,f883,f879]) ).
fof(f879,plain,
( spl22_99
<=> sP1(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_99])]) ).
fof(f883,plain,
( spl22_100
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_100])]) ).
fof(f279,plain,
( spl22_12
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_12])]) ).
fof(f473,plain,
( ~ function(sK16)
| sP1(sK16)
| ~ spl22_12
| ~ spl22_43 ),
inference(resolution,[],[f447,f281]) ).
fof(f281,plain,
( relation(sK16)
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f876,plain,
( spl22_98
| ~ spl22_25
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f423,f386,f343,f874]) ).
fof(f853,plain,
( spl22_97
| ~ spl22_8
| ~ spl22_92 ),
inference(avatar_split_clause,[],[f814,f798,f259,f850]) ).
fof(f850,plain,
( spl22_97
<=> relation_empty_yielding(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_97])]) ).
fof(f259,plain,
( spl22_8
<=> relation_empty_yielding(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_8])]) ).
fof(f814,plain,
( relation_empty_yielding(sK15)
| ~ spl22_8
| ~ spl22_92 ),
inference(superposition,[],[f261,f800]) ).
fof(f261,plain,
( relation_empty_yielding(empty_set)
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f848,plain,
( spl22_96
| ~ spl22_4
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f675,f662,f239,f846]) ).
fof(f675,plain,
( ! [X0] :
( apply(X0,sK4) = apply(relation_dom_restriction(X0,relation_dom(sK5)),sK4)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_4
| ~ spl22_74 ),
inference(resolution,[],[f663,f241]) ).
fof(f825,plain,
( spl22_95
| ~ spl22_3
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f674,f662,f234,f823]) ).
fof(f674,plain,
( ! [X0] :
( apply(relation_dom_restriction(X0,sK3),sK4) = apply(X0,sK4)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_3
| ~ spl22_74 ),
inference(resolution,[],[f663,f236]) ).
fof(f811,plain,
( spl22_94
| ~ spl22_10
| ~ spl22_22
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f428,f386,f329,f269,f808]) ).
fof(f808,plain,
( spl22_94
<=> sK15 = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_94])]) ).
fof(f428,plain,
( sK15 = sK21
| ~ spl22_10
| ~ spl22_22
| ~ spl22_33 ),
inference(forward_demodulation,[],[f426,f424]) ).
fof(f426,plain,
( empty_set = sK21
| ~ spl22_22
| ~ spl22_33 ),
inference(resolution,[],[f387,f331]) ).
fof(f806,plain,
( spl22_93
| ~ spl22_10
| ~ spl22_13
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f427,f386,f284,f269,f803]) ).
fof(f803,plain,
( spl22_93
<=> sK15 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_93])]) ).
fof(f427,plain,
( sK15 = sK17
| ~ spl22_10
| ~ spl22_13
| ~ spl22_33 ),
inference(forward_demodulation,[],[f425,f424]) ).
fof(f425,plain,
( empty_set = sK17
| ~ spl22_13
| ~ spl22_33 ),
inference(resolution,[],[f387,f286]) ).
fof(f801,plain,
( spl22_92
| ~ spl22_10
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f424,f386,f269,f798]) ).
fof(f795,plain,
( spl22_91
| ~ spl22_25
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f373,f355,f343,f793]) ).
fof(f793,plain,
( spl22_91
<=> ! [X0] : relation(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_91])]) ).
fof(f373,plain,
( ! [X0] : relation(sK11(X0))
| ~ spl22_25
| ~ spl22_28 ),
inference(resolution,[],[f356,f344]) ).
fof(f790,plain,
( spl22_90
| ~ spl22_25
| ~ spl22_27 ),
inference(avatar_split_clause,[],[f363,f351,f343,f788]) ).
fof(f788,plain,
( spl22_90
<=> ! [X0] : function(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_90])]) ).
fof(f363,plain,
( ! [X0] : function(sK11(X0))
| ~ spl22_25
| ~ spl22_27 ),
inference(resolution,[],[f352,f344]) ).
fof(f786,plain,
( ~ spl22_89
| ~ spl22_4
| spl22_5
| ~ spl22_69 ),
inference(avatar_split_clause,[],[f632,f628,f244,f239,f783]) ).
fof(f632,plain,
( ~ in(sK4,relation_dom(sK5))
| ~ sP0(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))
| spl22_5
| ~ spl22_69 ),
inference(resolution,[],[f629,f246]) ).
fof(f246,plain,
( ~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
| spl22_5 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f780,plain,
( spl22_88
| ~ spl22_10
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f374,f355,f269,f777]) ).
fof(f374,plain,
( relation(sK15)
| ~ spl22_10
| ~ spl22_28 ),
inference(resolution,[],[f356,f271]) ).
fof(f774,plain,
( spl22_87
| ~ spl22_4
| ~ spl22_46 ),
inference(avatar_split_clause,[],[f494,f458,f239,f771]) ).
fof(f771,plain,
( spl22_87
<=> element(sK4,relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_87])]) ).
fof(f494,plain,
( element(sK4,relation_dom(sK5))
| ~ spl22_4
| ~ spl22_46 ),
inference(resolution,[],[f459,f241]) ).
fof(f769,plain,
( ~ spl22_86
| ~ spl22_4
| ~ spl22_45 ),
inference(avatar_split_clause,[],[f492,f454,f239,f766]) ).
fof(f766,plain,
( spl22_86
<=> in(relation_dom(sK5),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_86])]) ).
fof(f492,plain,
( ~ in(relation_dom(sK5),sK4)
| ~ spl22_4
| ~ spl22_45 ),
inference(resolution,[],[f455,f241]) ).
fof(f764,plain,
( spl22_85
| ~ spl22_2
| ~ spl22_1
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f472,f446,f224,f229,f761]) ).
fof(f472,plain,
( ~ function(sK5)
| sP1(sK5)
| ~ spl22_1
| ~ spl22_43 ),
inference(resolution,[],[f447,f226]) ).
fof(f756,plain,
spl22_84,
inference(avatar_split_clause,[],[f187,f754]) ).
fof(f187,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ( apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
& in(sK12(X1,X2),relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f110,f111]) ).
fof(f111,plain,
! [X1,X2] :
( ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
& in(sK12(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f744,plain,
spl22_83,
inference(avatar_split_clause,[],[f220,f742]) ).
fof(f220,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,plain,
! [X2,X0,X1,X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f733,plain,
spl22_82,
inference(avatar_split_clause,[],[f186,f731]) ).
fof(f186,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK12(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f729,plain,
( ~ spl22_81
| ~ spl22_36
| spl22_60 ),
inference(avatar_split_clause,[],[f678,f561,f398,f726]) ).
fof(f561,plain,
( spl22_60
<=> empty(relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_60])]) ).
fof(f678,plain,
( ~ empty(sK5)
| ~ spl22_36
| spl22_60 ),
inference(resolution,[],[f563,f399]) ).
fof(f563,plain,
( ~ empty(relation_dom(sK5))
| spl22_60 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f718,plain,
spl22_80,
inference(avatar_split_clause,[],[f199,f716]) ).
fof(f199,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) )
& ( ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X1) )
| in(sK13(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f115,f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) )
& ( ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X1) )
| in(sK13(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f114]) ).
fof(f114,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(flattening,[],[f113]) ).
fof(f113,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f712,plain,
spl22_79,
inference(avatar_split_clause,[],[f221,f710]) ).
fof(f221,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f708,plain,
spl22_78,
inference(avatar_split_clause,[],[f166,f706]) ).
fof(f166,plain,
! [X3,X0,X1] :
( sP0(X0,X1)
| apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK7(X0,X1),X1) )
& ( ( sK7(X0,X1) = apply(X0,sK8(X0,X1))
& in(sK8(X0,X1),relation_dom(X0)) )
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK9(X0,X5)) = X5
& in(sK9(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f99,f102,f101,f100]) ).
fof(f100,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK7(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK7(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK7(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK7(X0,X1) = apply(X0,sK8(X0,X1))
& in(sK8(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK9(X0,X5)) = X5
& in(sK9(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f700,plain,
spl22_77,
inference(avatar_split_clause,[],[f165,f698]) ).
fof(f165,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f672,plain,
spl22_76,
inference(avatar_split_clause,[],[f198,f670]) ).
fof(f198,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f668,plain,
spl22_75,
inference(avatar_split_clause,[],[f197,f666]) ).
fof(f197,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f664,plain,
spl22_74,
inference(avatar_split_clause,[],[f192,f662]) ).
fof(f192,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f654,plain,
spl22_73,
inference(avatar_split_clause,[],[f164,f652]) ).
fof(f164,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f648,plain,
spl22_72,
inference(avatar_split_clause,[],[f196,f646]) ).
fof(f196,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f644,plain,
spl22_71,
inference(avatar_split_clause,[],[f162,f642]) ).
fof(f162,plain,
! [X0,X1,X5] :
( apply(X0,sK9(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f640,plain,
( spl22_70
| ~ spl22_3
| ~ spl22_46 ),
inference(avatar_split_clause,[],[f493,f458,f234,f637]) ).
fof(f637,plain,
( spl22_70
<=> element(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_70])]) ).
fof(f493,plain,
( element(sK4,sK3)
| ~ spl22_3
| ~ spl22_46 ),
inference(resolution,[],[f459,f236]) ).
fof(f630,plain,
spl22_69,
inference(avatar_split_clause,[],[f219,f628]) ).
fof(f219,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) ),
inference(equality_resolution,[],[f163]) ).
fof(f163,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f626,plain,
spl22_68,
inference(avatar_split_clause,[],[f161,f624]) ).
fof(f161,plain,
! [X0,X1,X5] :
( in(sK9(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f614,plain,
spl22_67,
inference(avatar_split_clause,[],[f195,f612]) ).
fof(f195,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f610,plain,
spl22_66,
inference(avatar_split_clause,[],[f194,f608]) ).
fof(f194,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f606,plain,
spl22_65,
inference(avatar_split_clause,[],[f193,f604]) ).
fof(f193,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f602,plain,
( ~ spl22_64
| ~ spl22_3
| ~ spl22_45 ),
inference(avatar_split_clause,[],[f491,f454,f234,f599]) ).
fof(f599,plain,
( spl22_64
<=> in(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_64])]) ).
fof(f491,plain,
( ~ in(sK3,sK4)
| ~ spl22_3
| ~ spl22_45 ),
inference(resolution,[],[f455,f236]) ).
fof(f588,plain,
spl22_63,
inference(avatar_split_clause,[],[f202,f586]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f584,plain,
spl22_62,
inference(avatar_split_clause,[],[f201,f582]) ).
fof(f201,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP2(X1,X0,X2) ),
inference(definition_folding,[],[f6,f91]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f580,plain,
spl22_61,
inference(avatar_split_clause,[],[f160,f578]) ).
fof(f160,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f564,plain,
( ~ spl22_60
| ~ spl22_4
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f444,f419,f239,f561]) ).
fof(f444,plain,
( ~ empty(relation_dom(sK5))
| ~ spl22_4
| ~ spl22_41 ),
inference(resolution,[],[f420,f241]) ).
fof(f559,plain,
spl22_59,
inference(avatar_split_clause,[],[f188,f557]) ).
fof(f188,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f555,plain,
spl22_58,
inference(avatar_split_clause,[],[f183,f553]) ).
fof(f183,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f551,plain,
spl22_57,
inference(avatar_split_clause,[],[f181,f549]) ).
fof(f549,plain,
( spl22_57
<=> ! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_57])]) ).
fof(f181,plain,
! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(f547,plain,
spl22_56,
inference(avatar_split_clause,[],[f179,f545]) ).
fof(f179,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f521,plain,
spl22_55,
inference(avatar_split_clause,[],[f190,f519]) ).
fof(f190,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f517,plain,
spl22_54,
inference(avatar_split_clause,[],[f189,f515]) ).
fof(f189,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f513,plain,
spl22_53,
inference(avatar_split_clause,[],[f175,f511]) ).
fof(f175,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f509,plain,
spl22_52,
inference(avatar_split_clause,[],[f158,f507]) ).
fof(f507,plain,
( spl22_52
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_52])]) ).
fof(f158,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f505,plain,
spl22_51,
inference(avatar_split_clause,[],[f157,f503]) ).
fof(f157,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f501,plain,
spl22_50,
inference(avatar_split_clause,[],[f148,f499]) ).
fof(f148,plain,
! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f53,f95]) ).
fof(f95,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f490,plain,
( ~ spl22_49
| ~ spl22_3
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f443,f419,f234,f487]) ).
fof(f443,plain,
( ~ empty(sK3)
| ~ spl22_3
| ~ spl22_41 ),
inference(resolution,[],[f420,f236]) ).
fof(f468,plain,
spl22_48,
inference(avatar_split_clause,[],[f222,f466]) ).
fof(f222,plain,
! [X0,X1] : sP2(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f200]) ).
fof(f200,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f118]) ).
fof(f464,plain,
spl22_47,
inference(avatar_split_clause,[],[f218,f462]) ).
fof(f218,plain,
! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) ),
inference(equality_resolution,[],[f159]) ).
fof(f159,plain,
! [X0,X1] :
( sP0(X0,X1)
| relation_rng(X0) != X1
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f460,plain,
spl22_46,
inference(avatar_split_clause,[],[f178,f458]) ).
fof(f178,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f456,plain,
spl22_45,
inference(avatar_split_clause,[],[f177,f454]) ).
fof(f177,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f452,plain,
spl22_44,
inference(avatar_split_clause,[],[f176,f450]) ).
fof(f176,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f448,plain,
spl22_43,
inference(avatar_split_clause,[],[f167,f446]) ).
fof(f167,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f64,f89,f88]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f441,plain,
( spl22_42
| ~ spl22_13
| ~ spl22_27 ),
inference(avatar_split_clause,[],[f365,f351,f284,f438]) ).
fof(f438,plain,
( spl22_42
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_42])]) ).
fof(f365,plain,
( function(sK17)
| ~ spl22_13
| ~ spl22_27 ),
inference(resolution,[],[f352,f286]) ).
fof(f421,plain,
spl22_41,
inference(avatar_split_clause,[],[f191,f419]) ).
fof(f191,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f417,plain,
spl22_40,
inference(avatar_split_clause,[],[f174,f415]) ).
fof(f174,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f413,plain,
( spl22_39
| ~ spl22_10
| ~ spl22_27 ),
inference(avatar_split_clause,[],[f364,f351,f269,f410]) ).
fof(f364,plain,
( function(sK15)
| ~ spl22_10
| ~ spl22_27 ),
inference(resolution,[],[f352,f271]) ).
fof(f408,plain,
spl22_38,
inference(avatar_split_clause,[],[f171,f406]) ).
fof(f171,plain,
! [X0] : element(sK11(X0),powerset(X0)),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f28,f106]) ).
fof(f106,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f404,plain,
spl22_37,
inference(avatar_split_clause,[],[f156,f402]) ).
fof(f156,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f400,plain,
spl22_36,
inference(avatar_split_clause,[],[f155,f398]) ).
fof(f155,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f396,plain,
spl22_35,
inference(avatar_split_clause,[],[f154,f394]) ).
fof(f154,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f392,plain,
spl22_34,
inference(avatar_split_clause,[],[f153,f390]) ).
fof(f153,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f388,plain,
spl22_33,
inference(avatar_split_clause,[],[f152,f386]) ).
fof(f152,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f384,plain,
spl22_32,
inference(avatar_split_clause,[],[f149,f382]) ).
fof(f382,plain,
( spl22_32
<=> ! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_32])]) ).
fof(f149,plain,
! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f380,plain,
spl22_31,
inference(avatar_split_clause,[],[f147,f378]) ).
fof(f147,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f371,plain,
( spl22_30
| ~ spl22_6
| ~ spl22_27 ),
inference(avatar_split_clause,[],[f362,f351,f249,f368]) ).
fof(f368,plain,
( spl22_30
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_30])]) ).
fof(f362,plain,
( function(empty_set)
| ~ spl22_6
| ~ spl22_27 ),
inference(resolution,[],[f352,f251]) ).
fof(f361,plain,
spl22_29,
inference(avatar_split_clause,[],[f170,f359]) ).
fof(f170,plain,
! [X0] : element(sK10(X0),X0),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] : element(sK10(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f9,f104]) ).
fof(f104,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK10(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f357,plain,
spl22_28,
inference(avatar_split_clause,[],[f151,f355]) ).
fof(f151,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f353,plain,
spl22_27,
inference(avatar_split_clause,[],[f150,f351]) ).
fof(f150,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f349,plain,
spl22_26,
inference(avatar_split_clause,[],[f173,f347]) ).
fof(f173,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f345,plain,
spl22_25,
inference(avatar_split_clause,[],[f172,f343]) ).
fof(f172,plain,
! [X0] : empty(sK11(X0)),
inference(cnf_transformation,[],[f107]) ).
fof(f341,plain,
spl22_24,
inference(avatar_split_clause,[],[f146,f339]) ).
fof(f146,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f337,plain,
spl22_23,
inference(avatar_split_clause,[],[f217,f334]) ).
fof(f334,plain,
( spl22_23
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_23])]) ).
fof(f217,plain,
function(sK21),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( function(sK21)
& empty(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f26,f133]) ).
fof(f133,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK21)
& empty(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f332,plain,
spl22_22,
inference(avatar_split_clause,[],[f216,f329]) ).
fof(f216,plain,
empty(sK21),
inference(cnf_transformation,[],[f134]) ).
fof(f327,plain,
spl22_21,
inference(avatar_split_clause,[],[f215,f324]) ).
fof(f324,plain,
( spl22_21
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_21])]) ).
fof(f215,plain,
relation(sK21),
inference(cnf_transformation,[],[f134]) ).
fof(f322,plain,
spl22_20,
inference(avatar_split_clause,[],[f214,f319]) ).
fof(f214,plain,
function(sK20),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f50,f131]) ).
fof(f131,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f317,plain,
spl22_19,
inference(avatar_split_clause,[],[f213,f314]) ).
fof(f213,plain,
relation(sK20),
inference(cnf_transformation,[],[f132]) ).
fof(f312,plain,
spl22_18,
inference(avatar_split_clause,[],[f212,f309]) ).
fof(f212,plain,
function(sK19),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f22,f129]) ).
fof(f129,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f307,plain,
spl22_17,
inference(avatar_split_clause,[],[f211,f304]) ).
fof(f211,plain,
relation(sK19),
inference(cnf_transformation,[],[f130]) ).
fof(f302,plain,
spl22_16,
inference(avatar_split_clause,[],[f210,f299]) ).
fof(f299,plain,
( spl22_16
<=> relation_empty_yielding(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_16])]) ).
fof(f210,plain,
relation_empty_yielding(sK18),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
( relation_empty_yielding(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f31,f127]) ).
fof(f127,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f297,plain,
spl22_15,
inference(avatar_split_clause,[],[f209,f294]) ).
fof(f209,plain,
relation(sK18),
inference(cnf_transformation,[],[f128]) ).
fof(f292,plain,
spl22_14,
inference(avatar_split_clause,[],[f208,f289]) ).
fof(f289,plain,
( spl22_14
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_14])]) ).
fof(f208,plain,
relation(sK17),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
( relation(sK17)
& empty(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f23,f125]) ).
fof(f125,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK17)
& empty(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f287,plain,
spl22_13,
inference(avatar_split_clause,[],[f207,f284]) ).
fof(f207,plain,
empty(sK17),
inference(cnf_transformation,[],[f126]) ).
fof(f282,plain,
spl22_12,
inference(avatar_split_clause,[],[f206,f279]) ).
fof(f206,plain,
relation(sK16),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( relation(sK16)
& ~ empty(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f27,f123]) ).
fof(f123,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK16)
& ~ empty(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f277,plain,
~ spl22_11,
inference(avatar_split_clause,[],[f205,f274]) ).
fof(f205,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f124]) ).
fof(f272,plain,
spl22_10,
inference(avatar_split_clause,[],[f204,f269]) ).
fof(f204,plain,
empty(sK15),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
empty(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f25,f121]) ).
fof(f121,plain,
( ? [X0] : empty(X0)
=> empty(sK15) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f267,plain,
~ spl22_9,
inference(avatar_split_clause,[],[f203,f264]) ).
fof(f203,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
~ empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f29,f119]) ).
fof(f119,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f262,plain,
spl22_8,
inference(avatar_split_clause,[],[f145,f259]) ).
fof(f145,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f257,plain,
spl22_7,
inference(avatar_split_clause,[],[f142,f254]) ).
fof(f142,plain,
relation(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f252,plain,
spl22_6,
inference(avatar_split_clause,[],[f140,f249]) ).
fof(f140,plain,
empty(empty_set),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f247,plain,
~ spl22_5,
inference(avatar_split_clause,[],[f139,f244]) ).
fof(f139,plain,
~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3))),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( ~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
& in(sK4,sK3)
& in(sK4,relation_dom(sK5))
& function(sK5)
& relation(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f52,f93]) ).
fof(f93,plain,
( ? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) )
=> ( ~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
& in(sK4,sK3)
& in(sK4,relation_dom(sK5))
& function(sK5)
& relation(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
inference(negated_conjecture,[],[f42]) ).
fof(f42,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
fof(f242,plain,
spl22_4,
inference(avatar_split_clause,[],[f137,f239]) ).
fof(f137,plain,
in(sK4,relation_dom(sK5)),
inference(cnf_transformation,[],[f94]) ).
fof(f237,plain,
spl22_3,
inference(avatar_split_clause,[],[f138,f234]) ).
fof(f138,plain,
in(sK4,sK3),
inference(cnf_transformation,[],[f94]) ).
fof(f232,plain,
spl22_2,
inference(avatar_split_clause,[],[f136,f229]) ).
fof(f136,plain,
function(sK5),
inference(cnf_transformation,[],[f94]) ).
fof(f227,plain,
spl22_1,
inference(avatar_split_clause,[],[f135,f224]) ).
fof(f135,plain,
relation(sK5),
inference(cnf_transformation,[],[f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 11:40:35 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (16725)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (16729)WARNING: value z3 for option sas not known
% 0.15/0.38 % (16730)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (16727)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (16731)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (16732)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (16729)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (16728)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (16733)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.21/0.40 TRYING [4]
% 0.21/0.44 TRYING [5]
% 0.21/0.44 TRYING [3]
% 0.21/0.50 TRYING [4]
% 0.21/0.50 TRYING [6]
% 1.89/0.62 TRYING [7]
% 2.03/0.63 TRYING [5]
% 3.88/0.90 TRYING [8]
% 4.17/0.99 TRYING [6]
% 7.84/1.48 TRYING [1]
% 7.84/1.48 TRYING [2]
% 7.84/1.48 TRYING [3]
% 7.84/1.48 TRYING [4]
% 7.84/1.51 TRYING [5]
% 8.49/1.56 TRYING [6]
% 9.09/1.67 TRYING [7]
% 11.38/1.99 TRYING [8]
% 28.77/4.47 TRYING [7]
% 30.97/4.80 TRYING [9]
% 37.74/5.74 TRYING [9]
% 43.34/6.53 % (16731)First to succeed.
% 43.84/6.59 % (16731)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16725"
% 43.84/6.60 % (16731)Refutation found. Thanks to Tanya!
% 43.84/6.60 % SZS status Theorem for theBenchmark
% 43.84/6.60 % SZS output start Proof for theBenchmark
% See solution above
% 43.84/6.63 % (16731)------------------------------
% 43.84/6.63 % (16731)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 43.84/6.63 % (16731)Termination reason: Refutation
% 43.84/6.63
% 43.84/6.63 % (16731)Memory used [KB]: 52868
% 43.84/6.63 % (16731)Time elapsed: 6.217 s
% 43.84/6.63 % (16731)Instructions burned: 19017 (million)
% 43.84/6.63 % (16725)Success in time 6.231 s
%------------------------------------------------------------------------------